Exploiting electron parity violationO. Moreno Exploiting electron parity violation Electroweak interactions p=0.04 β V n=−0.5 β V Electron scattering (a) (GF) 1 ⇥ f¯ µ µ5

Center for Theoretical Physics and Laboratory for Nuclear ScienceMassachusetts Institute of Technology, U.S.

Exploiting electron parity violation

O. Moreno

From Standard Model tests to dark matter detection predictions

Dpto. Estructura de la Materia & IPARCOS, Facultad CC. Físicas, Universidad Complutense de Madrid, Spain

Instituto de Estructura de la Materia,Consejo Superior de Investigaciones Científicas, Spain

T. W. Donnelly

• Electroweak interactions

• Parity-violating electron scattering

• Coherent neutrino scattering

• Connection between parity-violating electron scattering and coherent neutrino scattering

• WIMP direct detection

O. Moreno Exploiting electron parity violation

Summary


Electroweak interactions

04.0=pVβ

5.0−=nVβ

Electron scattering

(a)

(GF)

1

⇥¯f��µ � �µ�5

�⌧± f

⇤W±

µ (1)

h¯f⇣cfV �µ � cfA �µ�5

⌘fiZ0

µ (2)

⇥¯f qf�µ f

⇤Aµ (3)

A ⇡ � GFp2 2⇡ ↵

|Q2| aeA �nV

N

Z

Fn

Fp(4)

|⌫ai = cos ✓ |⌫1

i+ sin ✓ |⌫2

i (5)

|⌫bi = � sin ✓ |⌫1

i+ cos ✓ |⌫2

i (6)

mh = 1 keV (7)

⇠ = 40

o

(8)

Q� �mh = 1.47 keV Q� = 2.47 keV

�N�

N�⇡ 1p

N�> R ) N� > 1/R2

d�

dEe=

d�l

dEecos

2 ⇠ +d�h

dEesin

2 ⇠ (9)

R =

d�h/dEe

d�l/dEetan

2 ⇠ (10)

10

�8 � sin ⇠ � 10

�4

(11)

ml . eV (12)

(13)

mh ⇠ 1keV < Q� (14)

|⌫ei =X

l

Uel |⌫li+X

h

Ueh |⌫hi ) |⌫ei = cos ⇠ |⌫li+ sin ⇠ |⌫hi (15)

|⌫1

i , |⌫2

i , |⌫3

i , |⌫4

i (16)

✓⌫ee

◆,

✓⌫µµ

◆,

✓⌫⌧⌧

◆,

✓⌫s�

◆(17)

Axial - Vector ~10-5 GeV-2

Neutrino scattering

n(GF)

1

⇥¯f��µ � �µ�5

�⌧± f

⇤W±

µ (1)


⌘fiZ0

µ (2)

⇥¯f qf�µ f

⇤Aµ (3)

A ⇡ � GFp2 2⇡ ↵

|Q2| aeA �nV

N

Z

Fn

Fp(4)

|⌫ai = cos ✓ |⌫1

i+ sin ✓ |⌫2

i (5)

|⌫bi = � sin ✓ |⌫1

i+ cos ✓ |⌫2

i (6)

mh = 1 keV (7)

⇠ = 40

o

(8)

Q� �mh = 1.47 keV Q� = 2.47 keV

�N�

N�⇡ 1p

N�> R ) N� > 1/R2

d�

dEe=

d�l

dEecos

2 ⇠ +d�h

dEesin

2 ⇠ (9)

R =

d�h/dEe

d�l/dEetan

2 ⇠ (10)

10

�8 � sin ⇠ � 10

�4

(11)

ml . eV (12)

(13)

mh ⇠ 1keV < Q� (14)

|⌫ei =X

l

Uel |⌫li+X

h


|⌫1

i , |⌫2

i , |⌫3

i , |⌫4

i (16)

✓⌫ee

◆,

✓⌫µµ

◆,

✓⌫⌧⌧

◆,

✓⌫s�

◆(17)

~10-5 GeV-2Axial - Vector

Currents Couplings

1

⇥¯f��µ � �µ�5

�⌧± f

⇤W±

µ (1)


⌘fiZ0

µ (2)

⇥¯f qf�µ f

⇤Aµ (3)

A ⇡ � GFp2 2⇡ ↵

|Q2| aeA �nV

N

Z

Fn

Fp(4)

|⌫ai = cos ✓ |⌫1

i+ sin ✓ |⌫2

i (5)

|⌫bi = � sin ✓ |⌫1

i+ cos ✓ |⌫2

i (6)

mh = 1 keV (7)

⇠ = 40

o

(8)

Q� �mh = 1.47 keV Q� = 2.47 keV

�N�

N�⇡ 1p

N�> R ) N� > 1/R2

d�

dEe=

d�l

dEecos

2 ⇠ +d�h

dEesin

2 ⇠ (9)

