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

Understanding neutrino-nucleus interactions are essential to neutrino physics: for example consider a core-collapse supernova. Balantekin)and)Fuller,)Prog.)Part.)Nucl.)Phys.) 71 162)(2013) or)a)long?baseline)experiment

How can we accurately calculate neutrino-nucleus cross sections and beta decay rates? 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 g A /g V ? Neutrino#wave# function ! "#$ ≈ 1 +# '() − + , () , + ⋯ First5 allowed forbidden Second5 forbidden As the incoming neutrino energy increases, the contribution of the states which are not well-known increase, including first- and even second- forbidden transitions .

Example of an approach from the first principles: Using effective field theory for low-energy neutrino-deuteron scattering Below&the&pion&threshold& 3 S 1 ! 1 S 0 transition&dominates&and&one&only& needs&the&coefficient&of&the&two8body&counter&term,&L 1A (isovector two8 body&axial&current) L 1A can&be&obtained&by& comparing&the&cross&section& " (E)& =& " 0 (E)&+&L 1A " 1 (E)&with&cross8 section&calculated&using&other& approaches&or&measured& experimentally&(e.g.&use&solar& neutrinos&as&a&source).

Example of an approach from the first principles: Using effective field theory for low-energy neutrino-deuteron scattering Below$the$pion$threshold$ 3 S 1 ! 1 S 0 transition$dominates$and$one$only$ needs$the$coefficient$of$the$twoGbody$counter$term,$L 1A (isovector twoG body$axial$current) L 1A can$be$obtained$by$ comparing$the$cross$section$ " (E)$ =$ " 0 (E)$+$L 1A " 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$threshold$ 3 S 1 ! 1 S 0 transition$dominates$and$one$only$ needs$the$coefficient$of$the$twoGbody$counter$term,$L 1A (isovector twoG body$axial$current) L 1A can$be$obtained$by$ comparing$the$cross$section$ " (E)$ =$ " 0 (E)$+$L 1A " 1 (E)$with$crossG section$calculated$using$other$ approaches$or$measured$ experimentally$(e.g.$use$solar$ neutrinos$as$a$source). L 1A =3.9(0.1)(1.0)(0.3)(0.9) fm 3 at$ a$renormalization$scale$set$by$the$ physical$pion$mass Savage$et$al.,$PRL$119,$062002$(2017) Difficult$to$go$beyond$ twoGbody$systems! A.B.$Balantekin$and$H.$Yuksel,$PRC$ 68# 055801$(2003)

A new p-sd shell model (SFO) including up to 2-3 h Ω 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 − 5/2 − An example: ν e + 13 C 3/2 − 1/2+ 5/2+ 3/2 − Suzuki,,Balantekin,,Kajino, 1/2+ Phys.,Rev.,C, 86 ,,015502,(2012) 1/2 − GT 13 N IAS+GT 1/2 − 13 C CK,(circles),vs.,SFO,(lines), NC CC

! e + 13 C charged-current scattering Proton) emission 10 -40 Total g.s.0of0 σ (cm ² ) 10 -41 13 N 10 -42 Neutron)emission0and0 other0contributions 10 -43 0 10 20 30 40 50 Suzuki,0Balantekin,0Kajino,0Chiba,02019 arXiv:1904.11291 E (MeV)

̅ Comparison of charged-current cross sections 10 -39 ! " + $% C 10 -40 σ (cm ² ) 10 -41 ! " + $% C 10 -42 10 -43 0 10 20 30 40 50 E (MeV) Suzuki,'Balantekin,'Kajino,'Chiba,'2019

Neutrino Coherent Scattering ) ) !# $, # = ' ( !" 8+ , 2 − 2# + # ) 5 3 ) ) 3 4 # $ /01 2$ ) 3 ) = 2,# 3 4 = 6 − 1 − 4 sin ) < 4 = # /01 = 2$ + , For nearly spherical systems > !? ? ) sin ) 3? 5 3 ) = 1 @ A ? − 1 − 4 sin ) < 4 @ B ? 3 4 3?

) ) !# $, # = ' ( !" 8+ , 2 − 2# + # ) 5 3 ) ) 3 4 # $ /01 " $ ∝ $ ) + nuclear corrections 13 C 10 -12 E 2 10 -13 σ (fm ² ) PRELIMINARY exact 10 -14 12 C 13 C 10 -15 Suzuki, Balantekin, 10 -16 Kajino Chiba 0 20 40 60 80 100 120 140 E (MeV) Suzuki,<Balantekin,<Kajino,<Chiba,<2019

F ( Q 2 ) = 1 + η 2 Q 2 + η 4 Q 4 + · · · , σ ( E ) = G 2 ✓ ◆ 1 + 8 3 η 2 E 2 + 8 2 + 2 η 4 ) E 4 + · · · 4 π Q 2 W E 2 3( η 2 F − 2 ✓ E + 16 3 η 2 E 3 + 24 ◆ � 2 + 2 η 4 ) E 5 + · · · 3 ( η 2 + · · · M 10 -12 10 -13 σ (fm ² ) 10 -14 10 -15 10 -16 0 20 40 60 80 100 120 140 E (MeV)

Coherent elastic neutrino cross sections 5 x 10 -40 4 x 10 -40 13 C σ (cm ² ) 12 C 3 x 10 -40 2 x 10 -40 1 x 10 -40 0 0 100 200 300 400 500 Maximum recoil energy (keV)

