The flavor structure of nucleon sea from lattice QCD
Jiunn-Wei Chen National Taiwan U.
Collaborators: Saul D. Cohen, Tomomi Ishikawa, Xiangdong Ji, Luchang Jin, Huey-Wen Lin, Peng Sun, Yi-Bo Yang, Jianhui Zhang, Yong Zhao (LP3)
arXiv: 1402.1462 + 1603.06664 + 1609.08102 + 1702.00008 + 1706.01295 + 1708.05301+1710.01089
Feynman’s Parton Model
The momentum distributions of partons (quarks, antiquarks and gluons) become one dimensional distributions in the infinite
momentum frame.
Measuring Parton Distributions Using DIS experiments
Parton Distribution Function (PDF) in QCD
Parton Distribution Function (PDF) in QCD
The struck parton moves on a light cone at the leading order in the twist-expansion.
Current Status of Proton PDFs
How do momentum and spin distribute among partons?
• Exp: 1d mom. dist. largely mapped out (up to parameterizations of the functional forms);
largest sys. uncertainty in Higgs production.
improve 1d(spin)+3d: BNL, JLab, J-PARC, COMPASS, GSI, EIC, LHeC, ...
• Theory: Only first few moments could be computed directly from QCD!!!
PDFs from QCD---why is it so hard?
• Quark PDF in a proton:
• Non-perturbative, infinite dof, need lattice QCD
• Euclidean lattice: light cone operators cannot be distinguished from local operators
• Moments of PDF given by local twist-2
operators (twist = dim - spin); limited to first few moments but carried out successfully
.
Beyond the first few moments
• Smeared sources: Davoudi & Savage
• Gradient flow: Monahan & Orginos
• Current-current correlators: K.-F. Liu & S.-J.
Dong; Braun & Müller; Detmold & Lin;
QCDSF
• Xiangdong Ji (Phys. Rev. Lett. 110 (2013) 262002): quasi-PDF: computing the x
-dependence directly. (variation: pseudo-PDF, Radyushkin)
.
Ji’s idea
• Quark PDF in a proton:
• Boost invariant in the z-direction, rest frame OK
• Quark bilinear op. always on the light cone
• What if the quark bilinear is slightly away from the light cone (space-like) in the proton rest
frame?
• Then one can find a frame where the quark bilinear is of equal time but the proton is moving.
• Then one can find a frame where the quark bilinear is of equal time but the proton is moving.
d c
-1
b
H-g, bgL
z
t
• Then one can find a frame where the quark bilinear is of equal time but the proton is moving.
• Analogous to HQET: need power corrections &
matching---LaMET (Large Momentum Effective Theory)
Review: Ji’s LPDF (LaMET)
• Taylor expansion yields
op. symmetric but not traceless .
Review: Ji’s LPDF (LaMET)
• LHS: trace, twist-4
corrections, parametrized in this work
• RHS: trace
• One loop matching , OPE
What do we expect to see on the lattice?
• Suppose LPDF were the CTEQ PDF at
in the Fourier Space
First (isovector) LPDF Computation
• Lattice:
• Fermions: MILC highly improved staggered quarks (HISQ) Clover (valence)
• Gauge fields/links: hypercubic (HYP) smearing, 461 config.
• n = 1,2,3…
(high momentum smearing: Bali, Lang, Musch, Schafer)
Quasi-PDF (unpolarized)
n = 1, 2, 3.
Corrections
• Computed to all orders in
•
Corrections
• Twist-4:
Parameterized ( ) Additional complications? E.g.
Radyushkin
RG of Wilson Coefficient
Xiong, Ji, Zhang, Zhao (GPD: Ji, Schafer, Xiong, Zhang;
Xiong, Zhang) Factorization (Ma, Qiu; Li), Linear
divergence & LPT (Ishikawa, Ma, Qiu, Yoshida; JWC, Ji, Zhang; Xiong, Luu, Meissner; Rossi, Testa; Constantinou et al.), RI (Monahan & Orginos; Yong & Stewart;
Constantinou et al.), NPR(Constantinou et al.; LP3; Ji,
Zhang, Zhao; Ishikawa, Ma, Qiu, Yoshida; Green, Jansen, Steffens), E vs. M spaces (Carlson et al.; Briceno et al.)
Quasi-PDF (green) w/ loop (red) w/ loop + mass (blue)
n = 2 (upper) & 3
Unpolarized Isovector Proton PDF
Quark mass effect!
Follow-up works
(Alexandrou et. al.:1504.07455+1610.03689)
Isovector Proton Helicity and Transversity
(Alexandrou et.al., 1609.00172)
Isovector Proton Helicity
Isovector Proton Transversity
χQSM KPSY15 RCBG15 Lattice
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0
0 0.2 0.4 0.6 0.8
x
x(δu-δd)
.
More on the power divergence in
the matching kernel
.
Improved Quasi-PDF’s
(Ishikawa, Ma, Qiu, Yoshida; JWC, Ji, Zhang)
.
Improved Quasi-PDF’s
(Ishikawa, Ma, Qiu, Yoshida; JWC, Ji, Zhang)
All orders (Ji, Zhang, Zhao;
Ishikawa, Ma, Qiu, Yoshida)
NPR(RI/MOM)+1loop matching
LP3, 1706.01295
NPR w/o Pz corrections
Green, Jansen, Steffens, 1707.07152
Out[74]=
-3 -2 -1 1 2 3 x
0.5 1.0 1.5 2.0
fu-dHxL
Importance of the Long Tail
-3 -2 -1 1 2 3 x 0.5
1.0 1.5 2.0 2.5
fu-dHxL
1708.05301(LP3) attempts to address the long tail issue, physical pion mass (also 1710.6408 EMTC)
Outlook
• Further tests (non-singlet): long tail (L Pz large by taking Pz large? small x: large Nz); wee
partons (smaller quark mass); factorization proof.
Know whether it works within 5 years (~20%)?
• Singlet PDF’s: s, c, b and gluons Additional 3-5 yrs?
• If it works, complimentary to exp.: PDF (isov.
sea, small and large x’s, non-valence partons), DA, GPD, TMD …
Backup slides
Pion Light Cone DA-
Zhang, JWC, Ji, Jin, LinLaMET Param 1 Param 2 DSE Asymp
-1.0 -0.5 0.0 0.5 1.0 1.5
0.0 0.5 1.0 1.5
x ϕπ
No leading chiral log
JWC, Iain W. Stewart, Phys.Rev.Lett. 92 (2004) 202001
Comments on Radyushkin’s Pseudo-PDF
d c
-1
b
H-g, bgL
z t
Little z dependence
(Orginos, Radyushkin, Karpie, Zafeiropoulos)
Similar but could be complementary to quasi-PDF. Watch out the long tail.
Improved Quasi-PDF’s
Ishikawa, Ma, Qiu, Yoshida: x-space JWC, Ji, Zhang: p-space
.
Stewart & Zhang: NP RI/MOM renorm.
+ one-loop RI/MOM MS-bar matching
Helicity and Transversity
(isovector)
Quasi-PDF (Helicity and Transversity)
n = 1, 2, 3.
Quasi-PDF (green) w/ loop (red) w/ loop + mass (blue)
n = 2 (upper) & 3
