Abstract
I apply FDR—a recently introduced four-dimensional approach to quantum field theories (QFTs)—to the computation of the NLO QCD corrections to H rightarrow gg in the large top mass limit. The calculation involves all key ingredients of QCD—namely ultraviolet, infrared, and collinear divergences, besides alpha _S renormalization—and paves the way for successful use of FDR in massless one-loop QFT computations. I show in detail how the correct result emerges in FDR, and discuss the translation rules to dimensional regularization.
Highlights
Many of the difficulties of higher-order calculations in quantum field theories (QFTs) can be traced back to the treatment, in the framework of dimensional regularization (DR) [1], of the infinities arising in the intermediate steps of the computation
I present the first application of the FDR ideas in the context of fully massless QCD, where the issues related to gauge invariance are much more subtle than in the QED case
All CL/IR ln(μ2) and ln2(μ2) cancel in Eq (37), so that the remaining μ is directly interpreted as the renormalization scale. This is a typical procedure in FDR: since the UV infinities are subtracted from the very beginning, the unphysical left-over μ dependence is eliminated, on the perturbative level one is working at, by a finite renormalization, which fixes the bare parameters in terms of the observables [24]
Summary
Many of the difficulties of higher-order calculations in QFT can be traced back to the treatment, in the framework of dimensional regularization (DR) [1], of the infinities arising in the intermediate steps of the computation. The fact that the correct expression is reproduced shows that FDR is a valid and consistent approach in massless QFTs, and it gives confidence in its potential to simplify multi-leg/loop computations. There are five graphs contributing to the virtual part ΓV — without counting gluon wave-function corrections—and four diagrams for the real radiation ΓR. I separately compute, in FDR, the two pieces, showing how IR/CL divergences drop in the sum ΓV (H → gg) + ΓR(H → ggg)
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