Exotic ${\rho }^{\pm }{\rho }^0$ state photoproduction

Abstract

It is shown that the list of unusual mesons planned for a careful study in photoproduction can be extended by the exotic states $X^{\pm }(1600)$ with $I^G(J^{PC})=2^{+}(2^{++})$ which should be looked for in the ${\rho }^{\pm }{\rho }^0$ decay channels in the reactions $\gamma N\to {\rho }^{\pm }{\rho }^{0}N$ and $\gamma N\to {\rho }^{\pm }{\rho }^0\Delta$. The full classification of the ${\rho }^{\pm }{\rho }^0$ states by their quantum numbers is presented. A simple model for the spin structure of the $\gamma p\to f_2(1270)p$, $\gamma p\to a_2^0(1320)p$, and $\gamma N\to X^{\pm }(N,\Delta )$ reaction amplitudes is formulated and the tentative estimates of the corresponding cross sections at the incident photon energy $E_{\gamma }\approx 6$ GeV are obtained: $\sigma (\gamma p\to f_2(1270)p)\approx 0.12$ $\mu$b, $\sigma (\gamma p\to a_2^0(1320)p)\approx 0.25$ $\mu$b, $\sigma (\gamma N\to X^{\pm }N\to {\rho }^{\pm }{\rho }^{0}N)\approx 0.018$ $\mu$b, and $\sigma (\gamma p\to X^{-}{\Delta }^{++}\to {\rho }^{-}{\rho }^0{\Delta }^{++})\approx 0.031$ $\mu$b. The problem of the $X^{\pm }$ signal extraction from the natural background due to the other ${\pi }^{\pm }{\pi }^0{\pi }^{+}{\pi }^{-}$ production channels is discussed. In particular the estimates are presented for the $\gamma p\to h_1(1170){\pi }^{+}n$, $\gamma p\to {\rho }^{\prime +}n\to {\pi }^{+}{\pi }^0{\pi }^{+}{\pi }^{-}n$, and $\gamma p\to \omega {\rho }^{0}p$ reaction cross sections. Our main conclusion is that the search for the exotic $X^{\pm }(2^{+}(2^{++}))$ states is quite feasible at JEFLAB facility. The expected yield of the $\gamma N\to X^{\pm }N\to {\rho }^{\pm }{\rho }^{0}N$ events in a 30-day run at the 100% detection efficiency approximates $2.8\times 10^6$ events.

Comments: 19 pages, revtex, 1 figure in postscipt, some comments and references added, a few minor typos corrected, to be published in Phys. Rev. D