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Resumming Quark's Longitudinal Momentum Logarithms in LaMET Expansion of Lattice PDFs
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abstract
In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum ($p_z$) of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence through resumming logarithms of the type $\ln^n p_z/\mu$ in the matching coefficient, where $\mu$ is a fixed renormalization scale. The result enhances the accuracy of the expansion at moderate $p_z>1$ GeV, and at the same time, clearly shows that the partons cannot be approximated from quarks with $p_z\sim \Lambda_{\rm QCD}$ which are not predominantly collinear with the parent hadron momentum, consistent with power counting of the large-momentum effective theory. The same physics mechanism constrains the coordinate space expansion at large distances $z$, the conjugate of $p_z$, as illustrated in the example of fitting the moments of the PDFs.
Forward citations
Cited by 4 Pith papers
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Parton physics from a heavy-quark operator product expansion: Lattice QCD calculation of the fourth moment of the pion distribution amplitude
The fourth Mellin moment of the pion distribution amplitude is determined in the continuum limit for the first time in quenched QCD, giving <ξ^4> = 0.039(28)(11) at μ = 2 GeV.
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Resummation for Lattice QCD Calculation of Generalized Parton Distributions at Nonzero Skewness
A threshold factorization and resummation scheme for quasi-GPD matching in LaMET is derived and shown to be self-consistent on a GPD model.
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Unpolarized gluon PDF of the nucleon from lattice QCD at physical point in the continuum limit
A lattice QCD extraction of the nucleon gluon PDF using three lattice spacings, hybrid renormalization and NLO matching, extrapolated to the continuum and infinite-momentum limits, agrees with global fits while remain...
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Mapping Parton Distributions of Hadrons with Lattice QCD
A review of lattice QCD methods and results for x-dependent parton distribution functions and generalized parton distributions of hadrons.
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