✍ Scribed by Chikashi Iso; Hiroaki Yoshii
No coin nor oath required. For personal study only.
The general relation between pion electroproduction and vector meson production by pions is given under the assumption of the vector-meson-photon analogy model. We also propose how to check the off-mass-shell effect on the scattering amplitude for the nN + VN process.
In a series of papers (Z)--(3) we searched for relations among physical quantities of photoproduction and vector meson production, assuming the photon-vectormeson analogy model (4) (field-current identity model ( 5)), and got several relations among differential cross sections, polarization of nucleon, helicity density matrix of vector meson and joint decay helicity density matrix elements. As we noticed in the previous papers, in order to explain the differential cross section of yN ---f Z-N in terms of the rrN + VN process, we must consider the t-dependence of the helicity density matrix element 6: of the vector meson (1) (6) (7). The numerical comparison has been done by the present authors (I) and in several other papers ( 8)-(ZZ), and the agreement is fairly good.
Our analysis is quite general and independent of assumptions on the strong interaction dynamics, except for the assumption of field-current identities. However, as we noticed in the previous paper, when we try to compare our relations with experimental results, we must assume how to analytically continue the differential cross section of TN -+ VN from a nonzero mass to the photon mass.
The purpose of this paper is to find general relations between pion electroproduction and vector meson production by pions, and to propose how to check the off-mass-shell effect on the scattering amplitude of the TN --+ VN process.
In this paper we use the following notation: M, my and p are the mass of nucleon, vector meson and pion, respectively; we neglect the mass of the electron. W, 0, q and kv are the total pion-nucleon energy, scattering angle and momenta of pion and vector meson in the pion-nucleon center of mass system, respectively, and pi , pf and k are momenta of the initial and final electron, and virtual photon
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