Theory and Phenomenology of Coherent Elastic Neutrino Nucleus Scattering Gail McLaughlin NC State 1
Coherent Elastic Neutrino Nucleus Scattering (CE ν NS) • neutrino interacts with nucleus through neutral current • can’t see neutrino afterward, but could see small kick to nucleus Outline ν A Z • introduction • where CE ν NS is already in ν A use NC • future physics from CE ν NS 2
Basic cross section Coherent elastic neutrino nucleus scattering cross section � T � � 2 � dT ( E, T ) = G 2 Q 2 dσ 2 − 2 T − MT F 4 F 2 ( Q 2 ) W 2 π M E + E 2 E • E : neutrino energy, T : nuclear recoil 2 E 2 T M • Q 2 = ( E 2 − ET ) : squared momentum transfer • Q W = N − Z (1 − 4 sin 2 θ W ) : weak charge • F( Q 2 ) : form factor - largest uncertainty in cross section Assumes a spin zero nucleus, no non-standard model interactions 3
Making a theoretical prediction Fold cross section (previous slide) with incoming neutrino spectrum (e.g. left figure) to find nuclear recoil spectrum (right figure) Spectrum of nuclear recoils νs from π / µ decay at rest Flux 2400 0.035 Events/keV 2000 (delayed) ν 0.03 µ ν (delayed) e 1600 ν (prompt) 0.025 µ 1200 0.02 800 0.015 400 0.01 0 0.005 0 20 40 60 80 100 120 140 Recoil Energy (keV) 0 0 10 20 30 40 50 Neutrino energy (MeV) Fig. from Scholberg 2006 Fig. from Patton et al 2012 4
Coherent Elastic Neutrino Nucleus Scattering (CE ν NS) 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 5
Coherent Elastic Neutrino Nucleus Scattering (CE ν NS) 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 6
Supernovae Neutrinos long mean free path ν e core ν e ν ν ν ν µ µ τ τ short mean free path Schematic picture of neutrino emission from proto-neutron star Figure from J. Blondin Neutrinos are emitted from deep in the center 7
Coherent elastic neutrino nucleus scattering is an opacity source in supernova Figure from S. Bruenn 8
Coherent Elastic Neutrino Nucleus Scattering (CE ν NS) 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 9
Coherent Elastic Neutrino Nucleus Scattering (CE ν NS) for detecting supernova neutrinos 6 Background T=8 MeV Yield (Events per keV) 5 T=6 MeV 4 3 2 1 0 0 50 100 150 200 E (keV) spectra from ORNL group Event rates in CLEAN detector, Horowitz et al 2003 10
Coherent Elastic Neutrino Nucleus Scattering (CE ν NS) 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 11
CE ν NS proposed as a mechanism for probing sterile neutrino oscillations ( Anderson et al 2012, Formaggio et al 2012) Since CE ν NS 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 Dae δ alus Anderson et al 2012 12
Coherent Elastic Neutrino Nucleus Scattering (CE ν NS) 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 13
CE ν NS background is a limit on future dark matter sensitivity discussed in Snowmass Summary: WIMP Dark Matter Direct Detection 14
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 15
Beyond First Detection of CE ν NS 2400 Events/keV 2000 1600 • nonstandard ν 1200 interactions 800 400 • form factor 0 0 20 40 60 80 100 120 140 Recoil Energy (keV) 16
Beyond First Detection of CE ν NS 2400 Events/keV 2000 1600 • nonstandard ν 1200 interactions 800 400 • form factor 0 0 20 40 60 80 100 120 140 Recoil Energy (keV) 17
