Reducing full one-loop amplitudes to scalar integrals at the integrand level

By G. Ossola, Costas G.Papadopoulos, R. Pittau. 2006

716 citations recorded by the source corpus.

Abstract We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation.

Subfields: Electrical and Electronic Engineering, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4c29c1e2140d8f905ac6e04b139b6e0e7505fae2

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In Electrical and Electronic Engineering

In Nuclear and High Energy Physics

Citations in the corpus

Les Houches 2013: Physics at TeV Colliders: Standard Model Working Group Report (2014, methodology): “Working in a general multiparticle framework, 1-loop matrix elements are computed automatically, by using the OPP method [402] complemented by analytical formulas for calculating the contributions of the R2 rational terms [454], all implemented in HELAC-1LOOP [455].”
Handbook of LHC Higgs Cross Sections: 3. Higgs Properties (2013, methodology): “For the computation of the virtual corrections we use a code generated b y the program package G OSAM, which combines automated diagram generation and algebraic manip ul tion with integrand-level reduction techniques [133, 300, 301].”
On-the-fly reduction of open loops (2017, methodology): “For instance, the OPP method [5] is not applicable on-the-fly since it is based on the multiple poles of the entire integrand.”
QCD matrix elements + parton showers. The NLO case (2012, background): “These developments range from the (near) automation of cross section calculations for multi-particle final states at the next-to leading order [1–16] to the construction of algorithms that allow to use multi-particle calculations at leading and next-to-leading order to drive event simulation at the ”
Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes (2006, methodology): “A different method of constructing the master integral coefficients of one-loop amplitudes, from the values of the loop momentum that correspond to unitarity cuts, has been presented in [ 35 ].”
UFO - The Universal FeynRules Output (2011, methodology): “Furthermore, the same approach could be used in order to include other counterterm-like objects, such as the rational R2 terms [45–48] in the OPP approach [49,50].”
Electroweak and QCD corrections to top-pair hadroproduction in association with heavy bosons (2015, methodology): “– 3 – procedures for the computation of the one-loop matrix elements (automated in the module MadLoop [20, 33], which makes use of CutTools [45] with OPP and of IREGI [46] with TIR, and of an in-house implementation of the representation proposed in ref.”
Comix, a new matrix element generator (2008, neutral): “36 74 v2 [ he p- ph ] 2 4 N ov 2 00”
Weak corrections to Higgs hadroproduction in association with a top-quark pair (2014, methodology): “NLO results not matched to parton showers are obtained by adopting the FKS method [62, 63] for the subtraction of the singularities of the realemission matrix elements (automated in the module MadFKS [64]), and the OPP integralreduction procedure [65] for the computation of the one-loop matrix eleme”
Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order (2010, methodology): “It is based on the Helac-Phegas program to calculate all tree-order like ingredients and the OPP [55] reduction method.”
One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts (2011, methodology): “We use this example to introduce the connection between reduction procedures and the OPP/unitarity ideas [21].”
A framework for Higgs characterisation (2013, methodology): “For MadFKS this amounts to the ordinary Feynman rules; for MadLoop, to Feynman rules, UV counterterms, and special tree-level rules necessary to, and defined by, the OPP method, which are called R2.”
NLO QCD+EW predictions for V + jets including off-shell vector-boson decays and multijet merging (2015, methodology): “A sophisticated stability system is in place to rescue potential unstable phase-space points via a re-evaluation at quadrupole precision using CutTools [63], which implements the OPP method [64], together with the OneLOop library [65].”
Cuts of Feynman Integrals in Baikov representation (2017, methodology): “In the last years our understanding of the reduction of one-loop amplitudes to a set of Master Integrals (MI), a minimal set of FI that form a basis, either based on unitarity methods [9, 10, 11] or at the integrand level via the OPP method [12, 13], has drastically changed the way one-loop calculat”
NLO electroweak automation and precise predictions for W + multijet production at the LHC (2014, methodology): “1) to scalar integrals can be performed at the integrand level using the OPP method [86] as implemented in CutTools [87] or Samurai [88], which both rely on the OneLOop library [89] for the evaluation of scalar integrals.”