Supersymmetry after Higgs discovery (Status/Prospects)

Supersymmetry after Higgs discovery

Kick-off meeting : 08/30/2016 Masahiro Ibe (ICRR&IPMU)

(Status/Prospects)

Higgs is more like an elementary scalar

Higgs can be fit by the simplest implementation

V = - mhiggs2/2 h†h + λ/4 (h†h)2

mhiggs = λ1/2 v [ v=174.1GeV]

λ ~ 0.5mhiggs ~ 125GeV

( We knew v=174.1GeV before the discovery of Higgs )

V

hmh2

H

H† H

H† λ is expected to be very large (≃ 4π)

(Exceptional models : NGB Higgs → Top Yukawa coupling is difficult...)

e.g.) Naive composite Higgs :

Higgs exists

What have we learned from LHC results ?

No New Physics beyond the SM has been confirmed …

Wide range of alternatives to the Standard Model have been excluded…

[ Some tentative hints are/were reported though ]

[ e.g. Higgsless models ]

What have we learned from LHC results ?

Could the Standard Model Be the Ultimate Theory?

Quantum Gravity

Neutrino Masses

Dark Matter

Baryon Asymmetry of the Universe

Inflation

Strong CP problem

Answer is NO

Are some of these entries accessible at the LHC ?

Possibly, but not sure…

Most of the above entries can be solved in decoupled (ultra-violet) theories…

There should be new physics which addresses at least

Anomalies ( muon g-2, B-physics etc )

We want to know why the weak scale << MPL .

Let us suppose that the Higgs couples to X in the UV theories.

ΔL = λX |h|2 |X|2

→ Even aside from the quadratic divergence, the Higgs boson mass is sensitive to the UV scale mX !

→

If MW << MPL is explainable, there should be new physics close to MW which renders the SM being UV insensitive.

→ New Physics Accessible at the LHC !

Why New Physics at the LHC ?

[ No verifiable conflicts happen even if no new physics exist…]

Standard Model Superparticles

supersymmetry

Supersymmetric Standard Model

u c t

d s b

e ! "

# # #

$

ｇ

Z

We ! "

H

u c t

d s b

e ! "

# # #

$

ｇ

Z

We ! "

H

~ ~ ~ ~

~ ~ ~ ~

~ ~ ~ ~

~ ~ ~ ~

~

Higgs mass term = Higgsino mass term Higgsino mass term can be protected by the chiral symmetry!Hierarchy problem is solved if SUSY breaking is around Mw.

Higgs mass term can be protected !

same properties except for spins!

x2 x2

[ ’79 Maiani, ’81 Witten, ’81 Kaul ]

We just enlarge spacetime symmetry to supersymmetry !

Just by introducing the superpartners at around TeV, the gauge coupling unification become more precise!

Big Bonus !

Supersymmetric standard model is perfectly consistent with GUT !

SM MSSM (TeV)


Searchable at the LHC !

Supersymmetry = Spacetime symmetry

All the Standard Model particles are accompanied by superpartners.→ Lots of colored new particles (gluino, squarks)

at 13TeV, the cross section is x10 larger !


Big Blow to supersymmetry?

V = - mhiggs2/2 h†h + λ/4 (h†h)2

A combination of the SUSY breaking masses and the Higgsino mass

λ= (g’2+g2)/2 cos22βfrom gauge couplings

mH = λ1/2 v ~ mZ cos2β

The predicted Higgs boson mass is around Z-boson mass,

at the tree-level.

In the MSSM, the tree-level Higgs boson mass is given by the gauge coupling constants.

The Higgs boson ~ 125GeV requires multi-TeV SUSY ?


Tree-level quartic term: One-loop log enhanced:

-One-loop finite:

[’91 Okada, Yamaguchi, Yanagida, ’91 Haber, Hempfling, ’91 Ellis, Ridolfi, Zwirner ]

λ =14(g2

1 + g22) cos2 2β

2

The observed Higgs boson mass requires a rather large SUSY breaking effects!

The radiative corrections to the Higgs boson mass logarithmically depend on the stop masses.

m2h0 <

∼m2Z cos2 2β +

34π

y2t m2

t sin2 β

!log

m2t

m2t

+X2

t

m2t

− 112

X4t

m4t

"

~ ~

(Xt = At - μ cot β)



The simplest interpretation: mH ~ 125 GeV suggests that the sfermion (stop) masses are above O(10-1000)TeV [’91 Okada, Yamaguchi, Yanagida].

mh<115.5GeV

mh>127GeV

120GeV125GeV

130GeV

135GeV

10 102 103 1041

10

MSUSYêTeV

tanb

[’12, MI, Matsumoto,Yanagida (μH=O(Msusy))]

( mstop = 173.2 ± 0.9 GeV )


=vu

/ vd

The Higgs boson ~ 125GeV with a few TeV SUSY ?

[’12 Arvanitaki, Craig, Dimopoulos, Villadoro]

A large stop A-term (trilinear coupling) can enhance the Higgs boson mass !

Having a large stop A-term (trilinear coupling) at the low energy scale is not very easy.

which defines¶ running parameters at, ab, and aτ . In this approximation, the RG equations for theseparameters and b are

16π2 d

dtat = at

[18y∗t yt + y∗byb −

16

3g23 − 3g2

2 − 13

15g21

]+ 2aby

∗byt

+yt

[323

g23M3 + 6g2

2M2 +26

15g21M1

], (5.51)

16π2 d

dtab = ab

[18y∗byb + y∗t yt + y∗τyτ −

16

3g23 − 3g2

2 − 7

15g21

]+ 2aty

∗t yb + 2aτy

∗τyb

+yb

[323

g23M3 + 6g2

2M2 +14

15g21M1

], (5.52)

16π2 d

dtaτ = aτ

[12y∗τyτ + 3y∗byb − 3g2

2 − 9

5g21

]+ 6aby

∗byτ + yτ

[6g2

2M2 +18

5g21M1

], (5.53)

16π2 d

dtb = b

[3y∗t yt + 3y∗byb + y∗τyτ − 3g2

2 − 3

5g21

]

+µ[6aty

∗t + 6aby

∗b + 2aτy

∗τ + 6g2

2M2 +6

5g21M1

]. (5.54)

The β-function for each of these soft parameters is not proportional to the parameter itself, becausecouplings that violate supersymmetry are not protected by the supersymmetric non-renormalizationtheorem. So, even if at, ab, aτ and b vanish at the input scale, the RG corrections proportional togaugino masses appearing in eqs. (5.51)-(5.54) ensure that they will not vanish at the electroweak scale.

Next let us consider the RG equations for the scalar squared masses in the MSSM. In the approx-imation of eqs. (5.2) and (5.50), the squarks and sleptons of the first two families have only gaugeinteractions. This means that if the scalar squared masses satisfy a boundary condition like eq. (5.18)at an input RG scale, then when renormalized to any other RG scale, they will still be almost diagonal,with the approximate form

m2Q ≈

⎛

⎜⎝m2

Q10 0

0 m2Q1

0

0 0 m2Q3

⎞

⎟⎠ , m2u ≈

⎛

⎝m2

u10 0

0 m2u1

00 0 m2

u3

⎞

⎠ , (5.55)

etc. The first and second family squarks and sleptons with given gauge quantum numbers remainvery nearly degenerate, but the third-family squarks and sleptons feel the effects of the larger Yukawacouplings and so their squared masses get renormalized differently. The one-loop RG equations for thefirst and second family squark and slepton squared masses are

16π2 d

dtm2φi

= −∑

a=1,2,3

8Ca(i)g2a|Ma|2 +

6

5Yig

21S (5.56)

for each scalar φi, where the∑

a is over the three gauge groups U(1)Y , SU(2)L and SU(3)C , withCasimir invariants Ca(i) as in eqs. (5.28)-(5.30), and Ma are the corresponding running gaugino massparameters. Also,

S ≡ Tr[Yjm2φj

] = m2Hu

− m2Hd

+ Tr[m2Q − m2

L − 2m2u + m2

d+ m2

e ]. (5.57)

An important feature of eq. (5.56) is that the terms on the right-hand sides proportional to gauginosquared masses are negative, so∥ the scalar squared-mass parameters grow as they are RG-evolved from

¶Rescaled soft parameters At = at/yt, Ab = ab/yb, and Aτ = aτ/yτ are commonly used in the literature. We do notfollow this notation, because it cannot be generalized beyond the approximation of eqs. (5.2), (5.50) without introducinghorrible complications such as non-polynomial RG equations, and because at, ab and aτ are the couplings that actuallyappear in the Lagrangian anyway.

∥The contributions proportional to S are relatively small in most known realistic models.

45

which defines¶ running parameters at, ab, and aτ . In this approximation, the RG equations for theseparameters and b are

16π2 d

dtat = at

[18y∗t yt + y∗byb −

16

3g23 − 3g2

2 − 13

15g21

]+ 2aby

∗byt

+yt

[323

g23M3 + 6g2

2M2 +26

15g21M1

], (5.51)

16π2 d

dtab = ab

[18y∗byb + y∗t yt + y∗τyτ −

16

3g23 − 3g2

2 − 7

15g21

]+ 2aty

∗t yb + 2aτy

∗τyb

+yb

[323

g23M3 + 6g2

2M2 +14

15g21M1

], (5.52)

16π2 d

dtaτ = aτ

[12y∗τyτ + 3y∗byb − 3g2

2 − 9

5g21

]+ 6aby

∗byτ + yτ

[6g2

2M2 +18

5g21M1

], (5.53)

16π2 d

dtb = b

[3y∗t yt + 3y∗byb + y∗τyτ − 3g2

2 − 3

5g21

]

+µ[6aty

∗t + 6aby

∗b + 2aτy

∗τ + 6g2

2M2 +6

5g21M1

]. (5.54)

The β-function for each of these soft parameters is not proportional to the parameter itself, becausecouplings that violate supersymmetry are not protected by the supersymmetric non-renormalizationtheorem. So, even if at, ab, aτ and b vanish at the input scale, the RG corrections proportional togaugino masses appearing in eqs. (5.51)-(5.54) ensure that they will not vanish at the electroweak scale.

Next let us consider the RG equations for the scalar squared masses in the MSSM. In the approx-imation of eqs. (5.2) and (5.50), the squarks and sleptons of the first two families have only gaugeinteractions. This means that if the scalar squared masses satisfy a boundary condition like eq. (5.18)at an input RG scale, then when renormalized to any other RG scale, they will still be almost diagonal,with the approximate form

m2Q ≈

⎛

⎜⎝m2

Q10 0

0 m2Q1

0

0 0 m2Q3

⎞

⎟⎠ , m2u ≈

⎛

⎝m2

u10 0

0 m2u1

00 0 m2

u3

⎞

⎠ , (5.55)

etc. The first and second family squarks and sleptons with given gauge quantum numbers remainvery nearly degenerate, but the third-family squarks and sleptons feel the effects of the larger Yukawacouplings and so their squared masses get renormalized differently. The one-loop RG equations for thefirst and second family squark and slepton squared masses are

16π2 d

dtm2φi

= −∑

a=1,2,3

8Ca(i)g2a|Ma|2 +

6

5Yig

21S (5.56)

for each scalar φi, where the∑

a is over the three gauge groups U(1)Y , SU(2)L and SU(3)C , withCasimir invariants Ca(i) as in eqs. (5.28)-(5.30), and Ma are the corresponding running gaugino massparameters. Also,

S ≡ Tr[Yjm2φj

] = m2Hu

− m2Hd

+ Tr[m2Q − m2

L − 2m2u + m2

d+ m2

e ]. (5.57)

An important feature of eq. (5.56) is that the terms on the right-hand sides proportional to gauginosquared masses are negative, so∥ the scalar squared-mass parameters grow as they are RG-evolved from

¶Rescaled soft parameters At = at/yt, Ab = ab/yb, and Aτ = aτ/yτ are commonly used in the literature. We do notfollow this notation, because it cannot be generalized beyond the approximation of eqs. (5.2), (5.50) without introducinghorrible complications such as non-polynomial RG equations, and because at, ab and aτ are the couplings that actuallyappear in the Lagrangian anyway.

∥The contributions proportional to S are relatively small in most known realistic models.

45

[e.g. GMSB realization ’11 MI, Evans, Yanagida][see ’15 Kitano, Murayama, Tobioka with KK-effect]

Figure 4: The scalar mass scale in Split Supersymmetry as a function of tan � for a Higgs massfixed at 125.5 GeV for no and maximal stop mixing. The 1� error bands coming from the topmass measurement (which dominate over other uncertainties) are also shown.

high scale SUSY breaking models (as in gravity or anomaly mediation). The gluino RG e↵ectsbecome stronger as ⇤ is pushed up and it gets harder to have a stop much lighter than the gluino.

The bounds on the tuning from current direct stop searches are not competitive with the gluinoones, and thus do not pose a significant constraint on the parameter space. When m�3 � mt1 ,additional tuning is required because of the large correction to the stop mass from the gluino.Making the LSP heavier than 400 GeV to evade the gluino bounds does not improve the situation;a heavy LSP implies a large µ-term which increases the tree-level tuning of the theory. Fig. 2finally shows that the small window left for naturalness in SUSY will be probed already by theend of the 8 TeV LHC run, when the gluino searches are pushed above 1.5-1.8 TeV mass range.

The absence of evidence for sparticles suggests that either low-energy SUSY theories have to betuned, or sparticles are absent from the weak scale altogether. Why, then, does supersymmetricunification work so well if the sparticles responsible for it are not present? An answer to thisquestion comes from Split SUSY [7, 8], a theory motivated by the multiverse. In Split SUSY,scalar sparticles are heavy—at the SUSY breaking scale m0—whereas fermions (gauginos andhiggsinos) are lighter as they are further protected by the R-symmetry whose breaking scale canbe lower than m0. Choosing the fermion masses near a TeV, as dictated by the WIMP “miracle”,reproduces successful unification independent of the masses of scalar sparticles. So in Split onlythe gauginos and higgsinos may be accessible to the LHC, whereas the scalar masses can beanywhere between the GUT and the weak scale.

