[PPT] - Theory and Phenomenology of Coherent Elastic Neutrino Nucleus PowerPoint Presentation

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Theory and Phenomenology of Coherent Elastic Neutrino Nucleus Scattering

Gail McLaughlin NC State

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Coherent Elastic Neutrino Nucleus Scattering (CEνNS)

neutrino interacts with nucleus through neutral current
can’t see neutrino afterward, but could see small kick to nucleus

Outline

introduction
where CEνNS is already in

use

future physics from CEνNS

Z NC

ν ν

A A

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SLIDE 3

Basic cross section

Coherent elastic neutrino nucleus scattering cross section dσ dT (E, T) = G2

F

2π M

2 − 2T

E + T E 2 − MT E2

Q2

W

4 F 2(Q2)

E : neutrino energy, T : nuclear recoil
Q2 =

2E2T M (E2−ET ) : squared momentum transfer

QW = N − Z(1 − 4 sin2 θW ): weak charge
F(Q2): form factor - largest uncertainty in cross section

Assumes a spin zero nucleus, no non-standard model interactions

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Making a theoretical prediction

Fold cross section (previous slide) with incoming neutrino spectrum (e.g. left figure) to find nuclear recoil spectrum (right figure)

νs from π/µ decay at rest

Neutrino energy (MeV)

10 20 30 40 50

Flux

0.005 0.01 0.015 0.02 0.025 0.03 0.035 (delayed)

µ

ν (delayed)

e

ν (prompt)

µ

ν

Fig. from Scholberg 2006

Spectrum of nuclear recoils

400 800 1200 1600 2000 2400 20 40 60 80 100 120 140

Events/keV Recoil Energy (keV)

Fig. from Patton et al 2012

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Coherent Elastic Neutrino Nucleus Scattering (CEνNS) appears many places

A few of these

Opacity source in supernova neutrinos
Mechanism for detecting supernova neutrinos
Means for studying active-sterile oscillations
Background in dark matter detectors

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Coherent Elastic Neutrino Nucleus Scattering (CEνNS) appears many places

A few of these

Opacity source in supernova neutrinos
Mechanism for detecting supernova neutrinos
Means for studying active-sterile oscillations
Background in dark matter detectors

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SLIDE 7

Supernovae Neutrinos

Figure from J. Blondin

νe ν

e

short mean free path long mean free path

core ν ν ν ν

µ τ τ µ

Schematic picture of neutrino emission from proto-neutron star

Neutrinos are emitted from deep in the center

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SLIDE 8

Coherent elastic neutrino nucleus scattering is an opacity source in supernova

Figure from S. Bruenn

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Coherent Elastic Neutrino Nucleus Scattering (CEνNS) appears many places

A few of these

Opacity source in supernova neutrinos
Mechanism for detecting supernova neutrinos
Means for studying active-sterile oscillations
Background in dark matter detectors

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Coherent Elastic Neutrino Nucleus Scattering (CEνNS) for detecting supernova neutrinos

spectra from ORNL group 50 100 150 200 E (keV) 1 2 3 4 5 6 Yield (Events per keV) Background T=8 MeV T=6 MeV Event rates in CLEAN detector, Horowitz et al 2003

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Coherent Elastic Neutrino Nucleus Scattering (CEνNS) appears many places

A few of these

Opacity source in supernova neutrinos
Mechanism for detecting supernova neutrinos
Means for studying active-sterile oscillations
Background in dark matter detectors

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CEνNS proposed as a mechanism for probing sterile neutrino oscillations

( Anderson et al 2012, Formaggio et al 2012) Since CEνNS measures only neutral current it is insensitive to active flavor transformation, ideal for studying active sterile transformation Example: sensitivity to sterile oscil- lations using Ar at Daeδalus

Anderson et al 2012

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Coherent Elastic Neutrino Nucleus Scattering (CEνNS) appears many places

A few of these

Opacity source in supernova neutrinos
Mechanism for detecting supernova neutrinos
Means for studying active-sterile oscillations
Background in dark matter detectors

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CEνNS background is a limit

n future dark matter sensitivity

discussed in Snowmass Summary: WIMP Dark Matter Direct Detection

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Even though we are counting on this process, it has never been detected!

Why not? Large cross section but need to see the small recoil of the nucleus

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SLIDE 16

Beyond First Detection of CEνNS

nonstandard ν

interactions

form factor

400 800 1200 1600 2000 2400 20 40 60 80 100 120 140

Events/keV Recoil Energy (keV)

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SLIDE 17

Beyond First Detection of CEνNS

nonstandard ν

interactions

form factor

400 800 1200 1600 2000 2400 20 40 60 80 100 120 140

Events/keV Recoil Energy (keV)

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SLIDE 18

Nonstandard interactions

Some nonstandard interactions are currently poorly constrained. Examples are vector couplings for electron neutrinos with up and down quarks, ǫuV

ee and ǫdV ee , although there are other couplings that

contribute as well. To define the NSI, use eq from Barranco et al 2006, LNSI

νHadron = − GF √ 2

q=u,d

α,β=e,µ,τ

¯

ναγµ(1 − γ5)νβ

∗
εqL

αβ

¯

qγµ(1 − γ5)q

+ εqR

αβ

¯

qγµ(1 + γ5)q

(1)

The vector couplings are the only ones relevant for spin zero nuclei εqV

αβ = εqL αβ + εqR αβ.