Nonstandard interactions Some nonstandard interactions are currently poorly constrained. Examples are vector couplings for electron neutrinos with up and down quarks, ǫ uV ee and ǫ dV ee , although there are other couplings that contribute as well. To define the NSI, use eq from Barranco et al 2006, νHadron = − G F L NSI ν α γ µ (1 − γ 5 ) ν β � � � ¯ ∗ √ q = u,d 2 α,β = e,µ,τ � �� ε qL + ε qR qγ µ (1 − γ 5 ) q qγ µ (1 + γ 5 ) q � � � ¯ ¯ (1) αβ αβ The vector couplings are the only ones relevant for spin zero nuclei ε qV αβ = ε qL αβ + ε qR αβ . Limits are − 1 . 0 < ǫ uV ee < 0 . 6 and − 0 . 5 < ǫ dV ee < 1 . 2 18
Nonstandard interactions Continue considering example ǫ uV ee and ǫ dV ee . The zero order effect on CE ν NS is to change the standard model weak charge to an effective weak charge. ee ) + Z (1 − 4 sin 2 θ W + 4 ǫ uV Q W = N (1 − 2 ǫ uV ee − 4 ǫ dV ee + 2 ǫ dV ee ) Recall: � T � � 2 � dT ( E, T ) = G 2 Q 2 dσ 2 − 2 T − MT F 4 F 2 ( Q 2 ) W 2 π M E + E 2 E 19
Nonstandard interactions Changing the size of Q W 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. 20
Beyond First Detection of CE ν NS 2400 Events/keV 2000 1600 • nonstandard ν 1200 interactions 800 400 • form factor 0 0 20 40 60 80 100 120 140 Recoil Energy (keV) 21
Form factor Understanding the structure of the nucleus Form factor, F ( Q 2 ) is the Fourier transform of the density distributions of protons and neutrons in the nucleus. � sin ( Qr ) 1 � � ρ n ( r ) − (1 − 4 sin 2 θ W ) ρ p ( r ) F ( Q 2 ) = r 2 dr Q W Qr � R 2 � 1 / 2 SGII = 3.405 fm � R 2 � 1 / 2 G 202 = 3.454 fm density distributions 22
Form factor Form factor, F ( Q 2 ) is the Fourier transform of the density distributions of protons and neutrons in the nucleus. � sin ( Qr ) 1 � � ρ n ( r ) − (1 − 4 sin 2 θ W ) ρ p ( r ) F ( Q 2 ) = r 2 dr Q W Qr • Proton form factor term is suppressed by 1 − 4 sin 2 ( θ W ) • Neutron form factor is not suppressed CE ν NS can be used to determine the form factor Amanik et al 2009 23
Form factor � sin ( Qr ) 1 � � ρ n ( r ) − (1 − 4 sin 2 θ W ) ρ p ( r ) F ( Q 2 ) = r 2 dr Q W Qr • 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 Q 2 , extract A P V ∼ 0 . 65 × 10 − 6 then determine neutron radius, now also CREX at Jlab on Ca C ν NS recoil curve can be fit: neutron radius and higher moments 24
Nuclear-Neutron form factor from CE ν NS Taylor expand the sin( Qr ) form factor: Q W (1 − Q 2 n � + Q 4 ρ n ( r ) sin ( Qr ) 1 N F n ( Q 2 ) = r 2 dr ≈ 3! � R 2 5! � R 4 � n � − ... ) Q W Qr Moments of the den- � R 2 sity distribution, n � , � R 4 n � characterize the form factor. Patton et al 2012, 2013 25
Liquid argon scenario 4.50 n � 1 / 4 (fm) 4.00 3.50 3.5 tonnes argon 16m from SNS, � R 4 3.00 18m from Dae δ alus, 30m from ESS 2.50 for one year. Shows 40%, 91% and 4.50 97% confidence contours. Crosses n � 1 / 4 (fm) 4.00 are theory predictions. 3.50 � R 4 3.00 Fig. from Patton et al 2012 2.50 3.20 3.30 3.40 3.50 3.60 n � 1 / 2 (fm) � R 2 Band is measurement from neutron scattering. Top plot: normalization of neutrino flux not known, bottom plot normalization of neutrino flux known. 26
Xenon is more constraining 5.60 eff (fm) 5.40 5.20 n � 1 / 4 300 kg Xenon 16m from SNS, 18m 5.00 � R 4 4.80 from Dae δ alus, 30m from ESS for 4.60 one year. Shows 40%, 91% and 5.60 97% confidence contours. Crosses eff (fm) 5.40 5.20 are theory predictions. n � 1 / 4 5.00 � R 4 4.80 fig. from Patton et al 2012 4.60 4.60 4.70 4.80 4.90 5.00 5.10 n � 1 / 2 � R 2 eff (fm) Top plot: normalization of neutrino flux not known, bottom plot normalization of neutrino flux known. 27
Beyond NSIs and the form factor • Nonstandard ν interactions Q W = N + Z (1 − 4 sin 2 θ W ) • Form factor • sin 2 θ W • ν magnetic moment 28
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