DAPNIA-05-39 |
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Quantum interferences in the $\gamma\, N \rightarrow e^+e^- N$ reaction close to the vector meson production threshold |
M.F.M. Lutz, M. Soyeur |
The exclusive photoproduction of $e^+e^-$ pairs from nucleons close to the vector meson production threshold ($1.4<\\sqrt s <1.8$ GeV) results from two main processes: the emission of Bethe-Heitler pairs and the photoproduction of $\\rho^0$- and $\\omega$-mesons decayinginto $e^+e^-$ pairs. The Bethe-Heitler amplitudes are purely electromagnetic and reflect mostly the nucleon magnetic structure. The $\\gamma \\,N\\rightarrow e^+e^- N$ amplitudes arising from vector meson production and decay are derived from $\\gamma \\,N\\rightarrow \\rho^0 N$ and $\\gamma\\, N \\rightarrow \\omega N$ amplitudes supplemented by the Vector Meson Dominance assumption. The vector meson photoproduction amplitudes are calculated using a relativistic and unitary coupled-channel approach to meson-nucleon scattering. They depend sensitively on the coupling of vector fields to baryon resonances. The $\\gamma\\, N \\rightarrow e^+e^- N$ differential cross sections display interference patterns. The interference of Bethe-Heitler pair production with vector meson $e^+e^-$ decay is quite small in the domain of validity of our model for all angles of the emitted $e^+e^-$ pair. The interference of $\\rho^0$- and $\\omega$-mesons in the $e^+e^-$ channel can be large. It is constructive for the $\\gamma\\, p \\rightarrow e^+e^- p$ reaction and destructive for the $\\gamma\\, n \\rightarrow e^+e^- n$ reaction. We discuss the shape and magnitude of the $e^+e^-$ pair spectra produced in the $\\gamma \\,p \\rightarrow e^+e^- p$ and $\\gamma \\,n \\rightarrow e^+e^- n$ reactions as functions of the pair emission angle and of the total center of mass energy $\\sqrt s$. In the particular kinematics under consideration, our results suggest that the vector meson contribution can be determined quite accurately from experimental $e^+e^-$ spectra by subtracting the Bethe-Heitler term and neglecting the small interference of Bethe-Heitler pairs with vector meson $e^+e^-$ decays. |