Irreducible tensor approach to spin observables in the photoproduction of mesons with arbitrary spin-parity sπ

A theoretical formalism leading to elegant derivation of formulas for all spin observables is outlined for photoproduction of mesons with arbitrary spin-parity sπ. The salient features of this formalism, based on irreducible tensor techniques, are (i) the number of independent irreducible tensor amplitudes is 4(2s+1) (ii) a single compact formula is sufficient to express these amplitudes in terms of allowed electric and magnetic multipole amplitudes, and (iii) all the spin observables, including beam analyzing powers as well as the differential cross section, are expressible in terms of bilinear irreducible tensors of rank 0 to 2(s+1). The relationship between the irreducible tensor amplitudes and the helicity amplitudes is elucidated in general and explicit expressions for the helicity amplitudes are given in terms of the irreducible tensor amplitudes in the particular cases of pseudoscalar and vector meson photoproduction. The connection between the irreducible tensor amplitudes introduced here and the well-known Chew-Goldberger-Low-Nambu amplitudes for photoproduction of pseudoscalar mesons is also established