Sophia Borowka

SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop

Abstract SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present version 3.0 of the program, which has major improvements compared to version 2: it is faster, contains new decomposition strategies, an improved user interface and various other new features which extend the range of applicability. Program summary Program title: SecDec 3.0 Catalogue identifier: AEIR_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIR_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 123828 No. of bytes in distributed program, including test data, etc.: 1651026 Distribution format: tar.gz Programming language: Wolfram Mathematica, perl, Fortran/C++. Computer: From a single PC to a cluster, depending on the problem. Operating system: Unix, Linux. RAM: Depending on the complexity of the problem Classification: 4.4, 5, 11.1. Catalogue identifier of previous version: AEIR_v2_1 Journal reference of previous version: Comput. Phys. Comm. 184(2013)2552 Does the new version supersede the previous version?: Yes Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g. kinematic thresholds). Solution method: Algebraic extraction of singularities within dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter, where the coefficients are finite integrals over the unit-hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way. Reasons for new version: • Improved user interface. • Additional new decomposition strategies. • Usage on a cluster is much improved. • Speed-up in numerical evaluation times. • Various new features (please see below). Summary of revisions: • Implementation of two new decompositions strategies based on a geometric algorithm. • Scans over large ranges of parameters are facilitated. • Linear propagators can be treated. • Propagators with negative indices are possible. • Interface to reduction programs like Reduze, Fire, LiteRed facilitated. • Option to use numerical integrator from Mathematica. • Using CQUAD for 1-dimensional integrals to improve speed of numerical evaluations. • Option to include epsilon-dependent dummy functions. Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. Running time: Between a few seconds and several hours, depending on the complexity of the problem.

Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence.

We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.

Full top quark mass dependence in Higgs boson pair production at NLO

A bstractWe study the effects of the exact top quark mass-dependent two-loop corrections to Higgs boson pair production by gluon fusion at the LHC and at a 100 TeV hadron collider. We perform a detailed comparison of the full next-to-leading order result to various approximations at the level of differential distributions and also analyse non-standard Higgs self-coupling scenarios. We find that the different next-to-leading order approximations differ from the full result by up to 50 percent in relevant differential distributions. This clearly stresses the importance of the full NLO result.We study the effects of the exact top quark mass-dependent two-loop corrections to Higgs boson pair production by gluon fusion at the LHC and at a 100 TeV hadron collider. We perform a detailed comparison of the full next-to-leading order result to various approximations at the level of differential distributions and also analyse non-standard Higgs self-coupling scenarios. We find that the different next-toleading order approximations differ from the full result by up to 50 percent in relevant differential distributions. This clearly stresses the importance of the full NLO result.

Renormalization scheme dependence of the two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM.

Reaching a theoretical accuracy in the prediction of the lightest MSSM Higgs-boson mass,

Numerical multi-loop calculations: tools and applications

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Erratum: Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence [Phys. Rev. Lett. 117 , 012001 (2016)]

Mh, at the level of the current experimental precision requires the inclusion of momentum-dependent contributions at the two-loop level. Recently two groups presented the two-loop QCD momentum-dependent corrections to

Numerical evaluation of massive multi-loop integrals with SecDec

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