A. Garcia University of Washington

1

Cyclotron radiation detection to search for new

physics

Outline

• Energy versus precision frontiers

• Intro on chirality/helicity

• Precision needed in the LHC era

• Chirality-flipping as a signature

• Beta spectra as a probe

• Can it be done? Cyclotron radiation → microwaves

• Our experimental setup and recent progress

2

3

Energy versus Precision Frontier

LHC at CERN: energy frontier

Double beta decays

Electric Dipole Moments

Muon physics

Nuclear beta decays

In some cases, table-top

precision experiments can

compete with the LHC.

4

Shakespeare on Fundamental Physics

"I could be bounded in a nutshell,

and count myself a king of infinite space,

…."

- Hamlet, II.ii

Chirality and human conventions

5

Screws can be right handed or left handed.

Human conventions allow us to know

which sense to turn to take them in or out.

6

Surprising: Nature distinguishes chirality, at the molecular level.

Many organic molecules (glucose

and biological amino acids) are

chiral.

DNA double helix in its standard

form always twists like a right-

handed screw.

Chirality and molecules

7

Chirality and drug development -- the Thalidomide tragedy

Thalidomide: prescribed widely to pregnant women between 1957 and

1962 (reduced morning sickness).

However, taken during the first trimester of pregnancy, Thalidomide

prevented proper growth of fetus and result was thousands of children

around the world born with severe birth defects.

Thalidomide is a chiral molecule and the drug that was marketed was

a 50/50 mixture of left- and right-handed molecules. While the left-

handed molecule was effective, the right-handed one was highly toxic.

Chirality and molecules

Surprising: Nature distinguishes chirality, at the molecular level.

Symmetries in fundamental laws: discrete symmetries → Parity

Parity → inversion of spatial coordinates.

Vectors flip sign under P:

𝑃Ԧ𝑟 = −Ԧ𝑟𝑃 Ԧ𝑝 = − Ԧ𝑝

But, notice angular momentum does not

flip sign:

𝐿 = Ԧ𝑟 × Ԧ𝑝՜𝑃

−Ԧ𝑟 × − Ԧ𝑝 = 𝐿

Pseudo-vector

or Axial vector.

Scalars, like Energy, don’t flip sign under P.

But some scalars do:

Ԧ𝑎 . 𝑏 × Ԧ𝑐 ՜𝑃− Ԧ𝑎 . −𝑏 × −Ԧ𝑐 = − Ԧ𝑎 . 𝑏 × Ԧ𝑐 Pseudo-scalar.

8

Parity and 𝑬 field

𝑞 𝐸

𝑞𝐸

Under P:

𝜌 ⟶ 𝜌

𝐸 ⟶ −𝐸

9

Parity and 𝑩 field

𝐼 𝐵

Under P:

Ԧ𝐽 ⟶ − Ԧ𝐽

𝐵 ⟶ 𝐵

×

𝐼°𝐵

10

Examples of P conservation

• Harmonic oscillator even under P:

• Maxwell’s Eqs. under P:

Under P:

𝜌 ⟶ 𝜌

𝐸 ⟶ −𝐸Ԧ𝐽 ⟶ −Ԧ𝐽

𝐵 ⟶ 𝐵

Eqs. remain

unchanged

• Newton’s gravity eqs. remain unchanged:

11

Experimental Observation of Parity Violation

The idea that Parity could be

violated sounded ridiculous

to most physicists before

1957.

12

Experimental Observation of Parity Violation (1957)

)()( prprP

ppP

rrP

=

−=

−= P inverts coordinates and momenta,

but not angular momenta

electrons come opposite the polarization of 60Co.

13

⇑ 𝑱60Co

Ԧ𝑝𝑒

⇑ 𝑱60Co

Ԧ𝑝𝑒

Equivalent if P

is conserved

Experiment with polarized 60Co

Helicities and nuclear beta decays: Parity Violation

What makes electrons come out preferentially opposite the

polarization?

1) Conservation of Ang. Mom.: e and n

spins must align along the direction of

initial polarization.

2) e’s are left handed (momentum

preferentially opposite spin).

14

The Weak interaction couples

to left-handed fermions and

right-handed anti-fermions.

Helicity

Jp

Jp

=H

For a spin ½ particle H can be

Right (+) or Left (-).

15

Remarkable:

Anti-neutrinos and positrons emitted in beta decay are

Right-handed

Neutrinos and e’s emitted in beta decay

are Left-handed

Helicity

Jp

Jp

=H

For a spin ½ particle H can be

Right (+) or Left (-).

