Numerical evaluation of two-loop integrals with pySecDec

We describe the program pySecDec, which factorises endpoint singularities from multi-dimensional parameter integrals and can serve to calculate integrals occurring in higher order perturbative calculations numerically. We focus on the new features and on frequently asked questions about the usage of the program.Comment: 11 pages, to appear in the proceedings of the HiggsTools Final Meeting, IPPP, University of Durham, UK, September 201

The two-loop electroweak bosonic corrections to sin⁡2θeffb\sin^2\theta_{\rm eff}^{\rm b}

The prediction of the effective electroweak mixing angle $\sin^2\theta_{\rm eff}^{\rm b}$ in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the $Z{\bar b}b$ vertex. Numerical predictions are presented in the form of a fitting formula as function of $M_Z, M_W, M_H, m_t$ and $\Delta{\alpha}$, ${\alpha_{\rm s}}$. For central input values, we obtain a relative correction of $\Delta\kappa_{\rm b}^{(\alpha^2,\rm bos)} = -0.9855 \times 10^{-4}$, amounting to about a quarter of the fermionic corrections, and corresponding to $\sin^2\theta_{\rm eff}^{\rm b} = 0.232704$. The integration of the corresponding two-loop vertex Feynman integrals with up to three dimensionless parameters in Minkowskian kinematics has been performed with two approaches: (i) Sector decomposition, implemented in the packages FIESTA 3 and SecDec 3, and (ii) Mellin-Barnes representations, implemented in AMBRE 3/MB and the new package MBnumerics.Comment: 14 pp; v2: some explanations and Tab.2 added, version published in PL

Complete electroweak two-loop corrections to Z boson production and decay

This article presents results for the last unknown two-loop contributions to the $Z$-boson partial widths and $Z$-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where "bosonic" refers to diagrams without closed fermion loops. Together with the corresponding results for the $Z$-pole asymmetries $A_l, A_b$, which have been presented earlier, this completes the theoretical description of $Z$-boson precision observables at full two-loop precision within the Standard Model. The calculation has been achieved through a combination of different methods: (a) numerical integration of Mellin-Barnes representations with contour rotations and contour shifts to improve convergence; (b) sector decomposition with numerical integration over Feynman parameters; (c) dispersion relations for sub-loop insertions. Numerical results are presented in the form of simple parameterization formulae for the total width, $\Gamma_{\rm Z}$, partial decay widths $\Gamma_{e,\mu},\Gamma_{\tau},\Gamma_{\nu},\Gamma_{u},\Gamma_{c},\Gamma_{d,s},\Gamma_{b}$, branching ratios $R_l,R_c,R_b$ and the hadronic peak cross-section, $\sigma_{\rm had}^0$. Theoretical intrinsic uncertainties from missing higher orders are also discussed.Comment: 10 page

Static Pricing Problems under Mixed Multinomial Logit Demand

Price differentiation is a common strategy for many transport operators. In this paper, we study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap. Numerical experiments show the effectiveness of our method on a published, non-trivial, parking choice model

Slow rotation of a spherical particle inside an elastic tube

In this paper, we present an analytical calculation of the rotational mobility functions of a particle rotating on the centerline of an elastic cylindrical tube whose membrane exhibits resistance towards shearing and bending. We find that the correction to the particle rotational mobility about the cylinder axis depends solely on membrane shearing properties while both shearing and bending manifest themselves for the rotational mobility about an axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing frequency, the particle rotational mobility nearby a no-slip rigid cylinder is recovered only if the membrane possesses a non-vanishing resistance towards shearing. We further show that for the asymmetric rotation along the cylinder radial axis, a coupling between shearing and bending exists. Our analytical predictions are compared and validated with corresponding boundary integral simulations where a very good agreement is obtained.Comment: 23 pages, 7 figures and 107 references. Revised manuscript resubmitted to Acta Mec

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

SusHi 2.0 -- Higgs production cross sections in BSM models

A new upcoming version of SusHi is introduced. It features unified input for the Standard Model (SM) and beyond the SM models (BSM) parameters for higher-order total cross sections for Higgs production in gluon fusion, heavy-quark annhilation, as well as Higgsstrahlung. Like previous versions of SusHi, it provides links to codes like 2HDMC and FeynHiggs, but can also process standard SLHA output of spectrum generators like SOFTSUSY and SPheno.Comment: 10 pages, 4 figures, EPS-HEP202