相关论文: A general reduction method for one-loop N-point in…

The negative dimensional integration method (NDIM) is a technique where several difficulties concerning loop integration can be overcome. From usual covariant gauges to complicated Coulomb gauge integrals, and even the trickiest light-cone…

We present a new algorithm for the reduction of one-loop \emph{tensor} Feynman integrals with $n\leq 4$ external legs to \emph{scalar} Feynman integrals $I_n^D$ with $n=3,4$ legs in $D$ dimensions, where $D=d+2l$ with integer $l \geq 0$ and…

I give an efficient algorithm for the reduction of multi-leg one-loop integrals of rank one. The method combines the basic ideas of the spinor algebra approach with the dual vector approach and is applicable to box integrals or higher point…

We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We…

A set of one-loop vertex and box tensor-integrals with massless internal particles has been obtained directly without any reduction method to scalar-integrals. The results with one or two massive external lines for the vertex integral and…

We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…

Evaluation of three- and four-point diagrams with massless internal particles and arbitrary external momenta is considered. Exact results for some two-loop diagrams (planar and non-planar three-point contributions and the "double box"…

Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators…

We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…

In the calculation of cross sections for infrared-safe observables in high energy collisions at next-to-leading order, one approach is to perform all of the integrations, including the virtual loop integration numerically. One would use a…

This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…

Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop $N$-point corrections are needed. We study here the tensor reduction for Feynman integrals with $N \ge 6$. A general, recursive solution by…

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 perform a recursive reduction of one-loop $n$-point rank $R$ tensor Feynman integrals [in short: $(n,R)$-integrals] for $n\leq 6$ with $R\leq n$ by representing $(n,R)$-integrals in terms of $(n,R-1)$- and $(n-1,R-1)$-integrals. We use…

In this paper, we introduce a simple and efficient approach for the general reduction of one-loop integrals. Our method employs the introduction of an auxiliary vector and the identification of the tensor structure as an auxiliary…

The inclusive four-particle phase space integral of any $1\to 4$ matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this…

The soft and collinear singularities of general scalar and tensor one-loop N-point integrals are worked out explicitly. As a result a simple explicit formula is given that expresses the singular part in terms of 3-point integrals. Apart…

A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for…

We report on the computation of a class of integrals that appear when integrating the so-called iterated singly-unresolved approximate cross section of the NNLO subtraction scheme of [1-4], over the factorised phase space of unresolved…