16

Remarkable:

Anti-neutrinos and positrons emitted in beta decay are

Right-handed

Neutrinos and e’s emitted in beta decay

are Left-handed

A net helicity in particles emitted in a decay imply that

the interaction violates parity

17

Sorting this out took much

experimental effort and ingenuity

to come out of confusing times

Yang Gell-Mann Feynman

Marshak

Garwin

Lederman

Teledgi

Lee

Sudarshan

Charged weak current is left handed:

The modern context. The Standard Model and some open questions.

18

What is the mechanism for the mass of

neutrinos? (hints that it doesn’t work like for the

other particles)…

Can there be right-handed neutrinos from

nuclear beta decays?

Why are the number of generations for quarks

identical to those of leptons?

Answers should also illuminate “new physics”

19

Weak charged current in SM

𝐻𝑊 = ഥ𝜓𝜈𝐿 𝛾𝜇𝜓𝜇

𝐿−𝑔2

𝑀2 − 𝑞2ഥ𝜓𝑒𝐿 𝛾𝜇𝜓𝜈

𝐿

Projectors on chirality states:

𝑃𝐿 =1

21 + 𝛾5 ⇒ 𝜓𝑒

𝐿 = 𝑃𝐿𝜓𝑒

𝑃𝑅 =1

21 − 𝛾5 ⇒ 𝜓𝑒

𝑅 = 𝑃𝑅𝜓𝑒

Charged weak current in SM only sensitive to L:

ത𝜓𝑒𝑂𝜇𝜓𝜈 = ഥ𝜓𝑒

𝐿 𝛾𝜇𝜓𝜈𝐿

We can use this as a tool to search for

new physics.

Find “something that breaks this

symmetry”.

20

Weak charged current in SM

𝐻𝑊 = ഥ𝜓𝜈𝐿 𝛾𝜇𝜓𝜇

𝐿−𝑔2

𝑀2 − 𝑞2ഥ𝜓𝑒𝐿 𝛾𝜇𝜓𝜈

𝐿

Projectors on chirality states:

𝑃𝐿 =1

21 + 𝛾5 ⇒ 𝜓𝑒

𝐿 = 𝑃𝐿𝜓𝑒

𝑃𝑅 =1

21 − 𝛾5 ⇒ 𝜓𝑒

𝑅 = 𝑃𝑅𝜓𝑒

Charged weak current in SM only sensitive to L:

ത𝜓𝑒𝑂𝜇𝜓𝜈 = ഥ𝜓𝑒

𝐿 𝛾𝜇𝜓𝜈𝐿

We can use this as a tool to search for

new physics.

Find “something that breaks this

symmetry”.

Muon

current

electron

currentInteraction

propagator

𝑔 ≡ coupling

𝑀 ≡ W mass

21

Use “chirality flip” as a signature for new

physics

ത𝜓𝑒𝑂𝜇𝜓𝜈 ՜

?൝ഥ𝜓𝑒𝐿 𝛾𝜇𝜓𝜈

𝑅

ഥ𝜓𝑒𝑅 𝛾𝜇𝜓𝜈

𝐿

We can use this as a tool to search for

new physics.

Find “something that breaks this

symmetry”.

Credit: https://hackernoon.com/finding-a-needle-in-a-haystack-

5e024f931dc0

Chirality flipping?

Question coming back in

searching for

physics beyond the

Standard Model

Small contribution that

could be detected with

precision

experiments?

22

Leptoquarks:X: scalar; Y: VectorPredicted by Grand Unified Theories

Supersymmetric Theories

(with squarks, sleptons, and other supersymmetric sparticlessoverlined) ☺

Or maybe something not

considered so far.

Profumo, Ramsey-Musolf, Tulin

Phys. Rev. D 75, 075017 (2007)

23

Precision Frontier: ballpark precision needed for meaningful

contribution in LHC era.

General idea:

𝐻𝑡𝑜𝑡𝑎𝑙 = 𝐻𝑆𝑀 + 𝐻𝑛𝑒𝑤 = 𝐶𝑆𝑀 𝑂𝑆𝑀+ σ𝐶𝑛𝑒𝑤, 𝑖 𝑂𝑖

Effects of new physics

𝛿𝑂 ∼𝐶𝑛𝑒𝑤, 𝑖𝐶𝑆𝑀

2 𝑀𝑊

Λ

2

To reach Λ ∼10 TeV need

𝛿𝑂 ∼ 10−4

LEP and LHC imply new physics

probably beyond 1 TeV scale

24

Chirality-flipping interactions imply a distortion of beta spectra

Standard spectrum

Distortion due to new physics

𝑑𝑁

𝑑𝐸=

𝑑𝑁

𝑑𝐸𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑

1 + 𝑏𝑚

𝐸

`Fierz interference’

25

HOW TO? Beta spectra are known to be difficult to measure

• Many systematic errors

• Scattering probability → high at low energies

• Typical detectors –scintillators- rely on billions of processes

• Spectrometers suffer from scattering

Outlook: very hard to reach beyond LHC sensitivity with standard

technology.

