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Exclusive photoproduction of $\rho^0(770)$ mesons is studied using the H1detector at the $ep$ collider HERA. A sample of about 9 events is used tomeasure single- and double-differential cross sections for the reaction $\gammap \to \pi^{+}\pi^{-}Y$. Reactions where the proton stays intact (${m_Y{=}m_p}$)are statistically separated from those where the proton dissociates to alow-mass hadronic system ($m_p{<}m_Y{<}10$ GeV). The double-differential crosssections are measured as a function of the invariant mass $m_{\pi\pi}$ of thedecay pions and the squared $4$-momentum transfer $t$ at the proton vertex. Themeasurements are presented in various bins of the photon-proton collisionenergy $W_{\gamma p}$. The phase space restrictions are $0.5 < m_{\pi\pi} <2.2$ GeV, ${\vert t\vert < 1.5}$ GeV${}^2$, and ${20 < W_{\gamma p} < 80}$ GeV.Cross section measurements are presented for both elastic andproton-dissociative scattering. The observed cross section dependencies aredescribed by analytic functions. Parametrising the $m_{\pi\pi}$ dependence withresonant and non-resonant contributions added at the amplitude level leads to ameasurement of the $\rho^{0}(770)$ meson mass and width at $m_\rho = 770.8\{}^{+2.6}_{-2.7}$ (tot) MeV and $\Gamma_\rho = 151.3\ {}^{+2.7}_{-3.6}$ (tot)MeV, respectively. The model is used to extract the $\rho^0(770)$ contributionto the $\pi^{+}\pi^{-}$ cross sections and measure it as a function of $t$ and$W_{\gamma p}$. In a Regge asymptotic limit in which one Regge trajectory$\alpha(t)$ dominates, the intercept $\alpha(t{=}0) = 1.0654\{}^{+0.0098}_{-0.0067}$ (tot) and the slope $\alpha^\prime(t{=}0) = 0.233\{}^{+0.067 }_{-0.074 }$ (tot) GeV${}^{-2}$ of the $t$ dependence are extractedfor the case $m_Y{=}m_p$.

Measurement of Exclusive $\pi^{+}\pi^{-}$ and $\rho^0$ Meson Photoproduction at HERA