We present a stateoftheart calculation of the unpolarized pion valencequark distribution in the framework of largemomentum effective theory (LaMET) with improved handling of systematic errors as well as twoloop perturbative matching. We use lattice ensembles generated by the MILC collaboration at lattice spacing
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A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions xB → 0 and xB → 1. The extrapolated F2 ratio as quark momentum fraction xB → 1 is Fn 2 F p 2 → 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio when xB → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At highxB, the proton quark distribution function ratio d/u is derived from the F2 ratio and found to be d/u → 1/6. Our extrapolated values for both the Fn 2 F p 2 ratio and the d/u parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a DysonSchwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. One such example is nucleon wave functions composed of a linear combination of a quarkdiquark state and a threevalence quark correlated state with coefficients that combine to give the extrapolated F2 ratio at xB = 1.
A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio
data in the quark momentum fraction regions xB → 0 and xB → 1. The extrapolated F2 ratio as quark momentum
fraction xB → 1 is Fn
2
F p
2
→ 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio
when xB → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low
momentum fraction. At highxB, the proton quark distribution function ratio d/u is derived from the F2 ratio
and found to be d/u → 1/6. Our extrapolated values for both the Fn
2
F p
2
ratio and the d/u parton distribution
function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation
arguments, and a DysonSchwinger equation with a contact interaction model. In addition, it is possible to match
the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously
in the nucleon wave function. One such example is nucleon wave functions composed of a linear combination
of a quarkdiquark state and a threevalence quark correlated state with coefficients that combine to give the
extrapolated F2 ratio at xB = 1.
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 Award ID(s):
 2012413
 NSFPAR ID:
 10475807
 Publisher / Repository:
 PRC
 Date Published:
 Journal Name:
 Physical Review C
 Volume:
 107
 Issue:
 6
 ISSN:
 24699985
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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