flavor structure of the nucleon sea from lattice qcd jiunn-wei chen national taiwan u....
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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
• 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…
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?