High-Statistics Calculation of Nucleon Structure and Matrix Elements on Isotropic Clover Lattices Combined LHP & NME Proposal LHP: S.Syritsyn(PI), J.Green, M.Engelhardt, N.Hasan, S.Krieg,J.Negele, S.Meinel, A.Pochinsky NME: R.Gupta(PI), T.Bhattacharya, V.Cirigliano, B.Joo, H.-W.Lin, D.Richards, F.Winter, B.Yoon, (|LHP > + |NME > ): K.Orginos USQCD All-Hands Meeting, Fermilab May 1-2, 2015
Scientific Objectives Nucleon Structure with Isotropic Wilson Lattices Goal : Compute Nucleon Structure and Quark Matrix Elements with high statistical precision and robust control of systematic errors Wilson fermions are economical and permit higher statistics for better precision and noisy observables (TMDs, GPDs) experiments with newer techniques • controlling excited states • computing disconnected diagrams • exploring hadron states with high momentum JLab Isotropic clover-improved Wilson lattices: Traj. available Conn.cost per m 휋 m 휋 L ID a[fm] Volume %% conf.[NMEp] D4 0.085 32 3 x64 400 5.5 5100 500 Systematics Systematics D5 0.081 32 3 x64 300 4.0 2600 825 ~20% study [NMEp] study [NMEp] D6 0.080 48 3 x96 190 3.7 700 7,125 900 proposed in D7 0.080 64 3 x128 190 4.9 32,055 ~80% [LHPp] (++ by 07/01) D8 0.080 64 3 x128 140 4.1 Started Next Year ear (hopef hopefully) S. Syritsyn (LHP), R. Gupta (NME) Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2
Scientific Objectives Nucleon Structure Scientific Objectives In the Joint proposal, we will study (topics as expressed by in the initial proposals) LHP (before’15 : DWF with RBC) NME (before’15 : Wilson on HISQ) Vector (EM) Form Factors G E,M (including uding high momenta Q 2 ) and Radii (r 2E,M ) p,n Axial Vector Form Factors G ctors G A,P and Axial Coupling g A Scalar and Tensor C nsor Charges (g S,T ) u-d Generalized Form Factors, Moments of PDFs, Nucleon Spin Ordinary and Transverse Momentum- Dependent Parton Distributions Quark (chromo)EDM-induced nEDM Wilson Fermions will make affordable Variational analysis of Exc.States Study dep. on a , L , m ힹ � ( ≥ 190 MeV) Including Disconnected (light & ht & strange) Quark Contractions S. Syritsyn (LHP), R. Gupta (NME) Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2
Scientific Objectives Nucleon “Charges” g A,S,T [(P)N(D)ME, Lattice’14] g S,T “ charges” = couplings to BSM physics in precision meas. of β - decay [LANL] Clover-improved Wilson valence quarks on HISQ lattices g ( a, m π , L ) = g 0 + α a + β m 2 Extrapolation in a , L , m 휋 : π + γ e − m π L 1.35 1.35 1.35 1.30 1.30 1.30 Ï Ï Ï 1.25 1.25 Ï 1.25 Ï Ï ˜ ˜ ˜ u - d u - d ı · u - d · · ı ı Ï Ï g A Ï g A g A Û 1.20 Û Á · Û 1.20 1.20 Á · Á · 1.15 · 1.15 1.15 · · 1.10 1.10 1.10 0 0.03 0.06 0.09 0.12 0.00 0.05 0.10 0.15 3 4 5 6 7 M p 2 H GeV 2 L a H fm L M p L 1.5 1.5 1.5 ˜ ˜ ˜ · · · 1.0 1.0 1.0 Û Û Û ı ı · ı · Ï ·Ï Ï Á u - d u - d Á · u - d Á · · Ï Ï Ï g S 0.5 g S g S 0.5 0.5 Ï Ï Ï 0.0 0.0 0.0 0 0.03 0.06 0.09 0.12 0.00 0.05 0.10 0.15 3 4 5 6 7 M p 2 H GeV 2 L a H fm L M p L 1.20 1.20 1.20 1.15 1.15 1.15 Ï Ï Ï 1.10 1.10 1.10 u - d u - d u - d ˜ 1.05 ˜ ˜ 1.05 1.05 Ï Ï Ï g T · Ï g T · Á g T · Ï Ï Á · Á · · Û ı Û 1.00 · Û ı ı 1.00 · 1.00 · 0.95 0.95 0.95 0.90 0.90 0.90 0 0.03 0.06 0.09 0.12 0.00 0.05 0.10 0.15 3 4 5 6 7 M p 2 H GeV 2 L a H fm L M p L S. Syritsyn (LHP), R. Gupta (NME) Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2
