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<p>We present the analytic results for the non-singlet contributions to the three-loop mixed strong-electroweak <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <mrow> <msubsup> <mi>α</mi> <mi>s</mi> <mn>2</mn> </msubsup> <mi>α</mi> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({\alpha}_s^2\alpha \right) \)</EquationSource> </InlineEquation> virtual corrections to the quark form factors. The primary challenge of this computation arises from the presence of massive vector bosons within the loops. This significantly increases the complexity of the integration-by-parts reduction of the scalar integrals and complicates their evaluation via the method of differential equations. To obtain the physical results, we perform the appropriate ultraviolet renormalization and subtract the universal infrared divergences. The resulting finite remainders are expressed in terms of Harmonic Polylogarithms and Generalized Polylogarithms.</p>

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\( \mathcal{O}\left({\alpha}_s^2\alpha \right) \) corrections to quark form factor

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月19日

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  • Tanmoy Pati,
  • Narayan Rana,
  • V. Ravindran

摘要

We present the analytic results for the non-singlet contributions to the three-loop mixed strong-electroweak O α s 2 α \( \mathcal{O}\left({\alpha}_s^2\alpha \right) \) virtual corrections to the quark form factors. The primary challenge of this computation arises from the presence of massive vector bosons within the loops. This significantly increases the complexity of the integration-by-parts reduction of the scalar integrals and complicates their evaluation via the method of differential equations. To obtain the physical results, we perform the appropriate ultraviolet renormalization and subtract the universal infrared divergences. The resulting finite remainders are expressed in terms of Harmonic Polylogarithms and Generalized Polylogarithms.