Subleading effects in soft-gluon emission at one-loop in massive QCD

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Abstract
A bstract: We provide the last missing ingredient necessary to approximate one-loop amplitudes in QCD with massive quarks in the limit of vanishing energy of a single gluon up to terms suppressed by this energy. Our main result is a soft operator acting in color and spin space that manipulates the momenta of the hard partons while keeping them on-shell and respecting momentum conservation. Additionally, we provide a complete expression for the subleading term of the expansion of an arbitrary tree-level amplitude in the limit where the momenta of a massless quark and a massless anti-quark of the same flavor become collinear. This limit is necessary to obtain the one-loop soft approximation whenever the process involves such a quark-anti-quark pair. Interestingly, the result involves a high-energy limit.
Funding Information
  • Deutsche Forschungsgemeinschaft (396021762-TRR 257)
  • Deutsche Forschungsgemeinschaft (400140256-GRK 2497)

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