Related papers: One-loop Feynman Integral Reduction by Differentia…
As a key method to deal with loop integrals, Integration-By-Parts (IBP) method can be used to do reduction as well as establish the differential equations for master integrals. However, when talking about tensor reduction, the…
One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…
Passarino-Veltman (PV) reduction method has been proved to be very useful for the computation of general one-loop integrals. However, not much progress has been made when applying to higher loops. Recently, we have improved the PV-reduction…
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. The described methods for 3-point and 4-point integrals…
We briefly sketch the methods for a numerically stable evaluation of tensor one-loop integrals that have been used in the calculation of the complete electroweak one-loop corrections to $\Pep\Pem\to4 $fermions. In particular, the…
A new method for the reduction of one-loop tensor 5-point integrals to related 4-point integrals is proposed. In contrast to the usual Passarino-Veltman reduction and other methods used in the literature, this reduction avoids the…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic…
We describe a new, convenient, recursive tensor integral reduction scheme for one-loop $n$-point Feynman integrals. The reduction is based on the algebraic Davydychev-Tarasov formalism where the tensors are represented by scalars with…
Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…
We present a program that implements the OPP reduction method to extract the coefficients of the one-loop scalar integrals from a user defined (sub)-amplitude or Feynman Diagram, as well as the rational terms coming from the 4-dimensional…
In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
The \emph{conventional} Passarino-Veltman reduction is a systematic procedure based on the Lorentz covariance, which can efficiently reduce the one-loop tensor Feynman integrals in the relativistic quantum field theories (QFTs) at zero…
The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…
A unified formulation of one-loop tensor integrals is proposed for systematical calculations of finite volume corrections. It is shown that decomposition of the one-loop tensor integrals into a series of tensors accompanied by tensor…
We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…
The computational cost associated with reducing tensor integrals to scalar integrals using the Passarino-Veltman method is dominated by the diagonalisation of large systems of equations. These systems of equations are sized according to the…
We present a new systematic method to evaluate one-loop tensor integrals in conventional ultraviolet cutoff regularization. By deriving a new recursive relation that describes the momentum translation variance of ultraviolet integrals, we…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…