Spin O decay angular distribution for interfering mesons in electroproduction

Self analyzing meson electroproduction experiments are currently being planned for the CEBAF CLAS detector. These experiments deduce the spin polarization of outgoing unstable spin s (?)0 mesons from their decay angular distribution, W(θ,ψ). The large angular acceptance of the CLAS detector permits kinematic tracking of a sufficient number of these events to accurately determine electroproduction amplitudes from the deduced polarization. Maximum polarization information is obtained from W(θ,ψ) for decay into spin 0 daughters. The helicity of the decaying meson is transferred to the daughter's relative orbital angular momentum m-projection; none is open-quotes absorbedclose quotes into daughter helicities. The decaying meson's helicity maximally appears in W(θ,ψ). W(θ,ψ) for spin 0 daughters has been derived for (1) vector meson electroproduction and (2) general interfering mesons produced by incident pions. This paper derives W(θ,ψ) for electroproduction of two interfering mesons that decay into spin 0 daughters. An application is made to the case of interfering scalar and vector mesons. The derivation is an extension of work by Schil using the general decay formalism of Martin. The expressions can be easily extended to the case of N interfering mesons since interference occurs pairwise in the observable W (θ,ψ), a quadratic function of the meson amplitudes. The derivation uses the virtual photon density matrix of Schil which is transformed by a meson electroproduction transition operator, T. The resulting density matrix for the interfering mesons is then converted into a corresponding statistical tensor and contracted into the efficiency tensor for spin 0 daughters