7 research outputs found
Computation of in FDH and DRED: renormalization, operator mixing, and explicit two-loop results
The 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
-scalar contributions. In FDH and DRED there are additional
dimension-5 operators generating the vertices, where 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
to complete the study of the infrared divergence structure of two-loop
amplitudes in FDH and DRED
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
Regularization-scheme dependence of QCD amplitudes in the massive case
We investigate QCD amplitudes with massive quarks computed in the four-dimensional 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 velocity-dependent 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