This uncertainty in m0, which has been blurring the phenomenology and model building ofSplit, has come to an end with the discovery of the Higgs [4]. The Higgs mass mh correlates withm0 [7, 8] as shown in Fig. 3 [9], and for mh = 125.5 GeV the scalar sparticle masses are in the

4

-3 -2 -1 0 1 2 3110

115

120

125

130

135

Xt / mSUSY

mh(G

eV)

mSUSY=2TeV, tanβ=20

Feyn

Higg

s

Suspect

SUSY

HD

Figure 3: Comparison between the EFT computation (lower blue band) and two existing codes: FeynHiggs [41]and Suspect [39]. We used a degenerate SUSY spectrum with mass m

SUSY

in the DR-scheme with tan� = 20.The plot on the left is mh vs m

SUSY

for vanishing stop mixing. The plot on the right is mh vs Xt/mSUSY

form

SUSY

= 2 TeV. On the left plot the instability of the non-EFT codes at large mSUSY

is visible.

due to the missing 2-loop corrections in the top mass7. Note that, as discussed in the previoussection, the uncertainty in the EFT approach is dominated by the 3-loop top matching conditions,the 2-loop ones are thus mandatory in any precision computation of the Higgs mass. We checkedthat after their inclusion, the FeynHiggs code would perfectly agree with the EFT computationat zero squark mixing. At maximal mixing the disagreement would be reduced to 4 GeV, whichshould be within the expected theoretical uncertainties of the diagrammatic computation.

For comparison, in fig. 3 we also show the results obtained with a di↵erent code (Suspect [39])which uses a diagrammatic approach but unlike FeynHiggs, does not perform RGE improvementand its applicability becomes questionable for mSUSY in the multi TeV region.

3 Results

After having seen that the EFT computation is reliable for most of the relevant parameter spacewe present here some of the implications for the supersymmetric spectrum. Given the genericagreement with previous computations using the same approach, we tried to be as complemen-tary as possible in the presentation of our results, putting emphasis on the improvements of ourcomputation and novel analysis in the EFT approach.

3.1 Where is SUSY?

Fig. 4 represents the parameter space compatible with the experimental value of the Higgs mass inthe plane of (m1/2,m0) for zero (blue) and increasing values (red) of the stop mixing. For simplicitywe took degenerate scalar masses m0 as well as degenerate fermion masses m1/2 = M1,2,3 = µ. All

7It was brought to our attention that a similar observation was also made in [42].

11

mh=125.5GeVbands : top mass

uncertainties

fixed top mass band : computational uncertainties

[’15 Vega, Villadoro]

→ As a whole, msquark > TeV is required

[Extra matter can also enhance A-term see ’16 Moroi, Yanagida, Yokozaki]



Extra Vector Matter (e.g. 10 representation [’92 Moroi, Okada] )

for extra low energy matter multiplets beyond the above mentioned messenger. That is,

keeping perturbative unification at the GUT scale, we can still add

• up to one pair of 5+ 10

• up to three pairs of 5+ 5

• up to one pair of 10+ 10

along with an arbitrary number of gauge singlets.2

In the above lists, the first set of fields corresponds to a fourth-generation of matter.

The CMS collaboration, however, has ruled out a fourth generation for a Higgs boson

mass in the range 120� 600GeV at a 95%C.L. due to the Higgs production cross section

being too large [10]. Since we are interested in the Higgs boson mass in the range of

120 � 140GeV, we do not pursue this possibility, but rather concentrate on the other

two possibilities with vector-like multiplets3 (see discussion on the Higgs production cross

section in the case of vector-like extra matter in the appendixA). We assume that the

masses of these vector like fields are similar to the Higgsino masses, i.e. the so-called

µ-term, otherwise their masses should naturally be at the GUT scale.

The addition of a 10+ 10 is particularly interesting, since the doublet Higgs Hu may

couple to this extra matter via W = Hu1010. From this additional Higgs interaction, the

lightest Higgs boson mass can be increased due to radiative corrections [11]. The 5+ 5

mentioned above can also couple to Hu if we also introduce a singlet 1, W = Hu 5 1. In

the following, however, we mainly concentrate on the model with an extra 10+ 10. This

matter content is more advantageous since the gauge mediated contribution to the soft

masses of the 10+ 10 are much larger.

2.1 Constraints on extra matter

Here we concentrate on the constraints on the additional matter,

10 = (QE, UE, EE) , 10 = (QE, UE, EE) , (1)

where their Standard Model charge assignments should be clear. In terms of these fields,

the Yukawa interaction W = Hu1010 and invariant mass term W = MT10 10 can be

2 In this paper, we assume that the extra matter forms a complete multiplet.3 We may allow a pair of 5+ 10 and 5+ 10 keeping the perturbative unification when the messenger

scale is very high. This set of extra matter corresponds to a vector-like fourth generation of matter.

3

rewritten as,

W = MT QEQE +MT UEUE +MT EEEE + �uHuQEUE , (2)

where �u denotes a coupling constant. As a result of the Higgs coupling, the masses of

the additonal up-type quarks are split,

Mup�type

' MT ± �u sin �v

2, (3)

with the Higgs vacuum expectation value v ' 174GeV. The masses of the other extra

matter multiplets remain degenerated and are given by MT .

As we will show in the next section, the lightest Higgs boson mass is considerably

enhanced for �u ' 1. From this point on, we will assume that tan � = hHui / hHdi =

O(10), since we are interested in models with a relatively heavy lightest Higgs boson.4

In the superpotential in Eq. (2), we have implicitly assumed that the extra matter

does not mix with the matter multiplets of the MSSM. These couplings can be forbidden

by assuming some type of parity for which the extra matter is odd. If the mixing between

the MSSM and the extra matter are completely forbidden, however, some of the extra

charged particles can be stable, which conflicts with cosmological constraints. To avoid

such di�culties, we assume that the additional matter has a small amount of mixings

with the MSSM matter multiplets (5i=1�3

,10i=1�3

), such as

W = ✏iHu10i10+ ✏iHd5i10. (4)

Even with this small additional mixing the extra matter in 10 can decay into the MSSM

fields. The 10 field can also decay into the MSSM fields through the mass terms in

Eq. (2).5 Particulary, the lightest additional colored particle, which is an up-type quark,

can decay into a W -boson and a down-type quark.

The most stringent collider constraint on the mass of these heavy up-type quarks is

Mup�type

> 358GeV . (5)

4In our discussion, we could also include another Yukawa interaction W = �dHd10 10. This interac-tion, however, does not change our discussion even for �d ' �u as long as tan� = O(10).

5 The amplitudes of the FCNC process such as K0� K0 mixing caused by these terms are suppressedby ✏4. Thus, these terms do not cause FCNC problems for ✏ . 10�3.

4

Higgs quartic potential receives an additional radiative contributions !

→ 125GeV Higgs mass can be achieved as long as the extra matters have large SUSY soft masses in the TeV range.

If the soft masses of the MSSM and the extra matter have the same origin, the squarks are also in the TeV range though…



Singlet Extension (NMSSM)

W = λNHuHd +13κN3

We add a tree-level quartic term to the Higgs scalar potential :

16

3.7. Higgs-boson phenomenology

In contrast to the minimal supersymmetric extension of the SM we have in the next-to-minimal extension, NMSSM,due to the additional singlet superfield S two additional Higgs bosons as well as one additional singlino. In particularthe phenomenology of the Higgs bosons may be very di↵erent compared to the MSSM. This di↵erence is pointed outin this subsection. We start with considering one of the advantages of the NMSSM over the MSSM, namely the muchless restricted Higgs-boson sector. In the MSSM the lightest scalar Higgs boson is predicted to not exceed the Z-bosonmass,

(mMSSMH1

)2 < m2Z cos2(2�) . (3.36)

This bound is softened through quantum corrections. One-loop corrections to the lightest Higgs boson where stud-ied [60–63] as well as dominant two-loop corrections [41, 63]. The largest contribution comes from virtual top andstop loops, where the one-loop corrections read

(�mMSSMH1

)2 = cm4

t

v2ln

✓mtL

mtR

m2t

◆, (3.37)

with c of the order 1. Confronted with the experimental data, that is, LEP searches for light Higgs bosons in theMSSM we have the lower bound [64]

mMSSM, expH1

> 92 GeV . (3.38)

That is, we need, considering (3.36) and (3.37) rather large stop masses, which enter only logarithmically inthe radiative corrections, in order to increase the mass of the lightest scalar Higgs-boson in the MSSM. Onthe other hand, a large violation of the degeneracy of the superpartner top and stop masses reintroduces anew kind of unnatural fine-tuning. This is in particular disturbing since one of the main motivation for theintroduction of supersymmetry is to avoid this unnatural large quantum corrections to the scalar Higgs-bosonmass, which occur in the SM. Let us note that there is some debate about this argument and refer the reader tothe discussion in Martin [22]. We notice, that a large mass splitting of the superpartners would reintroduce theinitial naturalness problem we encounter in the SM. Therfore, we expect the superpartner particle masses not toexceed the scale of 1 TeV too much to be considered as natural. Another argument for superpartner masses not toexceed the scale of 1 TeV too much is the unification of gauge couplings, which is spoiled by very large mass splittings.

The situation in the NMSSM is quite di↵erent. Firstly, the tree-level mass bound (3.36) for the lightest Higgs bosonis no longer valid in the NMSSM. In the CP-conserving Higgs-boson sector case the lower bound is changed to [65]

(mNMSSMH1

)2 < m2Z

✓cos2(2�) +

2|�|2 sin2(2�)g21 + g22

◆. (3.39)

Thus, the upper limit of the lightest CP-even Higgs-boson mass is in general lifted compared to the MSSM (3.36).Secondly, the experimental bound (3.38) is also much weaker in the NMSSM [66–68]. This can be easily understood:the main detection strategy of the lightest scalar Higgs in the MSSM is based on Higgs-strahlung o↵ a Z-boson withsubsequent decay of the Higgs boson according to H1 ! bb and b-tagging in the detector; see Fig. 1. But in the

e�

e+

Z b

b

Z

H1

gHZZ

FIG. 1: Higgs-boson production via Higgs-strahlung and subsequent decay into a bb quark pair, as searched for at the LEPexperiment [64]. The coupling of the Higgs boson to the Z bosons is denoted by gHZZ and given for the NMSSM in App. D.

NMSSM the additional decay channel into a pair of pseudoscalar Higgs bosons, H1 ! A1A1, is open, reducing in

Accordingly, the tree-level Higgs mass is lifted :

Still, we need some radiative contributions to achieve 125GeV from the squarks in a TeV range.

( λ < 0.7 from perturbativity )2 4 6 8 10

80

90

100

110

120

130

tan b

mhêG

eV mh(tree)(λ = 0.7)

[see ’10 Maniatis for review]

[ For the scenarios where the lightest Higgs is not the observed one see ’13 Christensen, Han, Liu, Su ] .


→

( Rough estimation )

mh = 125GeV


Extended Gauge Symmetry [’06 Maloney, Pierce, Wacker]

If the gauge symmetry of the MSSM is extended, the Higgs obtains tree-level quartic D-term potential

j k

i

(a)

j k

i

(b)

i j

(c)

i j

(d)

ij

(e)

Figure 3.2: Supersymmetric dimensionful couplings: (a) (scalar)3 interaction vertex M∗inyjkn and (b)

the conjugate interaction M iny∗jkn, (c) fermion mass term M ij and (d) conjugate fermion mass term

M∗ij , and (e) scalar squared-mass term M∗

ikMkj.

(a) (b) (c) (d) (e)

(f) (g) (h) (i)

Figure 3.3: Supersymmetric gauge interaction vertices.

tion of Figure 3.1c is exactly of the special type needed to cancel the quadratic divergences in quantumcorrections to scalar masses, as discussed in the Introduction [compare Figure 1.1, and eq. (1.11)].

Figure 3.2 shows the only interactions corresponding to renormalizable and supersymmetric verticeswith coupling dimensions of [mass] and [mass]2. First, there are (scalar)3 couplings in Figure 3.2a,b,which are entirely determined by the superpotential mass parameters M ij and Yukawa couplings yijk,as indicated by the second and third terms in eq. (3.50). The propagators of the fermions and scalarsin the theory are constructed in the usual way using the fermion mass M ij and scalar squared massM∗

ikMkj. The fermion mass terms M ij and Mij each lead to a chirality-changing insertion in the

fermion propagator; note the directions of the arrows in Figure 3.2c,d. There is no such arrow-reversalfor a scalar propagator in a theory with exact supersymmetry; as depicted in Figure 3.2e, if one treatsthe scalar squared-mass term as an insertion in the propagator, the arrow direction is preserved.

Figure 3.3 shows the gauge interactions in a supersymmetric theory. Figures 3.3a,b,c occur onlywhen the gauge group is non-Abelian, for example for SU(3)C color and SU(2)L weak isospin in theMSSM. Figures 3.3a and 3.3b are the interactions of gauge bosons, which derive from the first termin eq. (3.57). In the MSSM these are exactly the same as the well-known QCD gluon and electroweakgauge boson vertices of the Standard Model. (We do not show the interactions of ghost fields, whichare necessary only for consistent loop amplitudes.) Figures 3.3c,d,e,f are just the standard interactionsbetween gauge bosons and fermion and scalar fields that must occur in any gauge theory because of theform of the covariant derivative; they come from eqs. (3.59) and (3.65)-(3.67) inserted in the kineticpart of the Lagrangian. Figure 3.3c shows the coupling of a gaugino to a gauge boson; the gaugino linein a Feynman diagram is traditionally drawn as a solid fermion line superimposed on a wavy line. InFigure 3.3g we have the coupling of a gaugino to a chiral fermion and a complex scalar [the first termin the second line of eq. (3.72)]. One can think of this as the “supersymmetrization” of Figure 3.3e or

28

D

j k

i

(a)

j k

i

(b)

i j

(c)

i j

(d)

ij

(e)




ikMkj.

(a) (b) (c) (d) (e)

(f) (g) (h) (i)




ikMkj. The fermion mass terms M ij and Mij each lead to a chirality-changing insertion in thefermion propagator; note the directions of the arrows in Figure 3.2c,d. There is no such arrow-reversalfor a scalar propagator in a theory with exact supersymmetry; as depicted in Figure 3.2e, if one treatsthe scalar squared-mass term as an insertion in the propagator, the arrow direction is preserved.


28

H H

H H

j k

i

(a)

j k

i

(b)

i j

(c)

i j

(d)

ij

(e)




ikMkj.

(a) (b) (c) (d) (e)

(f) (g) (h) (i)




ikMkj. The fermion mass terms M ij and Mij each lead to a chirality-changing insertion in the

fermion propagator; note the directions of the arrows in Figure 3.2c,d. There is no such arrow-reversalfor a scalar propagator in a theory with exact supersymmetry; as depicted in Figure 3.2e, if one treatsthe scalar squared-mass term as an insertion in the propagator, the arrow direction is preserved.


28

j k

i

(a)

j k

i

(b)

i j

(c)

i j

(d)

ij

(e)




ikMkj.

(a) (b) (c) (d) (e)

(f) (g) (h) (i)




ikMkj. The fermion mass terms M ij and Mij each lead to a chirality-changing insertion in thefermion propagator; note the directions of the arrows in Figure 3.2c,d. There is no such arrow-reversalfor a scalar propagator in a theory with exact supersymmetry; as depicted in Figure 3.2e, if one treatsthe scalar squared-mass term as an insertion in the propagator, the arrow direction is preserved.


