In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum () of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence through resumming logarithms of the type in the matching coefficient, where μ is a fixed renormalization scale. The result enhances the accuracy of the expansion at moderate GeV, and at the same time, clearly shows that the partons cannot be approximated from quarks with 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 , as illustrated in the example of fitting the moments of the PDFs.
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"full_name": "Su, Yushan",
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"affiliations": [
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"country": "USA",
"value": "Department of Physics, University of Maryland, College Park, USA"
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{
"country": "USA",
"value": "Center for Frontier Nuclear Science, Stony Brook University, Stony Brook, USA"
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"surname": "Holligan",
"email": "jeholligan@gmail.com",
"full_name": "Holligan, Jack",
"given_names": "Jack"
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"affiliations": [
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"country": "USA",
"value": "Department of Physics, University of Maryland, College Park, USA"
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"surname": "Ji",
"email": "xji@umd.edu",
"full_name": "Ji, Xiangdong",
"given_names": "Xiangdong"
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"affiliations": [
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"country": "China",
"value": "Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, China"
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"surname": "Yao",
"email": "feiyao@mail.bnu.edu.cn",
"full_name": "Yao, Fei",
"given_names": "Fei"
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"affiliations": [
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"country": "Hong Kong",
"value": "School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China"
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{
"country": "China",
"value": "Center of Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing, China"
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"surname": "Zhang",
"email": "zhangjianhui@cuhk.edu.cn",
"full_name": "Zhang, Jian-Hui",
"given_names": "Jian-Hui"
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"affiliations": [
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"country": "USA",
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"surname": "Zhang",
"email": "rayzhang@umd.edu",
"full_name": "Zhang, Rui",
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"source": "Elsevier",
"title": "Resumming quark's longitudinal momentum logarithms in LaMET expansion of lattice PDFs"
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"value": "In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum (<math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub></math>) of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence through resumming logarithms of the type <math><msup><mrow><mi>ln</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>\u2061</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>/</mo><mi>\u03bc</mi></math> in the matching coefficient, where \u03bc is a fixed renormalization scale. The result enhances the accuracy of the expansion at moderate <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>></mo><mn>1</mn></math> GeV, and at the same time, clearly shows that the partons cannot be approximated from quarks with <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>\u223c</mo><msub><mrow><mi>\u039b</mi></mrow><mrow><mi>QCD</mi></mrow></msub></math> 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 <math><msub><mrow><mi>p</mi></mrow><mrow><mi>z</mi></mrow></msub></math>, as illustrated in the example of fitting the moments of the PDFs."
}
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