g A Quenching Information from Neutrino Scattering

Transcription

1 g A Quenching Information from Neutrino Scattering Saori Pastore νeclipse Workshop Knoxville, TN, August 2017 Open Questions in Fundamental Symmetries and Neutrino Physics Majorana Neutrinos, Neutrinos Mass Hierarchy, bla CP-Violation in Neutrino Sector, Dark Matter WITH nnn Carlson & Gandolfi (LANL) - Schiavilla & Baroni (ODU/JLAB) - Wiringa & Piarulli & Pieper (ANL) Mereghetti & Dekens & Cirigliano (LANL) REFERENCES nnn PRC78(2008) PRC80(2009) PRL105(2010) PRC84(2011) PRC87(2013) PRC87(2013) PRL111(2013) PRC90(2014) JPhysG41(2014) PRC(2016) / 20

2 2 / 20 Electroweak Reactions * ω 10 2 MeV: Accelerator neutrinos * ω 10 0 MeV: EM decay, β-decay * ω 10 1 MeV: Astrophysical ν s, Stopped-π s expt l e,p µ e P µ f, Ψ f l q e,p µ e θe γ α q µ = p µ e p µ e = (ω,q) Z α j µ P µ i, Ψi

3 3 / 20 ω MeV: single β decay g eff A 0.70g A quenching required to bring theory in agreement with expt Rates g 2 A Fig. from Chou et al. PRC47(1993)163

4 4 / 20 Neutrinoless Double Beta Decay observation of 0νβ β-decay lepton # L=l l not conserved implications in matter-antimatter imbalance Majorana Demonstrator * detectors active material 76 Ge * 0νββ-decay τ 1/ years (age of the universe years) 1 ton of material to see (if any) 5 decays per year * also, if nuclear m.e. s are known, absolute ν-masses can be extracted * Rates g 4 A 2015 Long Range Plane for Nuclear Physics

5 5 / 20 Neutrinoless Double Beta Decay M 0νββ NR-EDF R-EDF QRPA Jy QRPA Tu QRPA CH+Ts IBM-2 SM Mi SM St-Md+Tk A J. Engels & J. Menendez - Rep. on Prog. in Physics 80(2017)046301

6 6 / 20 Neutrinoless Double Beta Decay CGT(q) (fm 1 ) Shell model 1b Shell model 1b+2b QRPA 1b * β decay energy and momentum are set by the Q-value MeV * 0νββ decay the scales is set by the interparticle distance of the two decay nucleon 100 MeV n p 0 ν M e ν M e q (MeV) n p J. Engels & J. Menendez * GT σ 1 σ 2 τ + 1 τ+ 2 /r Long Range Plane for Nuclear Physics

7 7 / 20 g A Quenching from Neutrino Scattering * Does the g A problem persist at moderate momenta? * How does the g A -quenching affect 0νβ β -decay matrix elements? * Data at moderate momenta from ν-scattering very valuable * LSND (stopped pions) data available on 12 C; C(ν e,e )N, C(ν µ, µ )N 2015 Long Range Plane for Nuclear Physics

8 8 / 20 Nuclear Physics Nuclei used as laboratories for precision tests of the standard model and in searches for beyond the standard model physics = An accurate understanding of nuclear structure and dynamics is required to extract new physics from nuclear effects l q l

9 9 / 20 Nuclear Interactions The nucleus is made of A non-relativistic interacting nucleons and its energy is A H = T+ V = i=1 t i + υ ij + V ijk +... i<j i<j<k where υ ij and V ijk are two- and three-nucleon operators based on EXPT data fitting and fitted parameters subsume underlying QCD π Aoki et al. Comput.Sci.Disc.1(2008) N N * One-pion-exchange: range 1 mπ * Two-pion-exchange: range 1 2 mπ * AV18+UIX / AV18+IL7 - QMC * NN(N3LO)+3N(N2LO) - QMC (π N ) by Maria Piarulli et al. PRC91(2015)024003

10 / 20 Energy Spectrum and Shape of Nuclei Energy (MeV) He 6 He 6 Li 7 Li 7/2 5/2 5/2 7/2 1/2 3/ He Argonne v 18 with Illinois-7 GFMC Calculations Li Li Be AV AV18 +IL7 5/2 1/2 3/2 Expt. 9 Be 7/2 + 5/2 + 7/2 7/2 3/2 3/ /2 + 3,2 + 1/ / / / Be Carlson et al. Rev.Mod.Phys.87(2015) B 12 C Carlson and Schiavilla Rev.Mod.Phys.70(1998)743 r r q Lovato et al. PRL111(2013)092501

