New predictions for inclusive heavy-quarkonium P-wave decays

We show that some NRQCD colour-octet matrix elements can be written in terms of (derivatives of) wave functions at the origin and non-perturbative universal constants once the factorization between the soft and ultrasoft scale is achieved by using an effective field theory where only ultrasoft degrees of freedom are kept as dynamical entities. This allows us to derive a new set of relations between inclusive heavy-quarkonium P-wave decays into light hadrons with different principal quantum number and with different heavy flavour. In particular, we can estimate the branching ratios of bottomonium P-wave states by using charmonium data.