Improved factorization for threshold resummation in heavy quark to heavy quark decays

Abstract

We consider the resummation of soft-gluon effects in heavy quark to heavy quark decays, namely the processes Q_1 rightarrow Q_2 , + , mathrm {(non,QCD, partons)}, where Q_1 and Q_2 are two different heavy quarks. We construct a new factorization scheme for threshold resummed spectra, which allows us to consistently evaluate the distribution of the final hadron invariant mass m_X in all the kinematic regions, i.e. when m_X is smaller, of the same order, or larger than the mass of the final quark Q_2. A dependence of the improved Coefficient function on the threshold variable is introduced, which can however be relegated to a small interval of this variable by means of the so-called Partition of Unity. We explicitly apply our improved scheme to the b rightarrow X_s , + gamma decay at next-to-leading logarithmic accuracy.