Elastic and proton-dissociative ρ⁰ photoproduction at HERA

Elastic and proton-dissociative ρ⁰ photoproduction (γp → p⁰p, γp → ρ⁰N, respectively, with p⁰ → π⁺π^-) has been studied in ep interactions at HERA for photon-proton centre-of-mass energies in the range 50 < W < 100 GeV and for |t| < 0.5 GeV², where t is the square of the four-momentum transfer at the proton vertex; the results on the proton-dissociative reaction are presented for masses of the dissociated proton system in the range M² _N < 0.1W². For the elastic process, the π⁺π^- invariant mass spectrum has been investigated as a function of t. As in fixed target experiments, the ρ⁰ resonance shape is asymmetric; this asymmetry decreases with increasing |t|, as expected in models in which the asymmetry is ascribed to the interference of resonant and non-resonant π⁺π^- production. The cross section has been studied as a function of W; a fit to the resonant part with the form W^a gives a = 0.16 ± 0.06 (stat.) ^+0.11 _-0.15 (syst.). The resonant part of the γp → π⁺π^-p cross section is 11.2 ± 0.1 (stat.) ^+1.1 _-1.2 (syst.) μb at 〈W〉 = 71.7 GeV. The t dependence of the cross section can be described by a function of the type A_ρ exp (-b_ρ|t| + c_ρt²) with b_ρ = 10.9 ± 0.3 (stat.) ^+1.0 _-0.5 (syst.) GeV^-2 and c_ρ = 2.7 ± 0.9 (stat.) ^+1.9 _-1.7 (syst.) GeV^-4. The t dependence has also been studied as a function of W and a value of the slope of the pomeron trajectory α _IP′ = 0.23 ± 0.15 (stat.) ^+0.10 _-0.07 (syst.) GeV^-2 has been deduced. The ρ⁰ spin density matrix elements r⁰⁴ ₀₀ r⁰⁴ _1-1 and ℜe[r⁰⁴ ₁₀] have been measured and found to be consistent with expectations based on s-channel helicity conservation. For proton-dissociative π⁺π^- photoproduction in the ρ⁰ mass range, the distributions of the two-pion invariant mass, W and the polar and azimuthal angles of the pions in the helicity frame are the same within errors as those for the elastic process. The t distribution has been fitted to an exponential function with a slope parameter 5.8 ± 0.3 (stat.) ± 0.5 (syst.) GeV^-2. The ratio of the elastic to proton-dissociative ρ⁰ photoproduction cross section is 2.0 ± 0.2 (stat.) ± 0.7 (syst.).