Nucleon Structure with clover-Wilson Fermions LHP proposal - PowerPoint PPT Presentation

Nucleon Structure with 
 clover-Wilson Fermions LHP proposal M.Engelhardt (PI), A.Gambhir, J.Green, 
 J.Negele, A.Pochinsky, S.Syritsyn(co-PI), 
 USQCD All-Hands Meeting, Jefferson Lab 
 Apr 28-30, 2017 


Nucleon Structure with Isotropic Wilson Lattices Goal : Study Flavor-Dependent Nucleon Structure at High Momentum with Stat.signal Improvement and Inclusion of Disconnected Quarks DISCO : disconnected diagrams with Hierarchical Probing and Deflation [A.Gambhir, K.Orginos] 
 with all lattice coordinate/momenta CONN3PT : Nucleon form factors with high momentum transfer with boosted nucleon operators TMD : Transverse-momentum dependent PDFs with boosted high-momentum initial/final states high-momentum limit for lattice Efficient quark-disconnected Transverse Momentum-Dependent 
 contributions ( DISCO ) parton dist. ( TMD ) nucleon states for high-Q 2 
 form factors( CONN3PT ) 
 M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

TMD Program Non-local lattice operator SIDIS ζ , µ ) = 1 Φ ( b, P, S, ˆ 2 h P, S | ¯ q (0) Γ U ( η v, b ) q ( b ) | P, S i $%+,&! ! -(.)&! #" " ! # "# with spacelike link path U = ! /$"&!0 '"()* " 1 111 1 1 ! #" " probes k ⟘ -moments 
 ! ! Z Z d 2 ~ k ⊥ k i f ( x, ~ k ⊥ ) dx (“shifts”) of TMDs ∼ !"#$%&! → l 0 + N ( P h ) + X l + N ( P ) − 0.1 Gen. Sivers Shift (SIDIS, u-d; GeV) Exp. Estimate, DWF-on-AsqTad; 0.12 fm, 518 MeV DWF; 0.084 fm, 297 MeV 0.0 Clover; 0.114 fm, 317 MeV !"#$%&! !"#$%&! '(!) '&"2#% -0.1 *+(,%-.3&'(0(&!1 *+(,%-./&/%!0"/1 " " -0.2 " " ! ! -0.3 ! ! " '2# ! .$40 -0.4 |b T | ≈ 0.35 fm ! -0.5 5"#$(-%4! 0 0.2 0.4 0.6 0.8 ! !$% ! !"# 0(/% ˆ τ ζ operator localized 
 P · v LC limit of spacelike staple ˆ at Euclidean time 𝜐 ζ = m N | v | → ∞ Collins-Soper parameter M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

TMD Program Non-local lattice operator SIDIS ζ , µ ) = 1 Φ ( b, P, S, ˆ 2 h P, S | ¯ q (0) Γ U ( η v, b ) q ( b ) | P, S i $%+,&! ! -(.)&! #" " ! # "# with spacelike link path U = ! /$"&!0 '"()* " 1 111 1 1 ! #" " probes k ⟘ -moments 
 ! ! Z Z d 2 ~ k ⊥ k i f ( x, ~ k ⊥ ) dx (“shifts”) of TMDs ∼ !"#$%&! → l 0 + N ( P h ) + X l + N ( P ) − 0.1 Gen. Sivers Shift (SIDIS, u-d; GeV) Exp. Estimate, DWF-on-AsqTad; 0.12 fm, 518 MeV DWF; 0.084 fm, 297 MeV 0.0 Clover; 0.114 fm, 317 MeV !"#$%&! !"#$%&! '(!) '&"2#% -0.1 *+(,%-.3&'(0(&!1 *+(,%-./&/%!0"/1 " " -0.2 " " ! ! -0.3 ! ! " '2# ! .$40 -0.4 Need large in/out 
 |b T | ≈ 0.35 fm ! -0.5 momentum states! 5"#$(-%4! 0 0.2 0.4 0.6 0.8 ! !$% ! !"# 0(/% ˆ τ ζ operator localized 
 P · v LC limit of spacelike staple ˆ at Euclidean time 𝜐 ζ = m N | v | → ∞ Collins-Soper parameter M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

