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

Abstract

A theoretical formalism leading to elegant derivation of formulae for all spin observables is outlined for photo production of mesons with arbitrary spin parity s π . 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 photo production. The connection between the irreducible tensor amplitudes introduced here and the well known CGLN amplitudes for photo production of pseudoscalar mesons is also established.

Decay of Polarized Delta

“…The dominance of ∆ in photo and electro-pion production has been known for a long time. Very recently, a theoretical formalism [14] for photo and electroproduction of mesons with arbitrary spin-parity s π has been outlined, which specializes to pion production for s π = 0 − . The excitation of a nucleon into ∆ through photoabsorption, involves electric quadrupole (E2) and magnetic dipole (M1) form factors, while electro-production involves a Coulomb form factor (C2) in addition.…”

“…×W (k111; Λl) C(11l; 000) (14) We note that I(q) and |f | 2 are already known, so that the spherically symmetric term with l = 0 in eq. ( 13) yields t 1 q .…”