Higgs-mass dependence of two-loop corrections to Delta r

The Higgs-mass dependence of the Standard Model contributions to the correlation between the gauge-boson masses is studied at the two-loop level. Exact results are given for the Higgs-dependent two-loop corrections associated with the fermions, i.e. no expansion in the top-quark and the Higgs-boson mass is made. The results for the top quark are compared with results of an expansion up to next-to-leading order in the top-quark mass. Agreement is found within 30% of the two-loop result. The remaining theoretical uncertainties in the Higgs-mass dependence of Delta r are discussed.Comment: 10 pages, LaTeX, minor changes, version to appear in Phys. Lett.

Reduction and evaluation of two-loop graphs with arbitrary masses

We describe a general analytic-numerical reduction scheme for evaluating any 2-loop diagrams with general kinematics and general renormalizable interactions, whereby ten special functions form a complete set after tensor reduction. We discuss the symmetrical analytic structure of these special functions in their integral representation, which allows for optimized numerical integration. The process Z -> bb is used for illustration, for which we evaluate all the 3-point, non-factorizable g^2*alpha_s mixed electroweak-QCD graphs, which depend on the top quark mass. The isolation of infrared singularities is detailed, and numerical results are given for all two-loop three-point graphs involved in this process

Analytical and numerical methods for massive two-loop self-energy diagrams

Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and especially four dimensions.This is done in three respects firstly results in terms of generalized, multivariable hypergeometric functions are presented giving explicit series for small and large momenta. Secondly the imaginary parts of these integrals are expressed as complete elliptic integrals.Finally one-dimensional integral representations with elementary functions are derived.They are very well suited for the numerical evaluations.Comment: 24 page

The effective electroweak mixing angle sin⁡2θeff\sin^2\theta_{eff} with two-loop fermionic contributions

We present the results from a calculation of the full electroweak two-loop fermionic contributions to the effective leptonic mixing angle of the $Z$ boson, $\sin^2\theta_{eff}$, in the Standard Model. On-shell renormalization and analytic calculations are performed for the three-point vertex functions at zero external momenta, whereas irreducible three-point integrals for non-vanishing external momenta are evaluated semi-analytically applying two different methods. Comparisons with a previous calculation show complete agreement.Comment: 15 pages, 5 figures, reference added, few typos correcte

Hadronic light-by-light corrections to the muon g-2: the pion-pole contribution

The correction to the muon anomalous magnetic moment from the pion-pole contribution to the hadronic light-by-light scattering is considered using a description of the pi0 - gamma* - gamma* transition form factor based on the large-Nc and short-distance properties of QCD. The resulting two-loop integrals are treated by first performing the angular integration analytically, using the method of Gegenbauer polynomials, followed by a numerical evaluation of the remaining two-dimensional integration over the moduli of the Euclidean loop momenta. The value obtained, a_{mu}(LbyL;pi0) = +5.8 (1.0) x 10^{-10}, disagrees with other recent calculations. In the case of the vector meson dominance form factor, the result obtained by following the same procedure reads a_{mu}(LbyL;pi0)_{VMD} = +5.6 x 10^{-10}, and differs only by its overall sign from the value obtained by previous authors. Inclusion of the eta and eta-prime poles gives a total value a_{mu}(LbyL;PS) = +8.3 (1.2) x 10^{-10} for the three pseudoscalar states. This result substantially reduces the difference between the experimental value of a_{mu} and its theoretical counterpart in the standard model.Comment: 27 pages, Latex, 3 figures. v2: version to be published in Phys. Rev. D, Note added and references updated (don't worry, sign has not changed

The effective electroweak mixing angle sin⁡2θeff\sin^2\theta_{eff} with two-loop bosonic contributions

We present the results for the full electroweak two-loop bosonic contributions to the effective leptonic mixing angle of the $Z$ boson, $\sin^2\theta_{\rm eff}$, in the Standard Model. A method applied to extract collinear divergences from two-loop vertex-functions is described. Comparisons of our results with those from a recent previous calculation show complete agreement.Comment: 14 pages, 3 figures, 4 table

Analysis of the vector and axialvector BcB_c mesons with QCD sum rules

In this article, we study the vector and axialvector $B_c$ mesons with the QCD sum rules, and make reasonable predictions for the masses and decay constants, then calculate the leptonic decay widths. The present predictions for the masses and decay constants can be confronted with the experimental data in the future. We can also take the masses and decay constants as basic input parameters and study other phenomenological quantities with the three-point vacuum correlation functions via the QCD sum rules.Comment: 14 pages, 16 figure

Dispersive calculation of the massless multi-loop sunrise diagram

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.Comment: 10 pages, 1 figure, LATEX, uses kluwer.cls, some references adde

Evaluating massive planar two-loop tensor vertex integrals

Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones in the two-loop corrections necessary, for instance, for the decay of the Z^0 boson. Instead of calculating particular decay processes, we present the new algorithm which allows one to calculate arbitrary NNLO calculations for massive planar two-loop vertex functions in the general mass case. All integration steps up to the last two ones are performed analytically and will be implemented under xloops as part of the Mainz xloops-GiNaC project. The last two integrations are done numerically using methods like VEGAS and Divonne. Thresholds originating from Landau singularities are found and discussed in detail. In order to demonstrate the numeric stability of our methods we consider particular Feynman integrals which contribute to different physical processes. Our results can be generalized to the case of the crossed topology.Comment: 51 pages in LaTeX, including 13 figures and 6 table