High-Q 2 Nucleon Form Factors in Experiments Form Factors at high momentum: 
 6 JLab@12GeV : 
 S n 0.3 2 S 4 p up to 18 GeV 2 ; 
 2 ( Q 2 ) u quark 0.2 q 2 Q 2 ➝ ∞ scaling; 
 F 2 κ q Q 4 F q 4 1 Q /F BJY - pQCD (2003) -1 q ! 2 0.1 F flavor separation 
 2 S = Q d quark " 0.75 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 u & d contributions 
 4 1.0 S d 1 ( Q 2 ) - u quark 2 to F 1,2 form factors q 1 F 4 [G.D.Cates et al., 
 Q Q 4 F q 2 0.5 S u PRL106:252003] d quark 2.5 " 0.0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1 2 3 4 5 6 7 8 2 2 Q [GeV ] 2 2 Q [GeV ] FIG. 3: The Q 2 -dependence for the u - and d -contributions to 1 G A (Q 2 ) are measured in 𝜉 -scattering, 𝝆 -production; 0.8 2 ) / G A (0) implications for neutrino flux norm. in IceCube, DUNE 0.6 Axial radius (r A2 )= 12 / m A2 : model dependence G A (Q 0.4 varying nuclear / G A shape models: m A =0.9 ... 1.4 GeV 0.2 Strange quark G sA,P (Q 2 ) : MiniBooNE 0 0 0.2 0.4 0.6 0.8 1 2 [GeV 2 ] Q [V.Bernard et at, J.Phys.G28:R1(2002)] M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

High-Momentum Nucleon States and Form Factors Nucleon operator on a lattice with Gaussian-"smeared" 2 � � S ψ quarks does not couple well to moving hadron x,y 1.5 1 � a � b � c 0.5 ⇥ abc � ⇥� � ⇤ N lat ( x ) = S u S d x C � 5 S u 0 x x -0.5 ⇤ ) 2 ] ⇥ exp ( � w 2 � S at-rest = exp[ � w 2 k 2 -1 4 ( i � lat ) -1.5 -2 2 4 1.5 1 y 0.5 0 reduced overlap with boosted WF -0.5 -1 2 x 1.5 1 0.5 -1.5 0 -0.5 -1 -2 -1.5 -2 Optimize smearing for boosted nucleon states 
 k x [orig. B.Musch] S boosted = exp[ � w 2 4 ( i � ⇤ � � k 0 ) 2 ] k y � ⇥ exp ( � w 2 � ( k lat � � 0 k 0 ) 2 k 0 ) 4 RQCD results for spectrum [G. Bali et al, arXiv:1602.05525] This Proposal ( CONN3PT ): continued study !'#$ of nucleon structure with boosted sources 
 34//#!55 97:;#!<=>/# 678#!55 ?@;;=9,!<=>/# !' m π =320 , 190 MeV with a=0.114, a=0.081 fm 0&1&1&2 !&#$ In Breit frame: !& 0&1&1(2 periodic BC ) ! *+,- k min ) 2 = 4 . 2 . . . 8 . 2GeV 2 opt = (6 � Q 2 0%1%1%2 !%#$ antiperiodic (twisting) 0"1"1"2 0&1(1(2 k min ) 2 = 1 . 1 . . . 2 . 1GeV 2 opt = (6 � Q 2 !% 0%1%1(2 0"1"1(2 + Include disconnected diagrams ( DISCO ) 
 !"#$ 0(1(1(2 Motivation : JLab @12 GeV will measure proton, !" 0"1(1(2 0%1(1(2 neutron form factors up to Q 2 = 12..18 GeV 2 !( !(#$ !" !"#$ !% !%#$ !& !&#$ ./.*+,- M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

