Nucleon Structure on a Lattice Sergey Syritsyn (Jefferson Lab)

Transcription

1 Nucleon Structure on a Lattice Sergey Syritsyn (Jefferson Lab) PhD, advisor: John Negele (MIT Center for Theoretical Physics) Postdoctoral Fellow (Nuclear Science Division, Berkeley National Lab) RIKEN Foreign Postdoctoral Researcher (Brookhaven National Lab) From Sep 2016 Nathan Isgur Fellow at Theory Center, Jefferson Lab Jefferson Lab Director's Seminar, December 2, 2015

2 Outline Nucleon Form Factors GE, GM on a lattice at the physical point Outlook: High-momentum Form Factors Strange quark contributions to the nucleon charge & magnetization Neutron-Antineutron Oscillations & BSM Physics Physics motivation Calculations at the physical point Summary Sergey N. Syritsyn

3 Sergey N. Syritsyn QCD on Lattice Numerical Path integral over quark & gluon fields q x q y... = D Glue D Quarks e S Glue q /D+m q q x q y... = D Glue e S Glue } Markov Chain Monte Carlo sampling Det /D + m /D + m 1 x,y... Euclidean lattice L U µ e ig aa µ U P e ig a2 F µν ( curl A µ ) Computation challenges: finite volume, simulations with light quarks, excited states in the correlatoin functions a quark covariant derivative

4 Sergey N. Syritsyn Hadron Spectrum & Structure in Lattice QCD Hadron Spectrum: C 2pt (T )=N(T ) N(0) = N N Euclidean lattice N(T )N(0) = n Z n 2 e E nt Hadron Matrix Elements: C O 3pt(T )=N(T )O(τ) N(0) = N O N + N O N e H QCDt evolution Each quark line = ( /D + m) 1 ψ N(T )O(τ)N(0) = n,m Z m e E n(t τ) n O me E mτ Z n Dealing with excited states : multi-exponential fits variational methods

5 Sergey N. Syritsyn Proton Electromagnetic Structure Electromagnetic probes e ±,! " G p E Alberico et al parametrization lattice data Distribution of charge... G E (Q 2 )=F 1 (Q 2 ) Q2 4M 2 N F 2 (Q 2 ) Proton electromagnetic form factors P + q qγ µ q P = ŪP +q F 1 (Q 2 ) γ µ + F 2 (Q 2 ) iσµν q ν 2M N U P Q 2 (GeV 2 ) 3.0 Alberico et al parametrization lattice data and magnetization G M (Q 2 )=F 1 (Q 2 )+F 2 (Q 2 ) Related to Fourier transform of charge and magnetization distribution in the nucleon (*) G p M On-going: continuum limit study Q 2 (GeV 2 ) Lattice data near the physical point (m! =149 MeV): [J.R.Green,SNS, et al (LHPc) PRD90: (2014)]

6 Sergey N. Syritsyn Proton Charge Radius Puzzle Proton radius discrepancy: 7! difference between e-p scattering and µ-p levels r p (fm) Sick CODATA 2006 Pohl et al Bernauer et al CODATA 2010 Zhan et al Antognini et al planned experiments JLab prad experiment MUSE@PSI : e ± / µ ± -p scattering Year [Muon Scattering Experiment Whitepaper (PSI), ] e-p data µ-p data (r 2 1) u d [fm 2 ] Lattice QCD preciction for ~10% uncertainty at physical point; agreement with muonium result after correcting excited states ChPT divergence (r 2 1 ) p (r 2 1) n HBChPT+ 32c64 fine 32c96 coarse 24c24 coarse 24c48 coarse 32c48 coarse 48c48 coarse µp +PDG PDG 2012 log m 2 π m π [GeV] Lattice data near the physical point (m! =149 MeV): [J.R.Green, SNS et al (LHPC), ]

7 Disconnected Light & Strange Quarks "Hierarchical probing": In sum over 2dk+1 vectors (d=3), nearest terms cancel exactly: N 1 zi (x)zi (y) = 0, N i x = y [K.Orginos, A.Stathopoulos] light strange t/a = F2 (disconn.) F1 (disconn.) Figure: [S.Meinel] F1disc < % of F1v Q2 (GeV2 ) t/a = F2disc < 2% of F2v m! =320 MeV strange light Q2 (GeV2 ) [J. Green, S. Meinel, SNS, et a(lhpc) PRD92 (2015) 3, ] Sergey N. Syritsyn Nucleon Structure on a Lattice JLab Director's Seminar, Dec 2, 2015

