Neutrinos & Nuclei 56th International meeting on Nuclear Physics in collaboration with: S. Pastore Beta Decay A. Lovato Accelerator Neutrinos (Quasi-elastic) D. Lonardoni Double Beta Decay S. C. Pieper R. Schiavilla R. B. Wiringa
Neutrinos Neutrinos proposed by Pauli in 1930 to conserve energy, momentum, and angular momentum in nuclear beta decay. n → p + e − + ¯ ν e In 1956 Reines and Cowan detected anti-neutrinos from Savannah River reactors: ν e + p → n + e + ¯ through coincidence of e+e- gamma rays and neutron capture. Reines was a LANL T-division employee at the time. Reines and Cowan were awarded the Nobel Prize in 1995. Reines and Cowan discovered the electron (anti-) neutrino. Later Lederman, Schwartz and Steinberger detected muon neutrino, receiving the Nobel Prize in 1988.
Nuclei Rutherford Geiger-Marsden apparatus (~1910)
Why study neutrino-nucleus scattering (accelerators) ? MicroBooNE MINERva SuperK mass differences, mixings from oscillations
Neutrinos Oscillations and Masses Neutrino oscillations first proposed in 1957 by Bruno Pontecorvo, Maki, Nakagawa, and Sakata in 1962 Neutrinos interact with matter in the flavor basis but propagate in the mass basis ( in vacuum ) Majorana CP-violating phase Mixing angles, CP violating phases, Majorana Phases + MSW effect from forward scattering in matter
Double Beta decay Why study Neutrinos and Nuclei Majorana nature of the neutrino Neutrinos and nuclei are fundamental to some of the largest and most exciting experiments and observations Coherent neutrino scattering at SNS Accelerator Neutrino Measurements: Supernovae/ Neutron star mergers and nucleosynthesis At high energies resonance and deep inelastic dominate
Recent Theory Status Until recently our understanding of neutrino nucleus interactions has been very limited Beta Decay Double Beta Decay 1.0 8 NR-EDF 7 R-EDF 0.77 0.8 QRPA Jy 0.744 6 QRPA Tu R(GT) Exp. 0.6 QRPA CH 5 IBM-2 SM Mi M 0 ν 0.4 4 SM St-M,Tk 3 0.2 2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1 R(GT) Th. overpredicted: g A quenching 1.27 ➡ ~ 1 0 Factor of >2 uncertainty Quasielastic Scattering MiniBooN How can we improve our understanding? Theory Under predicted by ~30%
Basic building blocks: Nuclear interactions and currents NN interactions LO ( ν = 0) NLO ( ν = 2) NNLO ( ν = 3) NN currents 3N interactions
Nuclei: Interactions and Currents 1 X X X p 2 H = i + V ij + V ijk 2 m i i<j i<j<k X X J = j 1; i + j 2 ; ij + ... i i<j 300 Reid Paris Urbana 200 AV18 v c 0,1 − 4v t t20 experiment Jlab R. Holt 0,1 100 (MeV) 0 − 100 v c 0,1 + 2v t 0,1 − 200 − 300 0 1 2 3 4 r (fm) Deuteron Potential Models with Different Spin Orientations Forrest, et al, PRC 1996
12 C calculations: computingnuclei.org GFMC for ground-state + current correlation matrix elements Ψ 0 = exp [ − H τ ] Ψ T 2 A = 4096 spin amplitudes x 12!/(6!6!) = 924 isospin amplitudes (charge basis) for each sample ADLB ~ 45 M core-hours Lusk, Pieper, … http://www.mcs.anl.gov/project/adlb-asynchronous-dynamic-load-balancer
Light Nuclear Spectra 15 -20 1 + 7/2 − 2 + 4 + 2 + 0 + 2 + 0 + 5/2 − 2 + -30 0 + 3 + 0 + 1 + 4 He 5/2 − 2 + 1 + 6 He 4 + 7/2 + 8 He 7/2 − 1 + 4 + 6 Li 3 + 5/2 + 1/2 − 0 + 5/2 − -40 2 + 1 + 7/2 − 3/2 − 1/2 − 3 + 3 + 2 + 7/2 − 3/2 − 1 + 7 Li 2 + 4 + 3/2 − 3 + 2 + -50 9 Li 3 + Energy (MeV) 1 + 3/2 + 4 + 2 + + … 8 Li 1 + 3,2 + 5/2 + 2 + 0 + 1 + Argonne v 18 0 + 1/2 − 3 + -60 8 Be 2 + 5/2 − 2 + 2 + 1/2 + 1 + with Illinois-7 0 + 3/2 − 1 + -70 10 Be 3 + GFMC Calculations 9 Be 10 B -80 0 + AV18 2 + -90 AV18 0 + Expt. +IL7 12 C -100 FIG. 2 GFMC energies of light nuclear ground and excited states for the AV18 and AV18+IL7 Hamiltonians compared to experiment. Carlson, et al, RMP 2015
Magnetic Moments Magnetic Moments and Transitions (q=0, Low energy) EM Transitions Wiringa, Pastore, Schiavilla, et al
