The total cross section for the photoproduction process with a leading proton in the final state has been measured at γp centre-of-mass energies W of 91, 181 and 231 GeV. The measured cross sections apply to the kinematic range with the transverse momentum of the scattered proton restricted to p T ≤ 0.2 GeV and 0.68 ≤ z ≤ 0.88, where z = E ′ p /E p is the scattered proton energy normalised to the beam energy. The cross section dσ γp→Xp ′ (W, z)/dz is observed to be independent of W and z within the measurement errors and amounts to (8.05±0.06 (stat)±0.89 (syst)) µb on average. The data are well described by a Triple Regge model in which the process is mediated by a mixture of exchanges with an effective Regge trajectory of intercept α i (0) = 0.33 ± 0.04 (stat) ± 0.04 (syst). The total cross section for the interaction of the photon with this mixture (γα i → X) can be described by an effective trajectory of intercept α k (0) = 0.99 ± 0.01 (stat) ± 0.05 (syst). Predictions based on previous triple Regge analyses of pp → pX data assuming vertex factorisation are broadly consistent with the γp data. The measured cross sections are compared with deep inelastic scattering leading proton data in the same region of z and p T for photon virtuality Q 2 > 2.5 GeV 2 . The ratio of the cross section for leading proton production to the total cross section is found to rise with Q 2 .To be submitted to Nucl. Phys. B
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