Abstract
A number of phenomenologically relevant processes at hadron colliders, such as Higgs and Z boson production in association with b quarks, can be conveniently described as scattering of heavy quarks in the initial state. We present a detailed analysis of this class of processes, identifying the form of the leading initial-state collinear logarithms that allow the relation of calculations performed in different flavour schemes in a simple and reliable way. This procedure makes it possible to assess the size of the logarithmically enhanced terms and the effects of their resummation via heavy-quark parton distribution functions. As an application, we compare the production of (SM-like and heavy) scalar and vector bosons in association with b quarks at the LHC in the four- and five-flavour schemes as well as the production of a heavy Z' in association with top quarks at a future 100 TeV hadron collider in the five- and six-flavour schemes. We find that, in agreement with a previous analysis of single heavy-quark initiated processes, the size of the initial-state logarithms is mitigated by a kinematical suppression. The most important effects of the resummation are a shift of the central predictions typically of about 20% at a justified value of the scale of each considered process and a significant reduction of scale variation uncertainties.
Highlights
JHEP09(2016)132 and the heavy quark is treated on the same footing as the light quarks: it contributes to the proton wave function and enters the running of the strong coupling constant αs
In this scheme the heavy quark mass is neglected in the matrix element and the collinear logarithms that may spoil the convergence of the perturbative expansion of the 4F scheme cross section are resummed to all orders in the evolution of the heavy quark parton density
A consistent and quantitative analysis of many processes involving one b quark in the initial state was performed and a substantial agreement between total cross sections obtained at next-to-leading order (NLO) in the two schemes found within the expected uncertainties
Summary
We start by considering Higgs boson production via bb fusion in the 4F scheme. The relevant partonic subprocess is g(p1) + g(p2) → b(k1) + H(k) + ̄b(k2),. The above results suggest that a “fair” comparison between calculations in the two schemes should be performed at factorisation/renormalisation scales smaller than the naıve choice μF = MH This evidence supports the conclusions drawn in previous studies [3], perhaps with a slightly larger value in the case of Higgs boson, μ ≈ MH /3 rather than MH /4. As observed in our previous work, at LO higher-order logarithms are important andb(1)(x, μ2) is a poor approximation of the fully resummed distribution function It overestimates the leading-log evolution of the b PDF by 20% at very small x and it underestimates it up to 30% at intermediate values of x. At NLO the explicit collinear logs present in a NLO 4F scheme calculation provide a rather accurate approximation of the whole resummed result at NLL; significant effects, of order up to 20%, appear predominantly at large values of x. A comparable behaviour was observed in ref. [18]
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