Any new ideas to measure electron’s energy?

26

Shakespeare on Fundamental Physics

"I could be bounded in a nutshell,

and count myself a king of infinite space,

were it not that I have bad dreams."

- Hamlet, II.ii

Thanks: Peter Doe 27

Overcoming “bad dreams”

KATRIN design:• Drawing on the experience of past experiments…

• Intense (1011 Bq) window-less gaseous T2 source.

• Hi resolution (0.93 eV) retarding potential spectrometer.

• Control of systematic errors.

28

If cyclotron period much shorter than

characteristic time for changes in B-field

intensity:2𝜋

𝜔≪

𝐵

𝛻𝐵

1

𝑣∥then flux of B through the cyclotron orbits is

constant of motion.

Cyclotron radius: 𝑅 =𝛾𝑚𝑣⊥

𝑞𝐵

Flux ∝ 𝐵𝑣⊥

𝐵

2=

𝑣⊥2

𝐵=

𝑣2 sin 𝜃 2

𝐵

(as B increases, 𝜃 increases)

Adiabatic invariance and pitch angle

29

Retarding spectrometer:

integrate number of e’s

that make it through an

electrostatic barrier.

Transverse (cyclotron)

motion not affected by E

field.

Improve sensitivity

minimizing transverse

motion → let trajectories

expand in low B field so

longitudinal comp. of Ԧ𝑝𝑒highest.

MAC-E filter

30

Retarding spectrometer:

integrate number of e’s

that make it through an

electrostatic barrier.

Transverse (cyclotron)

motion not affected by E

field.

Improve sensitivity

minimizing transverse

motion

MAC-E filter

High B field

Low B field

High B field

The magnetic field is decreased strongly to decrease the

transverse component of the momentum in the high-E field region

31

Recently KATRIN submitted their first

result:

Upper limit (at 90% c.l.) 𝑚𝜈 < 1.1 eV.

(4 weeks of running → next factor of 2

will take about 6 months.)

32

Project 8 collaboration gets

FWHM/E ~ < 10-3 resolution

for conversion electrons of

18-32 keV from 83Kr.

Beyond KATRIN?

New idea: cyclotron radiation emission spectroscopy

(CRES) 𝜔 =𝑞𝐵

𝐸/𝑐2

33

CRES technique: some details

Radiation amplitude proportional to

𝐸11 ∙ Ԧ𝐽

𝜔𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 = 𝜔𝑐𝑦𝑐𝑙𝑜𝑡𝑟𝑜𝑛 =𝑞𝐵

𝐸

𝑇𝐸11-mode 𝐸 lines

𝛽 trajectory

𝛽 undergoes cyclotron motion in 𝐵 field.

Using waveguide, radiation can be observed.

34

CRES technique

Electrons of ~ 18 keV from a gaseous

source let to decay within a 1 Tesla field.

Radiated power ≈ 10−15 Watts.

Frequency ≈ 27 Giga-Hertz

Tritium decay to get n mass.

Electrons emitted in an RF guide within

an axial B field.

Cyclotron freq. related to energy

𝜔𝑐 =𝑞𝐵

𝐸/𝑐2

PRL 114, 162501 (2015)

Cyclotron frequency reminder

35

𝑞 𝑣 𝐵 =𝑚 𝑣2

𝑅⟹ 𝜔 =

𝑣

𝑅=𝑞 𝐵

𝑚

Frequency independent

on K energy

for a non-relativistic particle:

𝑞 𝐵 =𝑚 𝑣 𝛾

𝑅⟹𝜔 =

𝑣

𝑅=

𝑞 𝐵

𝑚𝛾

for a relativistic particle:

Frequency depends on K

energy

𝜔 =𝑞 𝐵𝑐2

𝐾 +𝑚𝑐2Rough estimate:

𝐾=18 keV, 𝐵 = 1 Tesla

𝜔 ≈ 2 × 1011 rad/s

f ≈ 27 GHz microwaves

36

CRES technique

Power from a single electron

orbiting in a magnetic field

versus time and the

frequency extracted in 30 ms

bins.

