Direct reduction of multiloop multiscale scattering amplitudes

  title={Direct reduction of multiloop multiscale scattering amplitudes},
  author={Yefan Wang and Z. Li and Najam ul Basat},
  journal={Physical Review D},
We propose an alternative approach based on series representation to directly reduce multi-loop multi-scale scattering amplitude into set of freely chosen master integrals. And this approach avoid complicated calculations of inverse matrix and dimension shift for tensor reduction calculation. During this procedure we further utilize the Feynman parameterization to calculate the coefficients of series representation and obtain the form factors. Conventional methodologies are used only for scalar… Expand

Figures from this paper

Reduction of planar double-box diagram for single-top production via auxiliary mass flow
The single-top production is an important process at the LHC to test the Standard Model (SM) and search for the new physics beyond the SM. Although the complete next-to-next-to-leading order (NNLO)Expand
Two-loop leading-color helicity amplitudes for three-photon production at the LHC
We calculate all planar contributions to the two-loop massless helicity amplitudes for the process qq̄ → γγγ. The results are presented in fully analytic form in terms of the functional basisExpand
Multiloop corrections for collider processes using auxiliary mass flow
With a key improvement, the auxiliary mass flow method is now able to compute many badlyneeded Feynman integrals encountered in cutting-edge collider processes. We have successfully applied it toExpand
arXiv : Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
We compute the two-loop helicity amplitudes for the production of three photons at hadron colliders in QCD at leading-color. Using the two-loop numerical unitarity method coupled with analyticExpand
Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finiteExpand
Two-loop five-point integration-by-parts relations in a usable form
In this paper, we show that with the state-of-art module intersection IBP reduction method and our improved Leinartas’ algorithm, IBP relations for very complicated Feynman integrals can be solvedExpand
Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for the theExpand
Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
We introduce an algebro-geometrically motived integration-by-parts (IBP) re- duction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations inExpand
Integral reduction with Kira 2.0 and finite field methods
The new version 2.0 of the Feynman integral reduction program Kira is presented, featuring the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. Expand
Leading-color two-loop QCD corrections for three-photon production at hadron colliders
We compute the two-loop helicity amplitudes for the production of three photons at hadron colliders in QCD at leading-color. Using the two-loop numerical unitarity method coupled with analyticExpand


Hepta-cuts of two-loop scattering amplitudes
A bstractWe present a method for the computation of hepta-cuts of two loop scattering amplitudes. Four dimensional unitarity cuts are used to factorise the integrand onto the product of sixExpand
Recursive numerical calculus of one-loop tensor integrals
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a functionExpand
Reduction schemes for one-loop tensor integrals
Abstract We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e − → 4 fermions. TheExpand
Scattering amplitudes with open loops.
A new technique to generate scattering amplitudes at one loop using tensor-integral and Ossola-Papadopoulos-Pittau reduction results in a fully flexible, very fast, and numerically stable one-loop generator. Expand
Fusing gauge theory tree amplitudes into loop amplitudes
Abstract We identify a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities. One-loop amplitudes for masslessExpand
On the integrand-reduction method for two-loop scattering amplitudes
We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in theExpand
One-loop n-point gauge theory amplitudes, unitarity and collinear limits
Abstract We present a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory. As an example, we obtain the one-loop contribution toExpand
Numerical evaluation of six-photon amplitudes
We apply the recently proposed amplitude reduction at the integrand level method, to the computation of the scattering process 2? ? 4?, including the case of a massive fermion loop. We also presentExpand
A Systematic and Efficient Method to Compute Multi-loop Master Integrals
Abstract We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions.Expand
Full one-loop amplitudes from tree amplitudes
We establish an efficient polynomial-complexity algorithm for one-loop calculations, based on generalized D-dimensional unitarity. It allows automated computations of both cut-constructible andExpand