Fitting the b-quark PDF as a massive-b scheme: Higgs production in bottom fusion

Abstract

We show that a simple and accurate approach to the computation of hadron collider processes involving initial-state b quarks can be obtained by introducing an independently parametrized b PDF. We use the so-called FONLL method for the matching of a scheme in which the b quark is treated as a massless parton to that in which it is treated as a massive state, and extend it to the case in which the b quark PDF is not necessarily determined by perturbative matching conditions. This generalizes to hadronic collisions analogous results previously obtained for deep-inelastic scattering. The results corresponds to a "massive b" scheme, in which b mass effects are retained, yet the b quark is endowed with a PDF. We specifically study Higgs production in bottom fusion, and show that our approach overcomes difficulties related to the fact that in a standard massive four-flavor scheme b-quark induced processes only start at high perturbative orders. arXiv:1905.02207v2 [hep-ph] 18 Jul 20191 The treatment of heavy quark PDFs It has been recently shown [1] that for accurate phenomenology at the LHC it is advantageous to treat the charm parton distribution (PDF) on the same footing as light-quark PDFs, namely, to parametrize it and extract it from data, rather than to take it as radiatively generated from the gluon using perturbative matching conditions. This is likely to be due to the fact that matching conditions are only known to the lowest nontrivial order, which may well be subject to large higher order corrections, as revealed by the strong dependence of results on the choice of matching scale. On top of this, of course, the starting low-scale heavy quark PDFs could in principle also have a non-perturbative "intrinsic" component [2,3]. It is important to note that whether or not the heavy quark PDF has a nonperturbative component, and whether it is advantageous to parametrize the heavy quark PDF are separate issues: in fact in Ref. [1] it was shown that the main phenomenological advantage in parametrizing and fitting the charm PDF comes from a region in which any nonperturbative contribution to charm is likely to be extremely small.The case of the bottom quark PDF is, in this respect, particularly interesting. On the one hand, one may think that that the problem of large higher order corrections to the matching conditions is alleviated in this case by the larger value of the mass. However, on the other hand, there is a more subtle consideration. Namely, there are b-initiated hadron collider processes -some of which are especially relevant for new physics searches -such as Higgs production in bottom fusion, for which b quark mass effects might be nonnegligible [4][5][6]. This suggests the use of a scheme in which the b quark is treated as a massive final-state parton -hence not endowed with a PDF. In such a scheme the b-induced process necessarily starts at a higher perturbative order than in a scheme in which there exists a b PDF, because the b production process is included in the hard matrix element. As a consequence, th...

V and Heavy Flavour production: status and recent theoretical developments

“…The latter issue has instead recently been resolved [8]. Indeed it has been shown that a 5F massive scheme 1 can be consistently construct by simply constructing a parametrised b-PDF, and performing the FONLL matching between the 4FS and the 5FS: the matched FONLL result is indeed identical to what is defined in Ref.…”

Theoretical view on Heavy Flavours and jets

“…[19] for a methodology based on the idea of vetoing -hadrons, and to Refs. [20,21], for the formulation of a massive 5FS with consistent -quark PDFs to be used in association with massive initial states [22]. A promising avenue for matching 4FS and 5FS at the level of exclusive observable is based on multi-jet merging: the simulations in the 5FS are merged with the calculations of the production of -quark associated final states in the 4FS [23].…”

A massive variable flavour number scheme for the Drell-Yan process

“…Alternatively one can develop a scheme which combines these approaches, providing a uniform description of the scattering process across arbitrary energy scales-such a description is provided by a massive variable flavour number scheme. This topic has been studied in various contexts in the past [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], and with particular focus on the process of lepton-nucleon scattering [22][23][24][25][26][27][28][29][30][31]. In the latter case, it is well understood how to apply such a formalism to the description of nucleon structure functions.…”