Limits are −1.0 < ǫuV

ee < 0.6 and −0.5 < ǫdV ee < 1.2 18

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Nonstandard interactions

Continue considering example ǫuV

ee and ǫdV ee . The zero order effect on

CEνNS is to change the standard model weak charge to an effective weak charge. QW = N(1 − 2ǫuV

ee − 4ǫdV ee ) + Z(1 − 4 sin2 θW + 4ǫuV ee + 2ǫdV ee )

Recall: dσ dT (E, T) = G2

F

2π M

2 − 2T

E + T E 2 − MT E2

Q2

W

4 F 2(Q2)

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SLIDE 20

Nonstandard interactions

Changing the size of QW effectively changes overall magnitude of recoil

curve. Shows limits which could be

achieved after 100 kg/yr at SNS.

Scholberg 2006

Additional non-standard interactions such as the flavor changing neutral currents can be probed. Also, first order effect in changing relative contributions of neutron and proton form factor.

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Beyond First Detection of CEνNS

nonstandard ν

interactions

form factor

400 800 1200 1600 2000 2400 20 40 60 80 100 120 140

Events/keV Recoil Energy (keV)

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SLIDE 22

Form factor Understanding the structure of the nucleus

Form factor, F(Q2) is the Fourier transform of the density distributions of protons and neutrons in the nucleus. F(Q2) = 1 QW ρn(r) − (1 − 4 sin2 θW )ρp(r) sin (Qr) Qr r2dr density distributions R21/2

SGII = 3.405 fm

R21/2

G202 = 3.454 fm 22

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Form factor

Form factor, F(Q2) is the Fourier transform of the density distributions of protons and neutrons in the nucleus. F(Q2) = 1 QW ρn(r) − (1 − 4 sin2 θW )ρp(r) sin (Qr) Qr r2dr

Proton form factor term is suppressed by 1 − 4 sin2 (θW )
Neutron form factor is not suppressed

CEνNS can be used to determine the form factor Amanik et al 2009

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Form factor

F(Q2) = 1 QW ρn(r) − (1 − 4 sin2 θW )ρp(r) sin (Qr) Qr r2dr

Proton form factor can be measured by electromagnetic probes.
Neutron form factor is less well known:
Neutron scattering - many measurements - requires theory to go

from cross section to form factor

Parity violating electron scattering - PREX at Jlab Pb at one Q2,

extract AP V ∼ 0.65 × 10−6 then determine neutron radius, now also CREX at Jlab on Ca CνNS recoil curve can be fit: neutron radius and higher moments

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Nuclear-Neutron form factor from CEνNS

Taylor expand the sin(Qr) form factor: Fn(Q2) =

1 QW

ρn(r) sin (Qr)

Qr

r2dr ≈

N QW (1 − Q2 3! R2 n + Q4 5! R4 n − ...)

Moments

f

the den- sity distribution, R2

n,

R4

n

characterize the form factor.

Patton et al 2012, 2013

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SLIDE 26

Liquid argon scenario

2.50 3.00 3.50 4.00 4.50

R4

n1/4 (fm) 2.50 3.00 3.50 4.00 4.50 3.20 3.30 3.40 3.50 3.60

R4

n1/4 (fm)

R2

n1/2 (fm)

3.5 tonnes argon 16m from SNS, 18m from Daeδalus, 30m from ESS for one year. Shows 40%, 91% and 97% confidence contours. Crosses are theory predictions.

Fig. from Patton et al 2012

Band is measurement from neutron scattering. Top plot: normalization

f neutrino flux not known, bottom plot normalization of neutrino flux

known.

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Xenon is more constraining

4.60 4.80 5.00 5.20 5.40 5.60

R4

n1/4 eff (fm) 4.60 4.80 5.00 5.20 5.40 5.60 4.60 4.70 4.80 4.90 5.00 5.10

R4

n1/4 eff (fm)

R2

n1/2 eff (fm)

300 kg Xenon 16m from SNS, 18m from Daeδalus, 30m from ESS for

ne year. Shows 40%, 91% and

97% confidence contours. Crosses are theory predictions.

fig. from Patton et al 2012

Top plot: normalization of neutrino flux not known, bottom plot normalization of neutrino flux known.

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SLIDE 28

Beyond NSIs and the form factor

Nonstandard ν

interactions

Form factor
sin2 θW
ν magnetic moment

QW = N + Z(1 − 4 sin2 θW )

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SLIDE 29

Beyond NSIs and the form factor

Nonstandard ν

interactions

Form factor
sin2 θW
ν magnetic moment

MeV

4

10

3

10

2

10

1

10

Events per keV per yr per ton

20 40 60 80 100 120 140 160 180 200

Delayed flux Delayed flux

MeV

4

10

3

10

2

10

1

10

Events per keV per yr per ton

20 40 60 80 100 120 140 160 180 200

Prompt flux SM

10

10 × =1

ν

µ

10

10 × =6

µ

ν

µ Prompt flux fig from Scholberg 2006

Look for excess events at low recoil en- ergy using neutrinos from stopped π/µ

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Summary

Coherent elastic neutrino nucleus scattering is not yet detected,

but in many communities such as supernova simulation, supernova detection, active-sterile oscillations, dark matter detection it is assume to exist as predicted by standard model

Going beyond a first detection...

– non-standard interactions – form factor

and beyond these...

– Weinberg angle – neutrino magnetic moment

overall, a rich physics opportunity from the theory point of view

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