The straight streaks

correspond to the electron

losing energy (and orbiting

faster) as it radiates. The

jumps are due to collisions

with atoms in the imperfect

vacuum.

Notice noise and signal

PRL 114, 162501 (2015)

37

Advantages of the CRES technique

• Measures beta energy at creation, before complicated energy-loss mechanisms.

• Room photon or e scattering does not yield background.

• High resolution allows debugging of systematic uncertainties.

• 6He in gaseous form works well with the technique.

• Counts needed not a big demand on running time.

1) Take a wave during 30 ms.

Initial frequency 𝜔𝑐 =𝑞𝐵

𝐸/𝑐2→ E

Time bins ~ 30 ms.

2) Fourier analysis.

3) Plot peak frequency.

38

6He source at Seattle

1010 6He/s in clean lab in a

stable fashion.

Statistics

compare decay densities to neutron sources

UCN: 103 UCN/cc → ≈ 1 (decay/s)/cc

CN: 1010 CN/s cm2 →2 × 105 CN/cc ≈ 102 (decay/s)/cc6He: ≈ 106 (decay/s)/cc

40

Inject radioactivityRF systems

Read signals from

both ends →

overcome Doppler

shifts issues

41

6He in

Cryo cooler for T≈ 5 K

Low-Noise AmpsDecay volume

1-7 Tesla

superconducting

solenoid

6He in

6He-CRES apparatus

41

6He in

6He-CRES apparatus

42

coils

∆𝐵𝑧𝐵0

~10−3

6He-CRES apparatus:

trapping coils

Electrons with pitch angles 85°--90° get

trapped.

43

Apparatus assembled

44

Apparatus assembled

45

Testing RF assembly

TwistTransition

Polarizer

TrapPolarizer

Transition

Twist

Reflection and transmission in 18-24

GHz look very good

46

Monte Carlo simulations:

• 18-24 GHz

• Few days of running Extracting little b vs. B field

(assumed bMC = 0.01)

6He-CRES simulations

47

Obvious worry: efficiency

depends on energy.

Cross sectional view: guide with electron orbit. For this cyclotron radius there is a dead region shown in white.

Since blue area depends on energy there is a systematic distortion of the spectrum

Potential problems: “geometric effect”

48

Radii vs. B fieldCan use this to pin down geometric effect

Potential problems: “geometric effect”

Obvious worry: efficiency

depends on energy.

49

Radii vs. B fieldCan use this to pin down geometric effect

Geometric effect presently dominates uncertainty budget: ∆𝒃~𝟏𝟎−𝟑. Next phase → ion trap.

Potential problems: “geometric effect”

Obvious worry: efficiency

depends on energy.

50

6He-CRES: how to confirm a real signal?

Check on signature by measuring 14O and 19Ne:

Both 14O and 19Ne can be produced in similar quantities as 6He at CENPA.

19Ne source developed at Berkeley/Princeton appropriate.

14O as CO (Tfreeze = 68 K) Previous work at Louvain and TRIUMF.

SF6

51

19Ne source at Seattle Under development. Based on the

Berkeley/Princeton design, via

SF6(p,n).

Should deliver ~1010 19Ne/s in clean

lab.

SF6 in19Ne+SF6 out

beam

Al window

19Ne decay

52

Potential reach (Monte Carlo simulations)

Phase II

Phase III:Future development,Argonne National Lab., Texas A&M collaborators,couple to an ion trap

53

A series of workshops aimed at theory support for

“Beta decay as a probe of new physics”

ACFI (Amherst), Nov1-3, 2018https://www.physics.umass.edu/acfi/seminars-and-workshops/beta-decay-as-a-probe-of-new-physics

Vincenzo Cirigliano (Los Alamos National Laboratory)

Alejandro Garcia (University of Washington)

Rajan Gupta (Los Alamos National Laboratory)

Michael Ramsey-Musolf (UMass Amherst)

Albert Young (North Carolina State University)

ECT*(Trento), April 8-12, 2019 http://www.ectstar.eu/node/4435

Alejandro Garcia (University of Washington)

Doron Gazit (Hebrew University of Jerusalem)

Daniel Phillips (Ohio University)

Inst. Nucl. Theory (Seattle), Nov 4-8, 2019Brad Filippone (Caltech)

Alejandro Garcia (University of Washington)

Rajan Gupta (Los Alamos National Laboratory)

Albert Young (North Carolina State University)

https://arxiv.org/abs/1907.02164

54

• 2𝜈-2𝛽 decays

• single beta decays

• single electron capture decays

In 3 cases one can check all of the

above for the same nucleus:

good for understanding

overarching issues (role of p-p,

p-h correlations, deformation,

etc...)

