Integrand reduction of one-loop scattering amplitudes through Laurent series expansion

Abstract

We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integranddecomposition. In the asymptotic limit, the coefficients of the master integrals are the solutions of a diagonal system of equations, properly corrected by counterterms whose parametric form is known a priori. The Laurent expansion of the integrand is implemented through polynomial division. The extension of the integrand-reduction to the case of numerators with rank larger than the number of propagators is discussed as well.

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

“…This remarkable fact results from two equally important theoretical achievements. Namely, a universal formalism for the cancellation of infrared singularities [10][11][12][13][14], and a technique for the algorithmic evaluation of renormalised one-loop amplitudes [15][16][17][18][19][20][21][22][23][24][25], both of which must work in a process-and observable independent manner. At the NLO (as opposed to the NNLO and beyond) there is the further advantage that fixed-order computations can be matched to parton-shower event generators (with either the MC@NLO [26] or the POWHEG [27] method -see also refs.…”

“…(2.102), which implies that the difference V − V k is computed only in a fraction f k of the total number of point thrown. 25 For an explicit evaluation of eq. (2.102), we need to define what enters it.…”

Large NLO corrections in t t ¯ W ± $$ t\overline{t}{W}^{\pm } $$ and

“…are computed by dynamically switching between different kinds of techniques for integral reduction: the OPP [48], Laurent-series expansion [49], and tensor integral reduction [50][51][52]. These techniques have been automated in the module MadLoop [10], which is used for the generation of the amplitudes and in turn exploits CutTools [53], Ninja [54,55] and Collier [56], together with an in-house implementation of the OpenLoops optimisation [5].…”

Higgs boson pair productions in the Georgi-Machacek model at the LHC

“…In our simulations, events of Higgs boson pair production are generated with the loopinduced mode in Madgraph5 aMC@NLO [100][101][102][103][104] with m h = 125 GeV. The model file is adopted from the model database of FeynRules [105,106].…”