Abstract
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.
Highlights
We stress that in order to obtain the physical NNLO result of the cross section e+e− → γ ∗ → 2 jets it is in principle sufficient to only use the virtual corrections in (3.8) since all contributions related to the evanescent coupling ee drop out in the final result
Extending previous studies to double-real and real-virtual corrections, we have investigated the regularization-schemedependence of a physical cross section at NNLO
As a case study we have considered two-jet production in electronpositron annihilation since for this process all computations can be done analytically
Summary
An efficient way to regularize UV and IR divergences at the same time is to formally shift the dimension of loop and phase-space integrations from (strictly) four to d ≡4−2 ,. It was found that cdr and dred are unitary in the sense that this cancellation is ensured by integrating the corresponding squared matrix elements over the phase space This is related to the fact that in these two schemes ’regular’ and ’singular’ vector bosons are treated .. The argument that in dred the real corrections are consistently obtained by integrating the corresponding fourdimensional matrix element over the d-dimensional phase space is independent of the order of perturbation theory. In order to do so, we (re)derive the well-known analytic NNLO result [35,36] of the QCD corrections to e+e− → γ ∗ → 2 jets using cdr and dred, respectively, and show that the partonic cross section is a regularization-scheme independent quantity. This is the first time that dred is used for real (and real-virtual) corrections at NNLO
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