1. 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

2. 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….

3. 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.

4. 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..

5. Review: Ji’s LPDF Taylor expansion yields op. symmetric but not traceless.

6. Review: Ji’s LPDF LHS: trace, twist-4 corrections RHS: trace One loop matching an OPE.

7. What do we expect to see on the lattice? Suppose LPDF is the CTEQ PDF at

8. in the Fourier Space

9. 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…

11. Corrections Twist-4: Parameterized

12. Corrections Computed to all orders in Each moment rescaled by a factor

13. RG of Wilson Coefficient Relates. of different and

14. 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)

15. 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?)

16. Procedures Stepwise evolution with small steps Correcting for effect (to all orders) Extrapolating the effect

18. Quark mass effect!

19. Detmold, Melnitchouk, Thomas (2001)

21. 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?