A new paradigm for modeling the neutrino-nucleus cross section?

A new paradigm for modelling neutrino-nucleuscross sections?

Omar Benhar

INFN and Department of PhysicsUniversita “La Sapienza”

I-00185 Roma, Italy

NUINT11Dehradun, Uttarakhand, India. March 11th, 2011

Outline

Apologies

Theparadigm∗ of electron-nucleus scattering

Flux average

Are nucleon properties modified in nuclear matter?

2p-2h contributions

∗a philosophical or theoretical framework of any kind (Merriam-Webster)Omar Benhar (INFN, Roma) NUINT11 Dehradun 11/03/2011 2/ 14

Theparadigmof electron-nucleus scattering

The paradigm

⊲ Lepton kinematics fully determined⊲ Elementary interaction vertex (dσN ) determined by electron-protonand

electron-deuterondata (nuclear dynamics largely decoupled). No mediummodification of the nucleon form factors and structure functions.

Omar Benhar (INFN, Roma) NUINT11 Dehradun 11/03/2011 3/ 14

Theparadigmof electron-nucleus scattering

The paradigm

⊲ Lepton kinematics fully determined⊲ Elementary interaction vertex (dσN ) determined by electron-protonand

electron-deuterondata (nuclear dynamics largely decoupled). No mediummodification of the nucleon form factors and structure functions.

The simplest implementation: impulse approximation (IA)

⊲ At large momentum transfer electron-nucleus scattering reduces to theincoherent sum of scattering processes involving individual nucleons

Σi

2 2q,ω q,ω

i

x

JA →

A∑

i=1

j iN , |X〉 → |x, px〉 ⊗ |R, pR〉 .


Flux average

Bottom line: the scheme succesfully employed to describe theelectron-nucleus x-section over a broad range of beam energies fails toexplain the flux-averaged neutrino cross sectionIn neutrino interations the lepton kinematics isnot fully determined. Theflux-averaged double differential cross sections picks up contributions iatdifferent neutrino energies, corresponding to a variety of kinematicalregimes in which different reaction mechanisms dominate


“Flux averaged” electron-nucleus x-section

The electron scattering x-section off Carbon atθe= 37◦ has beenmeasured for a number of beam energies

Theoretical calculations accounting for the QE x-section at all beamenergies fail to explain the “flux integrated” cros section


Are the nucleon form factors modified in the nuclearmedium?

The answer to this question isinherently model dependent, since themodification is inferred from a comparison of the experimental data withtheoretical predictions.

Therefore, it is crucial for a proper interpretation of the experimentaldata that the theoretical calculations include contributions fromfinalstate interactionsas well as frommany-body terms in the nuclear currentand fromcorrelation effectsin the initial state

Electron scattering experiments have providedno evidence of mediummodifications of the vector form factors


Contributions of 2p2h final states

It has been suggested that 2p2h final states provide a large contributionto the neutrino cross section, that may explain the MiniBooNE datawithout any modifications of the nucleon axial mass

Two particle-two hole final states may be produced through differentmechanisms

1. Initial state correlations (taken into account in IA)2. Final state interactions (not taken into account in IA)3. Coupling to two-body current (not taken into account in IA)


2p2h final states from initial state correlations

Spectral lines corresponding to shell model states clearlyseen in highreeolution (e, e′p)

The measured strengths of the peaks corresponding to shell model statesare significantly les than unity (∼ 0.6 for valence states)

Emiss12.1

18.3

40.0(MeV)

1p1/2

3/21p

1s1/2

O16

10 20 40 70 100 200 0

20

40

60

80

100

120

140 o : (e,e’p)

x : (d,3He)

target mass

frac

tion

of IP

SM

lim

it [%

]


Missing strength. . .

Energy dependence of the spectroscopic strengths of shell model statesof 208Pb, measured in high resolution (e, e′p) at NIKHEF-K

Theoretical calculation obtained from LDA and nuclear matter spectralfunctions (no adjustable parameters involved)


. . . and correlation strength

JLAB E97-006 measured the strength in the 2p2h sectorstrong energy-momentum correlation

E ∼ Ethr +A− 2A− 1

k2

2m

80%

250

80 300

1.5%

5%

700

0

4.5%

8% 1%

Em(MeV)

pm(MeV/c)used region

0.2 0.3 0.4 0.5 0.6p

m [GeV/c]

10-3

10-2

10-1

n(p m

) [fm

3 sr-1

]

Measured correlation strength 0.61± 0.06, to be compared with thetheoretical predictions 0.64 (CBF) and 0.56 (G-Matrix)Correlated nucleons (most of the times a proton and a neutron) havemomenta> 250 MeV, pointing in opposite directions


Contribution to the inclusive cross section


A new paradigm? What does it mean?

Nieves et al (arXiv:1102.2777v1) state that ”In Ref.[22] itis suggestedthat the many body techniques successfully applied in QEelectron-nucleus scattering are not able to explain neutrino induced crosssections”

In the paper advocating the need of a new paradigm (arXiv:1012.2032),one of the authors of Ref.[22] arXiv:1012.2032 states that ”A newparadigm, . . . , should be based on a more flexible model of nucleareffects. Nuclear many-body theory provides a consistent framework forthe development of such a model”


Summary. . .

(1) It is a fact that the first element of the electron scattering paradigmcannot be applied to the analysis of flux-integrated cross sections


Summary. . .


(2) In order to determine whether the second element is applicable toneutrino scattering, the issue of the possible modificationof nucleonproperties in the nuclear medium must be resolved


Summary. . .



(3) Points (1) & (2) imply that the existing many-body techniques must beemployed to develop a model providing aconsistentdescription of allreaction mechanisms contributing to the flux integrated cross section inrelevant beam energy range


Summary. . .



(3) Points (1) & (2) imply that the existing many-body techniques must beemployed to develop a model providing aconsistentdescription of allreaction mechanisms contributing to the flux integrated cross section inrelevant beam energy range

(4) According to the above scheme, Nieveset aland Martiniet alare in factcontributing to the development of a new paradigm


. . . and outlook

(1) The analysis of neutrino data should focus on cross sectionsgiven interms of measured (not inferred) kinematical variables


. . . and outlook


(2) All proposed many-body approaches must provide aconsistent(i.e.based on the same dynamical model) description


. . . and outlook



(3) The determination of nuclear dynamics must be decoupled, asmuch aspossible, from the uncertainties associated with the solution of themany-body problem


. . . and outlook



(3) The determination of nuclear dynamics must be decoupled, asmuch aspossible, from the uncertainties associated with the solution of themany-body problem

(4) Theoretical predictions must be tested against electron scattering data


A new paradigm for modeling the neutrino-nucleus cross section?

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