28

H H

H H

superpartner of would-be NGB-

MZ’ : Mass of new gauge boson

If the soft masses of the MSSM and the gauge breaking sector have the same origin, the squarks are again in the TeV range.

We need a rather large g and at least TeV soft mass to the gauge symmetry breaking sector.


The observed Higgs boson mass disfavors the squark (stop) masses in the hundreds GeV range…

Although it’s a big blow, at the same time, the null SUSY discovery so far is not very surprising in view of the 125GeV Higgs.

This is a big blow to supersymmetry…[Before the LHC, we expected that the SUSY is easier to be discovered than the Higgs boson !!]

[ATLAS Summary, 13TeV ]

4 August 2016 K. Rosbach: third genera�on squarks with ATLAS@13 TeV 16

Summary & Conclusions

Stop searches updated with

available run 2 data.

Many final states & simplified

models covered.

No observation of SUSY...

… but some excesses that

will be interesting to follow as

more data is recorded!

[light stop search (ICHEP)]


How about the naturalness ?

Natural SUSY (mstop , mHu , mHd , μ ~ O(100)GeV )

Parameter regions are getting smaller by direct searches.

Model building is getting more complicated…(but should not give up this possibility)

The explanation of the Higgs boson mass is not easy.We need to avoid fine-tuning to achieve the natural spectrum.

[GeV]stopm200 400 600 800 1000 1200 1400

[GeV

]LS

Pm

0100200300400500600700800900

1000ATLAS Simulation Preliminary

=14 TeVs

0 and 1-lepton combined

discoveryσ>=60) 5µ (<-1300 fb>=60) 95% CL exclusionµ (<-1300 fb

discoveryσ>=140) 5µ (<-13000 fb>=140) 95% CL exclusionµ (<-13000 fb

ATLAS 8 TeV (1-lepton): 95% CL obs. limitATLAS 8 TeV (0-lepton): 95% CL obs. limit

[ATL-PHYS-PUB-2013-011 ]

4 August 2016 K. Rosbach: third genera�on squarks with ATLAS@13 TeV 16

Summary & Conclusions

Stop searches updated with

available run 2 data.

Many final states & simplified

models covered.

No observation of SUSY...

… but some excesses that

will be interesting to follow as

more data is recorded!

SUSY (in particular the stops) in the TeV range.

Is it natural to have <H> = 174 GeV from the TeV mass parameters ?

It is actually more or less a matter of taste.

We do not complain the naturalness once the squarks are discovered in the TeV range !

We look forward further searches at the LHC !

Mgluino > 1.8 TeV for Msquark ⨠ TeV (13TeV,13.3fb-1)

[ Future discovery reaches: Mgluino ~ Msquark ~ 2.8 TeV (14TeV, 300fb-1) Mgluino ~ Msquark ~ 3.2 TeV (14TeV, 3000fb-1) 　　　　　　　　　 Mgluino ~ Msquark ~ 6.8 TeV (33TeV, 3000fb-1) ]

Mgluino ~ Msquark >1.8 TeV (Run1)

[arXiv:1310.0077]

(Still, we would wonder why SUSY is not in the weak scale in this case.)


SUSY in the TeV range might be more natural than it appears.→ Focus point mechanism [’99 Feng, Matchev, Moroi]

When soft breaking parameters of O(MSUSY) at the UV satisfy a special (and motivated) condition, mHu2 can be much smaller than MSUSY .

mHu2 = ε MSUSY2 (ε << 1 )

the correct ⌦�, and present results in the (tan �,M1/2) plane, with every point satisfying⌦� ' 0.23. In Sec. VI we present results for b ! s� and Bs ! µ+µ� in the (tan �,M1/2)plane, and in Sec. VII we analyze implications for dark matter direct detection and showthat FP SUSY remains consistent with current null results. Finally, in Sec. VIII we showthat the observed deviations of (g�2)µ from SM expectations may be easily explained in FPSUSY (but not in the FP region). Our findings are summarized in Sec. IX. The robustnessof our numerical analyses is discussed in the Appendix.

II. FOCUS POINT SUPERSYMMETRY

In SUSY, the Z boson mass is determined at tree-level by the relation

1

2m2

Z = �µ2 +m2

Hd�m2

Hutan2 �

tan2 � � 1

��mweak

, (1)

where µ is the Higgsino mass parameter, m2Hd,u

are the soft SUSY-breaking Higgs mass

parameters, tan � ⌘ hH0ui/hH0

di is the ratio of Higgs boson vacuum expectation values, andall of these are evaluated at a renomalization group scale near mweak ⇠ 100 GeV � 1 TeV.For the moderate and large values of tan� required by current Higgs mass bounds, this maybe simplified to

1

2m2

Z ⇡ �µ2 �m2Hu

��mweak

. (2)

The weak-scale parameter m2Hu

depends on a set of fundamental parameters {ai}, typicallytaken to be grand unifed theory (GUT)-scale soft SUSY-breaking parameters, such as scalarmasses mf , gaugino masses Mi, and trilinear scalar couplings Ai. Naturalness requires thatmZ not be unusually sensitive to variations in the fundamental parameters ai. This doesnot necessarily imply ai ⇠ mZ for every i, however, because terms involving some ai in theexpression for m2

Z may be suppressed by small numerical coe�cients.In the class of FP SUSY models studied in Refs. [9–12], the fundamental GUT-scale

parameters satisfy�m2

Hu,m2

TR,m2

(T,B)L

�= m2

0 (1, 1 + x, 1� x) (3)

all other scalar masses <⇠ O(10 TeV) (4)

Mi, Ai<⇠ 1 TeV (5)

for moderate tan �, or�m2

Hu,m2

TR,m2

(T,B)L,m2

BR,m2

Hd

�= m2

0 (1, 1 + x, 1� x, 1 + x� x0, 1 + x0) (6)


Mi, Ai<⇠ 1 TeV (8)

for high tan �, where the top and bottom Yukawa couplings are comparable. In Eqs. (3)and (6), x and x0 are arbitrary constants, but for any values of x and x0, the weak-scale isinsensitive to variations in m0, even for multi-TeV m0. In other words, with these GUT-scale boundary conditions, renormalization group evolution takes m2

Huto values around m2

Z

at the weak scale, almost independent of its initial GUT-scale value. This “focusing” ofrenormalization group trajectories does not apply to the top and bottom squark masses or,

3

the correct ⌦�, and present results in the (tan �,M1/2) plane, with every point satisfying⌦� ' 0.23. In Sec. VI we present results for b ! s� and Bs ! µ+µ� in the (tan �,M1/2)plane, and in Sec. VII we analyze implications for dark matter direct detection and showthat FP SUSY remains consistent with current null results. Finally, in Sec. VIII we showthat the observed deviations of (g�2)µ from SM expectations may be easily explained in FPSUSY (but not in the FP region). Our findings are summarized in Sec. IX. The robustnessof our numerical analyses is discussed in the Appendix.

II. FOCUS POINT SUPERSYMMETRY

In SUSY, the Z boson mass is determined at tree-level by the relation

1

2m2

Z = �µ2 +m2

Hd�m2

Hutan2 �

tan2 � � 1

��mweak

, (1)

where µ is the Higgsino mass parameter, m2Hd,u

are the soft SUSY-breaking Higgs mass

parameters, tan � ⌘ hH0ui/hH0

di is the ratio of Higgs boson vacuum expectation values, andall of these are evaluated at a renomalization group scale near mweak ⇠ 100 GeV � 1 TeV.For the moderate and large values of tan� required by current Higgs mass bounds, this maybe simplified to

1

2m2

Z ⇡ �µ2 �m2Hu

��mweak

. (2)

The weak-scale parameter m2Hu

depends on a set of fundamental parameters {ai}, typicallytaken to be grand unifed theory (GUT)-scale soft SUSY-breaking parameters, such as scalarmasses mf , gaugino masses Mi, and trilinear scalar couplings Ai. Naturalness requires thatmZ not be unusually sensitive to variations in the fundamental parameters ai. This doesnot necessarily imply ai ⇠ mZ for every i, however, because terms involving some ai in theexpression for m2

Z may be suppressed by small numerical coe�cients.In the class of FP SUSY models studied in Refs. [9–12], the fundamental GUT-scale

parameters satisfy�m2

Hu,m2

TR,m2

(T,B)L

�= m2

0 (1, 1 + x, 1� x) (3)


Mi, Ai<⇠ 1 TeV (5)

for moderate tan �, or�m2

Hu,m2

TR,m2

(T,B)L,m2

BR,m2

Hd

�= m2

0 (1, 1 + x, 1� x, 1 + x� x0, 1 + x0) (6)


Mi, Ai<⇠ 1 TeV (8)

for high tan �, where the top and bottom Yukawa couplings are comparable. In Eqs. (3)and (6), x and x0 are arbitrary constants, but for any values of x and x0, the weak-scale isinsensitive to variations in m0, even for multi-TeV m0. In other words, with these GUT-scale boundary conditions, renormalization group evolution takes m2

Huto values around m2

Z

at the weak scale, almost independent of its initial GUT-scale value. This “focusing” ofrenormalization group trajectories does not apply to the top and bottom squark masses or,

3

[’99 Feng, Matchev, Moroi : mHu2 = mHd2 = mQ32 = mU32 >> gaugino mass][’13 Yokozaki, Yanagida : M3 : M2 = 0.4 : 1 in gaugino mediation]

[ Models in gauge mediation, see e.g. ’15 Murayama, Yokozaki, Yanagida ]

For a large tanβ, the weakscale is of O(mHu2 ) :

Higgsino searches in O(100)GeV range are important !


SUSY (in particular the stops) in the TeV range.

The weakscale can be obtained from the TeV SUSY naturally !

We do not think that <H> = 174GeV is naturally explained by the models the mass parameters of O(10-1000) TeV.

(may be a matter of taste again though…)

This is the simplest interpretation of the 125GeV Higgs boson mass.

One simple answer is : SUSY with O(10-1000)TeV is much much better than the Standard Model.

SM : mhiggs2/MGUT2 ~ 10-(24-28)

MSSM : mhiggs2/MSUSY2 ~ 10-(4–8)

Not very convincing though…


SUSY (in particular the stops) in the O(10-1000) TeV range.

Clearly, we need more consideration.So far, I do not have very convincing arguments...

Combination with Landscape/habitability arguments ? For <H> = 174GeV , it seems better to have SUSY in the electroweak scale.If some habitable conditions put lower limits on the SUSY scale, then the peak of the distribution of MSUSY can be much higher than MW.

(a) Landscape of vacua

mSUSY

Distribution of mSUSY

(b) Landscape of vacua of the flat universe

V0 ~ 0

(c) Landscape of vacua of vEW = 174GeV

~vEW

vEW ~174GeV

mSUSY


mSUSY


Figure 2: Schematic illustration of how to deduce the probable range of mSUSY. In each panel, the dotsdenote vacua. From (a) to (b), we restrict the landscape to vacua with an almost vanishing cosmologicalconstant, which, as we expect, leads to a sharply peaked distribution of mSUSY biased towards lowenergies. From (b) to (c), we restrict the landscape to vacua with an electroweak scale of vEW ' 174GeV,which results in a distribution peaked around vEW.

triggered by the sparticle masses in the MSSM ((c) in Fig. 2). As a result, we end up with a

distribution of mSUSY which peaks around vEW. This means once again that sparticle masses

most probably lie in the range of a few hundred GeV in view of electroweak naturalness.

In both approaches, we end up with more or less the same conclusion: mSUSY should be at

around a few hundred GeV. (In the following, we shall call the former approach the frequentist

approach and the later approach the Bayesian approach.) Here, it should be emphasized that

our deductions of the range of mSUSY are based on the principle of mediocrity [18], i.e., in both

approaches we have assumed that we are typical observers living in a typical habitable vacuum.

This is the reason why we obtained a similar conclusions in these two di↵erent approaches.

The big problem now is that the resultant ranges of mSUSY in both approaches are in tension

with the null discovery of sparticles at the LHC as well as with the observed Higgs boson mass.

This means that, unless we find a way to depart from the above argument and alter the ranges

deduced above, we almost lose ground on the postulation of low-scale SUSY from the standpoint

of electroweak naturalness.

The above conclusion should, however, change if there are crucial restrictions not accounted

for in the above argument. In the following, we are going to argue that the domain wall problem

related to R-symmetry breaking corresponds exactly to such a missing selection rule. Since

we are trying to shave the distribution function of mSUSY by applying the missing selection

7

~MW

(a) Landscape of vacua

mSUSY


(b) Landscape of vacua of the flat universe

V0 ~ 0

(c) Landscape of vacua of vEW = 174GeV

~vEW

vEW ~174GeV

mSUSY


mSUSY


Figure 2: Schematic illustration of how to deduce the probable range of mSUSY. In each panel, the dotsdenote vacua. From (a) to (b), we restrict the landscape to vacua with an almost vanishing cosmologicalconstant, which, as we expect, leads to a sharply peaked distribution of mSUSY biased towards lowenergies. From (b) to (c), we restrict the landscape to vacua with an electroweak scale of vEW ' 174GeV,which results in a distribution peaked around vEW.

triggered by the sparticle masses in the MSSM ((c) in Fig. 2). As a result, we end up with a

distribution of mSUSY which peaks around vEW. This means once again that sparticle masses

most probably lie in the range of a few hundred GeV in view of electroweak naturalness.

In both approaches, we end up with more or less the same conclusion: mSUSY should be at

around a few hundred GeV. (In the following, we shall call the former approach the frequentist

approach and the later approach the Bayesian approach.) Here, it should be emphasized that

our deductions of the range of mSUSY are based on the principle of mediocrity [18], i.e., in both

approaches we have assumed that we are typical observers living in a typical habitable vacuum.

This is the reason why we obtained a similar conclusions in these two di↵erent approaches.

The big problem now is that the resultant ranges of mSUSY in both approaches are in tension

with the null discovery of sparticles at the LHC as well as with the observed Higgs boson mass.

This means that, unless we find a way to depart from the above argument and alter the ranges

deduced above, we almost lose ground on the postulation of low-scale SUSY from the standpoint

of electroweak naturalness.

The above conclusion should, however, change if there are crucial restrictions not accounted

for in the above argument. In the following, we are going to argue that the domain wall problem

related to R-symmetry breaking corresponds exactly to such a missing selection rule. Since

we are trying to shave the distribution function of mSUSY by applying the missing selection

7

~MW

peak at mSUSY >>MW

Arguments depend on a lot of assumptions…Difficult to be confirmed experimentally…

Once additional light scalar bosons requiring fine-tuning are discovered, this explanation becomes much less convincing.

→


SUSY (in particular the stops) in the O(10-1000) TeV range.

