ar X iv : h ep - p h / 02 05 08 1 v 1 8 M ay 2 00 2 MPI - PhT / 2002 - 18 May 2002 TOP DECAY AND BOTTOM FRAGMENTATION IN NLO QCD

We apply the method of perturbative fragmentation to study bottom fragmentation in top decay. We present the energy spectrum of b-quarks and b-flavoured hadrons in top decay. A reliable understanding of bottom-quark fragmentation in top-quark decay (t → bW) will be fundamental to accurately measure the top properties, such as its mass, at present and future high-energy colliders. At the LHC, final states with leptons and J/ψ, where the leptons are W-decay products and the J/ψ comes from the decay of a b-flavoured hadron, will be a promising channel to reconstruct the top mass m t 1. The error is estimated to be ∆m t ≃ 1 GeV and the b-fragmentation is the largest source of uncertainty, accounting for about 0.6 GeV. In this paper we investigate bottom fragmentation in top decay within the framework of perturbative fragmentation 2 and use phenomenological models to describe the b-quark hadronization. According to the factorization theorem, the rate for the production of a b-hadron in top decay can be written, up to power corrections, as the following convolution: 1 Γ 0 dΓ dx B (x B , m t , m b) = 1 Γ 0 d ˆ Γ dx b In Eq. (1), Γ 0 is the Born width of the process t → bW , d ˆ Γ/dx b is the rate for the production of a massless b quark in top decay (coefficient function), D p (x b , m b , µ F) is the perturbative fragmentation function which expresses the transition from a massless b into a massive b quark, µ F is the factorization scale, D np is the non-perturbative fragmentation function. x b and x B are the normalized b-quark and b-hadron energy fractions in top decay 3 .