R =

d�h/dEe

d�l/dEetan

2 ⇠ (10)

10

�8 � sin ⇠ � 10

�4

(11)

ml . eV (12)

(13)

mh ⇠ 1keV < Q� (14)

|⌫ei =X

l

Uel |⌫li+X

h


|⌫1

i , |⌫2

i , |⌫3

i , |⌫4

i (16)

✓⌫ee

◆,

✓⌫µµ

◆,

✓⌫⌧⌧

◆,

✓⌫s�

◆(17)

Vector ~10-2

Electromagnetic + Weak neutral

Weak neutral


Parity-violating electron scattering

Polarized electron(clockwise)

Nuclear4target4

Mirror imagePolarized electron(anticlockwise)

q

q ≈ 2 E sin(q/2)

Parity-violating (helicity) asymmetry:

Definition




Definition

+

2

~10-6

Within plane wave Born approximation and for isospin-0 (N = Z), spin-0 targets, the ‘reference asymmetry’ is:

- Only one photon and one Z0 are exchanged. - Electron wave functions are not distorted by the target charge. - Target state is spin-0, isospin-0 (non isospin mixing).




Definition

Assumptions

1

A ⇡ � GFp2 2⇡ ↵

|Q2| aeA �nV

N

Z

Fn

Fp(1)

|⌫ai = cos ✓ |⌫1

i+ sin ✓ |⌫2

i (2)

|⌫bi = � sin ✓ |⌫1

i+ cos ✓ |⌫2

i (3)

mh = 1 keV (4)

⇠ = 40

o

(5)

Q� �mh = 1.47 keV Q� = 2.47 keV

�N�

N�⇡ 1p

N�> R ) N� > 1/R2

d�

dEe=

d�l

dEecos

2 ⇠ +d�h

dEesin

2 ⇠ (6)

R =

d�h/dEe

d�l/dEetan

2 ⇠ (7)

10

�8 � sin ⇠ � 10

�4

(8)

ml . eV (9)

(10)

mh ⇠ 1keV < Q� (11)

|⌫ei =X

l

Uel |⌫li+X

h


|⌫1

i , |⌫2

i , |⌫3

i , |⌫4

i (13)

✓⌫ee

◆,

✓⌫µµ

◆,

✓⌫⌧⌧

◆,

✓⌫s�

◆(14)

For N = Z nuclei:




Definition

• Determination of the neutron radius and neutron skin of heavy nuclei (PREX, CREX experiments), isospin mixing, neutron-rich matter equation of state, …

• Extrapolation to properties of neutron stars: radius, transition density, size of crust, …

NASA



Applications


0 0.5 1 1.5 2 2.5 3q [fm-1]

0

1

2

3

A [1

0-5]

120Sn

70 72 74 76 78 80 82Neutron number

0.12

0.14

0.16

0.18

0.20

0.22

Prot

on-n

eutro

n rm

s rad

ius d

iffer

ence

, rn-r

p [fm

]

120-132Sn

Neutron skin thickness

rn - rp

Nucleon densities (Form factors) PV asymmetry

0 1 2 3 4 5 6 7 8 9 10r [fm]

10-4

10-3

10-2

10-1

Den

sity

[fm

-3]

Proton densityNeutron density

120Sn


Applications


Possible relationship between nuclear structure and neutron star structure through the equation of state of neutron-rich matter: - The larger the neutron skin thickness of nuclei, the larger the

radius of neutron stars. - The larger the neutron skin thickness of nuclei, the smaller the

crust thickness of neutron stars.

University of Warwick/Mark Garlick


Applications

0 1 2 3 4 5 6 7 8 9r [fm]

10-2

10-1

Den

sity

[fm

-3]

Proton densityNeutron density

208Pb

• Accurate evaluation of the weak mixing angle, the size and momentum-dependence of higher-order electroweak radiative corrections, …

Related to the current interest in low-energy, high-luminosity polarized electron beams for high precision parity-violating experiments: MESA@Mainz, FEL@JLab, Cb@Cornell.

Accurate theoretical knowledge is required of the size and uncertainty of the nuclear and nucleon structure effects involved.



Applications

• Computation of nuclear and nucleon structure effects on the parity-violating observables in electron scattering. Focus on a carbon 12 target (spin 0, N = Z).

• Estimation of the theoretical uncertainties related to the previous calculations.

• Search for the optimal kinematic conditions to achieve the required theoretical and statistical uncertainties.



Analysis

Absolute effect of feature X



Analysis


Relative effect of feature X



Analysis


Relative effect of feature X

Relative uncertainty of feature X



Analysis

• Distortion of the electron wave function due to the Coulomb field created by the nuclear charge distribution: from plane-wave (PW) to distorted-wave (DW) calculations.