What do we get once we accept O(10-1000)TeV SUSY ?

This is the simplest interpretation of the 125GeV Higgs boson mass.

They can be often suppressed by symmetries such as R-symmetry !

Gaugino masses are not necessarily O(10-1000)TeV .

→ The models with O(10-1000)TeV SUSY are testable at the LHC !

Are those scenarios interesting ?

High Scale SUSY

There are interesting models which is motivated by consistencies in cosmology !

High Scale SUSY at 100TeV - PeV

Model building is very simple !Consistent with cosmology (good DM candidate, no Gravitino/Polonyi problem)

MSSM sector

R sector

Pure Gravity Mediation model

Fine-tuning problem between O(10-1000)TeV and O(100)GeV…

SUSY sector

They are connected by generic Planck suppressed operators with each other.

100TeV - 1000TeV

10TeV

1TeV

100GeV

sfermionsHeavy Higgs bosonsHiggsino

Gluino

Bino

Wino

Higgs boson

}

Fine-tuning

~ m3/2 = O(100)TeV

Gaugino Masses are One-Loop Suppressed !

[’04 Wells, 06’MI,Moroi,Yanagida,12 MI, Yanagida, ’12 Arkani-hamed, Gupta, Kaplan, Weiner, Zorawski…]

Loop suppressed

Gaugino Masses = Anomaly Mediation + Higgsino Mediation[‘99 Giudice, Luty, Murayama, Rattazzi, ’99 Gherghetta, Giudice, Wells]

Mini-Split Spectrum

Current limits via gluino production [‘12, Bhattacherjee, Feldstein, MI, Matsumoto, Yanagida]

Multi-jets + Missing pT search(conventional SUSY search)

mgluino > 1.8 TeV or mwino > 600GeV

For gluino→tt+wino or bb+wino, the constraints get a little more stringent.

[@95%CL: ATLAS-CONF-2015-062 13TeV, 3.2fb-1]

3

2

1

0.51000

Wino mass (GeV)

Glu

ino

mas

s (T

eV)

30010050

mbi

no <

mw

ino

8TeV&20.3fb-1(conventional)

7TeV&5fb-1 (track)

mwino < 400GeV[FERMI-LAT : dSph]

AMSB

mgluino > 1TeV or mwino > 800GeV

3

2

1

0.51000

Wino mass (GeV)

Glu

ino

mas

s (T

eV)

30010050

mbi

no <

mw

ino

8TeV&20.3fb-1(conventional)

7TeV&5fb-1 (track)

14TeV&300fb-1

(conventional)

14TeV&300fb-1(track)

AMSB

Prospects ?

Mgluino ~ 2.3 TeV (14TeV,300fb-1) Mgluino ~ 2.7 TeV (14TeV,3000fb-1) Mgluino ~5.8 TeV (33TeV, 3000fb-1)

[arXiv:1310.0077]

13TeV&13.3fb-1(ICHEP2016)put by hand


Direct Wino Production

Neutralino missing Et

Chargino track

slow pion

[GeV]1±r¾

m100 150 200 250 300 350 400 450 500 550 600

[MeV

]1r¾m6

140

150

160

170

180

190

200

ATLAS Preliminary

= 8 TeVs, -1 L dt = 20.3 fb0)theorym1 ±Observed 95% CL limit (

)expm1 ±Expected 95% CL limit (, EW prod.)-1 = 7 TeV, 4.7 fbsATLAS (

LEP2 exclusionTheory (Phys.Lett.B721 (2013) 252-260)

±

1r¾‘Stable’

> 0µ = 5, `tan

Hea

vy w

ino

limit

by Y

amad

a (2

009)

150

155

160

165

170

100 1000

δm

[MeV

]

mneutralino [GeV]

Hea

vy w

ino

limit

by Y

amad

a (2

009)

two-loopone-loop

Figure 5: The wino mass splitting δm as a function of mχ0 . The dark green

band shows δm at the one-loop level which is evaluated by Eq. (10) with uncertainty

induced by Q dependence, and the red band shows δm at two-loop which is evaluated

by Eq. (5) in MS scheme. The light green band shows the uncertainty for one-loop

result evaluated by Eq. (16). The uncertainties for the two-loop result induced by

the SM input parameters and the non-logarithmic corrections are negligible (see

Tab. 1). An arrow shows the result of Ref. [29], which is given by δm = 164.4 MeV

for mh = 125 GeV and mt = 163.3 GeV.

12

Limits (disappearing track search):

mwino > 130GeV (7TeV&5fb-1) using TRTmwino > 270GeV (8TeV&20fb-1) using SCT & TRT

→Prospects: Mwino ~ 500GeV (14TeV,300fb-1) Mwino ~ 650GeV (14TeV,3000fb-1) Mwino ~ 3TeV (100TeV,3000fb-1) [1407.7058, Cirelli, Sala, Taoso]

Main decay mode : χ± → χ0 + π± : τwino = O(10-10) sec.

[arXiv:1310.3675]

[arxiv:1210.2852]

[’12 Ibe,Mastumoto,Sato]



Wino dark matter is very successful !

500 1000 1500 2000 2500 3000106

107

108

109

1010

1011

M2êGeV

T RêGe

V

Figure 3: The required reheating temperature of universe as a function of the wino mass for theconsistent dark matter density. We have used the thermal relic density given in Refs. [14, 15].The color bands correspond to the 1� error of the observed dark matter density, ⌦h2 = 0.1126±0.0036 [29]. For a detailed discussion see also Ref. [10].

the gravitino number density which is proportional to the reheating temperature TR after

inflation,

⌦(NT )h2(M2

, TR) ' 0.16⇥✓

M2

300GeV

◆✓TR

1010 GeV

◆. (12)

The total relic density is given by,

⌦h2 = ⌦(TH)(M2

) + ⌦(NT )h2(M2

, TR) . (13)

Therefore, the wino which is lighter than 2.7TeV can be the dominant component of the

dark matter for an appropriate reheating temperature.

Fig. 3 shows the required reheating temperature of universe as a function of the wino

mass for the consistent dark matter density. The color bands correspond to the 1� error

of the observed dark matter density, ⌦h2 = 0.1126± 0.0036 [29]. It is remarkable that the

required reheating temperature is consistent with the lower bound on TR for the successful

thermal leptogenesis, TR & 109.5GeV [12].

Now, let us interrelate the wino dark matter density and the lightest Higgs boson mass.

As we have discussed, the lightest Higgs boson mass is determined for given MSUSY

=

O(m3/2) and tan �. The wino mass is, on the other hand, is given by,

M2

' 3⇥ 10�3 m3/2 , (14)

10

[’11 MI, Yanagida]Lo

g 10

[TR/

GeV

]

mwino/GeV

non-thermal DM from the gravitino decay

Thermal Wino dark matter Mwino ~ 2.8TeV

[’07 Hisano, Matsumoto, Nagai, Saito, Senarmi]

Non-thermal Wino dark matter from gravitino decay

Mwino < 1-1.5 TeVfor successful leptogenesis (TR > 109GeV).

Indirect search by gamma-ray from dwarf Spheroidal galaxies are promising !

Fermi-LAT 6 years data excluded the wino dark matter in

Mwino < 400 GeV (classical dSphs)

[For recent J-factor estimation ’16 Hayashi, Ichikawa, Matsumoto, MI, Ishigaki, Sugai]

Courtesy of S.Matsumoto

R-invariant Gauge Mediation

the minimal µ-term, we derive an upper bound on the gluino mass from the observed Higgs

boson mass by exploiting the predicted ratio between the gluino and the stop masses in the

R-invariant gauge mediation model. As a result of the upper bound, we find that a large

portion of parameter space can be tested by the LHC Run-II with an integrated luminosity

of 300 fb�1, unless model parameters are highly optimized to obtain a large gluino mass.

We also discuss whether the R-invariant direct gauge mediation model can explain the

3� excess of Z+jets+Emiss

T events reported by the ATLAS Collaboration [8]. We seek a

spectrum similar to the one in Ref. [9] where the gluino mainly decays into a gluon and a

Higgsino via one-loop corrections. With such a spectrum, the excess can be explained while

evading all the other constraints from SUSY searches at the LHC.

The paper is organized as follows. In section II, we discuss the consistency between

the R-invariant direct gauge mediation model and the minimal model of the µ-term. In

section III, we derive an upper bound on the gluino mass from the observed Higgs boson

mass. In section IV, we discuss whether the R-invariant direct gauge mediation can explain

the signal reported by the ATLAS Collaboration. The last section is devoted to the summary

of our discussions.

II. Bµ–PROBLEM IN R-INVARIANT DIRECT GAUGE MEDIATION MODEL

A. R-invariant Direct Gauge Mediation Model

We first review the minimal R-invariant direct gauge mediation model constructed in

Ref. [4, 5] (see also Ref. [10]). This model introduces NM sets of messenger fields, i, i,

0i and

0i, which are respectively 5, 5, 5 and 5 representations of the SU(5) gauge group

of the grand unified theory (GUT). The index i = 1, · · · , NM labels each set of messengers.

Messengers of each set directly couple to a supersymmetry breaking gauge singlet field S

in the superpotential,

W = WSUSY

+ kS i i +M

i 0i +M

¯

i 0i , (1)

where k denotes a coupling constant and M ,¯ are mass parameters. W

SUSY

encapsulates

a dynamical SUSY breaking sector such as those in Ref. [11–13] whose e↵ective theory is

3

R-invariant Gauge Mediation Model simply given by

WSUSY

' ⇤2S , (2)

where ⇤ denotes the associated dynamical scale. Due to the linear term of S in the super-

potential, the SUSY breaking field obtains a non-vanishing F -term expectation value. It

should be noted that the form of the superpotential in Eq. (1) is protected by an R-symmetry

with the charge assignments S(2), i(0), i(0), 0i(2) and 0

i(2),2 which gives the origin

of the name of the R-invariant direct gauge mediation (see also appendixA). Due to this

peculiar form of the superpotential, the SUSY breaking vacuum is not destabilized by the

couplings to the messenger fields.

It should be emphasized that the R-symmetry needs to be broken spontaneously to

generate non-vanishing MSSM gaugino masses. Such spontaneous R-symmetry breaking

can be achieved, for example, through a simple extension of the dynamical SUSY breaking

model [11, 12] with an extra U(1) gauge interaction [6]. See also Refs. [14–18] for radiative

R-symmetry breaking in more generic models.3 Altogether, we postulate that the SUSY

breaking field S obtains its expectation value,

hS(x, ✓)i = S0

+ F ✓2 , (3)

where S0

denotes the vacuum expectation value of the A-term of S and ✓ is the fermionic

coordinate of the superspace.

Due to the stability of the SUSY breaking vacuum, the model is viable even when the

reheating temperature of the Universe is very high. Thus, the model is consistent with

thermal leptogenesis with TR & 109GeV [22]. This feature should be compared with other

types of direct gauge mediation models where a SUSY breaking vacuum is destabilized by

messenger couplings such as

W = WSUSY

+ kS i i , (4)

(see e.g., Ref. [23]). In such cases, the thermal history of the Universe and/or the masses of

2 The charges are assigned up to U(1) messenger symmetries which are eventually broken by mixing with

MSSM fields.3 It is also possible to construct O’Raifeartaigh models where spontaneous SUSY and R-symmetry breakings

are achieved at tree level [19–21].

4

( S : SUSY breaking field, Ψ : Messengers )

[’97 Izawa, Nomura, Tobe, Yanagida]

→The SUSY vacuum in this model is stable !

MSSM Spectrum : Msfermion >> Mgaugino

[This is due to d/dS(det[MMess]) = 0 in R-invariant models and hence generic! ]

the messenger fields are severely restricted [3].4

B. Gauge Mediated Mass Spectrum

We now summarize the gauge mediated mass spectrum of MSSM particles. The most

distinctive feature of the MSSM spectrum in the R-invariant direct gauge mediation is that

gaugino masses vanish at the one-loop level to the leading order of the SUSY breaking pa-

rameter, O(kF/Mmess

) [4, 5] and are suppressed by a factor of O(k2F 2/M4

mess

) in comparison

with those in the conventional gauge mediation. In the following, we collectively denote the

mass scale of the messenger sector by Mmess

. Scalar masses, on the other hand, appear at

the leading order of the SUSY breaking parameter at the two-loop level. Therefore, gauge

mediated MSSM gaugino masses, Ma (a = 1, 2, 3), and MSSM scalar masses, mscalar

, are

roughly given by

Ma ⇠ g2a16⇡

kF

Mmess

⇥O✓

k2F 2

M4

mess

◆⇥ (0.1� 0.3) , (5)

mscalar

⇠ g2a16⇡

kF

Mmess

, (6)

where ga (a = 1, 2, 3) denote the gauge coupling constants of the MSSM gauge interactions.

A factor of O(0.1) at the end of Eq. (5) for the gaugino masses results from numerical

analyses (see Fig. 1 and the following discussions). As a result, the predicted spectrum is

hierarchical between gaugino masses and sfermion masses.

To date, searches for gluino pair production at the ATLAS and the CMS experiments

have put severe lower limits on the gluino mass at around 1.4TeV at 95%CL. The limits

are applicable for cases where the bino either is stable [25, 26] or decays into a photon and

a gravitino inside the detectors as the next-to-the lightest superparticle (NLSP) [27, 28]. To

satisfy this constraint, we infer that

kF

Mmess

⇥O✓

k2F 2

M4

mess

◆= 106�7 GeV , (7)

so that the gluino is su�ciently heavy (see Eq. (5)).

Due to the hierarchy between the gaugino masses and sfermion masses in Eqs. (5) and (6),

4 For phenomenological studies of this class of models after the LHC Run-I experiment, see e.g., Ref. [24].

5

the messenger fields are severely restricted [3].4

B. Gauge Mediated Mass Spectrum

We now summarize the gauge mediated mass spectrum of MSSM particles. The most

distinctive feature of the MSSM spectrum in the R-invariant direct gauge mediation is that

gaugino masses vanish at the one-loop level to the leading order of the SUSY breaking pa-

rameter, O(kF/Mmess

) [4, 5] and are suppressed by a factor of O(k2F 2/M4

mess

) in comparison

with those in the conventional gauge mediation. In the following, we collectively denote the

mass scale of the messenger sector by Mmess

. Scalar masses, on the other hand, appear at

the leading order of the SUSY breaking parameter at the two-loop level. Therefore, gauge

mediated MSSM gaugino masses, Ma (a = 1, 2, 3), and MSSM scalar masses, mscalar

, are

roughly given by

Ma ⇠ g2a16⇡

kF

Mmess

⇥O✓

k2F 2

M4

mess

◆⇥ (0.1� 0.3) , (5)

mscalar

⇠ g2a16⇡

kF

Mmess

, (6)

where ga (a = 1, 2, 3) denote the gauge coupling constants of the MSSM gauge interactions.

