Oscillations in q/m dataset

BASE startup meeting 24/01/2020

Contents

• Physics Cases• CPT and Lorentz violation (SME)

• Exotic interactions

• Weak Equivalence Principle (WEP)

• Variation of fundamental constants

• Dark matter

• Data analysis• Results at SME frequencies

• New strategy

Physics Cases - SME

CPT theorem

The invariance under the combined C, P and T symmetries implies for a particle and its antiparticle:

• same mass m

• same lifetime τ

• opposite charge q

• opposite magnetic moment μ

We are probing for physics beyond the standard model by comparing the proton/antiproton q/m and μ!

Physics Cases - SME

CPT theorem

Any quantum theory, formulated on flat spacetime is symmetric under the combined action of CPT transformations, provided the theory respects:

• Locality

• Unitarity (conservation of probability)

• Lorentz invariance

There may be violations of these assumptions in models of quantum gravity

Physics Cases - SME

CPT violation through Lorentz violation:• Spontaneous breaking of Lorentz symmetry

• No concrete microscopic model yet

• Effective field theory at low energy: SME

Standard Model Extension:• Conventional Dirac QED Lagrange density

• Add all terms that preserve U(1) gauge invariance

Physics Cases - SME

Minimal Standard Model Extension:

with

Lorentz violation is quantified by parameters

that are constant in an inertial frame

Physics Cases - SME

Minimal Standard Model Extension:

with

Lorentz violation is quantified by parameters

that are constant in an inertial frame

Dimension of mass

Dimensionless

Which are CPT odd?

Physics Cases - SME

Minimal Standard Model Extension:

with

Lorentz violation is quantified by parameters

that are constant in an inertial frame

Dimension of mass

Dimensionless

Which are CPT odd?

Physics Cases - SME

What to do with this Lagrangian?

Use perturbation theory to calculate the energy levels!

• Unperturbed we have relativistic Landau levels (charged particle in uniform magnetic field)

• The cyclotron frequency is

• The energy shifts can be calculated to first order by

Physics Cases - SME

What to do with this Lagrangian?

Use perturbation theory to calculate the energy levels!

• Unperturbed we have relativistic Landau levels (charged particle in uniform magnetic field)

• The cyclotron frequency is

• The energy shifts can be calculated to first order by

Cyclotron quantum number sign(q) sign( Ԧ𝑠 ∙ 𝐵)

Physics Cases - SME

What to do with this Lagrangian?

Use perturbation theory to calculate the energy levels!

• Unperturbed we have relativistic Landau levels (charged particle in uniform magnetic field)

• The cyclotron frequency is

• The energy shifts can be calculated to first order by

Cyclotron quantum number sign(q) sign( Ԧ𝑠 ∙ 𝐵)

∆𝑛 = 1, ∆𝑠 = 0

Physics Cases - SME

What to do with this Lagrangian?

Use perturbation theory to calculate the energy levels!

• Unperturbed we have relativistic Landau levels (charged particle in uniform magnetic field)

• The cyclotron frequency is

• The energy shifts can be calculated to first order by

Cyclotron quantum number sign(q) sign( Ԧ𝑠 ∙ 𝐵)

∆𝑛 = 1, ∆𝑠 = 0

Unperturbed eigenstate of 𝐸𝑛,𝑠SME perturbation of Hamiltonian

Physics Cases - SME

The energy shifts 𝛿𝐸𝑛,𝑠 are summarized in theappendix of [1], keeping only the terms relevant forthe cyclotron frequency in the minimal SME andusing some approximations:

[1]

0: 𝑡lab1: 𝑥lab2: 𝑦lab3: 𝑧lab along 𝐵

Physics Cases - SME

The energy shifts 𝛿𝐸𝑛,𝑠 are summarized in theappendix of [1], keeping only the terms relevant forthe cyclotron frequency in the minimal SME andusing some approximations:

[1]

CPT odd

0: 𝑡lab1: 𝑥lab2: 𝑦lab3: 𝑧lab along 𝐵

Physics Cases - SME

The energy shifts 𝛿𝐸𝑛,𝑠 are summarized in theappendix of [1], keeping only the terms relevant forthe cyclotron frequency in the minimal SME andusing some approximations:

[1]

CPT odd

0: 𝑡lab1: 𝑥lab2: 𝑦lab3: 𝑧lab along 𝐵

Lab frame is not an inertial frame…

Values of 𝑐𝜇𝜈 and 𝑔𝜆𝜇𝜈 are not constant!

Physics Cases - SME

The energy shifts 𝛿𝐸𝑛,𝑠 are summarized in theappendix of [1], keeping only the terms relevant forthe cyclotron frequency in the minimal SME andusing some approximations:

[1]

CPT odd

0: 𝑡lab1: 𝑥lab2: 𝑦lab3: 𝑧lab along 𝐵

Lab frame is not an inertial frame…

Values of 𝑐𝜇𝜈 and 𝑔𝜆𝜇𝜈 are not constant!

