Low Energy Neutrino Scattering: Supernovae Neutrino Energies J. Carlson Introduction Why is this interesting ? Decoupling regime S. Gandolfi (LANL) S. Pastori (LANL) Coherent Scattering R. Schiavilla (JLAB/ODU) Detection R. B. Wiringa (ANL) Scattering from nuclei S. C. Pieper (ANL) Deuteron A. Lovato (ANL) 4He (theory) Data and theory for 12C Conclusion
Accelerator Neutrinos MINOS SuperK MicroBooNE MINERva Advantages: Control over Energy, flux neutrino ‘beams’ can be sent over long distances Energies ~ 1 GeV
Contributions to Sum Rules Ground State (low-momentum piece): external momentum is large ( ≧ Fermi momentum) 12 C For a large momentum transfer to have an important matrix element, need contribution from pion-exchange interaction (correlations) or currents
Supernovae and Astrophysical Neutrinos Different Sources, time dependence, different epochs Kepler Supernova Can we make r-process nuclei in supernovae; and/or neutron-star mergers ? Need to understand low energy neutrinos in matter
Supernova Neutrino Spectra and Nucleosynthesis { Electron and anti-electron neutrinos n e + + p O n + e + . play a crucial role in supernova. Their energy spectrum impacts: n e + n O p + e – 1. Explosion mechanism 2. Nucleosynthesis 3. Detection Neutrino-sphere at high density. Neutron-rich matter at moderate entropy. R ~ 10-20 km PNS Neutrino driven wind at low- density and high entropy. R ~ 10 3 -10 4 km
After emission from the proto-neutron star surface Very few neutrinos scatter from e, n, p, ….; but collective oscillations may be important ! k Q O 10 10 0 � 2000 ! p 1600 45 � 10 9 P 1200 Radius (km) 800 10 8 ! q 400 90 � P νν (Survival Probability) P ¯ ν (Survival Probability) 0 ν ¯ 10 7 10 6 135 � cos ϑ 0 10 5 g cm − 3 180 � ν e ν e ¯ Cherry, Carlson, Friedland, ν τ ¯ ν τ ˜ f Fuller, Vlasenko PRL 2012 Duan, Fuller, Carlson, Qian, PRD 2006 and many more E ν (MeV) E ¯ ν (MeV) r 6 Different epochs and neutrino hierarchies can produce spectral swaps,… Much is unknown (scattering from nucleons and nuclei, …) Can also have lepton flavor violation (Vlasenko, Cirigliano, Fuller, 2014)
Neutrino Scattering from Nuclei Impacts explosion mechanism, r-proces, …. Necessary for interpreting neutrino observations How well do we understand it? Energies 50 MeV Typically going to excited states or low in the continuum � � � � Generic Neutral and Charged-Current Processes Momenta ~ 50-100 MeV/c = 0.25 - 0.5 fm -1
Inclusive electron scattering, measure electron kinematics only M � = � d � e � � d 2 � Q 4 d � e’ � q � 4 R L �� q � , � � d � e � dE e � 2 � R T �� q � , � � � , + � Q 2 1 � q � 2 + tan 2 � 12 C 2 2.7 fm e
Nuclear Interactions Chiral EFT and Phenomenological models investigating/improving predictive power 60 Argonne v 18 np Argonne v 18 pp 40 Argonne v 18 nn � (deg) SAID 7/06 np 20 0 1 S 0 -20 -40 0 100 200 300 400 600 500 E lab (MeV) NN interactions fit to huge database 3N interactions fit to nuclei
Higher Momenta: Form Factors 12 C elastic form factor 0 10 Currents: 1 + 2-nucleon currents + … -1 10 |F(q)| -2 10 π exp virtual pions, -3 10 ρ 1b π ρ 1b+2b deltas, … -4 10 0 1 2 3 4 -1 ) q (fm 10 -1 6 Z f tr ( k ) / k 2 (fm 2 ) 6 5 Elastic Processes and Low-Energy Transitions 4 3 2 Quasi-Elastic Inclusive Scattering 1 10 -2 0 0 0.2 0.4 k 2 (fm -2 ) f pt (k) 10 -3 VMC GFMC Experiment 10 -4 0 1 2 3 4 k (fm -1 )
2-Nucleon Currents and Low-Energy Transitions EM transitions Magnetic Moments A < 10 9 Be( 5 / 2 - → 3 / 2 - ) B(E2) lo 9 Be( 5 / 2 - → 3 / 2 - ) B(M1) ht 8 B(3 + → 2 + ) B(M1) n- 8 B(1 + → 2 + ) B(M1) ry 8 Li(3 + → 2 + ) B(M1) ls 8 Li(1 + → 2 + ) B(M1) ts 7 Be( 1 / 2 - → 3 / 2 - ) B(M1) ed 7 Li( 1 / 2 - → 3 / 2 - ) B(E2) Combination of correlations and currents ec- 7 Li( 1 / 2 - → 3 / 2 - ) B(M1) - 6 Li(0 + → 1 + ) B(M1) p = 2.792 n = -1.913 EXPT GFMC(IA) GFMC(MEC) 0 1 2 3 3 H = 2.979 3 He = -2.128 Ratio to experiment Pastore, Pieper, Schiavilla, Wiringa: arXiv 1406.2343, 1302.5091
