Neutrino Coherent Scattering, neutrino dipole moments, and - - PowerPoint PPT Presentation

Neutrino Coherent Scattering, neutrino dipole moments, and connection to cosmology

A.B. Balantekin

ACFI Workshop on Neutrino-Electron Scattering at Low Energies April 2019

Balantekin)and)Fuller,)Prog.)Part.)Nucl.)Phys.)71 162)(2013)

Understanding neutrino-nucleus interactions are essential to neutrino physics: for example consider a core-collapse supernova.

• r)a)long?baseline)experiment

For many aspects of SN physics we need to know what happens when a 10-40 MeV neutrino hits a nucleus? Where does the strength lie? What is gA/gV?

As the incoming neutrino energy increases, the contribution of the states which are not well-known increase, including first- and even second- forbidden transitions.

How can we accurately calculate neutrino-nucleus cross sections and beta decay rates?

!"#$ ≈ 1 +#'() − +

, () , + ⋯

Neutrino#wave# function allowed First5 forbidden Second5 forbidden

Example of an approach from the first principles: Using effective field theory for low-energy neutrino-deuteron scattering

Below&the&pion&threshold&3S1 ! 1S0 transition&dominates&and&one&only& needs&the&coefficient&of&the&two8body&counter&term,&L1A (isovector two8 body&axial&current) L1A can&be&obtained&by& comparing&the&cross&section&"(E)& =&"0(E)&+&L1A "1(E)&with&cross8 section&calculated&using&other& approaches&or&measured& experimentally&(e.g.&use&solar& neutrinos&as&a&source).

A.B.$Balantekin$and$H.$Yuksel,$PRC$68#055801$(2003)

Example of an approach from the first principles: Using effective field theory for low-energy neutrino-deuteron scattering

Below$the$pion$threshold$3S1 ! 1S0 transition$dominates$and$one$only$ needs$the$coefficient$of$the$twoGbody$counter$term,$L1A (isovector twoG body$axial$current) L1A can$be$obtained$by$ comparing$the$cross$section$"(E)$ =$"0(E)$+$L1A "1(E)$with$crossG section$calculated$using$other$ approaches$or$measured$ experimentally$(e.g.$use$solar$ neutrinos$as$a$source).

A.B.$Balantekin$and$H.$Yuksel,$PRC$68#055801$(2003)

Example of an approach from the first principles: Using effective field theory for low-energy neutrino-deuteron scattering

Below$the$pion$threshold$3S1 ! 1S0 transition$dominates$and$one$only$ needs$the$coefficient$of$the$twoGbody$counter$term,$L1A (isovector twoG body$axial$current) L1A can$be$obtained$by$ comparing$the$cross$section$"(E)$ =$"0(E)$+$L1A "1(E)$with$crossG section$calculated$using$other$ approaches$or$measured$ experimentally$(e.g.$use$solar$ neutrinos$as$a$source). Difficult$to$go$beyond$ twoGbody$systems!

L1A=3.9(0.1)(1.0)(0.3)(0.9) fm3 at$ a$renormalization$scale$set$by$the$ physical$pion$mass

Savage$et$al.,$PRL$119,$062002$(2017)

A new p-sd shell model (SFO) including up to 2-3 hΩ excitations which can describe well the magnetic moments and Gamow-Teller (GT) transitions in p-shell nuclei with a small quenching for spin g-factor and axial-vector coupling constant Suzuki,'Fujimoto,'Otsuka

5/2− 1/2+ 3/2− 1/2−

13N

5/2− 5/2+ 3/2− 1/2+ 1/2−

13C

GT IAS+GT

An example: νe+13C

Suzuki,,Balantekin,,Kajino, Phys.,Rev.,C,86,,015502,(2012)

CC NC

CK,(circles),vs.,SFO,(lines),

10 20 30 40 50 E (MeV) 10-43 10-42 10-41 10-40 σ (cm²)

Total Proton) emission g.s.0of0

13N

Neutron)emission0and0

• ther0contributions

!e + 13C charged-current scattering

Suzuki,0Balantekin,0Kajino,0Chiba,02019

arXiv:1904.11291

10 20 30 40 50 E (MeV) 10-43 10-42 10-41 10-40 10-39

σ (cm²)