A factor of O(0.1) at the end of Eq. (5) for the gaugino masses results from numerical

analyses (see Fig. 1 and the following discussions). As a result, the predicted spectrum is

hierarchical between gaugino masses and sfermion masses.

To date, searches for gluino pair production at the ATLAS and the CMS experiments

have put severe lower limits on the gluino mass at around 1.4TeV at 95%CL. The limits

are applicable for cases where the bino either is stable [25, 26] or decays into a photon and

a gravitino inside the detectors as the next-to-the lightest superparticle (NLSP) [27, 28]. To

satisfy this constraint, we infer that

kF

Mmess

⇥O✓

k2F 2

M4

mess

◆= 106�7 GeV , (7)

so that the gluino is su�ciently heavy (see Eq. (5)).

Due to the hierarchy between the gaugino masses and sfermion masses in Eqs. (5) and (6),

4 For phenomenological studies of this class of models after the LHC Run-I experiment, see e.g., Ref. [24].

5

bé

gé wéHé

EéR

LéL

QéL

DéR,UéR

0.80 0.85 0.90 0.95 1.001.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

k F ê HMYMY L

Log 1

0@MassêG

eVD

bé

gé

wéHé

EéR

LéL

QéL

DéR,UéR

0 1 2 3 4 51.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

kS0 ê MY MY

Log 1

0@MassêG

eVD

FIG. 1. The gauge mediated mass spectrum. The curves give the masses of various sparticles. In

the figure, we take M

= M¯

= 2 ⇥ 106GeV, NM = 1 and tan� = 10. In the left plot, we take

kS0

/p

M

M¯

= 1 and show the spectrum as a function of kF/(M

M¯

). In the right plot, we

take kF/(M

M¯

) = 0.9 and show the spectrum as a function of kS0

/p

M

M¯

.

R-symmetry breaking, while the scalar masses do not. In the region of kS0

/pM

M¯

> 1,

both the gaugino masses and the scalar masses are decreasing with kS0

/pM

M¯

. This is

because the messenger scale is dominated by kS0

as in the conventional gauge mediation in

that region.

For subsequent discussions, we split the messenger fields of SU(5) GUT multiplets into

the SM gauge group SU(3)C ⇥ SU(2)L ⇥ U(1)Y representations: 5 = (3�1/3,21/2) and

5 = (¯31/3,2�1/2), such as (0) = (D(0), L(0)) and (0) = (D(0), L(0)), respectively. Accordingly,

we also distinguish the parameters in Eq. (1) for each messenger using subscripts: kD and

kL, MD, ¯D and ML,¯L, respectively.

In the analysis of Refs. [7, 32], it is assumed that k’s and M ’s satisfy the so-called GUT

conditions at the GUT scale:

kD = kL , MD = ML , M¯D = M

¯L . (11)

In this paper, we do not impose these conditions in view of the fact that the doublets and

the triplets of the Higgs multiplets in the GUT models are required to split. In fact, the

doublet-triplet splitting in the Higgs sector is most naturally achieved in GUT models with

product gauge groups [33]. In those models, the GUT conditions in Eq. (11) are not expected

to be satisfied generically (see also Ref. [34] for a recent discussion). In the following, we

simply take k’s and M ’s of the D and the L-type messengers as independent parameters.

7

(Relative Size of spontaneous R-breaking)

tanβ = 10

[’15 Chiang, Harigaya,Ibe,Yanagida]

kF = 0.9 MΨ2


Upper limit on the gluino mass ! [’15 Chiang, Harigaya,Ibe,Yanagida]

kDS0êMD=1

NM=1

NM=2

MD=105GeVMD=106GeVMD=107GeV

0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.1

0.2

0.3

0.4

kDF ê MDMD

mgéêm s

top

FIG. 5. The ratio between the gluino mass and the stop mass, mstop

⌘ pm

˜t1m

˜t2, as a function

of kDF/(MDM ¯D) for NM = 1 and NM = 2. In the figure, we fix MD = M¯D and kDS0

= MD in

order to optimize the gluino mass.

10TeV to account for the observed Higgs boson mass, mh = 125.09± 0.21± 0.11GeV [28].

Thus, by remembering that the gluino mass is limited from above for a given squark mass,

the observed Higgs boson mass leads to an upper bound on the gluino mass.

To obtain the limit on the gluino mass from the observed Higgs boson mass, let us first

consider the ratio between the gluino mass and the stop mass, which is shown as a function

kDF/(MDM ¯D) for NM = 1 and NM = 2 in Fig. 5. Here we take kDS0

= (MDM ¯D)1/2 to

maximize the gluino mass, as given in Fig. 1. We have also checked that a heavier gluino

mass cannot be achieved even for MD 6= M¯D. The figure indicates that the ratio is a

monotonically increasing function of kDF/(MDM ¯D) and that mg/mstop

. 0.2 for NM = 1

and mg/mstop

. 0.3 for NM = 2.

From the observed Higgs boson mass, the stop mass is restricted to be in the O(10) TeV

regime. The left plot of Fig. 6 shows the Higgs boson mass as a function of the stop mass

for tan � & 50. In our analysis, we use SusyHD [46] to calculate the Higgs boson mass. The

band represents uncertainties of our prediction, originating from (i) higher-order corrections

of the Higgs mass calculation, (ii) uncertainties of Standard Model input parameters, and

(iii) choices of model parameters that a↵ect the SUSY spectrum other than stop masses. In

our analysis, we take the first uncertainty to be 1GeV to make our discussions conservative

(see also Ref. [46]). As for the uncertainties from Standard Model parameters, the top mass

15

The gaugino are lighter than the sfermions!Mgluino/Mstop < 0.2 - 0.3

NLSP = Stable Bino or Meta-stable Bino decaying into photon + gravitino

To reproduce 125GeV Higgs boson mass, Mstop < 20TeV (susyHD)

→ Gluino mass is bounded from above.

kDF êMD=2.5¥106GeVMD=MD

kDS0=MD

kDS0=MDê2

14TeV , 3000fb-1

14TeV , 300fb-1

0.5 0.6 0.7 0.8 0.9 1.01000

2000

3000

4000

5000

kDF êHMDMDL

mgé êG

eV

kDF êMD=1.8¥106GeVMD=MD

kDS0=MD

kDS0=MDê214TeV , 3000fb-1

14TeV , 300fb-1

33TeV , 3000fb-1

0.5 0.6 0.7 0.8 0.9 1.01000

2000

3000

4000

5000

6000

kDF êHMDMDL

mgé êG

eV

FIG. 7. The upper limit on the gluino mass as a function of kDF/(MDM ¯D) for NM = 1 (left) and

NM = 2 (right). Each plot corresponds to the stop mass around 20TeV, the upper limit obtained

from the Higgs boson mass. The blue curves show the upper limits for an optimal R-symmetry

breaking, kDS0

= (MDM ¯D)1/2, and the green curves show those for a less optimal R-symmetry

breaking, kDS0

= (MDM ¯D)1/2/2. The dashed lines are the expected 95%CL limits on the gluino

mass [48].

for NM = 1 unless the gluino mass is highly optimized. The figure also shows that a 33-TeV

hadron collider will cover almost the entire gluino mass range.

IV. Z+JETS+MISSING ET

Recently, the ATLAS Collaboration reported a 3� excess in the search for events with a

Z boson (decaying into a lepton pair) accompanied by jets and a large missing transverse

energy (Emiss

T ) [8]. They observed 29 events in a combined signal region with di-electrons

and di-muons at the Z-pole in comparison with an expected background of 10.6±3.2 events.

Although the significance of the signal is not su�ciently high at this point, many attempts

have been made to explain the excess using the MSSM [9, 49–52]. The signal requires colored

SUSY particles lighter than about 1.2TeV [49]. In this section, we briefly discuss whether

the R-invariant direct gauge mediation model can explain the reported signal.

As discussed in the previous section, the R-invariant direct gauge mediation model pre-

dicts a mass hierarchy between the gauginos and the scalars. Hence, the candidate colored

SUSY particle required for the signal is inevitably the gluino. For such a light gluino,

constraints from searches for SUSY particles with jets+Emiss

T are usually severe, and most

parameter region has been excluded [25, 26]. As shown in Ref. [9], however, a careful study

shows that the reported signal can be explained by the gluino production while evading all

17

(large tanβ is predicted due to a small B-term)

light Gravitino Mass region (m3/2 < O(10)eV)

light stable gravitino is very attractive from Cosmology

lighter gravitino might be preferred if we think of the naturalness problem from Cosmological Constant.

Recently, a severe upper limits are put from the CMB lensing and Cosmic Shear observations [’16 Osato, Sekiguchi, Shirasaki, Kamada, Yoshida]

CC = F2 - 3 m3/22 MPL2

m3/2 < 4.7 eV

I. INTRODUCTION

Low-scale gauge mediation models with a light gravitino mass, m3/2 < O(10) eV, is

very attractive, since the gravitino with a mass in this range does not cause astrophysical

nor cosmological problems [1–3]. In particular, such a light gravitino is consistent with

high reheating temperature which is essential for many baryogenesis scenarios as typified

in thermal leptogenesis [4] [see 5–7, for review]. A small gravitino mass is also motivated

since it may require a milder fine-tuning of the cosmological constant due to a smaller

supersymmetry (SUSY) breaking scale.

Recently, a severe upper limit on the mass of the light stable gravitino, m3/2 . 4.7 eV

(95%C.L.), has been put from CMB Lensing and Cosmic Shear [8]. With such a stringent

constraint, many models of low-scale gauge mediation are excluded when the squark masses

are required to be rather large to explain the observed Higgs boson mass, mH ' 125GeV [9].

For example, we immediately find that the above upper limit on the gravitino mass excludes

models in which the messenger fields couple to supersymmetry breaking sector perturba-

tively [10].

In this short note, we point out that the low-scale gauge mediation model can explain the

observed Higgs boson mass even for m3/2 . 4.7 eV when the messenger fields strongly couple

to the SUSY breaking sector. We also show that the gravitino mass cannot be smaller than

about 1 eV even in such models, which can be tested by future observations of 21 cm line

fluctuations [11].

II. MODELS WITH LOW-SCALE GAUGE MEDIATION

A. Low-scale gauge mediation and Higgs boson mass

In this note, we are interested in models with a gravitino mass in the eV range. For such

a light gravitino mass, the SUSY breaking scale must be low as,

pF ⇠ 65TeV ⇥

⇣m3/2

1 eV

⌘1/2

. (1)

Now, let us suppose that there are Nm pairs of and which are in the fundamental and

anti-fundamental representations of SU(5)GUT

� SU(3)C ⇥ SU(2)L ⇥ U(1)Y , respectively.

2

→

Stringent constraints on the SUSY masses in GMSB !

→ Closing this window is conceptually very important !

light Gravitino Mass region (m3/2 < O(10)eV)

g=1

m3ê2>4.7eVmgluino

<2.2TeV

Nmess=4tan b=40as=0.1185

mtop=173.21+0.87 GeV

105 106104

105

106

0.1

1.

10.

100.

MmessêGeV

F1ê2êGe

V

m3ê2êeV

mgluino<2.2TeV

m3ê2>4.7eVg=4p


mtop=173.21+0.87 GeV

105 106104

105

106

0.1

1.

10.

100.

MmessêGeV

F1ê2êGe

V

m3ê2êeV

FIG. 1. (Left) In the blue shaded region, the observed Higgs boson mass can be explained by thetop Yukawa radiative correction for y = 1. (Right) In the red shaded region, the observed Higgsboson mass can be explained by the top Yukawa radiative correction for y = 4⇡. In both panels,the upper left regions are excluded due to the tachyonic messenger fields, i.e. M2

m < Fm. Theregions with m

3/2 & 4.7 eV are excluded by the cosmological constraints. The green shaded regionsare excluded by the null results of searches for the tau slepton at the LHC. We take Nm = 4 andtan� = 40, although the results do not depend on tan� significantly as long as tan� = O(10).

Let us discuss whether the above soft masses can be consistent with the observed Higgs

boson mass, mH ' 125GeV. In the MSSM, the Higgs boson mass is constrained asmH . mZ

at the tree level, which is enhanced by the top Yukawa radiative corrections [12]. Then, the

observed Higgs boson mass, mH ' 125GeV, requires the squark masses (in particular the

stop masses) in multi-TeV range, which is in tension with the squark masses in Eq. (7) for

m3/2 < 4.7 eV.

In Fig. 1, we show the parameter region which is consistent with the observed Higgs

boson mass, mH = 125.09 ± 0.21 ± 0.11GeV [9]. In the figure, the Higgs boson mass is

consistently explained at the 2� level in the blue and red shaded regions for y = 1 and

y = 4⇡, respectively.1 Here, we take Nm = 4, so that the resultant squark masses are

as large as possible for given Mm and F while keeping the perturbativity of the gauge

coupling constants in the MSSM up to the scale of the grand unification. In our numerical

analysis, we use softsusy-3.7.3 [13] to solve the renormalization group evolution of the

1 In our analysis, we define the �2 estimator,

�2 =(mH � 125.09GeV)2

(0.21GeV)2 + (0.11GeV)2 + �m2

H

, (9)

where �mH denotes the theoretical uncertainty.4

The messenger fields couple to a SUSY breaking sector via a superpotential,

W = yZ +Mm . (2)

Here, the SUSY breaking sector is encapsulated in Z whose vacuum expectation value (VEV)

is assumed to be hZi = ✓2F . The coupling between the messenger fields and the SUSY

breaking sector is given by the term proportional to y. In this simple setup, the mass

splitting between the messenger scalars and the fermions is given by

Fm = yF . (3)

It should be noted that the mass splitting is required to be smaller than the messenger mass

scale, Mm, i.e.,

Fm < M2

m , (4)

to avoid the tachyonic messenger fields.

Below the messenger scale, the masses of superparticles are given by,

mgaugino

' Nm

✓g2

16⇡2

◆yF

Mm

, (5)

m2

sfermion

' 2C2

Nm

✓g2

16⇡2

◆2

✓yF

Mm

◆2

. (6)

Here, C2

is the quadratic Casimir invariant of representations of each sfermion, and g rep-

resents gauge coupling constant of the minimal SUSY Standard Model (MSSM). To satisfy

the cosmological constraint on the gravitino mass, m3/2 < 4.7 eV, the SUSY breaking scale is

required to bepF . 140TeV (see Eq. (1)). By combined with the non-tachyonic messenger

condition Eq. (4), we find that the soft terms are limited from above;

mgaugino

. Nm

✓g2

16⇡2

◆(yF )1/2 ' 0.9TeV ⇥Nm y1/2g2

⇣ m3/2

4.7 eV

⌘1/2

, (7)

m2

sfermion

. 2C2

Nm

✓g2

16⇡2

◆2

yF ' (1.3TeV)2 ⇥ C2

Nmg4y

⇣ m3/2

4.7 eV

⌘, (8)

at the messenger scale.