Inelastic Neutrino Scattering on 4 He Gazit and Barnea, PRL 2007 Multipole Expansion K max =15 Axial, Electric J=2 K max =13 AV18; AV18+UIX interaction K max =11 LIT [arb. units] K max =9 Axial, Magnetic J=1 Currents from chiral theory, continuity eq Axial, Longitudinal J=0 Vector, J=1 ⟨ σ 0 A ⟨ σ 0 ν x + σ 0 ν x ⟩ T [10 − 42 cm 2 ] x ⟩ T = 1 1 T [MeV] -20 0 20 40 60 80 100 2 AV8’ [3] AV18 AV18+UIX AV18+UIX+MEC σ R [MeV] 4 2.09(-3) 2.31(-3) 1.63(-3) 1.66(-3) 6 3.84(-2) 4.30(-2) 3.17(-2) 3.20(-2) 8 2.25(-1) 2.52(-1) 1.91(-1) 1.92(-1) 10 7.85(-1) 8.81(-1) 6.77(-1) 6.82(-1) 12 2.05 2.29 1.79 1.80 Integrated Cross section versus neutrino T 14 4.45 4.53 3.91 3.93 Some effect from interaction (A=4 binding) TABLE I: Temperature averaged neutral current inclusive Very little effect from 2-body currents (!?) inelastic cross-section per nucleon (in 10 − 42 cm 2 ) as a function of neutrino temperature (in MeV).
Neutrino Scattering from 12 C Hayes and Towner, PRC, 1999 Muon Electron Muon Photo- neutrino DIF neutrino DAR Capture absorption Closed shell 18.2 21.9 45.4 RPA +2p-2h 16.7 20.4 44.1 21.6 CRPA 17.6 14.4 38.0 Shell Model 13.8 12.5 42.2 23.6 Experiment 12.4(2) 14.4(4) 39.0(1) 21(2) At best ~10% uncertainty; no 2-body currents
Weak Processes in Larger Nuclei: Gamow-Teller Matrix Elements in Beta Decay 1.0 0.77 0.8 0.744 R(GT) Exp. 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 R(GT) Th. Martinez-Pinedo and Poves, PRC 1996 Shell Model Calculations of Beta Decay typically require a quenching (reduction) of g A by ~ 0.75 to reproduce experimental rates Not yet understood at a `microscopic’ level
Neutrino Detection from a Galactic Supernovae Scholberg 2012 TABLE II: Summary of neutrino detectors with supernova sensitivity. Neutrino event estimates are approximate for 10 kpc; note that there is significant variation by model. Not included are smaller detectors (e.g., reactor neutrino scintillator experiments) and detectors sensitive primarily to coherent elastic neutrino-nucleus scattering (e.g., WIMP dark matter search detectors). The entries marked with an asterisk are surface or near-surface detectors and will have larger backgrounds. Detector Type Mass (kt) Location Events Live period Baksan C n H 2 n 0.33 Caucasus 50 1980-present LVD C n H 2 n 1 Italy 300 1992-present Super-Kamiokande H 2 O 32 Japan 7,000 1996-present KamLAND C n H 2 n 1 Japan 300 2002-present MiniBooNE ∗ C n H 2 n 0.7 USA 200 2002-present Borexino C n H 2 n 0.3 Italy 100 2005-present IceCube Long string 0.6/PMT South Pole N/A 2007-present Icarus Ar 0.6 Italy 60 Near future HALO Pb 0.08 Canada 30 Near future SNO+ C n H 2 n 0.8 Canada 300 Near future MicroBooNE ∗ Ar 0.17 USA 17 Near future NO ν A ∗ C n H 2 n 15 USA 4,000 Near future LBNE liquid argon Ar 34 USA 3,000 Future LBNE water Cherenkov H 2 O 200 USA 44,000 Proposed MEMPHYS H 2 O 440 Europe 88,000 Future Hyper-Kamiokande H 2 O 540 Japan 110,000 Future LENA C n H 2 n 50 Europe 15,000 Future GLACIER Ar 100 Europe 9,000 Future
Conclusions/Outlook Supernovae neutrinos can teach us a lot about both neutrinos and supernovae Microscopic theory important for decoupling and propagation in the supernovae; and hence for energy deposition and potentially r-process Basic Theory ingredients understood More data essential - very limited at present Advances in many-body theory and computing essential Close relationship with many important issues Quasi-Elastic neutrino scattering Double-beta decay (Majorana neutrinos) Astrophysical Sources (neutron star mergers,…)
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