arXiv 2410.080892024-10-10hep-ph

QCD中的四圈分裂函数——胶子-胶子情形——

Four-loop splitting functions in QCD -- The gluon-gluon case --

G. Falcioni, F. Herzog, S. Moch, A. Pelloni, A. Vogt

备注：: 15 pages, LaTeX, 3 figures, 2 ancillary files (FORM file with results and FORTRAN subroutine). arXiv admin note: text overlap with arXiv:2404.09701

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AI总结：

通过离壳算符矩阵元重整化计算了微扰QCD第四阶胶子-胶子分裂函数P_{gg}的偶数N矩(N<=20)，构建了改进的四圈P_{gg}(x)近似，并证明N^3LO贡献在x>=10^-4时不超过1%。

摘要：

我们通过离壳算符矩阵元的重整化，在微扰QCD的第四阶计算了胶子-胶子分裂函数 P_{gg} 的偶数 N 矩 N <= 20。我们的结果是对一般紧致单李群解析推导得出的，与迄今为止针对该函数获得的所有结果一致，特别是与通过深度非弹性散射中的结构函数获得的最低五个矩一致。利用我们的新矩和所有可用的端点约束，我们构建了四圈 P_{gg}(x) 的改进近似，这应足以满足广泛的碰撞机物理应用。由这些以及相应的夸克到胶子分裂函数产生的对胶子分布标度导数的 N^3LO 贡献，在 alpha_s = 0.2 的标准参考尺度下，当 x >= 10^{-4} 时为 1% 或更小。

英文摘要：

We have computed the even-N moments N =< 20 of the gluon-gluon splitting function P_{gg} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop P_{gg}(x) that should be sufficient for a wide range of collider-physics applications. The N^3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1% or less at x >~ 10^{-4} at a standard reference scale with alpha_s = 0.2.

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