Comparison of charged-current cross sections !" + $%C ̅ !" + $%C

Suzuki,'Balantekin,'Kajino,'Chiba,'2019

Neutrino Coherent Scattering !" !# $, # = '(

)

8+ , 2 − 2# #

/01

+ # $

)

34

) 5 3) )

#

/01 =

2$) 2$ + , 34 = 6 − 1 − 4 sin) <4 = 3) = 2,# 5 3) = 1 34 > !? ?) sin) 3? 3? @A ? − 1 − 4 sin) <4 @B ? For nearly spherical systems

Suzuki, Balantekin, Kajino Chiba

PRELIMINARY

13C 12C

20 40 60 80 100 120 140 E (MeV) 10-16 10-15 10-14 10-13 10-12

σ (fm²)

Suzuki,<Balantekin,<Kajino,<Chiba,<2019

13C

exact E2 !" !# $, # = '(

)

8+ , 2 − 2# #

/01

+ # $

)

34

) 5 3) )

" $ ∝ $) + nuclear corrections

F(Q2) = 1 + η2Q2 + η4Q4 + · · · , σ(E) = G 2

F

4π Q2

W E 2

✓ 1 + 8 3η2E 2 + 8 3(η2

2 + 2η4)E 4 + · · ·

◆ − 2 M ✓ E + 16 3 η2E 3 + 24 3 (η2

2 + 2η4)E 5 + · · ·

◆ + · · ·

• 20

40 60 80 100 120 140 E (MeV) 10-16 10-15 10-14 10-13 10-12

σ (fm²)

100 200 300 400 500 Maximum recoil energy (keV) 1x10-40 2x10-40 3x10-40 4x10-40 5x10-40

σ (cm²)

Coherent elastic neutrino cross sections

13C 12C

Reactor neutrino experiments to measure the remaining mixing angle also measure the reactor neutrino flux

Daya Bay,& arXiv:1904.07812

PROSPECT(Collaboration,(J.(Phys.(G(43,(113001((2016)(

NEUTRINO-4 claim

arXiv:'1809.10561

Oscillation*Exclusion

PROSPECT() arXiv:1806.02784

An alternative solution:"

¹³C(ν, %&')¹²C٭(4.4-./)→¹²C(g.s.) + γ

Berryman,"Bradar,"Huber,"arXiv:"1803.08506

4.4 MeV prompt photon and proton recoils from thermalized neutron can mimic neutrinos around 5 MeV ; ;

10 20 30 40 50 60 E (MeV) 10-44 10-43 10-42 10-41 σ (cm²)

An alternative solution:"

¹³C(ν, %&')¹²C٭(4.4-./)→¹²C(g.s.) + γ

Berryman,"Bradar,"Huber,"arXiv:"1803.08506

4.4 MeV prompt photon and proton recoils from thermalized neutron can mimic neutrinos around 5 MeV

HOWEVER

56C+ ̅

8 →59 C+ ̅ % + n

; ;

All"states"in"12C g.s.in 12C 4.4"MeV"state"in"12C Suzuki,"Balantekin,"Kajino,"Chiba

State of the art SM calculation using SFO Hamiltonian which includes tensor and enhanced monopole interactions is too small. ➜This solution requires BSM physics. PRELIMINARY

Dirac magnetic moment Majorana magnetic moment

Introduce a magnetic moment operator, ˆ µ

σ ∝ νi ˆ µ νe

2 i

∑

= νe ˆ µ | ˆ µ νe

Example: Neutrino-electron scattering via magnetic moment

ˆ µ | = ˆ µ ˆ µT = − ˆ µ

A reactor experiment measuring electron antineutrino magnetic moment is an inclusive

• ne, i.e. it sums over all the

neutrino final states

dσ dTe = α 2π me

2 µeff 2

1 Te − 1 Eν " # $ % & ' µeff

2 =

Ueje

−iE jLµ ji j

∑

i

∑

2

Neutrino Magnetic Moment in the Standard Model Symmetry Principles ! µ" → 0 as #$ → 0

