b-Initiated processes at the LHC: a reappraisal

TL;DR

This paper critically reevaluates the use of 4-flavor and 5-flavor schemes in describing $b$-quark processes at the LHC, showing that both schemes can be effectively used together due to their complementary advantages.

Contribution

It provides a detailed analysis of the conditions under which 4-flavor and 5-flavor schemes are applicable, advocating for their combined use in different observables at the LHC.

Findings

4-flavor computations are perturbatively well-behaved.

Predictions in the two schemes largely agree.

Resummation effects are significant only at large Bjorken x.

Abstract

Several key processes at the LHC in the standard model and beyond that involve $b$ quarks, such as single-top, Higgs, and weak vector boson associated production, can be described in QCD either in a 4-flavor or 5-flavor scheme. In the former, $b$ quarks appear only in the final state and are typically considered massive. In 5-flavor schemes, calculations include $b$ quarks in the initial state, are simpler and allow the resummation of possibly large initial state logarithms of the type $\log \frac{{\cal Q}^2}{m_b^2}$ into the $b$ parton distribution function (PDF), ${\cal Q}$ being the typical scale of the hard process. In this work we critically reconsider the rationale for using 5-flavor improved schemes at the LHC. Our motivation stems from the observation that the effects of initial state logs are rarely very large in hadron collisions: 4-flavor computations are pertubatively well behaved and a substantial agreement between predictions in the two schemes is found. We identify two distinct reasons that explain this behaviour, i.e., the resummation of the initial state logarithms into the $b$-PDF is relevant only at large Bjorken $x$ and the possibly large ratios ${\cal Q}^2/m_b^2$'s are always accompanied by universal phase space suppression factors. Our study paves the way to using both schemes for the same process so to exploit their complementary advantages for different observables, such as employing a 5-flavor scheme to accurately predict the total cross section at NNLO and the corresponding 4-flavor computation at NLO for fully exclusive studies.