Electromagnetic form factors 12 C elastic form factor 0 10 -1 10 |F(q)| -2 10 Hoyle state transition form factor exp -3 10 ρ 1b 10 -1 ρ 1b+2b 6 Z f tr ( k ) / k 2 (fm 2 ) 6 -4 5 10 0 1 2 3 4 4 -1 ) q (fm 3 2 1 10 -2 0 2 Nucleon charge operators 0 0.2 0.4 k 2 (fm -2 ) f pt (k) (relativistic corrections) 10 -3 are small VMC GFMC Experiment 10 -4 0 1 2 3 4 k (fm -1 )
Quasi-elastic scattering: higher p, E Scaling with momentum transfer: ‘y’-scaling incoherent sum over scattering from single nucleons M � = � d � e � � d 2 � Q 4 d � � q � 4 R L �� q � , � � d � e � dE e � 2 � R T �� q � , � � � , + � Q 2 1 � q � 2 + tan 2 � 2 PWIA often good for q >> k F ; used in many fields (neutron scattering, …)
Quasi-Elastic electron scattering: 12 C transverse/longitudinal response from Benhar, Day, Sick, RMP 2008 data Finn, et al 1984 Scaled longitudinal vs. transverse scattering from 12C
Single-Nucleon Momentum Distributions 10 1 10 1 10 1 10 1 Preliminary AFDMC: 4 He AV6’ 4 He: AV6’ 10 0 10 0 10 0 10 0 AFDMC: 16 O AV6’ 16 O: AV6’ CVMC: 40 Ca AV18 4 He: N 2 LO R 0 =1.0 fm 10 -1 10 -1 10 -1 10 -1 16 O: N 2 LO R 0 =1.0 fm n p (k) / Z [ fm 3 ] n p (k) / Z [ fm 3 ] 4 He: N 2 LO R 0 =1.2 fm Different Nuclei 10 -2 10 -2 10 -2 10 -2 16 O: N 2 LO R 0 =1.2 fm 10 -3 10 -3 10 -3 10 -3 10 -4 10 -4 10 -4 10 -4 Chiral interactions 10 -5 10 -5 10 -5 10 -5 0.0 0.0 1.0 1.0 2.0 2.0 3.0 3.0 4.0 4.0 0.0 0.0 1.0 1.0 2.0 2.0 3.0 3.0 4.0 4.0 k [ fm -1 ] k [ fm -1 ] Lonardoni, Gandolfi, Wiringa, Pieper, et al Integrated Strength: 15-20 % above k F, Amplitude ~ 0.3-0.4 Scaling of the 1st kind (w/ p) Donnelly & Sick (1999)
Back to Back Nucleons (total Q~0) np pairs dominate over nn and pp 10 3 10 3 np, N 2 LO R 0 =1.0 fm 10 2 10 2 pp, N 2 LO R 0 =1.0 fm E Piasetzky et al. 2006 Phys. Rev. Lett. 97 162504. 10 1 10 1 np, N 2 LO R 0 =1.2 fm M Sargsian et al. 2005 Phys. Rev. C 71 044615. R Schiavilla et al. 2007 Phys. Rev. Lett. 98 132501. pp, N 2 LO R 0 =1.2 fm 10 0 10 0 R Subedi et al. 2008 Science 320 1475. n 12 (k) [ fm -1 ] 2-nucleon momentum 10 -1 10 -1 12 C distributions 10 -2 10 -2 10 B 10 5 8 Be 10 5 10 -3 10 -3 10 3 6 Li 10 5 10 3 10 1 4 He 10 -4 10 -4 16 O 10 5 10 3 ρ pN (q,Q=0) (fm 3 ) 10 1 10 5 10 -1 10 -5 10 -5 10 3 0 1 2 3 4 5 10 1 0.0 0.0 1.0 1.0 2.0 2.0 3.0 3.0 4.0 4.0 10 -1 10 3 k [ fm -1 ] 0 1 2 3 4 5 10 1 10 -1 0 1 2 3 4 5 10 1 10 -1 Lonardoni, et al, preliminary 0 1 2 3 4 5 10 -1 0 1 2 3 4 5 np vs. pp q (fm -1 ) Wiringa et al.; Carlson, et al, RMP 2015
Electron Scattering: Longitudinal and Transverse Response Transverse (current) response: X h 0 | j † ( q ) | f ih f | j ( q ) | 0 i δ ( w � ( E f � E 0 )) R T ( q, ω ) = f Longitudinal (charge) response: X h 0 | ρ † ( q ) | f ih f | ρ ( q ) | 0 i δ ( w � ( E f � E 0 )) R L ( q, ω ) = f π X X j = j i + j ij + ... i i<j Two-nucleon currents required by current conservation Response depends upon all the excited states of the nucleus
Sum Rules: Longitudinal Response Gives an indication of total strength, S ( q ) = h 0 | j † ( q ) j ( q ) 0 i but not energy dependence Energy dependence pion exchange Sum Rule final state interaction determined by PWIA pp correlations p p p + q - final states π final states p + q k p + q p + p p p
Vector Response Sum Rule: Constructive Interference between 1- and 2-body currents w/ tensor correlations p p PWIA p’ p k k p final state p + q - p’ + p’ + k p + q - k p + q π p k k p p’ p p π Large enhancement from combination of initial state correlations and two-nucleon currents ∝ σ i · k σ i · q ( σ j · k ) 2 ( τ i · τ j ) 2 v 2 π ( k ) similar in axial response
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EM observables well-reproduced What about neutrinos and weak currents? Vector and Axial currents: beta decay 5 response functions in inclusive scattering
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