Abstract
We compare threshold resummation in QCD, as performed using soft-collinear effective theory (SCET) in the Becher–Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross-sections. We consider various forms of the SCET result, which correspond to different choices of the soft scale μs that characterizes this approach. We derive a master formula that relates the SCET resummation to the QCD result for any choice of μs. We then use it first, to show that if SCET resummation is performed in N-Mellin moment space by suitable choice of μs it is equivalent to the standard perturbative approach. Next, we show that if SCET resummation is performed by choosing for μs a partonic momentum variable, the perturbative result for partonic resummed cross-sections is again reproduced, but, like its standard perturbative counterpart, it is beset by divergent behaviour at the endpoint. Finally, using the master formula we show that when μs is chosen as a hadronic momentum variable the SCET and standard approach are related through a multiplicative (convolutive) factor, which contains the dependence on the Landau pole and associated divergence. This factor depends on the luminosity in a non-universal way; it lowers by one power of log the accuracy of the resummed result, but it is otherwise subleading if one assumes the luminosity not to contain logarithmically-enhanced terms. Therefore, the SCET approach can be turned into a prescription to remove the Landau pole from the perturbative result, but the price to pay for this is the reduction by one logarithmic power of the accuracy at each order and the need to make assumptions on the parton luminosity.
Highlights
We compare threshold resummation in QCD, as performed using soft-collinear effective theory (SCET) in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic crosssections
In order to proceed to a comparison, it is necessary to discuss the dependence of the SCET resummation on the soft scale: in Section 3 we summarize how SCET results in Mellin space, or in momentum space, at either the partonic or hadronic level can be obtained by different choices of soft scale
A comparison is made possible through the derivation of a general relation between the SCET result and the standard result, by expressing the latter in terms of the convolution of the former with a function Cr which depends on the soft scale. We establish this result at next-to-next-to-leading logarithmic order: it provides a master formula which enables a full comparison of the QCD and SCET results, both from an analytic and a numerical point of view. This master formula can be used to prove the fact that if SCET resummation is performed in Mellin space it is completely equivalent to the standard approach, and in particular it has the same logarithmic accuracy at each order
Summary
The interest in the resummation of logarithmically enhanced contributions due to soft gluon radiation in perturbative QCD (threshold resummation, ) has been recently revived due to its relevance for many LHC processes, such as Higgs [1] or top [2] production. This master formula can be used to prove the fact that if SCET resummation is performed in Mellin space it is completely equivalent to the standard approach, and in particular it has the same logarithmic accuracy at each order This result was established already in Refs. We conclude that it is only for a particular class of luminosities that SCET with a hadronic choice of soft scale reproduces the perturbative result, and can be considered to be equivalent to the standard approach and to provide an alternative prescription to remove the divergence of the perturbative expansion Even when this is the case, the momentum-space SCET resummation prescription of Ref. Subleading terms which are induced by SCET resummation are suppressed by powers or logs of the hadronic scale: this feature of SCET resummation may be a limitation, because the partonic and hadronic scales, though related, do not coincide, and it may well be that the former is close to threshold while the latter is not [27]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
