大型强子对撞机（LHC）上顶夸克-反顶夸克对伴随W玻色子（t\bar{t}W）产生的双圈量子色动力学（QCD）振幅：领头色近似下的研究
Two-loop QCD amplitudes for $t\bar{t}W$ production at the LHC in the leading-colour approximation
AI总结：
该研究在领头色近似下数值计算LHC上t\bar{t}W产生的双圈QCD振幅，采用混合框架处理奇点与抵消项，经验证后提供对应硬函数用于相关QCD修正计算。
AI中文摘要：
我们在推广的领头色近似下，对大型强子对撞机（LHC）上顶夸克-反顶夸克对伴随W玻色子（t\bar{t}W）产生的双圈量子色动力学（QCD）散射振幅进行了数值计算，保留了顶夸克和W玻色子质量的精确依赖关系。我们未采用完全解析计算，而是采用了混合框架，将数值评估与强大的代数和解析控制相结合，可精确处理紫外和红外奇点以及中间的大抵消项。这通过将有限余项表示为一组带有有理系数的特殊函数来实现。这些特殊函数通过幂级数展开求解微分方程进行数值评估，而有理系数的值则通过有限场评估逐点重构。计算在't Hooft-Veltman方案中进行，并通过采用完全不同计算策略的常规维数正规化独立实现进行了验证。我们最终提供了色和极化求和后的硬函数，该函数在之前计算t\bar{t}W截面的次领头阶QCD修正时使用的相空间网格上进行了评估。
英文摘要：
We present a numerical computation of the two-loop QCD scattering amplitudes for the production of a top-antitop quark pair in association with a $W$ boson ($t\bar{t}W$) at the LHC in the generalised leading-colour approximation, retaining the exact dependence on the top-quark and $W$-boson masses. Rather than pursuing a fully analytic calculation, we employ a hybrid framework that combines numerical evaluation with strong algebraic and analytic control, allowing ultraviolet and infrared singularities as well as large intermediate cancellations to be treated exactly. This is achieved by expressing the finite remainder in terms of a set of special functions with rational coefficients. The special functions are evaluated numerically by solving differential equations through power-series expansions, while the values of the rational coefficients are reconstructed, point by point, from finite-field evaluations. The calculation is performed in the 't Hooft-Veltman scheme and validated against an independent implementation in conventional dimensional regularisation employing a substantially different computational strategy. We finally provide the colour- and polarisation-summed hard functions evaluated on the phase-space grid used in a previous computation of the next-to-next-to-leading-order QCD corrections to the $t\bar{t}W$ cross section.
