We present the even-N moments N≤20 of the fourth-order (N3LO) contribution Pgq(3)(x) to the quark-to-gluon splitting function in perturbative QCD. These moments, obtained by analytically computing off-shell operator matrix elements for a general gauge group, agree with all known results, in particular with the moments N≤10 derived before from structure functions in deep-inelastic scattering. Using the new moments and the available endpoint constraints, we construct approximations for Pgq(3)(x) which improve upon those obtained from the lowest five even moments. The remaining uncertainties of this function are now practically irrelevant at momentum fractions x>0.1. The resulting errors of the convolution of Pgq at N3LO with a typical quark distribution are small at x≳10−3 and exceed 1% only at x≲10−4 for a strong coupling αs=0.2. The present results for Pgq(3)(x) should thus be sufficient for most collider-physics applications.

中文翻译：

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QCD 中的四环分裂函数——夸克到胶子的情况


我们提出了微扰 QCD 中夸克到胶子分裂函数的四阶 (N3LO) 贡献 Pgq(3)(x) 的偶 N 矩 N≤20。这些矩是通过分析计算一般规范组的离壳算子矩阵元素而获得的，与所有已知结果一致，特别是与之前从深度非弹性散射中的结构函数导出的矩 N≤10 一致。使用新的矩和可用的端点约束，我们构建了 Pgq(3)(x) 的近似值，该近似值改进了从最低五个偶数矩获得的近似值。该函数的其余不确定性现在实际上与动量分数 x>0.1 无关。 Pgq 在 N3LO 处与典型夸克分布的卷积所产生的误差在 x≳10−3 处很小，并且仅在 x≲10−4 处对于强耦合 αs=0.2 超过 1%。因此，目前 Pgq(3)(x) 的结果对于大多数对撞机物理应用来说应该足够了。