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.
Highlights
The problem is somewhat alleviated if the massivescheme and massless-scheme computations are combined, with the b-PDF in the massless scheme assumed to be produced by perturbative matching conditions
An independently parametrized heavy quark PDF is included in the so-called FONLL method [12], which allows for the matching of a scheme in which the heavy quark mass is included but the heavy quark decouples from QCD evolution equations, and a massless scheme in which the heavy quark mass is neglected, but the heavy quark PDF couples to perturbative evolution
For the pure five-flavor scheme and for FONLL-BP we show the three curves corresponding to the three different choices for the b PDF discussed above, with a corresponding band: the central, thick, solid line represents the default μb = mb choice, while the edges of the band are drawn with dot-dash curves with decreasing thickness, with the thicker and the other two μb of the two corresponding to μb
Summary
The case of the bottom quark PDF is, in this respect, 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. Because the only data currently used for PDF determination in which heavy quark mass effects have a significant impact are deep-inelastic scattering data close to the charm production threshold, in these references only electroproduction was considered and only the parametrization of the charm was studied In these previous studies, an independently parametrized heavy quark PDF is included in the so-called FONLL method [12], which allows for the matching of a scheme in which the heavy quark mass is included but the heavy quark decouples from QCD evolution equations, and a massless scheme in which the heavy quark mass is neglected, but the heavy quark PDF couples to perturbative evolution. We compare predictions obtained within this approach with some plausible choices of the b-quark PDF to those obtained in the approach of Refs. [13,14], and argue that results with similar or better phenomenological accuracy can be obtained in a much simpler way within this new approach
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