The Higgs-boson mass used to be the only unknown input parameter of the electroweak contributions to ðg À 2Þ in the Standard Model. It enters at the two-loop level in diagrams with, e.g., top loops, W, or Z exchange. We reevaluate these contributions, providing analytic expressions and exact numerical results for the Higgs-boson mass recently measured at the LHC. Our final result for the full Standard Model electroweak contributions is ð153:6 AE 1:0Þ Â 10 À11 , where the remaining theory error comes from unknown three-loop contributions and hadronic uncertainties.

We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.

We consider variants of dimensional regularization, including the four-dimensional helicity scheme (fdh) and dimensional reduction (dred), and present the gluon and quark form factors in the fdh scheme at next-to-next-to-leading order. We also discuss the generalization of the infrared factorization formula to fdh and dred. This allows us to extract the cusp anomalous dimension as well as the quark and gluon anomalous dimensions at nextto-next-to-leading order in the fdh and dred scheme, using MS and DR renormalization. To obtain these results we also present the renormalization procedure in these schemes.

Abstract:We investigate the regularization-scheme dependence of scattering amplitudes in massless QCD and find that the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED) are consistent at least up to NNLO in the perturbative expansion if renormalization is done appropriately. Scheme dependence is shown to be deeply linked to the structure of UV and IR singularities. We use jet and soft functions defined in softcollinear effective theory (SCET) to efficiently extract the relevant anomalous dimensions in the different schemes. This result allows us to construct transition rules for scattering amplitudes between different schemes (CDR, HV, FDH, DRED) up to NNLO in massless QCD. We also show by explicit calculation that the hard, soft and jet functions in SCET are regularization-scheme independent.

Recently, first results were presented for two-loop corrections to the muon (g − 2) from fermion/sfermion loops in the MSSM. These corrections were shown to be generally large and even logarithmically enhanced for heavy sfermions. Here, full details of the calculation and analytical results are presented. Also, a very compact formula is provided which can be easily implemented and serves as a good approximation of the full result as a function of the fourteen most important input parameters. Finally, a thorough discussion of the numerical behaviour of the fermion/sfermion-loop corrections to (g − 2) µ is given. The discussion includes the case of very heavy SUSY masses as well as experimentally allowed scenarios with very light SUSY masses.

We present the heavy-to-light form factors with two different nonvanishing masses at next-to-next-to-leading order and study its expansion in the small mass. The leading term of this small-mass expansion leads to a factorized expression for the form factor. The presence of a second mass results in a new feature, in that the soft contribution develops a factorization anomaly. This cancels with the corresponding anomaly in the collinear contribution. With the generalized factorization presented here, it is possible to obtain the leading small-mass terms for processes with large masses, such as muon-electron scattering, from the corresponding massless amplitude and the soft contribution.

Abstract:We investigate QCD amplitudes with massive quarks computed in the fourdimensional helicity scheme (FDH) and dimensional reduction at NNLO and describe how they are related to the corresponding amplitudes computed in conventional dimensional regularization. To this end, the scheme dependence of the heavy quark and the velocitydependent cusp anomalous dimensions is determined using soft-collinear effective theory. The results are checked against explicit computations of massive form factors in FDH at NNLO. Our results complete the description of the scheme dependence of QCD amplitudes at NNLO.

The H → gg amplitude relevant for Higgs production via gluon fusion is computed in the four-dimensional helicity scheme (fdh) and in dimensional reduction (dred) at the two-loop level in the limit of heavy top quarks. The required renormalization is developed and described in detail, including the treatment of evanescent -scalar contributions. In fdh and dred there are additional dimension-5 operators generating the Hgg vertices, where g can either be a gluon or an -scalar. An appropriate operator basis is given and the operator mixing through renormalization is described. The results of the present paper provide building blocks for further computations, and they allow one to complete the study of the infrared divergence structure of two-loop amplitudes in fdh and dred.