Elastic and proton-dissociative $\rho^0$ photoproduction at HERA

Abstract.

Elastic and proton-dissociative $\rho^0$ photoproduction ($\gamma p \rightarrow \rho^0 p$, $\gamma p \rightarrow \rho^0 N$, respectively, with $\rho^0 \rightarrow \pi^+\pi^-$) has been studied in $ep$ interactions at HERA for photon-proton centre-of-mass energies in the range $50 < W < 100$ GeV and for $|t| < 0.5$ GeV$^2$, 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 $M_N^2 < 0.1 W^2$. For the elastic process, the $\pi^+\pi^-$ invariant mass spectrum has been investigated as a function of $t$. As in fixed target experiments, the $\rho^0$ 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 $\pi^+\pi^-$ production. The cross section has been studied as a function of $W$; a fit to the resonant part with the form $W^a$ gives $a=0.16\pm 0.06 \mbox{(stat.)} ^{+0.11}_{-0.15} \mbox{(syst.)}$. The resonant part of the $\gamma p \rightarrow \pi^+\pi^- p$ cross section is $11.2\pm 0.1 \mbox{(stat.)} ^{+1.1}_{-1.2} \mbox{(syst.)}$ $\mu$b at $\langle W\rangle=71.7$ GeV. The $t$ dependence of the cross section can be described by a function of the type $A_{\rho} \exp{(-b_{\rho} |t| + c_{\rho} t^2)}$ with $b_{\rho}= 10.9 \pm 0.3$ (stat.) $^{+1.0}_{-0.5}$ (syst.) GeV$^{-2}$ and $c_{\rho}= 2.7 \pm 0.9$ (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 $\alpha_{\mathbb{P}}^{\prime}= 0.23 \pm 0.15 \mbox{(stat.)} ^{+0.10}_{-0.07} \mbox{(syst.)}$ GeV$^{-2}$ has been deduced. The $\rho^0$ spin density matrix elements $r^{04}_{00}$, $r^{04}_{1-1}$ and ${\frak R}{e[r^{04}_{10}]}$ have been measured and found to be consistent with expectations based on $s$-channel helicity conservation. For proton-dissociative $\pi^+\pi^-$ photoproduction in the $\rho^0$ 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 $5.8 \pm 0.3 \mbox{(stat.)} \pm 0.5 \mbox{(syst.)}$ GeV$^{-2}$. The ratio of the elastic to proton-dissociative $\rho^0$ photoproduction cross section is $2.0 \pm 0.2 \mbox{(stat.)} \pm 0.7 \mbox{(syst.)}$.