High-Statistics Calculation of Nucleon Structure and Matrix Elements - - PowerPoint PPT Presentation

High-Statistics Calculation

• f Nucleon Structure and Matrix Elements
• n 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

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Scientific Objectives

• S. Syritsyn (LHP), R. Gupta (NME)

Nucleon Structure with Isotropic Wilson Lattices

ID a[fm] Volume

m휋 m휋 L

• Traj. available Conn.cost per

conf.[NMEp] %% D4 0.085 323x64 400 5.5 5100 500

Systematics

D5 0.081 323x64 300 4.0 2600 825 ~20%

Systematics study [NMEp]

D6 0.080 483x96 190 3.7 700 7,125

study [NMEp]

D7 0.080 643x128 190 4.9 900 (++ by 07/01) 32,055 ~80%

proposed in [LHPp]

D8 0.080 643x128 140 4.1 Started Next Year ear (hopef hopefully) 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: Goal : Compute Nucleon Structure and Quark Matrix Elements with high statistical precision and robust control of systematic errors

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Scientific Objectives

• S. Syritsyn (LHP), R. Gupta (NME)

Nucleon Structure Scientific Objectives

LHP (before’15 : DWF with RBC) NME (before’15 : Wilson on HISQ) Vector (EM) Form Factors GE,M (including uding high momenta Q2) and Radii (r2E,M)p,n Axial Vector Form Factors G ctors GA,P and Axial Coupling gA Scalar and Tensor C nsor Charges (gS,T)u-d Generalized Form Factors, Moments of PDFs, Nucleon Spin Ordinary and Transverse Momentum- Dependent Parton Distributions Quark (chromo)EDM-induced nEDM Variational analysis of Exc.States Study dep. on a, L, mힹ (≥190 MeV) Including Disconnected (light & ht & strange) Quark Contractions

In the Joint proposal, we will study (topics as expressed by in the initial proposals) Wilson Fermions will make affordable

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Scientific Objectives

• S. Syritsyn (LHP), R. Gupta (NME)

Nucleon “Charges” gA,S,T

· Ï Û ı · Ï Á · Ï ˜ 0.00 0.05 0.10 0.15 1.10 1.15 1.20 1.25 1.30 1.35 a HfmL gA

u-d

· Ï Û ı · Ï Á · Ï ˜ 0.03 0.06 0.09 0.12 1.10 1.15 1.20 1.25 1.30 1.35 Mp2 HGeV2L gA

u-d

· Ï Û ı · Ï Á · Ï ˜ 3 4 5 6 7 1.10 1.15 1.20 1.25 1.30 1.35 MpL gA

u-d

· Ï Û ı · Ï Á · Ï ˜ 0.00 0.05 0.10 0.15 0.0 0.5 1.0 1.5 a HfmL gS

u-d

· Ï Û ı · Ï Á · Ï ˜ 0.03 0.06 0.09 0.12 0.0 0.5 1.0 1.5 Mp2 HGeV2L gS

u-d

· Ï Û ı ·Ï Á · Ï ˜ 3 4 5 6 7 0.0 0.5 1.0 1.5 MpL gS

u-d

· Ï Û ı · Ï Á · Ï ˜ 0.00 0.05 0.10 0.15 0.90 0.95 1.00 1.05 1.10 1.15 1.20 a HfmL gT

u-d

· Ï Û ı · Ï Á · Ï ˜ 0.03 0.06 0.09 0.12 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Mp2 HGeV2L gT

u-d

· Ï Û ı · Ï Á · Ï ˜ 3 4 5 6 7 0.90 0.95 1.00 1.05 1.10 1.15 1.20 MpL gT

u-d

gS,T “charges” = couplings to BSM physics in precision meas. of β-decay [LANL] Clover-improved Wilson valence quarks on HISQ lattices Extrapolation in a, L, m휋 : [(P)N(D)ME, Lattice’14]

g(a, mπ, L) = g0 + αa + βm2

π + γe−mπL

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Scientific Objectives

• S. Syritsyn (LHP), R. Gupta (NME)

Nucleon Vector (EM) Form Factors

P + q| ¯ qγµq |P⇥ = ¯ UP +q h F1(Q2) γµ + F2 (Q2)iσµνqν 2MN i UP

Form Factors: (F1 / F2) scaling, (GE/GM), u-,d-contributions Proton radius: 7σ difference; JLab pRAD, MUSE (e±,µ± –p)

m휋=149 MeV data vs Phenomenology [J.Green et al(LHP), PRD90:074507(2014)]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 0.0 0.1 0.2 0.3 0.4 0.5 Gv

E

Q2 (GeV2) Alberico et al parametrization lattice data 1 2 3 4 5 6 0.0 0.1 0.2 0.3 0.4 0.5 Gv

M

Q2 (GeV2) Alberico et al parametrization lattice data

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 mπ [GeV] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 hr2

