Abstract
The complete expression for the intensity in pseudo-scalar meson photoproduction with a polarized beam, target, and recoil baryon is derived using a density matrix approach that offers great economy of notation. A Cartesian basis with spins for all particles quantized along a single direction, the longitudinal beam direction, is used for consistency and clarity in interpretation. A single spin-quantization axis for all particles enables the amplitudes to be written in a manifestly covariant fashion with simple relations to those of the well-known Chew-Goldberger-Low-Nambu formalism. Possible sign discrepancies between theoretical amplitude-level expressions and experimentally measurable intensity profiles are dealt with carefully. Our motivation is to provide a coherent framework for coupled-channel partial-wave analysis of several meson photoproduction reactions, incorporating recently published and forthcoming polarization data from Jefferson Lab.
Highlights
It is important to note that the sine and cosine terms in Eqs. 29 and 30 alter signs differently in going from the “theory” expressions to the “para” and “perp” settings, and this directly affects the signs of the extracted polarization observables
It is well known that the fifteen polarization observables occurring as bilinears in Eq 56 can be connected by various identities
We provide a detailed and self-contained description of the intensity profiles and amplitude-level expressions for the 15 polarization observables in pseudo-scalar meson photoproduction
Summary
“consistency relations” connecting the different spin observables These consistency relations provide important checks for both theoretical analyses and constraints in the case of future experiments which will have access to polarizations of the beam and target and recoil baryons. We aim to establish a consistent partial-wave-analysis formalism for recent [9,10,11,12,13] and future [14, 15] meson photoproduction data from CLAS, as well as all presently available polarization data from other experiments such as GRAAL [16, 17] and LEPS [18,19,20]. This article will provide a self-contained and comprehensive description of the formalism for pseudo-scalar meson photoproduction from the fundamental derivations and a careful treatment of the connection between theory and measurement of polarization observables
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