Scientific Objectives Nucleon Vector (EM) Form Factors F 1 ( Q 2 ) γ µ + F 2 ( Q 2 ) i σ µ ν q ν h i q γ µ q | P ⇥ = ¯ � P + q | ¯ U P + q U P 2 M N Form Factors: ( F 1 / F 2 ) scaling , ( G E /G M ), u-,d- contributions 6 1.1 Alberico et al parametrization Alberico et al parametrization lattice data 1.0 lattice data 5 0.9 0.8 4 0.7 M E G v G v 0.6 3 0.5 0.4 2 0.3 0.2 1 0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 Q 2 (GeV 2 ) Q 2 (GeV 2 ) m 휋 =149 MeV data vs Phenomenology [J.Green et al(LHP), PRD90:074507(2014)] 0 . 8 Proton radius: 7 σ difference; CLS-Mainz ’12 N f = 2 µp PDG 2012 RBC/UKQCD ’08, ’13 N f = 2 + 1 0 . 7 QCDSF ’11 N f = 2 LHPC ’10 N f = 2 + 1 PNDME ’13 N f = 2 + 1 + 1 JLab pRAD, MUSE (e ± ,µ ± –p) LHPC ’09 N f = 2 + 1 ETMC ’10 N f = 2 LHPC ’12 N f = 2 + 1 0 . 6 ETMC ’13 N f = 2 + 1 + 1 0 . 5 1 i u � d [fm 2 ] 0 . 4 h r 2 0 . 3 0 . 2 0 . 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 m π [GeV] S. Syritsyn (LHP), R. Gupta (NME) Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2
Scientific Objectives Nucleon Axial Form Factors 1 G A ( Q 2 ) γ µ γ 5 + G P ( Q 2 ) γ 5 q µ h i q γ µ γ 5 q | P ⇥ = ¯ � P + q | ¯ U P + q U P 2 M N 0.8 G A (Q 2 ) are measured in 휈 -scattering, 흅 -production; 2 ) / G A (0) 0.6 implications for neutrino flux norm. in IceCube, etc G A (Q 0.4 Axial radius (r A2 )= 12 / m A2 : model dependence 0.2 varying nuclear / G A shape models: m A =0.9 ... 1.4 GeV 0 Strange quark G sA,P (Q 2 ) : MiniBooNE 0 0.2 0.4 0.6 0.8 1 2 [GeV 2 ] Q [V.Bernard et at, J.Phys.G28:R1(2002)] G P (Q 2 ) induced pseudoscalar : 흁 capture (MuCAP) Physical m 휋 , chiral quarks [LHP & RBC collabs, Lattice’14] 2 . 0 60 phenomenology phenomenology T = 8 a T = 8 a T = 9 a T = 9 a 50 T = 10 a T = 10 a 1 . 5 T = 12 a T = 12 a summ summ 40 G A G P 1 . 0 30 20 0 . 5 10 0 . 0 0 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 Q 2 [GeV 2 ] Q 2 [GeV 2 ] S. Syritsyn (LHP), R. Gupta (NME) Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2
Scientific Objectives Nucleon Gen. F.F.s and Nucleon Spin n o ⇥ N ( p + q ) | T q,glue ( Q 2 ) | N ( p ) ⇤ � A 20 , B 20 , C 20 0 . 6 µ ν J u,d 0 . 5 h x i q = A q 20 (0) 0 . 4 J q,glue = 1 h i A q,glue (0) + B q,glue J u (0) 20 20 0 . 3 2 ETMC ’13 (Twisted Mass N f = 2(+1 + 1) QCDSF ’12 (Wilson-clover N f = 2 ) 0 . 2 J conn LHPC ’10 (Asqtad+DWF N f = 2 + 1 ) q LHPC ’10 (DWF N f = 2 + 1 ) J q = 1 0 . 1 LHPC ’13 (Wilson-clover N f = 2 + 1 ) X J glue + 2 , PRELIM N f = 2 + 1 DWF (LHP&RBC) 0 . 0 q J d − 0 . 1 J q = 1 2 ∆Σ q + L q − 0 . 2 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 m π [ GeV ] J u 0 . 6 0 . 4 ETMC ’13 (Twisted Mass N f = 2(+1 + 1) LHPC ’10 (DWF N f = 2 + 1 ) QCDSF ’12 (Wilson-clover N f = 2 ) PRELIM N f = 2 + 1 DWF (LHP&RBC) 0 . 5 LHPC ’10 (Asqtad+DWF N f = 2 + 1 ) 0 . 4 1 0 . 2 2 ∆Σ u + d 0 . 3 0 . 2 J conn L u+d , Σ u+d J u 0 . 0 q HERMES DD 0 . 1 HERMES Dual L u + d JLab DD 0 . 0 LHP’07 [0705.4295] − 0 . 2 − 0 . 1 QCDSF’07 [0710.1534] LHP’10 [1001.3620] − 0 . 2 ETMC N f = [1012.0857] J d χ QCD’13 [1312.4816] − 0 . 4 LHP&RBC m phys PRELIMINARY 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 π m π [ GeV ] − 0 . 4 − 0 . 2 0 . 0 0 . 2 0 . 4 discrepancy with 흌 QCD result for L u+d disconnected contributions are not included J d S. Syritsyn (LHP), R. Gupta (NME) Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2
Scientific Objectives Transverse Momentum-Dependent Distributions SIDIS Non-local lattice operator ζ , µ ) = 1 Φ ( b, P, S, ˆ 2 h P, S | ¯ q (0) Γ U ( η v, b ) q ( b ) | P, S i with spacelike link path U = probes k ⟘ -moments (“shifts”) of TMDs Z Z → l 0 + N ( P h ) + X d 2 ~ k ⊥ k i f ( x, ~ l + N ( P ) − k ⊥ ) dx ∼ valence DWF on Asqtad [B.Musch, P.Hägler, M.Engelhardt, J.Negele, A.Schäfer] 0.6 “light-cone” limit Sivers � Shift, u � d � quarks � 1 � � 0 � � GeV � P · v 0.4 ˆ ζ = m N | v | → ∞ 0.2 1 � � � 1 � � 1 � � f 0.0 � � 0.39, Ζ � 0.2 � b T � � 0.36 fm, operator localized 1T � m N f m Π � 518 MeV at Euclidean time 휏 � 0.4 � DY SIDIS � � 0.6 τ �� � 10 � 5 0 5 10 � Η � v � � lattice units � S. Syritsyn (LHP), R. Gupta (NME) Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2
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