8 Disconnected Light & Strange Quarks "Hierarchical probing": In sum over 2dk+1 vectors (d=3), nearest terms cancel exactly: N 1 zi (x)zi (y) = 0, N i [K.Orginos, A.Stathopoulos] 0.15 G0 HAPPEX GsE + ηgsm Figure: [S.Meinel] A4 lattice Experiment: Strange part in the elastic e p asymmetry (forward angles) Lattice: m! =320 MeV [J. Green, S. Meinel, SNS, et al (LHPc) PRD92 (2015) 3, ], x = y 0.0 Sergey N. Syritsyn Q2 (GeV2 ) Nucleon Structure on a Lattice Underway: disconnected & strange contributions to EM tensor and spin JLab Director's Seminar, Dec 2, 2015

9 Neutron-Antineutron Oscillations & BSM Motivation: One of Sakharov s conditions for baryogenesis Alternative to proton decay ("B=1) Which one (or both?) realized in nature? Probing BSM physics : "(B L)=2 Possible connections to lepton number violation: double beta decay, and seesaw neutrino mass mechanism [R.Mohapatra, R.Marshak (1980)] Past experimental searches: Quasi-free neutron conversion in flight B=1 P n n (t) (δmt) 2 =(t/τ n n ) 2 B=-1 Nuclear matter stability T d = Rτ 2 n n τ n n > sec ILL Grenoble reactor,1990 [M.Baldo-Ceolin et al, 1994)] τ n n > s τ n n > s τ n n > s [Soudan 2] [Super-K] [SNO] (limited by irreducible neutrino background) Experiment at ESS proposed to improve limits on osc.time x Sergey N. Syritsyn

10 Sergey N. Syritsyn Neutron Antineutron Operators Effective 6-quark operators From Beyond the Standard Model : interaction with a massive Majorana lepton, unified theories, etc [T.K.Kuo, S.T.Love, PRL45:93 (1980)] [R.N.Mohapatra, R.E.Marshak, PRL44:1316 (1980)] H n n = L eff = i E + V δm ci O 6q i δm E V +h.c. τ n n =(2δm) 1 δm = n d 4 x L eff n = i c i M 5 X n O 6q i n BSM scale suppression of 6-quark Dim-9 operators What is the scale for physics behind n#n? Sensitivity of matter to BN-violating terms is determined by nuclear scale physics and non-perturbative QCD Current lower bound on!n-n requires (*) MX few 10 2 TeV (*) Based on nucleon model-dependent matrix elements calculations

11 Sergey N. Syritsyn Neutron Antineutron Matrix Elements Effective operators: (R-,L-diquarks) 3 singlets in color & electroweak symmetries O 1 χ1 {χ 2 χ 3 } = Tijklmn s u it χ1 Cu j χ 1 d kt χ2 Cd l χ 2 d mt χ 3 Cd n χ 3 O 2 {χ1 χ 2 }χ 3 O 3 {χ1 χ 2 }χ 3 = Tijklmn s u it χ1 Cd j χ 1 u kt χ2 Cd l χ 2 d mt χ 3 Cd n χ 3 = Tijklmn a u it χ1 Cd j χ 1 u kt χ2 Cd l χ 2 d mt χ 3 Cd n χ 3 [T.Kuo, S.Love, PRL45:93 (1980)] χ 1,2,3 = R, L Chiral SU(2)L,R multiplet classification: SU(3) c U(1) em SU(2) L [(RRR) 3 ] OR(RR) 1 +4O2 (RR)R 3 R 0 L [(RRR) 1 ] O(RR)R 2 O1 R(RR) 3O3 (RR)R 1 R 0 L [R 1 (LL) 2 ] O(LL)R 2 O1 L(LR) 3O3 (LL)R 1 R 0 L [(RR) 1 L 0 ] 3O(LR)R 3 1 R 0 L [(RR) 2 L 1 ] (1) OL(RR) 1 2 R 1 L [(RR) 2 L 1 ] (2) O(LR)R 2 2 R 1 L [(RR) 2 L 1 ] (3) OR(LR) 1 +2O2 (RR)L 2 R 1 L + L R counterparts Chiral symmetry is essential for simple renormalization properties SU(2)L$U(1) -symmetric, non-vanishing

12 Sergey N. Syritsyn Lattice Calculation N (+) (t 2 ) O 6q (0) N ( ) ( t 1 ) e M n(t 2 +t 1 ) n O 6q n t 1,t 2,t 1 + t 2 t Initial calculation with anisotropic Wilson [M.Buchoff, C.Schroeder, J.Wasem, arxiv: (LATTICE2012)] CURRENT : Calculations with physical quarks masses & chiral symmetry [SNS et al (LATTICE2015)]

