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<p>We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a <i>W</i> boson at hadron colliders in the leading colour approximation. These Feynman integrals also contribute to Higgs or <i>Z</i>-boson production in association with a top pair. We employ the method of differential equations (DEs), facilitated by the use of finite field methods to handle the algebraic complexity stemming from the seven-scale kinematics. The presence of the top quark in the virtual propagators, in addition to the mass of the external <i>W</i> boson, gives rise to nested square roots and three elliptic curves. We obtain DEs that depend at most quadratically on the dimensional regulator <i>ϵ</i> for sectors where these analytic structures appear, and are <i>ϵ</i>-factorised otherwise. We express the DEs in terms of a minimal set of differential one-forms, separating the logarithmic ones. We solve the DEs numerically in the physical kinematic region, with the method of generalised power series expansions.</p>

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Two-loop Feynman integrals for leading colour \( t\overline{t}W \) production at hadron colliders

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月1日

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  • Matteo Becchetti,
  • Dhimiter Canko,
  • Vsevolod Chestnov,
  • Tiziano Peraro,
  • Mattia Pozzoli,
  • Simone Zoia

摘要

We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a W boson at hadron colliders in the leading colour approximation. These Feynman integrals also contribute to Higgs or Z-boson production in association with a top pair. We employ the method of differential equations (DEs), facilitated by the use of finite field methods to handle the algebraic complexity stemming from the seven-scale kinematics. The presence of the top quark in the virtual propagators, in addition to the mass of the external W boson, gives rise to nested square roots and three elliptic curves. We obtain DEs that depend at most quadratically on the dimensional regulator ϵ for sectors where these analytic structures appear, and are ϵ-factorised otherwise. We express the DEs in terms of a minimal set of differential one-forms, separating the logarithmic ones. We solve the DEs numerically in the physical kinematic region, with the method of generalised power series expansions.