1iud [fm2] µp PDG 2012 QCDSF ’11 Nf = 2 PNDME ’13 Nf = 2 + 1 + 1 ETMC ’10 Nf = 2 ETMC ’13 Nf = 2 + 1 + 1 CLS-Mainz ’12 Nf = 2 RBC/UKQCD ’08, ’13 Nf = 2 + 1 LHPC ’10 Nf = 2 + 1 LHPC ’09 Nf = 2 + 1 LHPC ’12 Nf = 2 + 1

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Scientific Objectives

• S. Syritsyn (LHP), R. Gupta (NME)

Nucleon Axial Form Factors

GA(Q2) are measured in 휈-scattering, 흅-production;

implications for neutrino flux norm. in IceCube, etc

Axial radius (rA2)=12 / mA2: model dependence

varying nuclear / GA shape models: mA=0.9 ... 1.4 GeV

Strange quark GsA,P(Q2) : MiniBooNE GP(Q2) induced pseudoscalar : 흁 capture (MuCAP)

P + q| ¯ qγµγ5q |P⇥ = ¯ UP +q h GA(Q2) γµγ5 + GP (Q2) γ5qµ 2MN i UP

0.0 0.1 0.2 0.3 0.4 0.5 Q2 [GeV2] 0.0 0.5 1.0 1.5 2.0 GA

phenomenology T = 8a T = 9a T = 10a T = 12a summ

0.0 0.1 0.2 0.3 0.4 0.5 Q2 [GeV2] 10 20 30 40 50 60 GP

phenomenology T = 8a T = 9a T = 10a T = 12a summ

Physical m휋, chiral quarks [LHP & RBC collabs, Lattice’14]

0.2 0.4 0.6 0.8 1

Q

2 [GeV 2]

0.2 0.4 0.6 0.8 1

GA (Q

2) / GA (0)

[V.Bernard et at, J.Phys.G28:R1(2002)]

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Scientific Objectives

• S. Syritsyn (LHP), R. Gupta (NME)

0.1 0.2 0.3 0.4 0.5 0.6 mπ[GeV ] −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Jconn

q

1 2∆Σu+d

Lu+d

ETMC ’13 (Twisted Mass Nf = 2(+1 + 1) QCDSF ’12 (Wilson-clover Nf = 2) LHPC ’10 (Asqtad+DWF Nf = 2 + 1) LHPC ’10 (DWF Nf = 2 + 1) PRELIM Nf = 2 + 1 DWF (LHP&RBC)

0.1 0.2 0.3 0.4 0.5 0.6 mπ[GeV ] −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Jconn

q

Ju Jd

ETMC ’13 (Twisted Mass Nf = 2(+1 + 1) QCDSF ’12 (Wilson-clover Nf = 2) LHPC ’10 (Asqtad+DWF Nf = 2 + 1) LHPC ’10 (DWF Nf = 2 + 1) LHPC ’13 (Wilson-clover Nf = 2 + 1) PRELIM Nf = 2 + 1 DWF (LHP&RBC)

Nucleon Gen. F.F.s and Nucleon Spin

−0.4 −0.2 0.0 0.2 0.4 Jd −0.4 −0.2 0.0 0.2 0.4 Ju

HERMES DD HERMES Dual JLab DD LHP’07 [0705.4295] QCDSF’07 [0710.1534] LHP’10 [1001.3620] ETMC Nf = [1012.0857] χQCD’13 [1312.4816] LHP&RBC mphys

π

PRELIMINARY

Ju Jd

disconnected contributions are not included Jq,glue = 1 2 h Aq,glue

20

(0) + Bq,glue

20

(0) i

Jglue + X

q

Jq = 1 2 , Jq = 1 2∆Σq + Lq hxiq = Aq

20(0)

⇥N(p + q)| T q,glue

µν

|N(p)⇤ n A20, B20, C20

• (Q2)

Ju,d Lu+d, Σu+d

discrepancy with 흌QCD result for Lu+d

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Scientific Objectives

• S. Syritsyn (LHP), R. Gupta (NME)

Transverse Momentum-Dependent Distributions

 

 



       

   

SIDIS

l + N(P) − → l0 + N(Ph) + X

              



 τ    

      

with spacelike link path U =

SIDIS DY SiversShift, ud quarks Ζ 0.39, bT 0.36 fm, mΠ 518 MeV 10 5 5 10

• 0.6

0.4 0.2 0.0 0.2 0.4 0.6 Ηv lattice units mN f

• 1T

1 1 f

• 1

1 0 GeV

valence DWF on Asqtad [B.Musch, P.Hägler, M.Engelhardt, J.Negele, A.Schäfer]

ˆ ζ = P · v mN |v| → ∞

“light-cone” limit

• perator localized

at Euclidean time 휏

Φ(b, P, S, ˆ ζ, µ) = 1

2hP, S| ¯ q(0) Γ U(ηv, b) q(b) |P, Si

Non-local lattice operator probes k⟘-moments (“shifts”) of TMDs

∼ Z dx Z d2~ k⊥ ki f(x,~ k⊥)

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Improvements

• S. Syritsyn (LHP), R. Gupta (NME)

Calculation Details and Improvements

Kinematics to access high-momentum form factors :

• include |psink|~1 GeV2 (up to Q2~4 GeV2 in Breit frame)
• TMDs also require high momentum in-,out-states |psink|=|psource|

