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

Momentum Dependent Two-Loop Corrections to the Neutral Higgs Boson Masses in the MSSM

The momentum dependent two-loop contributions of the order $\mathcal{O}$($\alpha_s \alpha_t$) to the masses in the Higgs-boson sector of the MSSM are computed. Adopting the Feynman-diagrammatic approach and using a mixed on-shell/$\overline{DR}$ renormalization scheme, the new corrections can directly be matched onto the higher-order corrections included in the code FeynHiggs. Two-loop diagrams involving several mass scales are evaluated with the program SecDec. The combination of the new momentum dependent two-loop contribution with the existing one- and two-loop corrections leads to an improved prediction of the light MSSM Higgs-boson mass with reduced theoretical uncertainty. The resulting shifts in the lightest Higgs-boson mass $M_h$ can extend up to the level of the current experimental uncertainty of about 500 MeV in the scenario considered in these proceedings.Comment: 8 pages, 3 figures, contribution to the proceedings of the Loops and Legs 2014 conferenc

Hyperelliptic genus 3 curves with involutions and a Prym map

We characterise genus 3 complex smooth hyperelliptic curves that contain two additional involutions as curves that can be build from five points in $\mathbb{P}^1$ with a distinguished triple. We are able to write down explicit equations for the curves and all their quotient curves. We show that, fixing one of the elliptic quotient curve, the Prym map becomes a 2:1 map and therefore the hyperelliptic Klein Prym map, constructed recently by the first author with A. Ortega, is also 2:1 in this case. As a by-product we show an explicit family of $(1, d)$ polarised abelian surfaces (for d > 1), such that any surface in the family satisfying a certain explicit condition is abstractly non-isomorphic to its dual abelian surface.Comment: 14 pages, comments welcom

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

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

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.Comment: 46 pages, version to appear in Comput.Phys.Com