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

By Pierpaolo Mastrolia, E. Mirabella, Tiziano Peraro. 2012

142 citations recorded by the source corpus.

A bstractWe present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. 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.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/32262c35256c230908a6ba552c267ff7f5e9499d

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In Applied Mathematics

1. Gudrun Heinrich
2. Stefan Dittmaier
3. Ansgar Denner
4. Stefano Pozzorini
5. Falko Dulat
6. M. Schönherr
7. P. Maierhöfer
8. Stefan Kallweit

In Atomic and Molecular Physics, and Optics

1. Gudrun Heinrich
2. Ansgar Denner
3. Stefan Dittmaier
4. G. Panico
5. R. Frederix
6. M. Zaro
7. Andrea Tesi
8. D. Pagani

In Numerical Analysis

1. Gudrun Heinrich
2. R. Frederix
3. M. Zaro
4. Ansgar Denner
5. Stefan Dittmaier
6. D. Pagani
7. Pierpaolo Mastrolia
8. Iain W. Stewart

Citations in the corpus

• Physics at a 100 TeV pp collider: Higgs and EW symmetry breaking studies (2016, methodology): “For the reduction of the tensor integrals at running time, we used NINJA [83, 84], which is an automated package carrying out the integrand reduction via Laurent expansion [85], and ONELOOP [86] for the evaluation of the scalar integrals.”
• Large NLO corrections in tt¯ W ± and tt¯ tt¯ hadroproduction from supposedly subleading EW contributions (2018, methodology): “J H E P 0 2 ( 2 0 1 8 ) 0 3 1 are computed by dynamically switching between different kinds of techniques for integral reduction: the OPP [48], Laurent-series expansion [49], and tensor integral reduction [50–52].”
• Handbook of LHC Higgs Cross Sections: 3. Higgs Properties (2013, background): “Moreover, the presence of effective couplings in the Lagrangian requires an extended version [303] of the integrand-level reduction, of which the present calculation is a first application .”
• Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, methodology): “Per default it uses Ninja [562, 563, 578], a package that performs the reduction on 23See http://feynrules.”
• Electroweak radiative corrections for collider physics (2019, methodology): “Ninja implements an alternative reduction algorithm based on the systematic application of Laurent series expansion [238].”
• Les Houches 2013: Physics at TeV Colliders: Standard Model Working Group Report (2014, methodology): “[3], here the newest developments regarding the evaluation of loop amplitudes with integrand reduction techniques based on Laurent expansion were used [397].”
• The automation of next-to-leading order electroweak calculations (2018, methodology): “The computations of one-loop amplitudes are carried out by switching dynamically between two integral-reduction techniques, OPP [52] or Laurent-series expansion [53], and TIR [54– 56].”
• Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report (2016, methodology): “These diagrams are then computed at running time with NINJA [339, 340], which is a reduction program based on the Laurent expansion of the integrand [338], and using ONELOOP [299] for the evaluation of the scalar one-loop integrals.”
• Scattering Amplitudes and the Positive Grassmannian (2012, unknown): “ linear combination of such basic integrals and nd ways of computing the coecients. This is known as the \unitarity-based method", [95{99] (for recent applications of these techniques, see e.g. [92,100]). In more modern language, the key idea is to use contour integrals to compute the coecients”
• GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond (2014, methodology): “a prominent example is the eective coupling of gluons to the Higgs boson), or in calculations involving spin-two particles beyond the leading order. These extensions are described in detail in Refs. [33,36,60] and are contained in the distribution of GoSam-2.0. The additional integrals will be calle”
• Scattering Amplitudes from Multivariate Polynomial Division (2012, background): “We closely follow the notation of [26, 35].”