Abstract
We study the transverse momentum of the leading jet in the limit where the jet radius is small, R ≪ 1. We introduce the leading-jet function to calculate this cross section for an inclusive jet sample, and the subleading-jet function when a loose veto on additional jets is imposed, i.e. {}_{PTJ}{underset{sim }{>}}_{P_T^{mathrm{veto}}} . These jet functions are calculated at next-to-leading order in QCD and the resummation of jet radius logarithms is explored. We present phenomenological results for Higgs + 1 jet production, for both the jet and Higgs transverse momentum distribution. We find that, while the R ≪ 1 limit of the cross section provides a good description of the full NLO result, even for values as large as R = 0.8, simply retaining the leading logarithm at this order does not. Indeed, the NLO contribution to the hard function and, to a lesser extent, non-logarithmic corrections to the jet function are sizable and must be included to obtain the correct cross section. In the inclusive cross section we find that the {alpha}_s^2 ln2R corrections are several precent, while in exclusive cross sections at large pT ,J and small R they can reach 20%. However, it is not clear how important the resummation of these logarithms is, given the presence of other large corrections at NNLO.
Highlights
Equation resums the logarithms of R, and we assess the importance of these corrections in Higgs + 1 jet production
While the R 1 limit of the cross section provides a good description of the full next-to-leading order (NLO) result, even for values as large as R = 0.8, retaining the leading logarithm at this order does not
It is clear from the ratio plots, that the NNLO leading logarithms (LL) corrections for R = 0.4 have a smaller impact on the quark jet function, where they are below 4%, than for the gluon where they approach 10% for larger zl
Summary
The differential cross section dσp(0p)→Hi describes the production of a Higgs boson and parton i at leading order in QCD with transverse momentum pT,i. As such, it contains the convolution with initial-state parton distribution functions, along with the usual sum over contributing partonic channels. We examine zl → 1 limit of the leading-jet functions, where almost all of the jet momentum is carried by a single parton This limit is interesting because of the soft singularity of QCD, and the NLO results for the jet functions reduce to.
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