3

g=1

m3ê2>4.7eVmgluino

<2.2TeV


mtop=173.21+0.87 GeV

105 106104

105

106

0.1

1.

10.

100.

MmessêGeV

F1ê2êGe

V

m3ê2êeV

mgluino<2.2TeV

m3ê2>4.7eVg=4p


mtop=173.21+0.87 GeV

105 106104

105

106

0.1

1.

10.

100.

MmessêGeV

F1ê2êGe

V

m3ê2êeV

FIG. 1. (Left) In the blue shaded region, the observed Higgs boson mass can be explained by thetop Yukawa radiative correction for y = 1. (Right) In the red shaded region, the observed Higgsboson mass can be explained by the top Yukawa radiative correction for y = 4⇡. In both panels,the upper left regions are excluded due to the tachyonic messenger fields, i.e. M2

m < Fm. Theregions with m

3/2 & 4.7 eV are excluded by the cosmological constraints. The green shaded regionsare excluded by the null results of searches for the tau slepton at the LHC. We take Nm = 4 andtan� = 40, although the results do not depend on tan� significantly as long as tan� = O(10).

Let us discuss whether the above soft masses can be consistent with the observed Higgs

boson mass, mH ' 125GeV. In the MSSM, the Higgs boson mass is constrained asmH . mZ

at the tree level, which is enhanced by the top Yukawa radiative corrections [12]. Then, the

observed Higgs boson mass, mH ' 125GeV, requires the squark masses (in particular the

stop masses) in multi-TeV range, which is in tension with the squark masses in Eq. (7) for

m3/2 < 4.7 eV.

In Fig. 1, we show the parameter region which is consistent with the observed Higgs

boson mass, mH = 125.09 ± 0.21 ± 0.11GeV [9]. In the figure, the Higgs boson mass is

consistently explained at the 2� level in the blue and red shaded regions for y = 1 and

y = 4⇡, respectively.1 Here, we take Nm = 4, so that the resultant squark masses are

as large as possible for given Mm and F while keeping the perturbativity of the gauge

coupling constants in the MSSM up to the scale of the grand unification. In our numerical

analysis, we use softsusy-3.7.3 [13] to solve the renormalization group evolution of the

1 In our analysis, we define the �2 estimator,

�2 =(mH � 125.09GeV)2

(0.21GeV)2 + (0.11GeV)2 + �m2

H

, (9)

where �mH denotes the theoretical uncertainty.4

yF~ Mm2 yF~ Mm2

Most parameter regions have been excluded by the LHC searches (stau NLSP) for perturbative models (y < O(1)).

For non-perturbative models with y = O(4π), there is an allowed parameter region.

Future LHC and the cosmological observation (21cm observations) play important roles!

[’16 MI, Yanagida]

mh = 125GeV

perturbative non-perturbative

Summary

The Higgs boson mass at 125GeV disfavors very natural and simple SUSY models.

The Standard Model is in very good shape... ( Higgs can be fit by the simple elementary doublet. )

In view of 125GeV Higgs boson mass, the null SUSY results so far are not very surprising/discouraging.

Although naturalness arguments become arguable than before, still SUSY is the most attractive model beyond the Standard Model.

[ SUSY can be consistent with the SM Yukawa intereactions. SUSY can be consistent with cosmology including inflation and baryogengesis such as leptogenesis. ]

We still have a lot of chances to see TeV SUSY at the LHC !

SummaryNatural SUSY models

Model building is more complicated than before…

TeV SUSY

Parameter regions are getting smaller by direct searches.→ Please let me know if you find good (and less complicated) models !

We just need to wait for further results from the LHC !(Once it is discovered, it requires some extension to the MSSM.)

High scale SUSY (in particular Pure Gravity Mediation Model)

This class of models is not only the simplest interpretation but also motivated by cosmological consistencies.

Naturalness requires more scrutiny…

Not only searchable at the LHC, the model can be tested via indirect searches of dark matter and precision measurements.

[ Orthogonal to the above classification, models which account for the muon g-2 are also important. ]

Back Up Slides


figure shows that the required µ-term is indeed smaller than the stop mass scale. It should

be also noted that a smaller µ-term is also possible when m2

Hu(M

mess

) is slightly larger at

the messenger scale. This property is important for the discussions in section IV.

D. Gravitino Dark Matter

In gauge mediation models, the gravitino is the lightest supersymmetric particle (LSP).

By assuming R-parity conservation, it can serve as a candidate for dark matter. In the

regime of much lighter than MeV, the gravitino is thermalized in the early Universe, and its

relic abundance is estimated to be

⌦3/2h

2 ' 0.1

✓100

g⇤(TD)

◆⇣ m3/2

100 eV

⌘. (20)

Here m3/2 is the gravitino mass, and g⇤(TD) ' 100 denotes the e↵ective massless degree of

freedom in the thermal bath at the decoupling temperature [42]

TD ⇠ max

"Mg, 160GeV

✓g⇤(TD)

100

◆1/2 ⇣ m

3/2

10 keV

⌘2

✓2TeV

M3

◆2

#. (21)

As discussed above, a successful R-invariant direct gauge mediation requires

(kF )1/2 = 106�7 GeV . (22)

By assuming that the SUSY breaking field S breaks supersymmetry dominantly, the grav-

itino mass is given by

m3/2 ' 10 keV ⇥

✓0.1

k

◆✓(kF )1/2

2⇥ 106 GeV

◆2

. (23)

In this case, the thermally produced gravitino abundance in Eq. (20) is too large to be

consistent with the observed dark matter density.9

This tension is removed when the above relic density is diluted by entropy production by

9 The gravitino with a mass m3/2 ' 100 eV is not cold dark matter but hot dark matter. Hence, it is not a

viable candidate for dark matter even if the thermal relic abundance is consistent with the observed dark

matter density.

13

Gravitino mass (for 125 GeV Higgs ) :

a factor of

� ' 100⇥✓

100

g⇤(TD)

◆⇣ m3/2

10 keV

⌘(24)

after the gravitino decouples from the thermal bath.10 As shown in Ref. [6], an appropriate

amount of entropy can be provided by, for example, the decay of long-lived particles in the

dynamical SUSY breaking sector.11 Interestingly, the gravitino in this mass range is a good

candidate for a slightly warm dark matter [7] enabled via an appropriate dilution factor.

Finally, let us comment on the decay length of the NLSP, which is the bino in most

parameter space of the R-invariant direct gauge mediation model. The bino NLSP mainly

decays into a gravitino and a photon/Z-boson with the branching ratios

�(b ! 3/2 + �) ' 1

48⇡

M5

1

M2

PLm2

3/2

cos2 ✓W , (25)

�(b ! 3/2 + Z) ' 1

48⇡

M5

1

M2

PLm2

3/2

sin2 ✓W . (26)

Here MPL

' 2.4 ⇥ 1018GeV denotes the reduced Planck scale, and ✓W is the weak mixing

angle. Altogether, the decay length of the bino NLSP is given by

c⌧˜B ' 0.6m⇥

✓500GeV

M1

◆5 ⇣ m

3/2

10 keV

⌘2

. (27)

Therefore, the bino may or may not decay inside the detectors, depending on the gravitino

mass and the NLSP mass.

III. UPPER BOUND ON THE GLUINO MASS

As alluded to before, the R-invariant direct gauge mediation model predicts a hierarchy

between gaugino masses and scalar masses. We have also argued that tan� is required to be

large, tan � & 50, if we further assume that the µ-term is provided by the minimal µ-term in

the superpotential, Eq. (12). For such a large tan �, the stop mass is restricted to be around

10 In general, if the dilution factor is provided by a late-time decay of a massive particle which dominates the

energy density of the Universe, it is given by � ' Tdom

/Tdecay

, where Tdom

is the temperature at which

the massive particle dominates the energy density of the Universe and Tdecay

is its decay temperature.

In order not to a↵ect the Big-Bang Nucleosynthesis, we require Tdecay

& O(1–10)MeV, and hence the

dilution factor is bounded from above by � < Tdom

/O(1–10)MeV.11 A mass of 106�7 GeV for the messenger is too light to provide a su�cient dilution factor [43] (see also

appendix A). For other mechanisms of entropy production after the decoupling of gravitinos, see Refs [44,

45].

14

Bino decay length :



Hu(M

mess








⌦3/2h

2 ' 0.1

✓100

g⇤(TD)

◆⇣ m3/2

100 eV

⌘. (20)



TD ⇠ max

"Mg, 160GeV

✓g⇤(TD)

100

◆1/2 ⇣ m

3/2

10 keV

⌘2

✓2TeV

M3

◆2

#. (21)


(kF )1/2 = 106�7 GeV . (22)



m3/2 ' 10 keV ⇥

✓0.1

k

◆✓(kF )1/2

2⇥ 106 GeV

◆2

. (23)






matter density.

13

Gravitino thermalization temperature :

Gravitino thermal dark matter density :



Hu(M

mess








⌦3/2h

2 ' 0.1

✓100

g⇤(TD)

◆⇣ m3/2

100 eV

⌘. (20)



TD ⇠ max

"Mg, 160GeV

✓g⇤(TD)

100

◆1/2 ⇣ m

3/2

10 keV

⌘2

✓2TeV

M3

◆2

#. (21)


(kF )1/2 = 106�7 GeV . (22)



m3/2 ' 10 keV ⇥

✓0.1

k

◆✓(kF )1/2

2⇥ 106 GeV

◆2

. (23)






matter density.

13

We need entropy production ! (slightly warm dark matter)

Supersymmetry in the TeV ranges

missing pT search (the gravitino LSP with m3/2 << O(1)keV )

Figure 1: Typical production and decay-chain processes for the gluino-pair production GGM model for which theNLSP is a bino-like neutralino.

case, the final decay in each of the two cascades in a GGM event would be predominantly �01 ! � + G,

leading to final states with �� + EmissT .

In addition to the bino-like �01 NLSP, a degenerate octet of gluinos (the SUSY partner of the SM gluon) is

taken to be potentially accessible with 13 TeV pp collisions. Both the gluino and �01 masses are considered

to be free parameters, with the �01 mass constrained to be less than that of the gluino. All other SUSY

masses are set to values that preclude their production in 13 TeV pp collisions. This results in a SUSYproduction process that proceeds through the creation of pairs of gluino states, each of which subsequentlydecays via a virtual squark (the 12 squark flavour/chirality eigenstates are taken to be fully degenerate)to a quark–antiquark pair plus the NLSP neutralino. Other SM objects (jets, leptons, photons) may beproduced in these cascades. The �0

1 branching fraction to � + G is 100% for m�01! 0 and approaches

cos2 ✓W for m�01� mZ , with the remainder of the �0

1 sample decaying to Z + G. For all �01 masses, then, the

branching fraction is dominated by the photonic decay, leading to the diphoton-plus-EmissT signature. For

this model with a bino-like NLSP, a typical production and decay channel for strong (gluino) productionis exhibited in Figure 1. Finally, it should be noted that the phenomenology relevant to this search has anegligible dependence on the ratio tan � of the two SUSY Higgs-doublet vacuum expectation values; forthis analysis tan � is set to 1.5.

2 Samples of simulated processes

For the GGM models under study, the SUSY mass spectra and branching fractions are calculated us-ing SUSPECT 2.41 [15] and SDECAY 1.3b [16], respectively, inside the package SUSY-HIT 1.3 [17]. TheMonte Carlo (MC) SUSY signal samples are produced using Herwig++ 2.7.1 [18] with CTEQ6L1 partondistribution functions (PDFs) [19]. Signal cross sections are calculated to next-to-leading order (NLO) inthe strong coupling constant, including, for the case of strong production, the resummation of soft gluonemission at next-to-leading-logarithmic accuracy (NLO+NLL) [20–24]. The nominal cross section and

3

[TeV]Λ70 80 90 100 110 120

βta

n

10

20

30

40

50

60=1

grav>0, Cµ=3,

5=250 TeV, NmessGMSB: M

)theorySUSYσ1 ± observed limit (τ2

)expσ1 ± expected limit (τ2ATLAS Run-1 exclusionAll limits at 95% CL

(160

0 G

eV)

g~

(180

0 G

eV)

g~ (200

0 G

eV)

g~ (220

0 G

eV)

g~ (240

0 G

eV)

g~

ATLAS

-1=13 TeV, 3.2 fbs

)theorySUSYσ1 ± observed limit (τ2

)expσ1 ± expected limit (τ2ATLAS Run-1 exclusionAll limits at 95% CL

Figure 9: Exclusion contours at the 95% confidence level for the gauge-mediated supersymmetry-breaking model,based on results from the 2⌧ channel. The red solid line and the blue dashed line correspond to the observed andmedian expected limits, respectively. The yellow band shows the one-standard-deviation spread of expected limitsaround the median. The e↵ect of the signal cross-section uncertainty in the observed limits is shown as red dottedlines. The previous ATLAS result [14] obtained with 20.3 fb�1 of 8 TeV data is shown as the grey filled area.

9 Summary

A search for squarks and gluinos has been performed in events with hadronically decaying tau leptons,jets and missing transverse momentum, using 3.2 fb�1 of pp collision data at

ps = 13 TeV recorded

by the ATLAS detector at the LHC in 2015. Two channels, with either one tau lepton or at least twotau leptons, are separately optimised. The numbers of observed events in the di↵erent signal regions arein agreement with the Standard Model predictions. Results are interpreted in the context of a gauge-mediated supersymmetry breaking model and a simplified model of gluino pair production with tau-rich cascade decay. In the GMSB model, limits are set on the SUSY-breaking scale ⇤ as a function oftan �. Values of ⇤ below 92 TeV are excluded at the 95% CL, corresponding to gluino masses below2000 GeV. A stronger exclusion is achieved for large values of tan �, where ⇤ and gluino mass values areexcluded up to 107 TeV and 2300 GeV, respectively. In the simplified model, gluino masses are excludedup to 1570 GeV for neutralino masses around 100 GeV, neutralino masses up to 700 GeV are excludedfor all gluino masses between 800 GeV and 1500 GeV, while the strongest neutralino-mass exclusionof 750 GeV is achieved for gluino masses around 1400 GeV. A dedicated signal region provides goodsensitivity to scenarios with a small mass di↵erence between the gluino and the neutralino LSP.

