  We show that the colour-singlet contributions to the hadroproduction of J/psi
in association with a W boson are sizable, if not dominant over the
colour-octet contributions. They are of two kinds, sg -> J/psi + c + W at
alpha^3_S alpha and q q'-bar -> gamma*/Z* W -> J/psi W at order alpha^3. These
have not been considered in the literature until now. Our conclusion is that
the hadroproduction of a J/psi in association with a W boson cannot be claimed
as a clean probe of the colour-octet mechanism. The rate are small even at the
LHC and it will be very delicate to disentangle the colour-octet contributions
from the sizable colour-singlet ones and from the possibly large
double-parton-scattering contributions. During this analysis, we have also
noted that, for reactions such as the production of a J/psi by light
quark-antiquark fusion, the colour-singlet contribution via an off-shell photon
is of the order of the expectation from the colour-octet contribution via an
off-shell gluon. This is relevant for inclusive production at low energies
close to the threshold. Such an observation also likely extends to other
processes naturally involving light-quark annihilation.
