Exclusive $\rho^0$ Meson Photoproduction with a Leading Neutron at HERA

A first measurement is presented of exclusive photoproduction of $\rho^0$ mesons associated with leading neutrons at HERA. The data were taken with the H1 detector in the years 2006 and 2007 at a centre-of-mass energy of 319 GeV and correspond to an integrated luminosity of 1.16/pb. The $\rho^0$ mesons with transverse momenta $p_T$0.35, are detected in the Forward Neutron Calorimeter having a polar angular acceptance < 0.75 mrad. Single- and double-differential cross sections are measured as a function of several variables. The data are interpreted in terms of a double peripheral process, involving pion exchange at the proton vertex followed by elastic photoproduction of a $\rho^0$ meson on the virtual pion. In the framework of one-pion-exchange dominance the elastic cross section of photon-pion scattering is extracted. The value of this cross section indicates significant absorptive corrections for the exclusive reaction $\gamma p \to \rho^0 n \pi^+$