Previous experiments limited by

energy resolution. CRES technique

would improve it by 100.

Applications: coupling CRES with radioactive ion trap.

Benchmarks for nuclear structure and 2𝜷 decays.

55

Suhonen et al. suggest extracting gA

using forbidden decays(PRC 96, 024317 (2017)).

CRES technique coupled to an ion trap with FRIB would allow for systematically measuring a broad range of spectra.

56

Phase I: proof of principle

2 GHz bandwidth.

Show detection of cycl. radiation from 6He.

Study power distribution.

magnet in place

some parts still being designed

vacuum systems under construction

daq system being debugged

Phase II: first measurement (b < 10-3)

6 GHz bandwidth.6He and 19Ne measurements.

Phase III: ultimate measurement (b < 10-4)

ion-trap for no limitation from geometric effect.

Mission until

Aug. 2020

Present status and outlook of 6He experiment at Seattle

57

Shakespeare on Fundamental Physics

"I could be bounded in a nutshell,

and count myself a king of infinite space,

were it not that I have bad dreams."

- Hamlet, II.ii

Translation: Experiments are difficult

and many a detail could give us

unanticipated headaches.

58

• Precision beta decay experiments may have sensitivity

beyond reach of LHC in some areas

• Need beta spectra determinations with precision ∼ 10−4.

• New Cyclotron Radiation Emission Spectroscopy technique

may yield it.

• Coupling to radioactive ion source could be powerful tool for

nuclear spectroscopy

Summary

59

Slides with details

60

Cirigliano et al.

Prog. Part. Nucl. Phys.

71, 93 (2013)

61

Project 8 timeline

• Have performed

proof-of-principle of

detection of cyclotron

radiation.

• Next phase: show

detection of molecular

tritium.

• Eventually: trap

atomic tritium

From Esfahani et al. arXiv:1703.02037

62

Standard Model+ non-SM-LL

chirality flipping

𝐻𝑉,𝐴 =

𝑖=𝑉,𝐴

ഥΨ𝑓 𝑂𝑖𝜇Ψ0 𝐶𝑖 + 𝐶𝑖′ ҧ𝑒𝐿 𝑂𝑖,𝜇𝜈𝑒

𝐿 + 𝐶𝑖 − 𝐶𝑖′ ҧ𝑒𝑅𝑂𝑖,𝜇𝜈𝑒𝑅

𝑂𝑖𝜇= ቊ

𝛾𝜇 𝑖 = 𝑉𝛾𝜇𝛾5 𝑖 = 𝐴

𝐻𝑆,𝑇 =

𝑖=𝑆,𝑇

ഥΨ𝑓 𝑂𝑖 Ψ0 𝐶𝑖 + 𝐶𝑖′ ҧ𝑒𝑅 𝑂𝑖𝜈𝑒𝐿 + 𝐶𝑖 − 𝐶𝑖′ ҧ𝑒𝐿𝑂𝑖𝜈𝑒

𝑅

𝑂𝑖 = ቊ1 𝑖 = 𝑆𝜎𝜇𝜈 𝑖 = 𝑇

LeptonicRight-handed

Scalar, Tensor

Helicity overlap

interference: 𝑚𝑒

𝐸𝑒

Nuclear beta decay phenomenology: beyond V-A ?

Helicity

Projection of spin

onto momentum

63

H=𝜎.𝑝

𝜎 𝑝

Not a Lorentz invariant:

moving faster than an R-

handed particle makes it

look L-handed

H= +1 H= −1

Chirality

A Lorentz invariant property

“relative” to helicity

64

The instantaneous velocity of a

particle:

But in QM: Δ𝑡 Δ𝐸 ∼ ℏ so

instantaneous velocity

𝑣 = limΔ𝑡՜0

Δ𝑥

Δ𝑡

𝑣 = ±𝑐

State

with

well-

defined

spin and

E,p.

Right-

chiral

Left-

chiral

A state with finite E,p and spin in a particular direction

can be expressed as linear comb. of the R and L

chirality states.

