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arXiv 2408.13486hep-ph
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重介子准分布振幅的幂次修正

Power corrections to quasi-distribution amplitudes of a heavy meson

Chao Han, Wei Wang, Jia-Lu Zhang, Jian-Hui Zhang

AI总结:

本文系统计算了重介子准分布振幅匹配到 QCD LCDAs 过程中的质量幂次修正和 QCD 标度幂次修正,采用矩关系、领头扭度投影算符及重整子模型,数值分析表明修正通常小于 20%,为格点 QCD 精确提取重介子 LCDAs 提供了重要指导。

摘要:

最近的研究表明,在重夸克极限下定义的重介子光锥分布振幅(LCDAs),可以通过在格点上模拟具有大介子动量 $P^z$ 的准分布振幅来提取。这一提取过程包含两步。第一步,将准分布振幅在大 $P^z$ 极限下匹配到 QCD LCDAs。第二步,将 QCD LCDAs 匹配到 HQET 中定义的所需 LCDAs。在本工作中,我们给出了第一步中的 $m_H^{2n}/(P^z)^{2n}$ 和 $Λ_\ ext{QCD}^2/(P^z)^2$ 修正,其中 $m_H$ 为重介子质量。为了处理 $m_H^{2n}/(P^z)^{2n}$ 修正,我们采用了两种方法:能够提供任意阶质量修正的矩关系,以及给出领头阶质量修正的领头扭度投影算符。对于 $Λ_\ ext{QCD}^2/(P^z)^2$ 修正,我们采用了一个重整子模型来处理由微扰级数发散引起的重整子不确定性。我们采用两种 QCD LCDAs 参数化形式进行数值分析。结果表明,这些修正在大多数区域通常小于 20%,在精确分析中应当被包含在内。这些发现将为未来重介子 LCDAs 的研究提供有价值的指导,特别是在格点 QCD 背景下,考虑这些修正对于提高结果的准确性和可靠性至关重要。

英文摘要:

It has been recently demonstrated that lightcone distribution amplitudes (LCDAs) for a heavy meson, defined in the heavy quark limit, can be extracted by simulating quasi-distribution amplitudes on the lattice with a large meson momentum $P^z$. This extraction involves a two-step procedure. In the first-step, the quasi-distribution amplitudes are matched onto the QCD LCDAs in the large $P^z$ limit. In the second step, the QCD LCDAs are matched onto the desired LCDAs defined in HQET. In this work, we present the $m_H^{2n}/(P^z)^{2n}$ and $Λ_\text{QCD}^2/(P^z)^2$ corrections in the first step with $m_H$ being the heavy meson mass. To account for $m_H^{2n}/(P^z)^{2n}$ corrections, we employ two methods: the moment relation that can provide mass corrections to all orders, and a leading-twist projector that gives the leading-order mass corrections. For the $Λ_\text{QCD}^2/(P^z)^2$ corrections, we employ a renormalon model that addresses the renormalon ambiguity stemming from the divergence of the perturbative series. We adopt two parametrizations for QCD LCDAs to conduct a numerical analysis. The results suggest that these corrections are typically smaller than 20\% in most regions, and should be included in a precision analysis. These findings will serve as a valuable guide for future studies on heavy meson LCDAs, particularly in the context of Lattice QCD, where accounting for such corrections is crucial for improving the accuracy and reliability of the results.

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