On the rational terms of the one-loop amplitudes

By G. Ossola, Costas G. Papadopoulos, R. Pittau. 2008

250 citations recorded by the source corpus.

The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n−4)-dimensional structure of the numerator of the one-loop amplitude can be derived by using appropriate Feynman rules within a tree-like computation. For the terms that originate from the reduction of the 4-dimensional part of the numerator, we present two different strategies and explicit algorithms to compute them.

Subfields: Artificial Intelligence, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/edc343717c79a3df1e5f61ad81cb3894ded716b5

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Citations in the corpus

A brief introduction to modern amplitude methods (2013, unknown): “ed as a byproduct of the computation of the cut part, by taking into account the extra-dimensional µ2 dependence appearing in the propagator denominators of the dimensionally-regulated loop integrand [45]. The remaining R2 terms come from µ2 dependence in the numerator of the loop integrand. As in t”
On-the-fly reduction of open loops (2017, background): “As is well known [2,59], these so-called rational terms of type R1 can arise only in the presence of 1/(D−4) poles of ultraviolet type.”
The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations (2014, background): “In particular, one can show [158] that the computation of R2 is equivalent to that of a tree-level amplitude, constructed with a universal set of theory-dependent rules (see ref.”
Automated event generation for loop-induced processes (2015, background): “Conversely, R2 counterterms [28–30], originating from the 4-dimensional nature of the reduction methods applied in MadLoop, must be included.”
NLO electroweak automation and precise predictions for W + multijet production at the LHC (2014, methodology): “Corresponding Feynman rules have been derived for QED in [90], for QCD in [93] and for the complete EW Standard Model in [94–97].”
Handbook of LHC Higgs Cross Sections: 3. Higgs Properties (2013, methodology): “This is a non-trivial check, also taking into account that P OWHEL, like HELAC-NLO, uses the OPP method [133, 134] complemented by rational terms of kind R2 [198] to compute one-loop amplitudes, whereas the authors of [184] rely on tensor-reduction techn iques.”
Recursive generation of one-loop amplitudes in the Standard Model (2012, background): “A rational term is dubbed R1-term if it results from the ǫ-dependence of the denominators of the loop integrals and it is called R2-term if it is generated by a O(ǫ) term in the numerator of the Feynman amplitude [71].”
Electroweak radiative corrections for collider physics (2019, methodology): “The results for the contributions of the 4-point functions are slightly more complicated and involve (q̌2)2 terms [197, 239].”
Automation of one-loop QCD computations (2011, background): “In exactly the same way one deals with the computation of R1 [30].”