24

neutralino NLSP (missing pT + photons)

stau NLSP (missing pT + tau)

Mgluino >1.6 - 1.8 TeV( Msquark >> TeV )

[arXiv:1607.05979]

q

q

�01

⌧

�01 ˜

p

p

q ⌧⌧

G

q ``

G

(a) GMSB

g

g

�±1

⌧/⌫⌧

�02 ⌧/⌫⌧

p

p

q q ⌫⌧/⌧⌧/⌫⌧

�01

qq ⌧/⌫⌧

⌧/⌫⌧

�01

(b) Simplified model

Figure 1: Diagrams illustrating the two SUSY scenarios studied in this analysis. In the GMSB model, the scalarlepton ˜ is preferentially a scalar tau ⌧1 for high values of tan �.

As in previous ATLAS searches [13, 14], the GMSB model is probed as a function of ⇤ and tan �, andthe other parameters are set to Mmes = 250 TeV, N5 = 3, sign(µ) = 1 and Cgrav = 1. For this choiceof parameters, the NLSP is the lightest scalar tau (⌧1) for large values of tan �, while for lower tan �values, the ⌧1 and the superpartners of the right-handed electron and muon (eR, µR) are almost degeneratein mass. The squark–antisquark production mechanism dominates at high values of ⇤. A typical GMSBsignal process is displayed in Fig. 1(a). The value of Cgrav corresponds to prompt decays of the NLSP.The region of small ⇤ and large tan � is unphysical since it leads to tachyonic states.

The other signal model studied in this analysis is a simplified model of gluino pair production [19] in an R-parity-conserving scenario. It is inspired by generic models such as the phenomenological MSSM [20,21]with dominant gluino pair production, light ⌧1 and a �0

1 LSP. Gluinos are assumed to undergo a two-stepcascade decay leading to tau-rich final states, as shown in Fig. 1(b). The two free parameters of the modelare the masses of the gluino (mg) and the LSP (m�0

1). Assumptions are made about the masses of other

sparticles, namely the ⌧1 and ⌫⌧ are mass-degenerate, and the �02 and �±1 are also mass-degenerate, with

m�±1 = m�02=

12

(mg + m�01) , m⌧1 = m⌫⌧ =

12

(m�±1 + m�01). (1)

Gluinos are assumed to decay to �±1 qq0 and �02qq with equal branching ratios, where q, q0 denote generic

first- and second-generation quarks. Neutralinos �02 are assumed to decay to ⌧⌧ and ⌫⌧⌫⌧ with equal

probability, and charginos �±1 are assumed to decay to ⌫⌧⌧ and ⌧⌫⌧ with equal probability. In the last stepof the decay chain, ⌧ and ⌫⌧ are assumed to decay to ⌧�0

1 and ⌫⌧�01, respectively. All other SUSY particles

are kinematically decoupled. The topology of signal events depends on the mass splitting between thegluino and the LSP. The sparticle decay widths are assumed to be small compared to sparticle masses,such that they play no role in the kinematics.

4

Mgluino >2 - 2.3 TeV( GMSB : Nm = 3 )

Mgluino >1.5 - 1.6 TeV( Msquark >> TeV )

ATLAS-CONF-2016-066

via gluino production

via gluino,squark production

via gluino production

Supersymmetry in the TeV ranges

stable stau search (GMSB with m3/2 > O(100)keV )

12 7 Results

Table 6: Summary of the pT, Ias, 1/b, and mass thresholds, the observed and predicted yieldspassing these criteria, and the resulting expected (Exp.) and observed (Obs.) cross section limitsfor modified Drell–Yan models of various charge signals. The signal efficiency and theoretical(Th.) cross section are also listed.

Mass Requirements Yields Signal s (pb)pT ( GeV) Ias 1/b M ( GeV) Predicted Data Eff. Th. Exp. Obs.

Modified Drell–Yan |Q| = 1e particles with the tracker+TOF analysis200 65 0.175 1.250 80 0.226 ± 0.046 0 0.304 1.1E-01 4.4E-03 4.4E-03400 65 0.175 1.250 200 0.014 ± 0.003 0 0.417 7.3E-03 3.2E-03 3.2E-03600 65 0.175 1.250 320 0.002 ± 0.000 0 0.462 1.2E-03 2.9E-03 2.9E-03800 65 0.175 1.250 460 0.000 ± 0.000 0 0.486 2.6E-04 2.8E-03 2.8E-031000 65 0.175 1.250 590 0.000 ± 0.000 0 0.486 7.6E-05 2.9E-03 2.9E-031800 65 0.175 1.250 1010 0.000 ± 0.000 0 0.250 1.0E-06 5.5E-03 5.5E-032600 65 0.175 1.250 1230 0.000 ± 0.000 0 0.026 0.0E+00 5.6E-02 5.6E-02

Modified Drell–Yan |Q| = 2e particles with the tracker+TOF analysis200 65 0.175 1.250 0 0.901 ± 0.182 0 0.211 3.0E-01 8.7E-03 6.1E-03400 65 0.175 1.250 90 0.164 ± 0.033 0 0.410 2.3E-02 3.2E-03 3.2E-03600 65 0.175 1.250 200 0.014 ± 0.003 0 0.482 3.5E-03 2.8E-03 2.8E-03800 65 0.175 1.250 300 0.003 ± 0.001 0 0.488 8.0E-04 2.6E-03 2.6E-031000 65 0.175 1.250 370 0.001 ± 0.000 0 0.450 2.4E-04 3.0E-03 3.0E-031800 65 0.175 1.250 420 0.001 ± 0.000 0 0.141 4.0E-06 9.6E-03 9.6E-032600 65 0.175 1.250 540 0.000 ± 0.000 0 0.040 0.0E+00 3.3E-02 3.3E-02

Mass (GeV)1000 2000

(pb)

σ95

% C

L lim

it on

4−10

3−10

2−10

1−10

1

10

210

310 (13 TeV)-12.4 fbCMSPreliminary

Tracker - Only

Theoretical Predictiongluino (NLO+NLL)stop (NLO+NLL)stau; dir. prod. (NLO)stau (NLO)|Q| = 1e (LO)|Q| = 2e (LO)

Theoretical Predictiongluino (NLO+NLL)stop (NLO+NLL)stau; dir. prod. (NLO)stau (NLO)|Q| = 1e (LO)|Q| = 2e (LO)

gg~gluino; 50% gg~gluino; 10% g; CSg~gluino; 10%

stopstop; CSstau; dir. prod.stau|Q| = 1e|Q| = 2e

Mass (GeV)1000 2000

(pb)

σ95

% C

L lim

it on

4−10

3−10

2−10

1−10

1

10

210

310 (13 TeV)-12.4 fbCMSPreliminary

Tracker + TOF

Theoretical Predictiongluino (NLO+NLL)stop (NLO+NLL)stau, dir. prod. (NLO)stau (NLO)|Q| = 1e (LO)|Q| = 2e (LO)

gg~gluino; 50% gg~gluino; 10%

stopstau; dir. prod.stau|Q| = 1e|Q| = 2e

Figure 4: Cross section upper limits at 95% CL on various signal models for the tracker-onlyanalysis (left) and tracker+TOF analysis (right) at

ps = 13 TeV. In the legend, ’CS’ stands for

charged suppressed interaction model.via gluino production (assuming GMSB with Nm = 3)

via direct (Drell-Yan) production (assuming GMSB with Nm = 3)

Mstau > 480 GeV via gluino,squark production

(GMSB Nm = 3, Mgluino > 3.3TeV)

Mstau > 340 GeV (Run1)via Drell-Yan production

(Mgluino,squark >> TeV )

CMS PAS EXO-15-010

»Lêm 3ê2»=1

»Lêm 3ê2»=2

»Lêm3ê2»=

3

»Lêm3ê2»=

4

»Lêm3ê2»=0

arg@LD=0

arg@LD=p

arg@LD=p5pê6

2pê3

pê2pê3pê6

Bino LSP

0 1 2 3 40.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

mwinoêmwinoAMSB

mbinoêm bi

noAMSB

m3ê2=MS=50TeV

-4 -2 0 2 410

20

50

100

200

500

1000

2000

Lêm3ê2

mgauginoêGe

V

Figure 3: (Left) The ratios of the wino and bino masses with and without the Higgsino

contributions for given values of L. We have used a phase convention that m3/2 is real

and positive. The red lines show the |L| dependences for given phases of L, while the blue

lines show the arg[L] dependences for given values of |L|. (The dashed blue lines show the

values of |L| in between the ones for the two solid lines.). In the gray shaded region for

|L/m3/2| & 3, the wino is no more the LSP. (Right) The L dependences of the gaugino

masses for m3/2 = M

SUSY

= 50TeV for L > 0 (arg[L] = 0) and L < 0 (arg[L] = ⇡).

Higgsino contributions for given values of L (left panel). The figure shows that the

wino mass can be about twice as heavy as the anomaly mediated contribution for

|L/m3/2| ' 1 which is expected in the pure gravity mediation model. It should be

noted that the wino becomes no more the LSP where the Higgsino threshold contri-

bution dominates. In such cases, the relic density of dark matter easily exceed the

observed one due to the highly suppressed annihilation cross section of the bino for

O(100)GeV. Fortunately, however, the figure shows that the bino becomes LSP only

for |L/m3/2| > 3 which is less likely in the pure gravity mediation model. Therefore,

in the pure gravity mediation model, the LSP is mostly wino-like, although the wino

mass obtains a comparable contribution from the Higgsino threshold e↵ects.7

In Fig. 4, we show the contour plot of the wino mass. In the figure, the blue shaded

region shows the current experimental constraints on the wino mass mwino

� 88GeV

7 In general, a relative phase between L and m3/2 is a free parameter, and hence, the three

gauginos have di↵erent phases. Such gaugino phases, however, do not cause serious CP-problems,

since the Higgsinos as well as the sfermions are expected to be very heavy in the pure gravity

mediation model. Interestingly, the relative phase of O(1) may lead to the visible electron electric

dipole moment of de/e ⇠ 10�30 cm [22] for the µ-term in the tens to hundreds TeV range, which

can be reached in future experiments [26].

7

AMSB

mwino>mbino

mwino>mgluino

Lêm 3ê2=

1

Lêm 3ê2=2

Lêm 3ê2=3

200 400 600 800 1000500

1000

1500

2000

2500

3000

mwinoêGeV

mgluinoêGe

V

Gaugino Masses = Loop-suppressed (AMSB + Heavy Higgs Mediation)

GluinoBino

Wino

L/m3/2

mgluino = 2.5x10-2m3/2

mwino = 3.0x10-3( m3/2 + L )mbino = 9.6x10-3( m3/2 + L/11 )

for m3/2 =O(100)TeV.

The wino is the LSP in the most parameter space.

The gluino can be lighter than the prediction in AMSB for L/m3/2 = O(1).

[’12, MI, Matsumoto,Yanagida (μH=O(Msusy) )]

Purely AMSB


L = O(m3/2) : Higgsino mediation effect

Hu Hd

⟨H⟩

H γW

γ

f

Hd Hu

⟨H⟩

H γW

γ

f

Figure 4: Feynman diagrams contributing to the fermion EDM in Split Supersymmetry.To better illustrate the structure of the interactions, we consider current eigenstates withinsertions of M2, µ, and ⟨H⟩ denoted by crosses. Two other diagrams with reversed directionsof chargino arrows are not shown.

= (2 − ln x) x +!

5

3− ln x

"

x2

6+ O(x3). (123)

Here KQED is the leading-logarithm QED correction in the running from the scale of the

heavy particles to mf (or mn for the neutron EDM) [39]

KQED = 1 − 4α

πln

mH

mf. (124)

We work in a general basis in which gu, gd, M2, and µ are all complex. The matrices U and

V are defined such that U∗Mχ+V † is diagonal with real and positive entries, where Mχ+ is

the chargino mass matrix

Mχ+ =!

M2

√2MW gu/g√

2MW gd/g µ

"

. (125)

We can explicitly write the matrices U and V as

U =!

cReiφ1 sRei(φ1−δR)

−sReiφ2 cRei(φ2−δR)

"

V =!

cL sLe−iδL

−sL cLe−iδL

"

(126)

tan 2θL,R =2|XL,R|

1 + |XR,L|2 − |XL,R|2, eiδL,R =

XL,R

|XL,R|, (127)

XL =

√2MW (g∗

uM2 + gdµ∗)

g(|M2|2 − |µ|2), XR =

√2MW (g∗

dM2 + guµ∗)

g(|M2|2 − |µ|2), (128)

where sL,R ≡ sin θL,R and cL,R ≡ cos θL,R. The phases φ1 and φ2 are chosen such that mχ+i

are real and positive. Using the diagonalization properties of the matrices U and V , we

33

Hu Hd

⟨H⟩

H γW

γ

f

Hd Hu

⟨H⟩

H γW

γ

f

Figure 4: Feynman diagrams contributing to the fermion EDM in Split Supersymmetry.To better illustrate the structure of the interactions, we consider current eigenstates withinsertions of M2, µ, and ⟨H⟩ denoted by crosses. Two other diagrams with reversed directionsof chargino arrows are not shown.

= (2 − ln x) x +!

5

3− ln x

"

x2

6+ O(x3). (123)

Here KQED is the leading-logarithm QED correction in the running from the scale of the

heavy particles to mf (or mn for the neutron EDM) [39]

KQED = 1 − 4α

πln

mH

mf. (124)

We work in a general basis in which gu, gd, M2, and µ are all complex. The matrices U and

V are defined such that U∗Mχ+V † is diagonal with real and positive entries, where Mχ+ is

the chargino mass matrix

Mχ+ =!

M2

√2MW gu/g√

2MW gd/g µ

"

. (125)

We can explicitly write the matrices U and V as

U =!

cReiφ1 sRei(φ1−δR)

−sReiφ2 cRei(φ2−δR)

"

V =!

cL sLe−iδL

−sL cLe−iδL

"

(126)

tan 2θL,R =2|XL,R|

1 + |XR,L|2 − |XL,R|2, eiδL,R =

XL,R

|XL,R|, (127)

XL =

√2MW (g∗

uM2 + gdµ∗)

g(|M2|2 − |µ|2), XR =

√2MW (g∗

dM2 + guµ∗)

g(|M2|2 − |µ|2), (128)

where sL,R ≡ sin θL,R and cL,R ≡ cos θL,R. The phases φ1 and φ2 are chosen such that mχ+i

are real and positive. Using the diagonalization properties of the matrices U and V , we

33

deêe = 10-27cm

deêe = 10-28cm

deêe = 10-29cm

deêe = 10-30cmtanb = 3de µ sin2b

2.0 2.2 2.4 2.6 2.8 3.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Log10@M2êGeV D

Log 1

0@mêGe

VD

Physical CP-violation is suppressed by O(m3/2).

EDM via one-loop slepton diagrams is suppressed by mslepton-2 .

EDM are dominated by two-loop diagrams in which the light Higgs boson is circulating (suppressed by μH-1sin2β)

The current limits de/e < 8.7 x10-29cm is reaching to μH of O(104) TeV !

