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

Бандаж робочого колеса турбінного ступеня

Бандаж робочого колеса турбінного ступеня містить бандажну стрічку з отворами, що відповідають формі шипів робочих лопаток, просунутих в отвори бандажної стрічки, та допоміжне кільце з ущільнювальними гребенями на його зовнішній поверхні, яке надіте на бандажну стрічку. На зовнішній торцевій частині шипів робочих лопаток виконані виступи циліндричної, сферичної або конічної форми. На внутрішній частині допоміжного кільця з ущільнювальними гребенями створені лунки, розміри яких відповідають формі і розмірам зазначених виступів над шипами робочих лопаток

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

Higgs boson pair production in gluon fusion at NLO 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.Comment: Version published in PRL, v2: results at 13 TeV (v1 was at 14 TeV), minor correction to virtual part included, conclusions unchange

Projective geometry and the quaternionic Feix-Kaledin construction

Starting from a complex manifold S with a real-analytic c-projective structure whose curvature has type (1,1), and a complex line bundle L with a connection whose curvature has type (1,1), we construct the twistor space Z of a quaternionic manifold M with a quaternionic circle action which contains S as a totally complex submanifold fixed by the action. This extends a construction of hypercomplex manifolds, including hyperkaehler metrics on cotangent bundles, obtained independently by B. Feix and D. Kaledin. When S is a Riemann surface, M is a self-dual conformal 4-manifold, and the quotient of M by the circle action is an Einstein-Weyl manifold with an asymptotically hyperbolic end, and our construction coincides with a construction presented by the first author in a previous paper. The extension also applies to quaternionic Kaehler manifolds with circle actions, as studied by A. Haydys and N. Hitchin.Comment: 28 pages, (v2) added material on Swann bundles, quaternionic Kaehler metrics and the Haydys-Hitchin correspondence, (v3) refereed version, restructured content, to appear in TAM

pySecDec: a toolbox for the numerical evaluation of multi-scale integrals

We present pySecDec, a new version of the program SecDec, which performs the factorization of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of the program is now written in the form of python modules, which allow a very flexible usage. The optimization of the C++ code, generated using FORM, is improved, leading to a faster numerical convergence. The new version also creates a library of the integrand functions, such that it can be linked to user-specific codes for the evaluation of matrix elements in a way similar to analytic integral libraries

Large scale analytic calculations in quantum field theories

We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.Comment: 25 pages Latex, 1 style fil

Estimated Risk for Altered Fetal Growth Resulting from Exposure to Fine Particles during Pregnancy: An Epidemiologic Prospective Cohort Study in Poland

The purpose of this study was to estimate exposure of pregnant women in Poland to fine particulate matter [≤2.5 μm in diameter (PM(2.5))] and to assess its effect on the birth outcomes. The cohort consisted of 362 pregnant women who gave birth between 34 and 43 weeks of gestation. The enrollment included only nonsmoking women with singleton pregnancies, 18–35 years of age, who were free from chronic diseases such as diabetes and hypertension. PM(2.5) was measured by personal air monitoring over 48 hr during the second trimester of pregnancy. All assessed birth effects were adjusted in multiple linear regression models for potential confounding factors such as the size of mother (maternal height, prepregnancy weight), parity, sex of child, gestational age, season of birth, and self-reported environmental tobacco smoke (ETS). The regression model explained 35% of the variability in birth weight (β = −200.8, p = 0.03), and both regression coefficients for PM(2.5) and birth length (β = −1.44, p = 0.01) and head circumference (HC; β = −0.73, p = 0.02) were significant as well. In all regression models, the effect of ETS was insignificant. Predicted reduction in birth weight at an increase of exposure from 10 to 50 μg/m(3) was 140.3 g. The corresponding predicted reduction of birth length would be 1.0 cm, and of HC, 0.5 cm. The study provides new and convincing epidemiologic evidence that high personal exposure to fine particles is associated with adverse effects on the developing fetus. These results indicate the need to reduce ambient fine particulate concentrations. However, further research should establish possible biologic mechanisms explaining the observed relationship