Applications of the loop-tree duality

Abstract

We describe a new method to perform NLO calculations, combining real and virtual amplitudes at the integrand level, with a fully local compensation between them in the IR, and between the virtual integrand and properly defined counter-terms in the UV, in such a way that physical observables can be computed in 4 dimensions. One of the advantages of the method is that all the scattering amplitudes are integrated simultaneously, without the need for tensor reduction, or projection onto sets of master integrals. As such, it could offer great progress in the automation of NLO calculations, where the actual bottle-necks are the complexity of the analytical calculations for multi-leg processes, and the numerical stability of the result. Loops and Legs in Quantum Field Theory

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

“…The four-dimensional unsubtraction (fdu) [103][104][105][106][107] approach constitutes an alternative to the traditional subtraction method. It is based on the loop-tree duality (LTD) theorem [108][109][110][111], which establishes a connection among loop and dual integrals, the latter being similar to standard phase-space integrals.…”

Four-dimensional unsubtraction with massive particles

“…LTD has also been used recently to deal with integral representations of virtual and real subtraction terms [13], including the description of initial-state singularities, that are grouped together and then are integrated numerically.The main purpose of this article is to extend the LTD four-dimensional unsubtraction method presented in Refs. [36,37,38,39,40] to deal with massive particles. From the kinematical point of view, the mass of the particles slightly modifies the momentum mapping used to perform the real-virtual combination and this changes the IR-divergent structure.…”

May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

“…With the aim of by-passing these difficulties, the fourdimensional unsubtraction (fdu) [42][43][44][45][46] approach constitutes a radically-new alternative to the traditional subtraction technique. It is based on the loop-tree duality (ltd) theorem [47][48][49][50], which establishes a connection among loop and dual integrals.…”