[’04 Arkani-hamed,Dimopoulos,Giudice, Rommanio]

[1310.7534 ACME : ThO]

High Scale SUSY at 100TeV - PeV For detailed analyses [`15 Hisano, Kobayashi,Kuramoto, Kuwahara]

� �� -��-��-��-��-��-��-��-��-��-��-��-��-��-��

��-��-��-��-��-��-��-��-��-��-��-��-��-��-

�� [�/�]

��-� ��[�� ]

��-� ��[��]

COHERENT NEUTRIN O SCATTERING CO

HERENT NEU

TRI NO SCATTERING COHERENT NEUTRINO SCATTERING

CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

DAMA SIMPLE (2012)

ZEPLIN-III (2012)COUPP (2012)

LUX (2013)

CDMSlite (2013) SuperCDMS LT (2014)

8BNeutrinos

Atmospheric and DSNB Neutrinos

7BeNeutrinos

COHERENT NEUTRIN O SCATTERING CO

HERENT NEU

TRI NO SCATTERING COHERENT NEUTRINO SCATTERING

CRESST (2014)

EDELWEISS (2011)

DAMIC (2012)

9

Impact on direct detection sensitivity

• First detection of CNS! • Diversifying toward solar neutrino physics (J. Billard et al., arXiv:1409.0050)

Julien Billard (IPNL) - Moriond EW

(J. Billard et al., PRD 89 (2014))

Figure 4 – The neutrino background to direct DM searches.

So far we observed Dark Matter gravity. We only have upper bounds on any other DMinteraction with matter and among itself. In cosmology, this lack of interactions is what al-lows DM to cluster forming galaxies, while normal matter is still interacting with non-clusteringphotons. Cosmological data are reproduced if DM has a primordial inhomogeneity of adia-batic type: a single dominant primordial perturbation equal for all components of the universe.Loosely speaking, this suggests some connection with matter. The assumption that DM is athermal relic favours M

DM

<⇠ 100 TeV: then DM could be discovered in direct, indirect, collidersearches around 2010 or maybe later. We passed the golden moment where Pamela, Fermi,AMS, CDMS, Xenon, LHC started to produce data: backgrounds are starting to become alimitation.

2.1 Dark Matter searches are reaching the backgrounds

Direct searches for DM with electro-weak mass improved by 3 orders of magnitude in thepast decade and are now 3-4 orders of magnitude above the irreducible ⌫ background, as shownin fig. 4. This was discussed by J. Billard1 who proposed how, in case of no signal above thebackground, we might survive to the crash on the ground, relying on seasonal variations (DMrates are maximal in June, while solar ⌫ rates are maximal in January), multiple experiments,directionality of scattered particles. Various authors explore how to improve searches for sub-GeV DM particles: present bounds are still far from the irreducible ⌫ backgrounds.

Indirect searches aim at detecting in cosmic rays an excess of e+, p, � possibly producedby DM annihilations or decays. In the past years such cosmic rays have been observed at weakscale energies, and no undisputable evidence of a DM excess above the astrophysical fluxes wasfound. The uncertain uncertainties on such backgrounds to DM searches are now the limitingfactor: it will be di�cult to clarify the tentative claims and to improve the searches. Once alldata will be available, it will maybe possible to better understand galactic astro-particle physics,improving DM searches.

Searches at colliders mostly rely on the classical DM signal

missing energy + something to tag the event (a jet, a �, ...). (7)

At a hadron collider, this signal can be easily seen if DM is produced with QCD-like cross section,like in supersymmetric models. On the other hand, the same signal can be easily missed below

Wino Dark Matter Search (direct detections, χN→χN )

Coupling to H and Z are highly suppressed for μH =O(10-100) TeV at the tree-level.

Wino-Nucleon @ higher loop level σp-N = (10-47)cm2 ( much smaller than the current reach...)

h0

χ∼ 0 χ∼ 0 χ∼ 0 χ∼ 0χ∼− χ∼−

W-W-

W-

q q’ q

(a) (b)

q q

Figure 1: One-loop contributions to effective interactions of Wino LSP and light quarks.

χ∼ 0 χ∼ 0χ∼−

Q/q

Q’/q’W- W-

g g

χ∼ 0 χ∼ 0χ∼−

W-W-

Q

Q’

g g

(b) (c)

h0

χ∼ 0 χ∼ 0χ∼−

W-

(a)

Qg

g

Figure 2: Two-loop contributions to interactions of Wino LSP and gluon. Here, Q and qrepresent heavy and light quarks, respectively.

are zero, as

gH(x) ≃ −2π ,

gAV(x) ≃√x

6π ,

gT1(x) ≃π

3,

gT2(x) ≃ −√x

6. (18)

Next, let us discuss the effective interactions of the Wino LSP and gluon. As wediscussed in the previous section, the O(αs) correction to fG in Eq. (3) is relevant at theleading order though it is induced by two-loop order. Three types of diagrams in Fig. 2contribute to fG. The diagram (a) includes heavy quark loop (Q = c, b, t). The heavyquark content of the nucleon is related to the gluon condensate as [22]

⟨N |mQQQ|N⟩ = −αs

12π⟨N |Ga

µνGaµν |N⟩ . (19)

6

h0

χ∼ 0 χ∼ 0 χ∼ 0 χ∼ 0χ∼− χ∼−

W-W-

W-

q q’ q

(a) (b)

q q

Figure 1: One-loop contributions to effective interactions of Wino LSP and light quarks.

χ∼ 0 χ∼ 0χ∼−

Q/q

Q’/q’W- W-

g g

χ∼ 0 χ∼ 0χ∼−

W-W-

Q

Q’

g g

(b) (c)

h0

χ∼ 0 χ∼ 0χ∼−

W-

(a)

Qg

g

Figure 2: Two-loop contributions to interactions of Wino LSP and gluon. Here, Q and qrepresent heavy and light quarks, respectively.

are zero, as

gH(x) ≃ −2π ,

gAV(x) ≃√x

6π ,

gT1(x) ≃π

3,

gT2(x) ≃ −√x

6. (18)

Next, let us discuss the effective interactions of the Wino LSP and gluon. As wediscussed in the previous section, the O(αs) correction to fG in Eq. (3) is relevant at theleading order though it is induced by two-loop order. Three types of diagrams in Fig. 2contribute to fG. The diagram (a) includes heavy quark loop (Q = c, b, t). The heavyquark content of the nucleon is related to the gluon condensate as [22]

⟨N |mQQQ|N⟩ = −αs

12π⟨N |Ga

µνGaµν |N⟩ . (19)

6

One-loop diagrams which contribute to the Wino-nucleon scatterings.

Darwin (multi-ton Argon/Xe detector) will reach down to 10-47cm2 for WIMP mass below 300GeV.

The irreducible background from atmospheric neutrinos at about 10-48cm2. [arxiv:1003.5530][’10 Hisano, Ishiwata, Nagata]

[’10 Hisano, Ishiwata, Nagata]

DM mass :

σp-N/cm2


To avoid this problem, we need to assume that the messenger fields couple to a secondary

SUSY breaking as realized in models of “cascade SUSY breaking” [22] (see also [23–25] for

earlier works). There, a secondary SUSY breaking field S couples to the primary SUSY

breaking field Z with hZi = F✓2 only through the Kahler potential,

K = |Z|2 + |S|2 +

⇤2

|Z|2|S|2 + · · · , (11)

where ⇤ is the dynamical scale of the SUSY breaking sector (see [22] for more details). By

using the Naive Dimensional Analysis (NDA) [26, 27], the coe�cient is expected to be of

O((4⇡)2) when both Z and S take part in the strong dynamics with the dynamical scales

of O(⇤). By using the NDA, the primary SUSY breaking scale is also estimated to be4

FZ ⇠ ⇤2

4⇡. (12)

As a result, the term proportional to leads to a soft SUSY breaking mass of S,5

m2

S ' �

⇤2

⇥ F 2

Z ⇠ �⇤2 . (13)

Now, let us suppose that S and the messenger fields are composite states of some dynamics

so that they couple in the superpotential

W ' k

⇤n�3

Sn +�

⇤n�3

Sn�2 · · · , (14)

with n � 3.6 By the NDA again, we expect k = O((4⇡)n�2) and � = O((4⇡)n�2). Then,

the scalar potential of S is roughly given by,

V ⇠ m2

S|S|2 +k2

⇤2n�6

|S|2n�2 , (15)

3 This limit is put by assuming Nm = 3 in [20]. For Nm = 4, the constraint might become slightly more

stringent due to a relative smallness of the squark mass for Nm = 3. When, the NLSP is the lightest

neutralino, the lower limit on the gluino mass is slightly tighter, mgluino

& 1.6–1.7TeV, which has been

put by the null results of searches for the photons with missing energy [21].4 If we assume IYIT SUSY breaking model [28, 29], this is achieved when the coupling between the gauge

singlet and SP (Nc) fundamental quarks are of O(4⇡).5 Here, we assume > 0 for simplicity, although a model in [22] is viable even for < 0.6 A model with n = 5 is achieved in [22].

6





K = |Z|2 + |S|2 +

⇤2

|Z|2|S|2 + · · · , (11)





FZ ⇠ ⇤2

4⇡. (12)


m2

S ' �

⇤2

⇥ F 2

Z ⇠ �⇤2 . (13)



W ' k

⇤n�3

Sn +�

⇤n�3

Sn�2 · · · , (14)



V ⇠ m2

S|S|2 +k2

⇤2n�6

|S|2n�2 , (15)







6





K = |Z|2 + |S|2 +

⇤2

|Z|2|S|2 + · · · , (11)





FZ ⇠ ⇤2

4⇡. (12)


m2

S ' �

⇤2

⇥ F 2

Z ⇠ �⇤2 . (13)



W ' k

⇤n�3

Sn +�

⇤n�3

Sn�2 · · · , (14)



V ⇠ m2

S|S|2 +k2

⇤2n�6

|S|2n�2 , (15)







6





K = |Z|2 + |S|2 +

⇤2

|Z|2|S|2 + · · · , (11)





FZ ⇠ ⇤2

4⇡. (12)


m2

S ' �

⇤2

⇥ F 2

Z ⇠ �⇤2 . (13)



W ' k

⇤n�3

Sn +�

⇤n�3

Sn�2 · · · , (14)



V ⇠ m2

S|S|2 +k2

⇤2n�6

|S|2n�2 , (15)







6





K = |Z|2 + |S|2 +

⇤2

|Z|2|S|2 + · · · , (11)





FZ ⇠ ⇤2

4⇡. (12)


m2

S ' �

⇤2

⇥ F 2

Z ⇠ �⇤2 . (13)



W ' k

⇤n�3

Sn +�

⇤n�3

Sn�2 · · · , (14)



V ⇠ m2

S|S|2 +k2

⇤2n�6

|S|2n�2 , (15)







6

which leads to the VEVs of S,

hSi ⇠ ⇤

4⇡, hFSi ⇠ ⇤2

4⇡. (16)

Putting these VEVs into the superpotential in Eq. (14), the messenger fields obtain their

masses and the mass splittings,

Mm ⇠ ⇤, Fm ⇠ ⇤2 ⇠ 4⇡FZ , (17)

which corresponds to y = O(4⇡). In this way, we can construct a model in which the

messenger fields and the SUSY breaking couple strongly without causing vacuum stability

problem.7

C. Higgs boson mass beyond the MSSM

So far, in this note, we have confined ourselves to the MSSM where the Higgs boson

mass is explained by the top Yukawa radiative corrections. Here, let us comment on the

extensions of the SUSY standard model which can enhance the Higgs boson mass without

requiring large squark masses.

First, let us consider the so-called NMSSM [31, for review] in which a newly introduced

singlet field couples to the Higgs doublets in the MSSM. When the singlet–Higgs coupling

is rather large, the observed Higgs boson mass can be explained even for relatively light

squarks. However, in the presence of multiple messenger fields, the upper limit on the

singlet–Higgs coupling from the Landau pole problem is severer than in the models without

the messenger fields. As a result, if we require perturbativity to the NMSSM up to the grand

unification scale, the Higgs boson mass cannot be explained in the models with low-scale

gauge mediation (with y = O(1)) even for the NMSSM [10].8

As another example to enhance the Higgs boson mass, it is also possible to introduce

vector-like matter fields coupling to the Higgs doublets [32–40]. In those extensions, however,

the more the vector-like matters are added, the severer upper limit on the messenger number

7 See also [30] for another strongly interacting messenger model.8 Here, we assume that the NMSSM respects the Z

2

symmetry. If we allow Z3

violating terms, it is possible

to explain mH ' 125GeV without having the Landau pole problem. In such cases, however, we generically

su↵er from tadpole problem and fine tuning problems.

7

which leads to the VEVs of S,

hSi ⇠ ⇤

4⇡, hFSi ⇠ ⇤2

4⇡. (16)

Putting these VEVs into the superpotential in Eq. (14), the messenger fields obtain their

masses and the mass splittings,

Mm ⇠ ⇤, Fm ⇠ ⇤2 ⇠ 4⇡FZ , (17)

which corresponds to y = O(4⇡). In this way, we can construct a model in which the

messenger fields and the SUSY breaking couple strongly without causing vacuum stability

problem.7

C. Higgs boson mass beyond the MSSM

So far, in this note, we have confined ourselves to the MSSM where the Higgs boson

mass is explained by the top Yukawa radiative corrections. Here, let us comment on the

extensions of the SUSY standard model which can enhance the Higgs boson mass without

requiring large squark masses.

First, let us consider the so-called NMSSM [31, for review] in which a newly introduced

singlet field couples to the Higgs doublets in the MSSM. When the singlet–Higgs coupling

is rather large, the observed Higgs boson mass can be explained even for relatively light

squarks. However, in the presence of multiple messenger fields, the upper limit on the

singlet–Higgs coupling from the Landau pole problem is severer than in the models without

the messenger fields. As a result, if we require perturbativity to the NMSSM up to the grand

unification scale, the Higgs boson mass cannot be explained in the models with low-scale

gauge mediation (with y = O(1)) even for the NMSSM [10].8

As another example to enhance the Higgs boson mass, it is also possible to introduce

vector-like matter fields coupling to the Higgs doublets [32–40]. In those extensions, however,

the more the vector-like matters are added, the severer upper limit on the messenger number

7 See also [30] for another strongly interacting messenger model.8 Here, we assume that the NMSSM respects the Z

2

symmetry. If we allow Z3

violating terms, it is possible

to explain mH ' 125GeV without having the Landau pole problem. In such cases, however, we generically

su↵er from tadpole problem and fine tuning problems.

7

Strongly coupled Gauge Mediation

Cascade SUSY breaking

Messenger Coupling

Supersymmetry after Higgs discovery (Status/Prospects)

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