Tiziano Peraro

GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond

We present the version 2.0 of the program package GoSam for the automated calculation of one-loop amplitudes. GoSam is devised to compute one-loop QCD and/or electroweak corrections to multi-particle processes within and beyond the Standard Model. The new code contains improvements in the generation and in the reduction of the amplitudes, performs better in computing time and numerical accuracy, and has an extended range of applicability. The extended version of the “Binoth-Les-Houches-Accord” interface to Monte Carlo programs is also implemented. We give a detailed description of installation and usage of the code, and illustrate the new features in dedicated examples.

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

A bstractWe correct an error affecting eq. (6.11) of the article.

Ninja: Automated Integrand Reduction via Laurent Expansion for One-Loop Amplitudes

Abstract We present the public C++ library Ninja , which implements the Integrand Reduction via Laurent Expansion method for the computation of one-loop integrals. The algorithm is suited for applications to complex one-loop processes. Program summary Program title: Ninja Catalogue identifier: AETO_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AETO_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 74303 No. of bytes in distributed program, including test data, etc.: 530944 Distribution format: tar.gz Programming language: C++. Computer: Any computer with a compliant C++ compiler. Operating system: Unix-like (tested on Linux and Mac OS). RAM: Several thousands of bytes (it can vary depending on the complexity of the computation) Classification: 4.4, 11.1. External routines: A library of one-loop Master Integrals: OneLOop, LoopTools, or any other library implementing a suitable interface Nature of problem: Computation of one-loop integrals contributing to scattering amplitudes. Solution method: Semi-numerical implementation of the integrand reduction via Laurent expansion, using a simplified polynomial division algorithm. Running time: Depending on the number of integrals and their complexity, between less than a millisecond up to several seconds per phase-space point, for the computation of a full amplitude.

Scattering amplitudes from multivariate polynomial division

Abstract We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Grobner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.

Multiloop integrand reduction for dimensionally regulated amplitudes

Abstract We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary dimensionally regulated loop integrals with any number of loops and external legs, which can be used to obtain the decomposition of any integrand analytically with a finite number of algebraic operations. The general results are illustrated by applications to two-loop Feynman diagrams in QED and QCD, showing that the proposed reduction algorithm can also be seamlessly applied to integrands with denominators appearing with arbitrary powers.

GoSam applications for automated NLO calculations

We present applications of the program GoSAM for the automated calculation of one-loop amplitudes. Results for NLO QCD corrections to beyond the Standard Model processes as well as Higgs plus up to three-jet production in gluon fusion are shown. We also discuss some new features of the program.

GoSam @ LHC: algorithms and applications to Higgs production

We elaborate on GoSam, a code-writer for automated one-loop calculations. After recalling its main features, we present a selection of phenomenological results recently obtained, giving relevance at the evaluation of NLO QCD corrections to the production of a Higgs boson in association with jets and heavy quarks.

Integrand reduction at NLO and beyond

The integrand-level methods for the reduction of scattering amplitudes are powerful techniques for the analysis and the computation of loop integrals, which have already been successfully applied and automated at one-loop. Moreover, some very interesting progress has recently been made towards the higher-loop extension of such techniques. In this presentation, we review the basics principles of integrand-reduction methods within a coherent framework we developed, which can be applied to any integrand at any number of loops and is based on simple concepts of algebraic geometry, such as multivariate polynomial division. We particularly focus on semianalytic and algebraic techniques, such as the Laurent series expansion which we exploited to improve the one-loop reduction with the library NINJA, and the multi-loop divide-and-conquer approach which can always be used to find the integrand decomposition of any Feynman graph in a finite number of algebraic operations.

Automated one-loop calculations with GoSam 2.0

We present the program package GoSam which is designed for the automated calculation of one-loop amplitudes for multi-particle processes in renormalisable quantum field theories. The amplitudes, which are generated in terms of Feynman diagrams, can be reduced using either D-dimensional integrand-level decomposition or tensor reduction. GoSam can be used to calculate one-loop QCD and/or electroweak corrections to Standard Model processes and offers the flexibility to link model files for theories Beyond the Standard Model. A standard interface to programs calculating real radiation is also implemented. We demonstrate the flexibility of the program by presenting examples of processes with up to six external legs attached to the loop.We present the version 2.0 of the program GOSAM, which is a public program package to compute one-loop corrections to multi-particle processes. The extended version of the “Binoth-LesHouches-Accord” interface to Monte Carlo programs is also implemented. This allows a large flexibility regarding the combination of the code with various Monte Carlo programs to produce fully differential NLO results, including the possibility of parton showering and hadronisation. We describe the new features of the code and illustrate the wide range of applicability for multiparticle processes at NLO, both within and beyond the Standard Model.