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.
