Progress in bottom - quark fragmentation

I review recent progress on bottom-quark fragmentation in e + e − annihilation, top-quark decay and H → b ¯ b processes. I discuss the implementation of collinear and soft resummation, and the inclusion of non-perturbative information taken from LEP and SLD data. Heavy-quark physics is currently one of the major fields of investigation in experimental and theoretical particle physics. In order to investigate heavy-quark phenomenology, fixed-order calculations are reliable as long as one considers inclusive observables, such as total cross sections. For less inclusive quantities, one needs to resum large contributions, which correspond to collinear or soft parton radiation. In this talk I will investigate bottom-quark production in e + e − → b ¯ b processes, top-quark decay t → bW , and Standard Model Higgs decay H → b ¯ b. In particular, I wish to study the energy distribution of b quarks and b-flavoured hadrons in such processes. The results will be expressed in terms of the b normalized energy fraction x b , which is given, e.g. in Higgs decay H → b ¯ b(g), by: 2 x b = 2p b · p H m 2 H. (1) The differential distribution for the production of a massive b quark at next-to-leading order (NLO) in the strong coupling constant α S is given by the following general result: 1 Γ 0 dΓ dx b = δ(1 − x b) + α S (µ) 2π P qq (x b) ln m 2 H m 2 b + A(x b) + O m 2 b m 2 H p. (2) In Eq. (2) Γ 0 is the width of the Born process, µ is the renormalization scale, A(x b) is a function independent of m b , p ≥ 1, P qq (x b) is the Altarelli–Parisi splitting function: P qq (x b) = C F 1 + x 2 b 1 − x b +. (3) Equation (2) is formally equal to the bottom energy spectrum in top decay or e + e − processes: one will just have to replace m H with the top mass or the centre-of-mass energy √ s of the e + e − collision. Function A(x b) is instead process-dependent. Equation (2) presents a large mass logarithm ∼ α S ln(m 2 H /m 2 b), which needs to be resummed to all orders to improve the prediction. To achieve …