Standard Model (Dirac)

µij = − eGF 8 2π 2 (mi + mj) UiUj

* f (r ) 

∑

f (r

) ≈ − 3

2 + 3 4 r

 +…,

r

 =

m MW $ % & ' ( )

2

Standard Model (only) contribution to the Dirac neutrino magnetic moment measured at reactors

A.B.B.$&$ N.$Vassh A.B.B.,$N.$Vassh,$PRD$89#(2014)$073013

Cosmological$limits

Dirac Majorana

Reactors vs. solar Cerenkov detectors

A.B.B. & N. Vassh AIP Conf.Proc. 1604 (2014) 150 arXiv:1404.1393

Extension of the red giant branch in globular clusters

Globular(cluster(M5((! μν<(4.5(× 10712 μB(95%(C.L.)

arXiv:1308.4627

µ!=10-12µB µ!=10-11µB µ!=10-10µB

electroweak

weak magnetic

dσ dT = GF

2me

2π gV + gA

( )

2 + gV − gA

( )

2 1− T

Eν " # $ % & '

2

+ gA

2 − gV 2

( ) meT

Eν

2

( ) * * + ,

• + πα 2µ 2

me

2

1 T − 1 Eν " # $ % & '

gv = 2sin2θW +1/ 2 gA = +1/ 2 for electron neutrinos −1/ 2 for electron antineutrinos " # $ % $ νj νe γ e− e−

n± = g 2π

( )

3

d3p

∫

1 e(E±µ)/T +1 ⇒ ρb = −e n− − n+

( )

Introducing a charge Ze at r = 0 will create a potential φ ρa = −e π 2 d3p

∫

1 e(E−eφ−µ)/T +1 − 1 e(E+eφ+µ)/T +1 $ % & ' ( ) ∇2φ = −4π ρa − ρb + Zeδ3(r) $ % ' ( ∇2φ = − − 1 λD

2 φ + 2π

∂2 ∂µ 2 ρb ,

• .

/ 1 eφ

( )

2 + 4πZeδ3(r)

$ % & ' ( )+O eφ

( )

3

( )

1 4πλD

2 = e2 ∂

∂µ n− − n+

[ ] ⇒ φ(r) = Ze

r exp −r / λD

( )

Explicitly verified in Q.E.D. only up to third order.

Classical screening in an electron- positron plasma

1 λD

2 = −Π00 k0 = 0, k → 0

( )

= −e2T d3p 2π

( )

3

∫

np

∑

Tr γ 0G(p)Γ0(p, p)G(p)

( )

= −e2T d3p 2π

( )

3

∫

np

∑

Tr γ 0G(p)∂G−1 ∂µ (p)G(p) ( ) * + ,

• = e2 ∂

∂µ T d3p 2π

( )

3

∫

np

∑

Tr γ 0G(p)

( )

= e2 ∂n ∂µ ( ) * + ,

• T

= e2 ∂2 ∂µ 2 P(µ,T)

Quantum derivation in finite-temperature Q.E.D. Note that the pressure is so far calculated only to order e3 at finite temperature

Magnetic scattering of neutrinos and electrons

dσ dTe = α 2π me

2

Ueje

−iE jLµ ji j

∑

i

∑

2

# $ % % & ' ( ( 1 Te − 1 Eν ) * + ,

• .

σ (s) = π 2α 2µν

2

me

2

tmax s − me

2 − s − me 2

s + log s − me

2

( )

2

s tmax " # $ $ % & ' ' tmax = −2me me

2 + 1

λD

2 − me

( ) * * + ,

• In the laboratory

In relativistic e+e- plasma

Vassh, Grohs, Balantekin, Fuller,

• Phys. Rev. D 92,

125020 (2015)

Vassh, Grohs, Balantekin, Fuller,

• Phys. Rev. D 92, 125020 (2015)

The effect of the neutrino magnetic moment on neutrino decoupling in the BBN epoch

dσ dT = GF

2me

2π gV + gA

( )