13 [(RRR)3] [(RRR)1] [(RR)2L1] (1) [(RR)2L1] (2) [(RR)2L1] (3) [(RR)0L1] [(RR)1L0] [(LLL)3] [(LLL)1] [(LL)2R1] (1) [(LL)2R1] (2) [(LL)2R1] (3) [(LL)0R1] [(LL)1R0] [(RRR)3] [(RRR)1] [(RR)2L1] (1) [(RR)2L1] (2) [(RR)2L1] (3) [(RR)0L1] [(RR)1L0] [(LLL)3] [(LLL)1] [(LL)2R1] (1) [(LL)2R1] (2) [(LL)2R1] (3) [(LL)0R1] [(LL)1R0] Renormalization : RI-(S)MOM on a lattice (G I ) ijklmn αβγδη (x, p 1...p 6 )=O I dn η (p 6 ) d m (p 5 ) d l δ(p 4 ) d k γ(p 3 )ū j β (p 2)ū i α(p 1 ) p 1 = p 3 = p 5 = p p 2 = p 4 = p 6 = p Ext.momenta assigned to match the 2-loop pert.qcd calculation [M.Buchoff, M.Wagman, arxiv: ] u(p) d( p) is not an SU(2) doublet: mix 3R 1R, etc Fix: symmetrize external momenta 1 5 O6q ū(+p)ū(+p) d(+p) d( p) d( p) d( p) O6q ū(+p)ū( p) d(+p) d(+p) d( p) d( p) O6q ū( p)ū( p) d(+p) d(+p) d(+p) d( p) [(RRR) 3 ] [(RRR) 1 ] [(RR) 2 L 1 ] (1) [(RR) 2 L 1 ] (2) [(RR) 2 L 1 ] (3) [(RR) 0 L 1 ] [(RR) 1 L 0 ] [(LLL) 3 ] [(LLL) 1 ] [(LL) 2 R 1 ] (1) [(LL) 2 R 1 ] (2) [(LL) 2 R 1 ] (3) [(LL) 0 R 1 ] [(LL) 1 R 0 ] p 2!(5.6 GeV) 2 [(RRR) 3 ] [(RRR) 1 ] [(RR) 2 L 1 ] (1) [(RR) 2 L 1 ] (2) [(RR) 2 L 1 ] (3) [(RR) 0 L 1 ] [(RR) 1 L 0 ] [(LLL) 3 ] [(LLL) 1 ] [(LL) 2 R 1 ] (1) [(LL) 2 R 1 ] (2) [(LL) 2 R 1 ] (3) [(LL) 0 R 1 ] [(LL) 1 R 0 ] Input to pert. QCD matching [M.Buchoff, M.Wagman, arxiv: ] Sergey N. Syritsyn

14 Lattice->MSbar Conversion R Z SI (µ) =Z lat (µ)/( Z(µ) Z(2GeV) )MS Fit Z + αa 2 µ 2 (RRR) 3 (RRR) 1 (RR) 2 L 1 2 R 1 L R 1 (LL) 0 (RR) 1 L µ 2 [GeV 2 ] Perturbative 1-loop running from W.Caswell et al PLB122:373 (1983)] Syst.error : difference between 2 4 GeV and 4 6 GeV fits Sergey N. Syritsyn

15 Sergey N. Syritsyn Preliminary Results & Comparison to Bag Model Lattice Results, PRELIMINARY MS(2 GeV) O Bag A LQCD Bag A Bag B [10 5 GeV 6 ] [10 5 GeV 6 ] [10 5 GeV 6 ] MIT Bag model results from [S.Rao, R.Shrock, PLB116:238 (1982)] N-Nbar oscillation is x(5-10) more sensitive to BSM physics than previously thought! Outlook: Finalize the current results (physical quarks with chiral symmetry) Use finer discretization to eliminate potential cutoff effects LQCD Bag B [(RRR) 3 ] [(RRR) 1 ] 45.4(5.6) [R 1 (LL) 0 ] 44.0(4.1) [(RR) 1 L 0 ] -66.6(7.7) [(RR) 2 L 1 ] (1) -2.12(26) [(RR) 2 L 1 ] (2) 0.531(64) [(RR) 2 L 1 ] (3) -1.06(13)

16 Summary Lattice QCD methods are mature enough for reliable nucleon structure calculations, and... offer multiple avenues to explore nucleon structure to complement experiments, and... are crucial for experiments that use nucleons as a lab for new physics searches. Sergey N. Syritsyn