For 𝑣 ≈ 𝑐: chirality ≡ helicity

𝑢↑ 𝐸, 𝑝 =1 +

𝑝𝐸

2𝜙↑ +𝑐 +

1 −𝑝𝐸

2𝜙↑ −𝑐

𝐻𝐴 = ഥΨ𝑓𝛾𝜇𝛾5Ψ0 2𝐶𝐴 ҧ𝑒𝐿𝛾𝜇𝛾5 𝜈𝑒

𝐿 +ഥΨ𝑓 𝜎

𝜇𝜈Ψ0 𝐶𝑇 + 𝐶𝑇′ ҧ𝑒𝑅𝜎𝜇𝜈𝜈𝑒

𝐿 + 𝐶𝑇 − 𝐶𝑇′ ҧ𝑒𝐿𝜎𝜇𝜈𝜈𝑒𝑅

65

Nuclear beta decay: Fierz interference and other correlations

Decay rate:

Standard Model

chirality flipping

b-n correlation

Fierz interference

𝑏 ≈ ± 𝐶𝑇 + 𝐶𝑇′ /𝐶𝐴

𝑎 ≈ −1

31 −

𝐶𝑇2 + 𝐶′𝑇

2

2 𝐶𝐴2

Example for axial decay of unpolarized parent

𝑑𝑤 ≈ 𝑑𝑤0 1 + 𝑏𝑚

𝐸𝑒+ 𝑎

Ԧ𝑝𝑒𝐸𝑒

∙Ԧ𝑝𝜈𝐸𝜈

Precision beta decay versus others:

Can “precision” compete with “energy”?

66

Best limits now from LHC.

Will not improve significantly

with next run.

IS THIS THE END OF

SEARCHING FOR THIS

PROBE OF FUNDAMENTAL

PHYSICS?

F. Wauters et al.

PRC 89, 025501

(2014)

67

Apparatus being assembled

Coils winding

Assembling cryo

cooler connection

to RF

Magnet connected

for He recirculation,

cooled and biased

RF components

being tested

68

Potential problems:

Response to mono-energetic

𝛽’s depends on field

𝜔(arb. units)

69

Potential problems:

Response to mono-energetic

𝛽’s depends on field

Coil fields are small and

well determined. Under control

∆𝐵𝑧𝐵0

~10−3

∆𝜔𝑐𝜔𝑐

~10−3

70

Potential problems: scattering

Misidentification due to scattering?

71

Misidentification due to scattering?

• Veto events with predecessors.

• Energy loss dominated by inelastic scattering on H2 (≈14 eV).

• Larger jumps possible, but small probability.

• Can be carefully characterized varying H2 pressure.

Potential problems: scattering

72

Axial motion generates sidebands that

can distort frequency spectrum.

Correct 𝜔 missing.

Potential problems: Doppler effect

Phase changes due to axial motion

73

Axial motion generates sidebands that

can distort frequency spectrum.

Correct 𝜔 missing.

Potential problems: Doppler effect

Misidentify events

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Reading only from one end:

Doppler effect generates

sidebandsReading from both ends and

making product

Correct 𝜔 missing.Correct 2𝜔 strong.

Strategy to bypass Doppler effect issues.

Potential problems: Doppler effect

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Nuclear structure issues to reach 𝑏 < 10−3

Recoil-order corrections and the SM contribution to little b

Weak CC nucleon current:𝑝|𝑉𝜇|𝑛 = 𝑝|𝑔𝑉𝛾

𝜇 + 𝑔𝑊𝑀 𝜎𝜇𝜈𝑞𝜈|𝑛𝑝|𝐴𝜇|𝑛 = 𝑝|𝑔𝐴𝛾

𝜇𝛾5 + 𝑔𝑃 𝑞𝜇𝛾5|𝑛

Dominant factor in recoil-order correction is interference between WM and GT:

𝑅 𝐸 ≈ 𝑅02 𝐸

𝑚−

𝐸0

𝑚−

𝑚

𝐸

with𝑅0 ≈2𝑚

3𝑀

𝑊𝑀

𝜎∼ 10−3.

For 6He: 𝑅0 determined to ∼ 2% by connection to g decay of analogue in 6Li.

Other recoil-order correction (pseudo-induced term) suppressed for 6He.

How about 19Ne? 14O?

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Radiative corrections

Order-𝛼

From Hayen et al.Rev.Mod.Phys. 90, 015008 (2018)

inner bremsstrahlung

Order-𝑍𝛼2

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Likely something not considered so far…

From Cirigliano, Gonzalez-Alonso, GraesserJ. High Energy Phys. 02, 046 (2013)Modern context: EFT connection to hep.

the fields

the 𝑑 = 6 ops.