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

PROSPECT() arXiv:1806.02784 Oscillation*Exclusion

; ; An alternative solution :" ¹³ C(ν, % & ')¹²C ٭ (4.4-./)→¹²C(g.s.) + γ 4.4 MeV prompt photon and proton recoils Berryman,"Bradar,"Huber,"arXiv:"1803.08506 from thermalized neutron can mimic neutrinos around 5 MeV

; ; An alternative solution :" ¹³ C(ν, % & ')¹²C ٭ (4.4-./)→¹²C(g.s.) + γ 4.4 MeV prompt photon and proton recoils Berryman,"Bradar,"Huber,"arXiv:"1803.08506 from thermalized neutron can mimic neutrinos around 5 MeV HOWEVER State of the art SM calculation using SFO All"states"in" 12 C Hamiltonian which 10 -41 includes tensor and g.s.in 12 C enhanced monopole interactions is too 10 -42 σ (cm ² ) small. 4.4"MeV"state"in" 12 C ➜ This solution 10 -43 requires BSM physics. PRELIMINARY 10 -44 8 → 59 C+ ̅ 56 C+ ̅ % + n 10 20 30 40 50 60 Suzuki,"Balantekin,"Kajino,"Chiba E (MeV)

Introduce a magnetic moment operator, ˆ µ Example: Neutrino-electron scattering via magnetic moment µ | ˆ 2 ∑ ν i ˆ = ν e ˆ σ ∝ µ ν e µ ν e i µ | = ˆ Dirac magnetic moment ˆ µ µ T = − ˆ ˆ Majorana magnetic moment µ " % = α 2 π d σ 1 − 1 A reactor experiment 2 2 µ eff $ ' measuring electron antineutrino dT e m e T e E ν # & magnetic moment is an inclusive 2 one, i.e. it sums over all the 2 = − iE j L µ ji ∑ ∑ neutrino final states U ej e µ eff i j

Neutrino Magnetic Moment in the Standard Model µ ij = − eG F * f ( r ∑ 8 2 π 2 ( m i + m j ) U  i U  j  ) Symmetry Principles  ! µ " → 0 as # $ → 0 2 $ '  ) ≈ − 3 2 + 3 m   + … , f ( r 4 r r  = & ) M W % ( Standard Model (Dirac)

Standard Model (only) contribution to the Dirac neutrino magnetic moment measured at reactors A.B.B.,$N.$Vassh,$PRD$ 89# (2014)$073013 Cosmological$limits A.B.B.$&$ N.$Vassh

Reactors vs. solar Cerenkov detectors Dirac Majorana 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(( ! μ ν <(4.5(× 10 712 μ B (95%(C.L.) arXiv:1308.4627

µ ! =10 -10 µ B electroweak µ ! =10 -11 µ B µ ! =10 -12 µ B

( + 2 " % 2 m e d σ dT = G F 2 1 − T ) m e T 2 + g V − g A 2 − g V ( 2 * - ( ) ( ) g V + g A + g A weak $ ' 2 2 π E ν E ν * - # & ) , " % + πα 2 µ 2 T − 1 1 magnetic $ ' 2 m e E ν # & g v = 2sin 2 θ W + 1/ 2 " + 1/ 2 for electron neutrinos $ g A = # − 1/ 2 for electron antineutrinos $ % ν j e − γ ν e e −

Classical screening in an electron- positron plasma g 1 d 3 p ∫ ( ) n ± = e ( E ± µ )/ T + 1 ⇒ ρ b = − e n − − n + 3 ( ) 2 π Introducing a charge Ze at r = 0 will create a potential φ $ ' ρ a = − e 1 1 d 3 p ∫ e ( E − e φ − µ )/ T + 1 − & ) e ( E + e φ + µ )/ T + 1 π 2 % ( ∇ 2 φ = − 4 π ρ a − ρ b + Ze δ 3 ( r ) $ ' % ( $ ' , ∂ 2 / ∇ 2 φ = − − 1 2 + 4 π Ze δ 3 ( r ) ( ) 3 ( ) ( ) 2 φ + 2 π 1 e φ ) + O e φ ∂ µ 2 ρ b & . λ D - 0 % ( 1 ] ⇒ φ ( r ) = Ze 2 = e 2 ∂ [ ( ) ∂ µ n − − n + r exp − r / λ D 4 πλ D Explicitly verified in Q.E.D. only up to third order.

Quantum derivation in finite-temperature Q.E.D. 1 2 = −Π 00 k 0 = 0, k → 0 ( ) λ D d 3 p Tr γ 0 G ( p ) Γ 0 ( p , p ) G ( p ) ( ) = − e 2 T ∑ ∫ 3 ( ) 2 π n p ( + d 3 p Tr γ 0 G ( p ) ∂ G − 1 = − e 2 T ∑ ∫ ∂ µ ( p ) G ( p ) * - 3 ( ) 2 π ) , n p d 3 p = e 2 ∂ Tr γ 0 G ( p ) ( ) ∑ ∫ ∂ µ T 3 ( ) 2 π n p ( + = e 2 ∂ 2 = e 2 ∂ n ∂ µ 2 P ( µ , T ) * - ∂ µ ) , T Note that the pressure is so far calculated only to order e 3 at finite temperature