Numerical Computation of Two-loop Box Diagrams with Masses

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass configurations. As an example, the computation of two-loop planar and non-planar box diagrams is shown. The results are confirmed by comparisons with other techniques, including the reduction method, and by a consistency check using the dispersion relation.Comment: 16 pages, 8 figure

Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves

We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from algebraic geometry, this idea provides a new highly efficient algorithm for integral reduction. We demonstrate the power of this method via several complicated two-loop diagrams with internal massive legs. No explicit elliptic or hyperelliptic integral computation is needed for our method.Comment: minor changes: more references adde

Numerical evaluation of multi-loop integrals by sector decomposition

In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines. Here we show how to extend this algorithm to Feynman diagrams with massive propagators and arbitrary propagator powers. As applications, we present numerical results for the master 2-loop 4-point topologies with massive internal lines occurring in Bhabha scattering at two loops, and for the master integrals of planar and non-planar massless double box graphs with two off-shell legs. We also evaluate numerically some two-point functions up to 5 loops relevant for beta-function calculations, and a 3-loop 4-point function, the massless on-shell planar triple box. Whereas the 4-point functions are evaluated in non-physical kinematic regions, the results for the propagator functions are valid for arbitrary kinematics.Comment: 15 pages latex, 11 eps figures include

Automation of electroweak corrections for LHC processes

For the Run 2 of the LHC next-to-leading order electroweak corrections will play an important role. Even though they are typically moderate at the level of total cross sections they can lead to substantial deviations in the shapes of distributions. In particular for new physics searches but also for a precise determination of Standard Model observables their inclusion in the theoretical predictions is mandatory for a reliable estimation of the Standard Model contribution. In this article we review the status and recent developments in electroweak calculations and their automation for LHC processes. We discuss general issues and properties of NLO electroweak corrections and present some examples, including the full calculation of the NLO corrections to the production of a W boson in association with two jets computed using GoSaM interfaced to MadDipole.Comment: LaTex, 60 pages, 8 Figure

μ−e\mu-e conversion in nuclei within the CMSSM seesaw: universality versus non-universality

In this paper we study $\mu-e$ conversion in nuclei within the context of the Constrained Minimal Supersymmetric Standard Model, enlarged by three right handed neutrinos and their supersymmetric partners, and where the neutrino masses are generated via a seesaw mechanism. Two different scenarios with either universal or non-universal soft supersymmetry breaking Higgs masses at the gauge coupling unification scale are considered. In the first part we present a complete one-loop computation of the conversion rate for this process that includes the photon-, $Z$-boson, and Higgs-boson penguins, as well as box diagrams, and compare their size in the two considered scenarios. Then, in these two scenarios we analyse the relevance of the various parameters on the conversion rates, particularly emphasising the role played by the heavy neutrino masses, $\tan \beta$, and especially $\theta_{13}$. In the case of hierachical heavy neutrinos, an extremely high sensitivity of the rates to $\theta_{13}$ is indeed found. The last part of this work is devoted to the study of the interesting loss of correlation between the $\mu-e$ conversion and $\mu \to e \gamma$ rates that occurs in the non-universal scenario. In the case of large $\tan \beta$ and light $H^0$ Higgs boson an enhanced ratio of the $\mu-e$ to $\mu \to e \gamma$ rates, with respect to the universal case is found, and this could be tested with the future experimental sensitivities.Comment: 48 pages, 15 figures. Minor typos corrected and some references adde