11 Nuclear Currents 1b 2b l l q l l ρ = q j = A i=1 ρ i + ρ ij +..., i<j A j i + j ij +... i=1 i<j * In Impulse Approximation IA nuclear currents are expressed in terms of those associated with individual protons and nucleons, i.e., ρ i and j i, 1b-operators L p S p Sn * Two-body 2b currents essential to satisfy current conservation q j=[h, ρ]=[t i + υ ij + V ijk, ρ] q γ N N +... * Villars, Myiazawa, Chemtob, Riska, Schiavilla, Marcucci, / 20

12 12 / 20 Electromagnetic Currents from Chiral Effective Field Theory LO : j ( 2) eq 2 NLO : j ( 1) eq 1 N 2 LO : j ( 0) eq 0 * 3 unknown Low Energy Constants: fixed so as to reproduce d, 3 H, and 3 He magnetic moments N 3 LO: j (1) eq unknownlec s Pastore et al. PRC78(2008) & PRC80(2009) & PRC84(2011) * analogue expansion exists for the Axial nuclear current - Baroni et al. PRC93 (2016) *

13 13 / 20 Magnetic Moments and M1 Transitions 9 Be( 5 / 2-3 / 2 - ) B(E2) 4 9 Be( 5 / 2-3 / 2 - ) B(M1) µ (µ N ) p 7 Li 9 3 H 9 B Li 6 Li* 10 B 8 2 Li H 6 Li 8 B 10 B* GFMC(1b) GFMC(1b+2b) 9 EXPT 7 Be 9 C Be n 3 He EXPT GFMC(1b) 8 B( ) B(M1) 8 B( ) B(M1) 8 Li( ) B(M1) 8 Li( ) B(M1) 7 Be( 1 / 2-3 / 2 - ) B(M1) 7 Li( 1 / 2-3 / 2 - ) B(E2) 7 Li( 1 / 2-3 / 2 - ) B(M1) 6 Li( ) B(M1) GFMC(1b+2b) Ratio to experiment Pastore et al. PRC87(2013) & PRC90(2014)024321, Datar et al. PRL111(2013)062502

14 14 / 20 ω MeV: single β decay g eff A 0.70g A quenching required to bring theory in agreement with expt We use g A = from PDG Fig. from Chou et al. PRC47(1993)163

15 15 / 20 Single beta decay in A 10 Nuclei 10 C 10 B 7 Be 7 Li(ex) 7 Be 7 Li(gs) 6 He 6 Li 3 H 3 He Ratio to EXPT gfmc 1b gfmc 1b+2b(N4LO) Chou et al Shell Model - 1b g A = from PDG in preparation * Two-body currents are found to provide a small (negligible) contribution * Significant reduction from correlations * no quenching required - limited to the light systems we studied

16 16 / 20 Single beta decay in A 10 Nuclei 10 C 10 B 7 Be 7 Li(ex) 7 Be 7 Li(gs) 6 He 6 Li Ratio to EXPT H 3 He gfmc 1b gfmc 1b+2b(N4LO) Chou et al Shell Model - 1b Preliminary - 1b - with NV2+3 (Piarulli & Wiringa) g A = from PDG in preparation * Two-body currents are found to provide a small (negligible) contribution * Significant reduction from correlations * no quenching required - limited to the light systems we studied

17 17 / 20 Double beta-decay m.e. s in 8 He(0 + ;2) 8 Be(0 + ;0): A test case II Axial τ + 1 τ+ 2 σ 1 σ Tensor τ + 1 τ+ 2 S 12 Density [fm (-1) ] Standard Axial = π Tensor = ππ Tensor = ππ Axial = π Axial = * Preliminary * r [fm] π ππ CT WITH Emanuele Mereghetti & Dekens & Cirigliano & Graesser & Wiringa et al.

18 18 / 20 Summary and Outlook We discussed the role played by correlations and many-body currents in β- and υ0ββ-decay m.e. s of A 10 nuclei * Two-body currents provide negligible quenching in the β-decay m.e. s we studied * Large reduction from correlations found in β-decay m.e. s * υ0ββ-decay involves different energy scale, g A -quenching likely to be different * Data very valuable at moderate momenta * GFMC calculations computationally limited to A=12 (data on C valuable) * AFDMC pushing microscopic picture to A 40 (data on O, Ca, LAr valuable) Outlook * Understand quantitatively and qualitatively g A quenching * Benchmark both single- and double-beta decay m.e. s * Characterize two-body currents entering double-beta decay m.e. s

