Transcript 投影片 1 - University of Adelaide
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…
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.
Review: Ji’s LPDF
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• Taylor expansion yields op. symmetric but not traceless
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…
• Twist-4:
Corrections
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?