Transform to canonical inertial frame: Sun-centered celestial-equatorial frame (SCCEF) with coordinates T, X, Y, Z

Physics Cases - SME

Transformation of 𝑐𝜇𝜈 and 𝑔𝜆𝜇𝜈 to Sun-Centered Celestial-Equatorial Frame:

Each Lorentz index (𝜆, 𝜇, 𝜈) transforms with Λ

R is rotation matrix due to Earth’s rotation

𝛽 is boost due to Earth’s trajectory around the Sun

Physics Cases - SME

Transformation of 𝑐𝜇𝜈 and 𝑔𝜆𝜇𝜈 to Sun-Centered Celestial-Equatorial Frame:

Each Lorentz index (𝜆, 𝜇, 𝜈) transforms with Λ

becomes a complicated expression involving almost all 𝑔𝐿𝑀𝑁 and 𝑐𝑀𝑁 with time-dependent factors involving the sidereal frequency 𝜔 and the annual frequency Ω

Physics Cases - SME

Transformation of 𝑐𝜇𝜈 and 𝑔𝜆𝜇𝜈 to Sun-Centered Celestial-Equatorial Frame:

Results in a time-dependent expression for 𝛿𝜔𝑐𝜔𝑐

with

characteristic frequencies 𝜔 and Ω and theirharmonics (2𝜔, 3𝜔) and sidebands (Ω ± 𝜔, Ω ± 2𝜔,Ω ± 3𝜔) .However, not all coefficients𝑔𝐿𝑀𝑁 are independent physicalobservables

Convert to tilde coefficients [2]!These are the ones you can find in the data tables

[2]

Physics Cases - SME

Tilde coefficients: large set is still unconstrained!

Physics Cases - SME

Last note:

In principle we have to take into account that theRubidium reference clock in the experiment can alsohave Lorentz violating effects. However these effectsare already well constrained.

Physics Cases – Exotic interactions

• Spacetime torsion: • spacetime can have torsion (geodesics can helix around

each other),

• torsion couples to SM fields,

• results in SME-like terms because torsion would violate Lorentz symmetry

• Non-metricity:• Very similar reasoning

Physics Cases – Exotic interactions

Fifth force:

MWDM formalism describes long-range potentials associated with any generic spin-0 or spin-1 boson exchange

Yukawa potential modifies gravitational potential

Physics Cases - WEP

Weak Equivalence Principle states that the inertial mass 𝑚𝐼 is equal to the gravitational mass 𝑚𝐺

Dirac equation predicts that the inertial mass of a particle and its antiparticle are the same

CPT theorem says that the inertial masses of particle and antiparticle are the same

But what about the gravitational masses? Or equivalently, the free fall acceleration of matter and antimatter?

Physics Cases - WEP

Our Weak Equivalence Test:

Effective gravitational potential for matter: 𝑈

Effective gravitational potential for antimatter: 𝛼𝑔𝑈

Clock running in gravitational potential acquires a gravitational redshift (or time dilation), so

Here we assumed that the inertial masses of 𝑝 and ҧ𝑝 are the same and we use the Local Supercluster to determine 𝑈/𝑐2 =3 × 10−5

Physics Cases - WEP

To avoid the assumption of CPT invariance and the estimate of the absolute gravitational potential, measure at different values of 𝑈!

∆𝑈

𝑐2= 3 × 10−10

This would generate a yearly modulation of the cyclotronfrequency!

One caveat: we have to assume there is no CPT violatingeffect with annual modulation due to the boost resulting fromthe Earth’s trajectory around the Sun

Physics Cases - WEP

We are not the first ones to do this, this has been studied in other systems:

• Ultrarelativistic electrons and positrons: Cherenkov radiation in vacuum at LEP and vacuum single photon decay sets 4% limit on 𝑚𝐺

𝑚𝐼

• 𝐾0 and ഥ𝐾0 : annual variation of decay parameters, WEP holds to 10−8

Physics Cases – “Constants”

Fundamental constant:

Any parameter not determined by the theory in which it appears

Example in SM: fine structure constant 𝛼, electron mass 𝑚𝑒, Higgs vev

Variation in time and space

Value of constant could be determined by theory beyond SM and GR in which dimensionless constants become dynamical.

• They are expectation value of this dynamical field, f.e. dilaton (string theory).

• Variation of gauge couplings like 𝛼 could arise due to variation of size extra dimensions (string theory)

• Some models can be coupled to dark energy (chameleon, quintessence), some to dark matter (dilaton)

• If one constant varies, typically all vary

28

Physics Cases – “Constants”

It could be that there is a difference between the coupling of these scalar fields with matter and antimatter, although none of the theories would predict that…

The cyclotron frequency contains 𝛼 (because of the charge) and the mass of the proton

Time signature depends on the theory:• Most commonly searched for is a slow linear drift• Coupling to the gravitational potential

29

Physics Cases – Dark Matter

What we currently believe:

• Milky Way is embedded within and rotates through a spherical dark matter halo

• Dark matter is cold, meaning that it is moving with velocities much smaller than the speed of light

• Observational limits permit a mass of DM constituents between 10−24eV and 1048GeV

Physics Cases – Dark Matter

Let’s focus on light dark matter:

It can form a coherently oscillating classical field with the frequency given by its mass and interact with SM particles through different portals.

Oscillating g-factor

Oscillating mass

Oscillating 𝛼

Physics Cases – Dark Matter

One candidate for dark matter is virialized ultralight fields (VULFs) that interact through the portals

Giving an oscillating mass and fine structure constant

Data Analysis – SME frequencies

Combine 2017II and 2018I data

Frequency Amplitude P-value

𝜔⨁ 52(18) 0.025

2𝜔⨁ 13(18) 0.779

3𝜔⨁ 13(18) 0.814

Ω 14(57) 0.925

Ω − 𝜔⨁ 36(19) 0.164

Ω + 𝜔⨁ 35(18) 0.177

Ω − 2𝜔⨁ 18(18) 0.618

Ω + 2𝜔⨁ 28(18) 0.315

Data Analysis – New Strategy

New analysis procedure (work in progress)

1. More conservative cut on contaminants

2. Average multiple axial frequencies for one cyclotron frequency based on Allan deviation

3. Flag magnetic field jumps

4. Higher order cyclotron drift correction

5. Simultaneous fit of all SME frequencies