• Isospin mixing in the nucleus due to the Coulomb interaction acting differently on protons and neutrons.

• Strangeness content of the nucleons modifying the isoscalar (but not the isovector) nuclear responses.

• Meson exchange currents among the nucleons affecting differently the isoscalar and the isovector nuclear responses.

• Inelastic transitions to excited nuclear states differing significantly from the ground state (e.g. different nominal isospin).



Analysis

Contribution to PV asymmetry

Relative size

Relative uncertainty

Coulomb distortion of projectile wave function 3 % 0.01 %

Nuclear isospin mixing (electromagnetic origin) 0.4 % 0.05 %

Nucleon strangeness content (mainly electric) 0 - 1 % 1%

Meson exchange currents < 0.1 % < 0.1 %

Inelastic contributions < 0.1 % --

Summary of sizes and uncertainties (150 MeV incident electron energy, 25º - 45º scattering angle range)



Analysis

• Weak neutral current process, neutrino in and neutrino out: only nuclear recoil can be detected.

• The target nucleus remains in its ground state (elastic scattering).

• The cross section is roughly proportional to A2.

• Larger when the wavelength corresponding to the momentum transfer is similar to the nuclear size (q ≲ 70 MeV for 12C).

• It is the only elastic contribution for even-even nuclear targets, and usually dominant for other targets.

(ERL, qg0)


Coherent neutrino scattering

Definition

• Determination of electroweak constants at low momentum transfer as well as higher-order corrections.

• Testing the universality of the weak interaction for charged and neutral leptons.

• Analysis of structure details of the target (e.g. axial structure).

• Astrophysical processes (e.g. stellar core collapse, supernova neutrinos).

• Extension to direct detection of certain types of dark matter particles.


Coherent neutrino scattering

Applications

• Relationship between coherent electron-nucleus and coherent neutrino-nucleus cross-sections in PWBA:

• Relationship between their relative uncertainties:


Parity violating electron and coherent neutrino scatterings

- Coulomb distortion.

- Effect of higher order corrections.

- Non-SM couplings of neutrinos to Z0.

Deviations from this prediction


Parity violating electron and coherent neutrino scatterings

WI(M)Ps: Weak interacting (massive) particles - Weak-like interactions (like neutrinos): the current has vector and

axial components. - May have much heavier masses than Standard Model neutrinos. - Examples: supersymmetric particles (neutralinos),

sterile neutrinos.1

|⌫a > = cos ✓ |⌫1 > +sin ✓ |⌫2 > (1)

(2)

|⌫b > = � sin ✓ |⌫1 > +cos ✓ |⌫2 > (3)

✓⌫ee

◆,

✓⌫µµ

◆,

✓⌫⌧⌧

◆,

✓⌫s�

◆(4)

1

|⌫ai = cos ✓ |⌫1i+ sin ✓ |⌫2i (1)

(2)

|⌫bi = � sin ✓ |⌫1i+ cos ✓ |⌫2i (3)

|⌫1i , |⌫2i , |⌫3i , |⌫4i (4)

✓⌫ee

◆,

✓⌫µµ

◆,

✓⌫⌧⌧

◆,

✓⌫s�

◆(5)Standard Model ?


WI(M)P direct detection

Flavor eigenstates

Mass eigenstates

1

|⌫ai = cos ✓ |⌫1i+ sin ✓ |⌫2i (1)

|⌫bi = � sin ✓ |⌫1i+ cos ✓ |⌫2i (2)

|⌫1i , |⌫2i , |⌫3i , |⌫4i (3)

✓⌫ee

◆,

✓⌫µµ

◆,

✓⌫⌧⌧

◆,

✓⌫s�

◆(4)

WIMP - 12C elastic scattering differential cross sections as a function of momentum transfer q (proportional to nuclear recoil energy), for several WIMP velocities b and WIMP mass 100 MeV.

Vector component

Axial component



Parity violationin electron scattering

Nuclear structure: radius, neutron skin,

isospin mixing

Nuclear matter equation of state, neutron star radius and structure

Nucleon structure: form factors,

strangeness content

Standard Model tests and parameters Neutrino-nucleus

coherent scattering



Conclusions

References:

PRC 89 (2014) 015501, JPG 42 (2015) 034006, NPA 828 (2009) 306, JPG 37 (2010) 064019, PRC 92 (2015) 055504, NPB 866 (2013) 177 , AIPCP 1541 (2013) 167, arXiv:1603.05932v1

Documents

Exploiting electron parity violationO. Moreno Exploiting electron parity violation Electroweak interactions p=0.04 β V n=−0.5 β V Electron scattering (a) (GF) 1 ⇥ f¯ µ µ5