Variational method to reduce excited states :

• 2x2 nucleon correlators with varied source smearing
• ptimize nucleon operators both zero/low and high momentum states

Improved sampling with All-Mode-Averaging :

• exact low-mode deflation OR truncated multigrid solver
• ~4,000 (exact+sloppy) samples for the lightest mힹ=190 MeV

Disconnected quark loops (light and strange) with variance reduction :

• hierarchical probing
• low-eigenmode deflation

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Improvements

• S. Syritsyn (LHP), R. Gupta (NME)

Nucleon Excited States and SNR

Stochastic noise grows rapidly with T, especially with light pions [Lepage’89]:

Signal hN(T) ¯ N(0)i ⇠ e−MNT Noise h|N(T) ¯ N(0)|2i |hN(T) ¯ N(0)i|2 ⇠ e−3mπT Signal/Noise ⇠ e−(MN− 3

2 mπ)T

Physical point: SNR ~ x(1/2) every (2a)

[LHP, PLB734 290 (2014)]

Multi-exp. fits of T-dependence : determined by the largest T Variational method: (–)expensive ~(Nop)2, (+)greatly extend plateaus [CSSM] Proposal : explore and compare cost / benefit variational vs traditional

0.10 0.15 0.20 0.25 0.30 mπ [GeV] 0.00 0.05 0.10 0.15 0.20 0.25 hxiud

BChPT CTEQ6

0.93 1.16 1.39 fm summ.

0.10 0.15 0.20 0.25 0.30 mπ [GeV] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (r2

1)u−d [fm2]

HBChPT+∆ µp + PDG PDG 2012

1.39 1.16 0.93 fm summ.

tsink − tsource = 0.93, 1.16, 1.39 fm

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Improvements

• S. Syritsyn (LHP), R. Gupta (NME)

Disconnected Quark Contractions

Hierarchical probing [K.Orginos, A.Stathopoulos, ’13] : In sum over 2dk+1 vectors (d=3), dist(x,y) ≤ 2k terms cancel exactly: zi ! zi ξ , ξ(x) = random Z2-vector

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Q2 (GeV2)

−0.07 −0.06 −0.05 −0.04 −0.03 −0.02 −0.01 0.00

F2 (disconn.)

t/a = 10 strange light 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Q2 (GeV2)

0.000 0.002 0.004 0.006 0.008 0.010 0.012

F1 (disconn.)

t/a = 10 light strange

Disconnected diagrams with JLab isotropic Clover [S.Meinel’s USQCD project ’13; in prep.]

1 ≤ X

a

|xa − ya| ≤ 2k : 1 N

N

X

i

zi(x)zi(y)† ≡ 0

NEW: reduce variance by treating low modes

• f exactly [K.Orginos et al]

( / D

† /

D)

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Request

• S. Syritsyn (LHP), R. Gupta (NME)

Total Request for the Joint Proposal

Computing resources request was updated to reflect non-overlapping goals in the proposals : [common] connected and disconnected 3pt correlators on the lightest pion ensemble mힹ=190 MeV : 32.8M [NMEp] calculations with the heavier pion masses: +8.2M [LHPp] additional contractions (GFFs, TMDs) the lightest pion ensemble: +9.5M [common] exploration of variational method and source tuning: +6M Computing resources request was updated to reflect non-overlapping goals in the proposals : LHP requested 43M NME requested 47M Total combined request : 56.5M

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2

• S. Syritsyn (LHP), R. Gupta (NME)

Summary

High-statistics, high precision nucleon structure calculations with very wide scope

proton form factors and charge radius proton spin puzzle applications to BSM and CPV searches parton distributions

Exploration of new techniques crucial for calculations at the physical point Equal emphasis on Connected and Disconnected (Light and Strange) contributions to the nucleon structure We are hopeful that the USQCD will support not only this proposal, but also generation of physical point Wilson-clover lattices

Nucleon Structure with Wilson Clover Lattices USQCD All-Hands Meeting, Fermilab, May1&2 Improvements

• S. Syritsyn (LHP), R. Gupta (NME)

Code Performance [NMEp]

Multi-GPU DD scaling (Titan)

512 1024 1536 2048 2560 3072 3584 4096 4608 Titan Nodes (GPUs) 50 100 150 200 250 300 350 400 450 TFLOPS BiCGStab: 72

3x256

DD+GCR: 72

3x256

BiCGStab: 96

3x256

DD+GCR: 96

3x256

Strong Scaling, QUDA+Chroma+QDP-JIT(PTX)

• B. Joo, F. Winter (JLab), M. Clark (NVIDIA)

0" 50" 100" 150" 200" 250" 300" 32" 64" 128"

Wall$clock$(me$(s)$$ XK$Nodes$

light"quark,"MG,"CPU,"8"cores/node" light"quark,"MG,"CPU,"16"cores/node" light"quark,"BiCGStab,"GPU+1"core/node" strange"quark,"BiCGStab,"GPU+1"core/node"

Comparison of AMG (QDP-MG) to usual Krylov iteration methods