2 + gV − gA

( )

2 1− T

Eν " # $ % & '

2

+ gA

2 − gV 2

( ) meT

Eν

2

( ) * * + ,

• + πα 2µ 2

me

2

1 T − 1 Eν " # $ % & '

Decoupling temperature of three flavors

0.4 0.6 0.8 1.0 1.2 Tνe,dec [MeV] 0.4 0.6 0.8 1.0 1.2 1.4 Tντ,dec [MeV]

0.2450 0.2452 0.2455 0.2458 . 2 4 6 0.2462 0.2466

0.4 0.6 0.8 1.0 1.2 1.4 Tνµ,dec [MeV]

0.2435 . 2 4 4 0.2448 0.2456 0.2464

Contours of constant YP

T!µ,dec=0.245 MeV T!e,dec=0.245 MeV

YP ≡ 4nHe np + nn

1 2 3 4 5 6 7 8 µeµ [10−10µB] 1 2 3 4 5 6 7 8 µeτ [10−10µB]

0.2440 . 2 4 4 5 0.2450 0.2455 0.2460 . 2 4 6 5

1 2 3 4 5 6 7 8 µµτ [10−10µB]

0.2440 0.2445 0.2450 0.2455 0.2460 0.2465 . 2 4 7 0.2475

Contours of constant YP µµ!=10"10µ# µeµ=10"10µ#

10−10 µeµ [µB] 10−10 µµτ [µB]

3 . 5 3 . 1 3 . 2 3 . 3 3.400 3.600 3.200 3.300 3 . 4 3.600 3 . 8

Contours of constant Neff µe!=10"10 µ# µe!=4.9x10'10 µ#

Planck: Neff = 3.30 ± 0.27 ⇒ µ ≤ 6×10−10µB

ρrelativistic = π 2 15 T

γ 4 1+ 7

8 Neffective 4 11 ! " # $ % &

4/3

' ( ) ) * + , ,

!" !# = %&

'

8) * 2 − 2# #

• ./

+ # 1

'

23

' 45 2' ' +

)6'7eff

'

:' ;<

'

1 # − 1 1 4

> 2' '

Including magnetic moment in coherent neutrino scattering 7eff

'

= ?

@

?

A

B < or E A FG@HIJ7A@

'

Note that this is a different combination than what is measured at reactors or solar neutrino experiments!

Γi→j = µ

2

8π mi

2 − mj 2

mi $ % & & ' ( ) )

3

= 5.308s−1 µeff µB $ % & ' ( )

2 mi 2 − mj 2

mi

2

$ % & & ' ( ) )

3

mi eV $ % & ' ( )

3

Sterile neutrino decay and Big Bang Nucleosynthesis

Kusakabe, A.B.B., Kajino, and Pehlivan, Phys. Rev. D 87, 085045 (2013)

How can we tell if the neutrinos are Dirac

• r Majorana particles?
• Neutrinoless double beta decay –only possible for

Majorana neutrinos

Meyer Racah

0!"" decay

Majorana mass 2!"" 0!""

How can we tell if the neutrinos are Dirac

• r Majorana particles?
• Neutrinoless double beta decay –only possible for

Majorana neutrinos

• Capturing cosmic background neutrinos. At least

two of them are non-relativistic where what kind

• f mass you have matters. Very difficult

experiments with significant uncertainties due to the lack of knowledge of the local neutrino density.

How can we tell if the neutrinos are Dirac

• r Majorana particles?
• Neutrinoless double beta decay –only possible for

Majorana neutrinos

• Capturing cosmic background neutrinos. At least

two of them are non-relativistic where what kind

• f mass you have matters. Very difficult

experiments with significant uncertainties due to the lack of knowledge of the local neutrino density.

• Measure angular distribution in decays.

How can we tell if the neutrinos are Dirac

• r Majorana particles?
• Measure angular distribution in decays.

The decay angular distribution is isotropic in the Majorana case, and not isotropic in the Dirac case. Next speaker, B. Kayser, will show how this conclusion follows from general symmetry arguments.