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One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions

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arxiv 2204.08343 v4 pith:2VEKSM2L submitted 2022-04-18 hep-lat

Chien-Yu Chou , Jiunn-Wei Chen This is my paper · ORCID
classification hep-lat
keywords schemematchingpartonrenormalizationdistributiondistributionsfunctionshadrons
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Large momentum effective theory allows extraction of hadron parton distribution functions in lattice QCD by matching them to quark bilinear matrix elements of hadrons with large momenta. We calculate the matching kernels for the unpolarized, helicity, and transversity isovector parton distribution functions and skewless generalized parton distributions of all hadrons in the hybrid-RI/MOM scheme. This renormalization scheme uses RI/MOM when the Wilson line length is less then $z_s$, otherwise a mass subtraction scheme is used. By design, the non-hybrid scheme is recovered as $z_s \to \infty$. In the opposite limit, $z \to 0$, the self renormalization scheme is obtained. When the parameters $p_z^R=0$ and $\mu^R z_s \ll 1$, the hybrid-RI/MOM scheme coincides with the hybrid-ratio scheme times the charge of the PDF. We also discuss the subtlety related to the commutativity of Fourier transform and $\epsilon$ expansion in the $\bar{\text{MS}}$ scheme.

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Cited by 5 Pith papers

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  1. Light Cone Distribution Amplitude for the $\Lambda$ Baryon from Lattice QCD

    hep-lat 2024-11 conditional novelty 7.0 of 10

    The first lattice QCD extraction of the Lambda baryon's light-cone distribution amplitude via LaMET yields a momentum-fraction distribution peaked at small light-quark momenta.

  2. Isolating Scheme Dependence of Quasi-PDFs in the RI/MOM Scheme

    hep-ph 2026-07 accept novelty 5.0 of 10

    Two new finite renormalization schemes for quasi-PDFs cancel all RI/MOM reference-momentum dependence from the renormalized quasi-PDF, counterterm, and matching coefficient at one loop.

  3. Disentangling Scheme Dependence in Quasi-PDFs with a Transverse-Momentum Cutoff

    hep-ph 2026-07 accept novelty 5.0 of 10

    In the minimal TMC scheme, one-loop nonsinglet quasi-PDFs separate into explicit cutoff (and boundary UV) counterterms plus a remainder that carries the collinear IR pole and finite matching kernel.

  4. Conformal Mapping in Matching Quark Correlation Functions to Parton Distribution Functions

    hep-ph 2024-11 conditional novelty 4.0 of 10

    Conformal mapping of the Borel-transformed matching kernel reduces the scale-variation error band for quark correlation function to PDF matching by up to 40%.

  5. Mapping Parton Distributions of Hadrons with Lattice QCD

    hep-lat 2025-06 accept

    A review of lattice QCD methods and results for x-dependent parton distribution functions and generalized parton distributions of hadrons.

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