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

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

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

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

Loopedia, a Database for Loop Integrals

Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of SPIRES or arXiv in the sense that it admits searching for integrals by graph-theoretical objects, e.g. its topology.Comment: 16 pages, lots of screenshot

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

Probing the scalar potential via double Higgs boson production at hadron colliders

We present a sensitivity study on the cubic and quartic self couplings in double Higgs production via gluon fusion at hadron colliders. Considering the relevant operators in the Standard Model Effective Field Theory up to dimension eight, we calculate the dominant contributions up to two-loop level, where the first dependence on the quartic interaction appears. Our approach allows to study the independent variations of the two self couplings and to clearly identify the terms necessary to satisfy gauge invariance and to obtain UV-finite results order by order in perturbation theory. We focus on the bb¯ γγ signature for simplicity and provide the expected bounds for the cubic and quartic self couplings at the 14 TeV LHC with 3000 fb −1 (HL-LHC) and for a future 100 TeV collider (FCC-100) with 30 ab −1 . We find that while the HL-LHC will provide very limited sensitivity on the quartic self coupling, precision measurements of double Higgs production at a FCC-100 will offer the opportunity to set competitive bounds. We show that combining information from double and triple Higgs production leads to significantly improved prospects for the determination of the quartic self coupling

Factors for of the formation of the quality of professional training of a skilled worker

В статті розглянуто особливості формування якості професійної підготовки здобувачів освіти в закладах професійної (професійно-технічної) освіти в умовах реалізації Закону України «Про освіту». Розглянута важливість проектування освітнього процесу закладів професійної (професійно-технічної) освіти на основі результатів навчання, які мають оцінюватися як навчальні досягнення здобувачів освіти та формують їх професійну компетентність, що, в свою чергу, забезпечує підвищення конкурентоздатності випускників на ринку праці.The article considers the peculiarities of the formation of the quality of the professional training of applicants for education in the institutions of vocational (vocational) education in the conditions of implementation of the Law of Ukraine "On Education". Considered the importance of designing the educational process of professional (vocational) education institutions based on learning outcomes, which should be evaluated as educational achievements of the education providers and form their professional competence, which, in turn, ensures higher competitiveness of graduates in the labor market