19 19 / 20 Outlook l q l j 1b j 1b > 0 j 1b j 2b vπ v 2 π > 0

20 20 / 20 Institute for Nuclear Theory (INT) Program - Seattle - Summer 2018 Fundamental Physics with Electroweak Probes of Light Nuclei June 12 - July 13, 2018 S. Bacca, R. J. Hill, S. Pastore, D. Phillips Contacts saori.pastore@gmail.com saori@lanl.gov

21 EXTRA SLIDES 21 / 20

22 22 / 20 ω GeV: Accelerator Neutrinos LBNF T2K neutrinos oscillate they have tiny masses = BSM physics Beyond the Standard Model Simplified 2 flavors picture: ( m P(ν µ ν e )=sin 2 2θsin 2 2 ) L 2E ν * Unknown * ν-mass hierarchy, CP-violation, accurate mixing angles [x cm 2 ] Neutrino-Nucleus scattering CCQE on 12 C Ankowski, SF Athar, LFG+RPA Benhar, SF GiBUU Madrid, RMF Martini, LFG+RPA Nieves, LFG+SF+RPA RFG, M A =1 GeV RFG, M A =1.35 GeV Martini, LFG+2p2h+RPA E ν [GeV] Alvarez-Ruso arxiv: DUNE, MiniBoone, T2K, Minerνa... active material * 12 C, 40 Ar, 16 O, 56 Fe,... *

23 23 / 20 ω GeV: Dark Matter Direct Detection Dark Matter : Direct Detection χ χ??? SM SM CDMS Dark Matter Beam Production and Direct detection: χ+ A χ+ A Dark Matter is detected via scattering on nuclei in the detector Detection of Sub-GeV Dark Matter requires knowledge of nuclear responses A. A. Aguilar-Arevalo et al. arxiv:

24 24 / 20 Three-body Axial Currents from χeft A. Baroni et al. PRC93(2016) & PRC94(2016)024003

25 25 / 20 SNPA Two-body Axial Currents 1) One body has GT, relativistic corrections, PS from pion-pole diagrams 2) Two-body currents 2.a) Major contribution from -excitation current 2.b) Negligible contributions from Aπ, Aρ, Aπρ 3) AN coupling fixed to tritium beta-decay 4) 3% additive correction from -current Chemtob, Rho, Towner, Riska, Schiavilla, Marcucci... see, e.g., Marcucci et al. PRC63(2001) and references therein

26 26 / 20 Error Estimate µ (µ N ) GFMC(IA) GFMC(FULL) EXPT n p 2 H 3 H 3 He 6 Li 6 Li* 7 Li 7 Be 8 Li 8 B 9 Li 9 Be 9 B 9 C 10 B 10 B* m.m. THEO EXP 9 C -1.35(4)(7) (5) 9 Li 3.36(4)(8) (6) EE et al. error algorithm Epelbaum, Krebs, and Meissner EPJA51(2015)53 [ δ N3LO =max Q 4 µ LO, Q 3 µ LO µ NLO, Q 2 µ NLO µ N2LO, ] Q 1 µ N2LO µ N3LO [ mπ Q=max Λ, p ] Λ * N3LO- corrections can be large * * SNPA and χeft currents qualitatively in agreement, χeft isoscalar currents provide better description exp data * Pastore et al. PRC87(2013)035503

27 27 / 20 χeft currents: a closer look A=7 Captures gs ex LO N2LO N3LO(OPE) N3LO(CT) N4LO(2b) N4LO(3b) TOT(2b+3b) * Large cancellations due to positive CT at N3LO with c D fixed to GT m.e. of tritium In preparation

28 28 / 20 Convergence and cutoff dependence Tritium β-decay 1.08 Cumulative m.e. / EXP GT + N2LO (1b RC) + N3LO (OPE - c 3 c 4 ) + N3LO (CT c D ) + N4LO (OPE) + N4LO (MPE) + N4LO (3b) EXP GT (LO) Cutoff MeV * 2% additive contribution from two-body currents A. Baroni et al. PRC93(2016) & PRC94(2016)024003

29 29 / 20 Back-to-back np and pp Momentum Distributions ρ pn (q,q=0) (fm 3 ) 12 C B 5 8 Be Li He q (fm -1 ) Wiringa et al. PRC89(2014) JLab, Subedi et al. Science320(2008)1475 Nuclear properties are strongly affected by two-nucleon interactions!

