Numerical evaluation of massive multi-loop integrals with SecDec

The program package SecDec is presented, allowing the numerical evaluation of multi-loop integrals. The restriction to Euclidean kinematics of version 1.0 has been lifted: thresholds can be handled by an automated deformation of the integration contour into the complex plane. Other new features of the program, which go beyond the standard decomposition of loop integrals, are also described. The program is publicly available at http://secdec.hepforge.org.Comment: 6 pages, proceedings of the 11th DESY workshop "Loops and Legs in Quantum Field Theory", April 2012, Wernigerode, German

Numerical multi-loop calculations with the program SecDec

SecDec is a program which can be used for the evaluation of parametric integrals, in particular multi-loop integrals. For a given set of propagators defining the graph, the program constructs the graph polynomials, factorizes the endpoint singularities, and finally produces a Laurent series in the dimensional regularization parameter, whose coefficients are evaluated numerically. In this talk we discuss various features of the program, which extend the range of applicability. We also present a recent phenomenological example of an application entering the momentum dependent two-loop corrections to neutral Higgs boson masses in the MSSM.Comment: 9 pages, 5 figures; contribution to the proceedings of the conference ACAT 2014 (Advanced Computing and Analysis Techniques in physics), Prague, Czech Republic, September 201

Two-loop massless QCD corrections to the g+g→H+Hg+g \rightarrow H+H four-point amplitude

We compute the two-loop massless QCD corrections to the four-point amplitude $g+g \rightarrow H+H$ resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.Comment: 3 figure

Systematic approximation of multi-scale Feynman integrals

An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman integrals, allowing for fast numerical evaluation. The results are valid in all kinematical regions, both above and below thresholds, up to in principle arbitrary orders in the dimensional regulator. The scope of the algorithm is demonstrated by presenting results for selected two-loop threepoint and four-point integrals with an internal mass scale that appear in the two-loop amplitudes for Higgs+jet production

Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters

Higher-order corrections to the Higgs-boson masses within the MSSM are desirable for accurate predictions currently testable at the LHC. From the comparison of the prediction with the measured value of the mass of the discovered Higgs signal, constraints on the available parameter space can be inferred. In order to improve on the accuracy of current predictions, all two-loop corrections involving the strong coupling are computed for the Higgs-boson mass spectrum of the MSSM with complex parameters. Apart from the dependence on the strong coupling, these contributions depend on the weak coupling, leading to terms of $\mathcal{O}{\left(\alpha\alpha_s\right)}$, or on Yukawa couplings, leading to terms of $\mathcal{O}{\left(\sqrt{\alpha_{q_1}}\sqrt{\alpha_{q_2}}\alpha_s\right)}$, ($q_{1,2}=t,b,c,s,u,d$; flavor-violation effects are neglected). The full dependence on the external momentum at the two-loop level and on all relevant mass scales is taken into account. The calculation is performed in the Feynman-diagrammatic approach such that there is flexibility in the choice of the employed renormalization scheme. For the phenomenological results presented here, a renormalization scheme consistent with higher-order corrections included in the code FeynHiggs is adopted. For the evaluation of the results, a total of 513 two-loop two-point integrals with up to five different mass scales are computed fully numerically using the program SecDec. A comparison with existing results in the limit of real parameters and / or vanishing external momentum is carried out, and the impact of the new results for the lightest neutral Higgs-boson mass of the MSSM is discussed with respect to their dependence on the phases of the complex parameters. The new results will be included in the public code FeynHiggs