Signal Gain : Traditional vs. Boosted Smearing Nucleon Effective Energy: m π = 320 MeV, a=0.081 fm, 32 3 x64 1 . 6 1 . 6 p 2 = 0 . 000 [0 0 0] p 2 = 0 . 000 [0 0 0] ~ boosted [0 0 3]+[0 0 -3] ~ boosted [0 0 3]+[0 0 -3] p 2 = 0 . 196 [0 0 1] p 2 = 0 . 196 [0 0 1] boosted [0 0 3]+[0 0 -2] boosted [0 0 3]+[0 0 -2] ~ ~ p 2 = 0 . 393 [0 0 2] p 2 = 0 . 393 [0 0 2] boosted [0 0 3]+[0 0 -1] boosted [0 0 3]+[0 0 -1] 1 . 4 ~ 1 . 4 ~ p 2 = 0 . 589 [0 0 3] p 2 = 0 . 589 [0 0 3] boosted [0 0 3]+[0 0 0] boosted [0 0 3]+[0 0 0] ~ ~ 1 . 2 1 . 2 E eff ( t ) E eff ( t ) 1 . 0 1 . 0 0 . 8 0 . 8 0 . 6 0 . 6 0 . 4 0 . 4 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 t t w=4.96 (N=40) w=6.56 (N=70) Gaussian smearing each quark is boosted with the same k=[0 0 1] [SNS, Lattice 2016] w=5.55 (N=45) chosen for preliminary structure study M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

Q 2 Dependence of F 1u and F 1d 6 T = 8 a T = 8 a 1 . 4 T = 9 a T = 9 a T = 10 a T = 10 a summ 5 summ 2-exp fit 1 . 2 2-exp fit 1 . 0 4 Q 4 F U Q 4 F D 0 . 8 1 1 3 0 . 6 2 0 . 4 1 0 . 2 PRELIMINARY PRELIMINARY 0 0 . 0 0 2 4 6 8 10 0 2 4 6 8 10 Q 2 [GeV 2 ] Q 2 [GeV 2 ] expect F 1 (Q 2 )~ Q 4 scaling [Lepage, Brodsky (1979)] [SNS, Lattice 2016] Both form factors overshoot experiment (x3-4) M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

Q 2 Dependence of F 1u and F 1d u quark d quark 6 T = 8 a T = 8 a 1 . 4 T = 9 a T = 9 a T = 10 a T = 10 a summ 5 summ 2-exp fit 1 . 2 2-exp fit 1 . 0 4 Q 4 F U Q 4 F D 0 . 8 1 1 3 0 . 6 2 0 . 4 1 0 . 2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 PRELIMINARY PRELIMINARY 1.0 0 u quark 0 . 0 0 2 4 6 8 10 0 2 4 6 8 10 q 1 Q 2 [GeV 2 ] Q 2 [GeV 2 ] F 4 Q 0.5 [G.D.Cates, C.W.de Jager, d quark 2.5 " S.Riordan, B.Wojtsekhovski, 0.0 PRL106:252003, arXiv:1103.1808] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 2 2 Q [GeV ] expect F 1 (Q 2 )~ Q 4 scaling [Lepage, Brodsky (1979)] [SNS, Lattice 2016] Both form factors overshoot experiment (x3-4) M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017 1.0

Q 2 F 2 /F 1 for Proton 6 T = 8 a T = 9 a T = 10 a 5 summ 2-exp fit 4 2 /F P 1 3 Q 2 F P 2 1 PRELIMINARY 0 0 2 4 6 8 10 Q 2 [GeV 2 ] expect Q 2 F 1 (Q 2 )/F 2 (Q 2 ) ~ log[ Q 2 / Λ 2 ] scaling 
 [Belitsky, Ji, Yuan (2003)] Qualitative behavior of F1u, F1d agrees with phenomenology [SNS, Lattice 2016] M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017

Q2F2/F1, Comparison to pQCD scaling 6 a=0.081 fm a=0.114 fm 5 4 6 S 2 /F P n 1 2 S 4 p 3 Q 2 F P 2 1 BJY - pQCD (2003) 2 2 0 1 2 3 4 5 6 7 8 [G.D.Cates, C.W.de Jager, 2 2 Q [GeV ] 1 S.Riordan, B.Wojtsekhovski, PRL106:252003, arXiv:1103.1808] PRELIMINARY 0 0 2 4 6 8 10 Q 2 [GeV 2 ] expect Q 2 F 1 (Q 2 )/F 2 (Q 2 ) ~ log[ Q 2 / Λ 2 ] scaling 
 [Belitsky, Ji, Yuan (2003)] Qualitative behavior of F1u, F1d agrees with phenomenology [SNS, Lattice 2016] M.Engelhardt(PI), LHPc Nucleon Structure with Wilson Clover Fermions USQCD Meeting, JLab, Apr 28-30, 2017