30 30 / 20 Electromagnetic Currents from Nuclear Interactions (SNPA currents) q j=[h, ρ]= [ t i + υ ij + V ijk, ρ ] 1) Longitudinal component fixed by current conservation 2) Plus transverse phenomenological terms j = j (1) π transverse + j (2) (v) + + q π ρω + j (3) (V ) N N Villars, Myiazawa (40-ies), Chemtob, Riska, Schiavilla... see, e.g., Marcucci et al. PRC72(2005) and references therein

31 31 / 20 Currents from nuclear interactions Satisfactory description of a variety of nuclear em properties in A 12 2 H(p,γ) 3 He capture 0.5 S(E) (ev b) LUNA Griffiths et al. Schmid et al E CM (kev) Marcucci et al. PRC72, (2005)

32 32 / 20 0νβ β decay 0νβ β -decay matrix elements and the role of two-nucleon correlations Majorana Demonstrator Berna U. *Preliminary results*

33 33 / 20 Double beta-decay m.e. s in 12 Be(0 + ;2) 12 C(0 + ;0): A test case *Preliminary* Be(0 + ;2) -> 12 C(0 + ;0) - AV18+UX ρ V = τ + 1 τ+ 2 /r 12 Jf ρ V Ji =.063 f ρ V i =.0545 ρ 12 (r) (fm -4 ) ρ A = 1 2 τ + 1 τ+ 2 /r 12 f ρ A i = Jf ρ A Ji = r (fm) * <ρ V> corr <ρ V > uncorr 0.86 * <ρ A> corr <ρ A > uncorr 0.72

34 34 / 20 Magnetic Moments in A 10 Nuclei - bis Predictions for A>3 nuclei 4 µ (µ N ) p 7 Li 9 3 H 9 B Li 6 Li* 10 B 8 Li 2 H 6 Li 8 B 10 B* GFMC(IA) GFMC(FULL) 9 EXPT 7 Be 9 C Be n 3 He p n 9 Be 9 C -3 µ N (IA)= i [(L i + g p S i )(1+τ i,z )/2+g n S i (1 τ i,z )/2] 9 C ( 9 Li) dominant spatial symmetry [s.s.] = [432] = [α, 3 He( 3 H),pp(nn)] Large MEC 9 Be ( 9 B) dominant spatial symmetry [s.s.] = [441] = [α,α,n(p)] PRC87(2013)035503

35 Outlook The microscopic description of nuclei successfully reproduces EXPT data provided that many-body effects in nuclear interactions and EM currents are accounted for. J.Phys.G41(2014) S.Bacca&S.P. EM structure and dynamics of light nuclei Charge and magnetic form factors of A 10 systems M1/E2 transitions in light nuclei Radiative captures, photonuclear reactions... Role of -resonances in MEC (EM current consistent with the chiral -full NN potential developed by M. Piarulli et al. PRC91(2015)024003) Fully consistent χeft calculations with MEC for A>4 (based on, e.g., PRC91(2015)024003) Zemach moments of light nuclei with MEC Electroweak structure and dynamics of light nuclei Test axial currents (chiral and conventional) in light nuclei (A. Baroni et al. PRC93(2016)015501) Incorporate pion production mechanisms in STA Strong reactions in nuclei QMC calculations of nuclear reactions 35 / 20

36 36 / 20 χeft EM currents at N3LO: fixing the EM LECs d S, d V 1, dv 2 c S, c V d V 1, d V 2 Isovector Five LECs: d S, d1 V, and dv 2 could be determined by pion photo-production data on the nucleon d2 V and dv 1 are known assuming -resonance saturation Left with 3 LECs: Fixed in the A = 2 3 nucleons sector Isoscalar sector: * d S and c S from EXPT µ d and µ S ( 3 H/ 3 He) Isovector sector: * model I = c V from EXPT npdγ xsec. or * model II = c V from EXPT µ V ( 3 H/ 3 He) m.m. our choice Note that: χeft operators have a power law behavior introduce a regulator to kill divergencies at large Q, e.g., C Λ = e (Q/Λ)n,...and also, pick n large enough so as to not generate spurious contributions ( ) Q n C Λ Λ

37 Predictions with χeft EM currents for A = 2 3 systems np capture xsec. (using model II) / µ V of A=3 nuclei (using model I) bands represent nuclear model dependence (N3LO/N2LO AV18/UIX) γ np µ V ( 3 H/ 3 He) mb LO NLO N2LO N3LO (no LECs) N3LO (full) EXP n.m. Λ (MeV) Λ (MeV) npdγ xsec. and µ V ( 3 H/ 3 He) m.m. are within 1% and 3% of EXPT Two-body currents important to reach agreement with exp data Negligible dependence on the cutoff entering the regulator exp( (k/λ) 4 ) PRC87(2013) / 20