Direct Extraction Of One Loop Rational Terms
arXiv:0806.4600 · doi:10.1088/1126-6708/2009/01/049
Abstract
We present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop amplitudes in terms of products of massive tree amplitudes. We find that the rational terms in $4-2\e$ dimensions can be determined from quadruple, triple and double cuts without the need for independent pentagon contributions using a massive integral basis. The additional mass-dependent integral coefficients may then be extracted from the large mass limit which can be performed analytically or numerically. We check the method by computing the rational parts of all gluon helicity amplitudes with up to six external legs. We also present a simple application to amplitudes with external massless fermions.
35 pages, 6 figures. Major revisions: new analytic results for gluon amplitudes and new section on treatment of massless fermions. References added and typos corrected. Accepted for publication in JHEP
References in corpus (17)
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
- Direct extraction of one-loop integral coefficients
- Full one-loop amplitudes from tree amplitudes
- A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
- On the Rational Terms of the one-loop amplitudes
- D-dimensional unitarity cut method
- NLO QCD corrections to tri-boson production
- On Triple-Cut of Scattering Amplitudes
- Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
- Optimizing the Reduction of One-Loop Amplitudes
- One-loop phi-MHV amplitudes using the unitarity bootstrap
- Integral Coefficients for One-Loop Amplitudes
- Closed-Form Decomposition of One-Loop Massive Amplitudes
- One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case
- Analytic Structure of Three-Mass Triangle Coefficients
- Polynomial Structures in One-Loop Amplitudes