Measurement of exclusive $\pi^+ \pi ^-$ and $\rho^0$ meson photoproduction at HERA

Exclusive photoproduction of ${{\rho ^0}} (770)$ mesons is studied using the H1 detector at the ep collider HERA. A sample of about 900,000 events is used to measure single- and double-differential cross sections for the reaction $\gamma p \rightarrow \pi ^{+}\pi ^{-}Y$. 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~{{\text {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\le m_{\pi \pi } \le 2.2~{{\text {GeV}}} $, $\vert t\vert \le 1.5~{{\text {GeV}^2}} $, and $20 \le W_{\gamma p} \le 80~{{\text {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 ${{\rho ^0}} (770)$ meson mass and width at $m_\rho = 770.8{}^{+2.6}_{-2.7}~({\text {tot.}})~{{\text {MeV}}} $ and $\Gamma _\rho = 151.3 {}^{+2.7}_{-3.6}~({\text {tot.}})~{{\text {MeV}}} $, respectively. The model is used to extract the ${{\rho ^0}} (770)$ contribution to 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 $\alpha (t{=}0) = 1.0654\ {}^{+0.0098}_{-0.0067}~({\text {tot.}})$ and the slope $\alpha ^\prime (t{=}0) = 0.233 {}^{+0.067 }_{-0.074 }~({\text {tot.}}) ~{{\text {GeV}^{-2}}} $ of the t dependence are extracted for the case $m_Y{=}m_p$.