Analytic structure of one-loop coefficients
arXiv:1301.7510 · doi:10.1007/JHEP05(2013)104
Abstract
By the unitarity cut method, analytic expressions of one-loop coefficients have been given in spinor forms. In this paper, we present one-loop coefficients of various bases in Lorentz-invariant contraction forms of external momenta. Using these forms, the analytic structure of these coefficients becomes manifest. Firstly, coefficients of bases contain only second-type singularities while the first-type singularities are included inside scalar bases. Secondly, the highest degree of each singularity is correlated with the degree of the inner momentum in the numerator. Thirdly, the same singularities will appear in different coefficients, thus our explicit results could be used to provide a clear physical picture under various limits (such as soft or collinear limits) when combining contributions from all bases.
40 pages. Some discussions and references updated
References in corpus (15)
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
- D-dimensional unitarity cut method
- Uniqueness of two-loop master contours
- Direct Extraction Of One Loop Rational Terms
- Taming Tree Amplitudes In General Relativity
- Scattering Amplitudes from Multivariate Polynomial Division
- Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
- Tensorial Reconstruction at the Integrand Level
- Double-Cut of Scattering Amplitudes and Stokes' Theorem
- Integral Coefficients for One-Loop Amplitudes
- Polynomial Structures in One-Loop Amplitudes
- An Integrand Reconstruction Method for Three-Loop Amplitudes
- Unitarity Method with Spurious Pole
- Generalised Unitarity At One-Loop With Massive Fermions