Measurement of exclusive π${}^{+}$π${}^{-}$ and ρ${}^0$ meson photoproduction at HERA

Exclusive photoproduction of ρ${}^0$(770) mesons is studied using the H1 detector at the ep collider HERA. A sample of about 900000 events is used to measure single- and double-differential cross sections for the reaction γp→π${}^{+}$π${}^{\text{â}}\text{ˆ}\text{’}$Y. Reactions where the proton stays intact (m${}_Y$=m${}_p$) are statistically separated from those where the proton dissociates to a low-mass hadronic system (m${}_p$< m${}_Y$< 10 GeV). The double-differential cross sections are measured as a function of the invariant mass m${}_{\pi \pi }$ of the decay pions and the squared 4-momentum transfer t at the proton vertex. The measurements are presented in various bins of the photon-proton collision energy W${}_{\gamma p}$. The phase space restrictions are 0.5 < m${}_{\pi \pi }$< 2.2 GeV, |t| < 1.5 GeV${}^2$, and 20 < W${}_{\gamma p}$< 80 GeV. Cross section measurements are presented for both elastic and proton-dissociative scattering. The observed cross section dependencies are described by analytic functions. Parametrising the m${}_{\pi \pi }$ dependence with resonant and non-resonant contributions added at the amplitude level leads to a measurement of the ρ${}^0$(770) meson mass and width at m${}_{\rho }$=770.8${}_{\text{â}\text{ˆ}\text{’}2.7}^{+2.6}$ (tot) MeV and Γ${}_{\rho }$=151.3${}_{\text{â}\text{ˆ}\text{’}3.6}^{+2.7}$ (tot) MeV, respectively. The model is used to extract the ρ${}^0$(770) contribution to the π${}^{+}$π${}^{\text{â}}\text{ˆ}\text{’}$ cross sections and measure it as a function of t and W${}_{\gamma p}$. In a Regge asymptotic limit in which one Regge trajectory α(t) dominates, the intercept α(t=0)=1.0654${}_{\text{â}\text{ˆ}\text{’}0.0067}^{+0.0098}$ (tot) and the slope α′(t=0)=0.233${}_{\text{â}\text{ˆ}\text{’}0.074}^{+0.067}$ (tot) GeV${}^{\text{â}\text{ˆ}\text{’}2}$ of the t dependence are extracted for the case m${}_Y$=m${}_p$.