| Summary: | Abstract We consider the resummation of soft-gluon effects in heavy quark to heavy quark decays, namely the processes $$Q_1 \rightarrow Q_2 \, + \, \mathrm {(non\,QCD\, partons)}$$ Q 1 → Q 2 + ( non QCD partons ) , where $$Q_1$$ Q 1 and $$Q_2$$ 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 $$m_X$$ m X in all the kinematic regions, i.e. when $$m_X$$ m X is smaller, of the same order, or larger than the mass of the final quark $$Q_2$$ 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 $$b \rightarrow X_s \, + \gamma $$ b → X s + γ decay at next-to-leading logarithmic accuracy.
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