The leading jet transverse momentum in inclusive jet production and with a loose jet veto

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. p T,J p veto T . 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 2 s ln 2 R corrections are several precent, while in exclusive cross sections at large p T,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. 1 Factorization formulae where a different number of jet functions appear at different orders in perturbation theory have also been obtained in refs. [23,24].2 Indeed, we extract dσpp→Hij by expanding eq. (2.2) to NLO, and subtracting the contribution involving the NLO jet function. This is discussed in detail in section 4.1.

Leading jets and energy loss

“…The factorization in eq. (2.5) holds up to power corrections O(R 2 ) which are usually found to be small even for large values of R [24,73]. The first two symbols ⊗ in eq.…”

“…The O(α s ) correction of the leading and subleading jet functions was first discussed in ref. [24]. Here we denote the leading jet function by J i (z 1 , QR, µ) which depends on the momentum fraction z 1 of the leading jet relative to the initial scale Q of the fragmenting quark or gluon, see the right panel of figure 1.…”

“…In refs. [18,24] an iterative approach was used starting with the LO jet function as the initial condition of the evolution. However, this approach is impractical when the whole NLO jet function is evolved and when additional threshold logarithms are resummed to all orders which is discussed in more detail in section 4 below.…”

“…The non-linear RG equation resums logarithms of the jet radius R. In ref. [24], these results were extended by including the full fixed order jet function at next-to-leading order (NLO). In addition, the jet functions were incorporated using a complete factorization formula at NLO which was obtained within Soft Collinear Effective Theory (SCET) [25][26][27][28][29].…”

“…Here we further extend the work of ref. [24] by evolving the entire NLO jet function using a parton shower Monte Carlo approach and we include the resummation of threshold logarithms [30,31] which dominate the cross section when the momentum fraction carried by the leading jet relative to the initial parton approaches unity. In addition, we focus specifically on cross sections where an additional reference scale Q is measured such that we can directly measure the momentum fraction of the leading jet relative to Q.…”