Application of perturbative quantum chromodynamics to processes with heavy quarks

Abstract

In this thesis we discuss application of perturbative QCD to processes involving bottom and top quarks. We begin by considering the semileptonic B-meson decay to charmed final states B → Xcℓνℓ. We calculate two-loop QCD corrections to the partonic contribution to this process, given by the free b-quark decay b → cℓνℓ. We consider cases where the charged lepton in the final state is massless (e) or massive (τ ). We review techniques used in the computation of O(α2s) corrections to inclusive semileptonic b → c transitions and present extensive numerical studies of the two-loop QCD effects in b → cℓ¯νℓ decays, for ℓ = e, τ . Next, we explore determination of the top quark mass at hadron colliders, by studying correlations between kinematics of top quark decay products and the top quark mass. Some of these observables are anticipated to yield one percent accuracy (or better) in the extracted value of the top quark mass mt. The residual uncertainties in mt are mostly theoretical; they are usually estimated using parton shower Monte Carlo programs whose reliability at this level of precision is difficult to assess. We employ perturbative QCD at next-to-leading order to describe these observables and estimate the uncertainties in the values of mt that are extracted from them. We contrast these estimates with the results obtained by means of traditional parton showers for a few observables, often discussed in the context of high-precision top quark mass measurements at the LHC. We find that the parton showers are good in estimating central values, but that perturbative QCD provides us with both accurate central values and a trustworthy estimate of the uncertainties in the extracted value of the top quark mass mt.