  Diffractive photoproduction of vector mesons, gamma p --> V Y, where Y is a
proton-dissociative system, has been measured in ep interactions with the ZEUS
detector at HERA using an integrated luminosity of 25 pb^-1. The differential
cross section, ds/dt, is presented for -t<12 GeV^2, where t is the square of
the four-momentum transferred to the vector meson. The data span the range in
photon-proton centre-of-mass energy, W, from 80 GeV to 120 GeV. The t
distributions are well fit by a power law, ds/dt ~ (-t)^{-n}. The slope of the
Pomeron trajectory, measured from the W dependence of the rho^0 and phi cross
sections in bins of t, is consistent with zero. The ratios ds_(gamma p --> phi
Y)/dt to ds_(gamma p --> rho^0 Y)/dt and ds_(gamma p --> J/psi Y)/dt to
ds_(gamma p --> rho^0 Y)/dt increase with increasing -t. Decay-angle analyses
for rho^0, phi and J/psi mesons have been carried out. For the rho^0 and phi
mesons, contributions from single and double helicity flip are observed. The
results are compared to expectations of theoretical models.
