A unitarity compatible approach to one-loop amplitudes with massive fermions

Abstract

We explain how one-loop amplitudes with massive fermions can be computed using only on-shell information. We first use the spinor-helicity formalism in six dimensions to perform generalised unitarity cuts in $d$ dimensions. We then show that divergent wavefunction cuts can be avoided, and the remaining ambiguities in the renormalised amplitudes can be fixed, by matching to universal infrared poles in $4-2\epsilon$ dimensions and ultraviolet poles in $6-2\epsilon$ dimensions. In the latter case we construct an effective Lagrangian in six dimensions and reduce the additional constraint to an on-shell tree-level computation.

33 pages, 7 figures, 1 table (v2 updated acknowledgments)

References in corpus (16)

• FeynRules - Feynman rules made easy
• New Developments in FeynCalc 9.0
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Full one-loop amplitudes from tree amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Amplitudes and Spinor-Helicity in Six Dimensions
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Closed-Form Decomposition of One-Loop Massive Amplitudes
• QCD corrections to the hadronic production of a heavy quark pair and a W-boson including decay correlations
• Next-to-leading order QCD predictions for top-quark pair production with up to three jets
• Unitarity and On-Shell Recursion Methods for Scattering Amplitudes

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