<p>The associated production of a photon and a top-antitop quark pair <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mfenced close=")" open="("> <mrow> <mi>t</mi> <mover accent="true"> <mi>t</mi> <mo stretchy="true">¯</mo> </mover> <mi>γ</mi> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ \left(t\overline{t}\gamma \right) $</EquationSource> </InlineEquation> is important for measuring the top-quark charge and probing the top-photon interaction, and it requires improved theoretical predictions. We focus on the calculation of two-loop amplitudes for <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>t</mi> <mover accent="true"> <mi>t</mi> <mo stretchy="true">¯</mo> </mover> <mi>γ</mi> </math></EquationSource> <EquationSource Format="TEX">$ t\overline{t}\gamma $</EquationSource> </InlineEquation> production at hadron colliders. The infrared singularities with full top-quark mass dependence are derived from universal anomalous dimensions combined with one-loop massive amplitudes expanded to higher orders in the dimensional regulator <i>ϵ</i>. The finite remainders are approximated in the high-energy boosted limit using the mass-factorization formula. To validate our approach, we compare approximate one-loop amplitudes up to <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>ϵ</mi> <mn>2</mn> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{O}\left({\epsilon}^2\right) $</EquationSource> </InlineEquation>, as well as the two-loop infrared poles, against our exact results. The results in this paper serve as an important step toward next-to-next-to-leading order predictions for <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mi>t</mi> <mover accent="true"> <mi>t</mi> <mo stretchy="true">¯</mo> </mover> <mi>γ</mi> </math></EquationSource> <EquationSource Format="TEX">$ t\overline{t}\gamma $</EquationSource> </InlineEquation> production.</p>

Two-loop QCD amplitudes for $ t\overline{t}\gamma $ production at hadron colliders

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2026年4月1日

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Guoxing Wang,
Li Lin Yang

摘要

The associated production of a photon and a top-antitop quark pair $(t \bar{t} γ)$ $ \left(t\overline{t}\gamma \right) $ is important for measuring the top-quark charge and probing the top-photon interaction, and it requires improved theoretical predictions. We focus on the calculation of two-loop amplitudes for $t \bar{t} γ$ $ t\overline{t}\gamma $ production at hadron colliders. The infrared singularities with full top-quark mass dependence are derived from universal anomalous dimensions combined with one-loop massive amplitudes expanded to higher orders in the dimensional regulator ϵ. The finite remainders are approximated in the high-energy boosted limit using the mass-factorization formula. To validate our approach, we compare approximate one-loop amplitudes up to $O (ϵ^{2})$ $ \mathcal{O}\left({\epsilon}^2\right) $ , as well as the two-loop infrared poles, against our exact results. The results in this paper serve as an important step toward next-to-next-to-leading order predictions for $t \bar{t} γ$ $ t\overline{t}\gamma $ production.

Two-loop QCD amplitudes for \( t\overline{t}\gamma \) production at hadron colliders

摘要