γ5\gamma_{5} in FDH

We investigate the regularization-scheme dependent treatment of $\gamma_{5}$ in the framework of dimensional regularization, mainly focusing on the four-dimensional helicity scheme (FDH). Evaluating distinctive examples, we find that for one-loop calculations, the recently proposed four-dimensional formulation (FDF) of the FDH scheme constitutes a viable and efficient alternative compared to more traditional approaches. In addition, we extend the considerations to the two-loop level and compute the pseudo-scalar form factors of quarks and gluons in FDH. We provide the necessary operator renormalization and discuss at a practical level how the complexity of intermediate calculational steps can be reduced in an efficient way.Comment: 28 pages, 7 figure

Small-mass effects in heavy-to-light form factors

We present the heavy-to-light form factors with two different non-vanishing 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.Comment: 20 pages, 4 figures, 1 ancillary file, published versio

Two-loop results on the renormalization of vacuum expectation values and infrared divergences in the FDH scheme

Recent progress in the understanding of vacuum expectation values and of infrared divergences in different regularization schemes is reviewed. Vacuum expectation values are gauge and renormalization-scheme dependent quantities. Using a method based on Slavnov-Taylor identities, the renormalization properties could be better understood. The practical outcome is the computation of the beta functions for vacuum expectation values in general gauge theories. The infrared structure of gauge theory amplitudes depends on the regularization scheme. The well-known prediction of the infrared structure in CDR can be generalized to the FDH and DRED schemes and is in agreement with explicit computations of the quark and gluon form factors. We discuss particularly the correct renormalization procedure and the distinction between MSbar and DRbar renormalization. An important practical outcome are transition rules between CDR and FDH amplitudes.Comment: 8 pages, proceedings for Loops and Legs in Quantum Field Theory 2014, Weimar, German

SCET approach to regularization-scheme dependence of QCD amplitudes

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 soft-collinear 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.Comment: 46 pages, 6 figure

Computation of H→ggH\to gg in FDH and DRED: renormalization, operator mixing, and explicit two-loop results

The $H\to gg$ 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. The required renormalization is developed and described in detail, including the treatment of evanescent $\epsilon$-scalar contributions. In FDH and DRED there are additional dimension-5 operators generating the $H g g$ vertices, where $g$ can either be a gluon or an $\epsilon$-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 to complete the study of the infrared divergence structure of two-loop amplitudes in FDH and DRED

GM2Calc: Precise MSSM prediction for (g−2)(g - 2) of the muon

We present GM2Calc, a public C++ program for the calculation of MSSM contributions to the anomalous magnetic moment of the muon, $(g-2)_\mu$. The code computes $(g-2)_\mu$ precisely, by taking into account the latest two-loop corrections and by performing the calculation in a physical on-shell renormalization scheme. In particular the program includes a $\tan\beta$ resummation so that it is valid for arbitrarily high values of $\tan\beta$, as well as fermion/sfermion-loop corrections which lead to non-decoupling effects from heavy squarks. GM2Calc can be run with a standard SLHA input file, internally converting the input into on-shell parameters. Alternatively, input parameters may be specified directly in this on-shell scheme. In both cases the input file allows one to switch on/off individual contributions to study their relative impact. This paper also provides typical usage examples not only in conjunction with spectrum generators and plotting programs but also as C++ subroutines linked to other programs.Comment: 27 pages, 4 figures, 4 listings; version sent to EPJ

Dimensional schemes for cross sections at NNLO

So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of physical cross sections at next-to-next-to-leading order. As a case study we consider two-jet production in electron-positron annihilation and describe how to compute the various parts separately in different schemes. In particular, we verify that using dimensional reduction the double-real corrections are obtained simply by integrating the four-dimensional matrix element over the phase space. In addition, we confirm that the cross section is regularization-scheme independent.Comment: 20 pages, 2 figure