| Summary: | 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 > ~ P T veto $$ {}_{PTJ}{\underset{\sim }{>}}_{P_T^{\mathrm{veto}}} $$ . 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 α s 2 $$ {\alpha}_s^2 $$ ln2 R 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.
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