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Dispersive derivation of the pion distribution amplitude
Physical Review D ( IF 5 ) Pub Date : 2022-08-12 , DOI: 10.1103/physrevd.106.034015
Hsiang-nan Li

We derive the dependence of the leading-twist pion light-cone distribution amplitude (LCDA) on a parton momentum fraction x by directly solving the dispersion relations for the moments with inputs from the operator product expansion (OPE) of the corresponding correlation function. It is noticed that these dispersion relations must be organized into those for the Gegenbauer coefficients first in order to avoid the ill-posed problem appearing in the conversion from the moments to the Gegenbauer coefficients. Given the values of various condensates in the OPE, we find solutions for the pion LCDA, which are convergent and stable in the Gegenbauer expansion. Moreover, the solution from summing contributions up to 18 Gegenbauer polynomials is smooth, and can be well approximated by a function proportional to xp(1x)p with p0.45 at the scale μ=2GeV. Turning off the condensates, we get the asymptotic form for the pion LCDA as expected. We then solve for the pion LCDA at a different scale μ=1.5GeV with the condensate inputs at this μ, and demonstrate that the result is consistent with the one obtained by evolving the Gegenbauer coefficients from μ=2GeV to 1.5 GeV. That is, our formalism is compatible with the QCD evolution. The strength of the above framework that goes beyond analyses limited to only the first few moments of a LCDA in conventional QCD sum rules is highlighted. The precision of our results can be improved systematically by including higher-order and higher-power terms in the OPE.

中文翻译:

介子分布幅度的色散推导

我们推导出前扭转π介子光锥分布幅度(LCDA)对部分子动量分数的依赖性X通过使用相应相关函数的算子乘积展开 (OPE) 的输入直接求解矩的离散关系。需要注意的是,为了避免矩量到格根鲍尔系数的转换中出现不适定问题,必须首先将这些色散关系组织成格根鲍尔系数。给定 OPE 中各种冷凝物的值,我们找到了 pion LCDA 的解,它们在 Gegenbauer 展开中收敛且稳定。此外,对多达 18 个 Gegenbauer 多项式的贡献求和的解是平滑的,并且可以通过与Xp(1-X)pp0.45在规模μ=2锗钒. 关闭冷凝物,我们得到了π介子 LCDA 的渐近形式,如预期的那样。然后我们求解不同尺度的介子 LCDAμ=1.5锗钒与冷凝水输入在此μ, 并证明该结果与通过将 Gegenbauer 系数从μ=2锗钒至 1.5 GeV。也就是说,我们的形式主义与 QCD 演化兼容。上述框架的强度超出了传统 QCD 总和规则中仅限于 LCDA 前几个时刻的分析。通过在 OPE 中包含高阶和高幂项,可以系统地提高我们结果的精度。
更新日期:2022-08-12
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