Flavor Structure of the Nucleon Sea from Lattice QCD

Jiunn-Wei Chen

National Taiwan U.

Collaborators: Huey-Wen Lin, Saul D. Cohen, Xiangdong Ji

arXiv: 1402.1462

Lattice PDF: from Moments to the Sea

• Quark PDF in a proton:

• Euclidean lattice: light cone operators cannot be distinguished from local operators

• Moments of PDF given by ME of local twist-2 operators; LPDF limited to first few moments; Sea quarks cannot be isolated

• until X. Ji’s proposal came alone in 2013…

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Review: PDF

• Quark PDF in a proton:

• Taylor expansion yields symmetric traceless twist-2 operators:

• 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.

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Review: Ji’s LPDF

• Taylor expansion yields

op. symmetric but not traceless

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Review: Ji’s LPDF

• LHS: trace, twist-4 corrections

• RHS: trace • One loop matching• an OPE.

What do we expect to see on the lattice?

• Suppose LPDF is 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…

Corrections

• Twist-4:

Parameterized

Corrections

• Computed to all orders in• Each moment rescaled by a factor

RG of Wilson Coefficient

• Relates . of different and

One loop matching

• If is not a smooth limit, then additional operator has to be added to match the theories with infinite or finite

• This could be due to the limits of taking the transverse momentum cut-off and the longitudinal momentum to infinity do not commute.

• One loop matching of the non-singlet case suggests the limit is smooth (Xiong, Ji, Zhang, Zhao)

One loop matching

• Daughter parton’s momentum can be larger than the mother’s at finite . Thus, can be of any value, not bounded by unity. Only

is possible and the limit is smooth. • This also helps to regularize the double pole in the kernel. • Still need to match to scheme and do lattice perturbation (with the

smeared action; gauge fixing breaks gauge symmetry?)

Procedures

• Stepwise evolution with small steps

• Correcting for effect (to all orders)

• Extrapolating the effect

Quark mass effect!

Detmold, Melnitchouk, Thomas (2001)

Outlook

• Wee partons, a good test to this approach---smaller quark mass

• If it works, lots of things to do: LCW, PDF, GPD, TMD (maybe)…

• Boosting a problem w/ finite T?

• Observables related to new physics search at LHC? Jet physics?