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<p>We compute the soft function at NLO and NNLO for a one-parameter family of event shapes we call C-angularity. This family contains C-parameter as a specific choice of the parameter, in close analogy with how conventional angularity contains thrust as a special case. By construction, C-angularity and angularity coincide in the collinear limit such that the anomalous dimensions are equal. However, unlike angularity, C-angularity is a continuously differentiable function of the final state momenta, which makes the analytic calculation of the C-angularity soft function simpler. We obtain analytical results for the C-angularity soft function and anomalous dimension as an expansion in the C-angularity parameter <i>a</i>, to third and fourth order in <i>a</i> respectively. These expansions yield results that are accurate at the few per mille level for −1 ≤ <i>a</i> &lt; 1.</p>

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Analytical results for the C-angularity soft function at NNLO

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月21日

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  • Alexander Bennett,
  • Emmet P. Byrne,
  • Jonathan R. Gaunt,
  • Elsa C. Lang

摘要

We compute the soft function at NLO and NNLO for a one-parameter family of event shapes we call C-angularity. This family contains C-parameter as a specific choice of the parameter, in close analogy with how conventional angularity contains thrust as a special case. By construction, C-angularity and angularity coincide in the collinear limit such that the anomalous dimensions are equal. However, unlike angularity, C-angularity is a continuously differentiable function of the final state momenta, which makes the analytic calculation of the C-angularity soft function simpler. We obtain analytical results for the C-angularity soft function and anomalous dimension as an expansion in the C-angularity parameter a, to third and fourth order in a respectively. These expansions yield results that are accurate at the few per mille level for −1 ≤ a < 1.