### 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*(δ*u*-*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

*f** _{u-d}*HxL

### Importance of the Long Tail

-3 -2 -1 1 2 3 *x*
0.5

1.0 1.5 2.0 2.5

*f** _{u-d}*HxL

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