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<p>Large-momentum effective theory (LaMET) provides an approach to directly calculate the <i>x</i>-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton’s momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness <i>ξ</i> is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for [−1 + <i>x</i><sub>0</sub><i>,</i> −<i>ξ</i> − <i>x</i><sub>0</sub>] ∪ [−<i>ξ</i> + <i>x</i><sub>0</sub><i>, ξ</i> − <i>x</i><sub>0</sub>] ∪ [<i>ξ</i> + <i>x</i><sub>0</sub><i>,</i> 1 − <i>x</i><sub>0</sub>], where <i>x</i><sub>0</sub> is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.</p>

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Resummation for lattice QCD calculation of generalized parton distributions at nonzero skewness

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月24日

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  • Jack Holligan,
  • Huey-Wen Lin,
  • Rui Zhang,
  • Yong Zhao

摘要

Large-momentum effective theory (LaMET) provides an approach to directly calculate the x-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton’s momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness ξ is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for [−1 + x0, −ξ − x0] ∪ [−ξ + x0, ξ − x0] ∪ [ξ + x0, 1 − x0], where x0 is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.