Reduction with Degenerate Gram matrix for One-loop Integrals
arXiv:2205.03000 · doi:10.1007/JHEP08(2022)110
Abstract
An improved PV-reduction method for one-loop integrals with auxiliary vector has been proposed in \cite{Feng:2021enk,Hu:2021nia}. It has also been shown that the new method is a self-completed method in \cite{Feng:2022uqp}. Analytic reduction coefficients can be easily produced by recursion relations in this method, where the Gram determinant appears in denominators. The singularity caused by Gram determinant is a well-known fact and it is important to address these divergences in a given frame. In this paper, we propose a systematical algorithm to deal with this problem in our method. The key idea is that now the master integral of the highest topology will be decomposed into combinations of master integrals of lower topologies. By demanding the cancellation of divergence for obtained general reduction coefficients, we solve decomposition coefficients as a Taylor series of the Gram determinant. Moreover, the same idea can be applied to other kinds of divergences.
arXiv comment46 pages, no figures
References in corpus (32)
- One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
- Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
- Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- Dimensionally Regulated Pentagon Integrals
- Reduction schemes for one-loop tensor integrals
- One-Loop Amplitudes for e^+ e^- to Four Partons
- Scalar one-loop integrals for QCD
- FIRE6: Feynman Integral REduction with Modular Arithmetic
- Dimensionally Regulated One-Loop Integrals
- Reduction of one-loop tensor 5-point integrals
- A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
- D-dimensional unitarity cut method
- Techniques for the calculation of electroweak radiative corrections at the one-loop level and results for W-physics at LEP200
- One-Loop Amplitudes Of Gluons In SQCD
- Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
- Algebraic reduction of one-loop Feynman graph amplitudes
- Reduction formalism for dimensionally regulated one-loop N-point integrals
- Reduction method for dimensionally regulated one-loop N-point Feynman integrals
- Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
- Numerical Evaluation of Six-Photon Amplitudes
- One-Loop Tensor Integrals in Dimensional Regularisation
- Integral Coefficients for One-Loop Amplitudes
- Closed-Form Decomposition of One-Loop Massive Amplitudes
- Polynomial Structures in One-Loop Amplitudes
- Single Cut Integration
- Analytic Tadpole Coefficients of One-loop Integrals
- One-loop Feynman Integral Reduction by Differential Operators
- PV-Reduction of Sunset Topology with Auxiliary Vector
- Reduction of General One-loop Integrals Using Auxiliary Vector
- Universal Treatment of Reduction for One-Loop Integrals in Projective Space
- Analytic structure of one-loop coefficients
Cited by in corpus (5)
- Generation Function For One-loop Tensor Reduction
- Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals
- Nontrivial One-loop Recursive Reduction Relation
- OPITeR: A program for tensor reduction of multi-loop Feynman Integrals
- Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices