  Photon diffractive dissociation, $\gamma p \to Xp$, has been studied at HERA
with the ZEUS detector using $ep$ interactions where the virtuality $Q^2$ of
the exchanged photon is smaller than 0.02 GeV$^2$. The squared four-momentum
$t$ exchanged at the proton vertex was determined in the range $0.073<|t|<0.40$
GeV$^2$ by measuring the scattered proton in the ZEUS Leading Proton
Spectrometer. In the photon-proton centre-of-mass energy interval $176<W<225$
GeV and for masses of the dissociated photon system $4<M_X<32$ GeV, the $t$
distribution has an exponential shape, $dN/d|t| \propto \exp{(-b|t|)}$, with a
slope parameter $b=6.8 \pm 0.9$~(stat.)~$ ^{+1.2}_{-1.1}$~(syst.)~GeV$^{-2}$.
