Quark Model for Photoproduction of Baryons

A quark ($Q$) model of photoproduction of positive- and negative-parity baryons in association with a meson octet is proposed. According to this model, the basic mechanism for photoproduction is represented by a $U$-spin-invariant process $\gamma +Q\to Q+\Pi$ at each quark, $\Pi$ being a meson octet. The matrix elements of this basic amplitude are taken between appropriate $3Q$ states representing the initial proton and a final baryon, according to the multiplet structure ${56}^{+}$ of $\mathrm{SU}\left(6\right)\mathrm{}$ and (70,${(70,3)}^{-}$ of $\mathrm{SU}\left(6\right)\mathrm{}\otimes O\left(3\right)\mathrm{}$ for the positive-parity and negative-parity baryonic states, respectively. The $\mathrm{SU}\left(3\right)\mathrm{}$ sum rules based on $U$-spin invariance of the amplitudes are verified. Several additional sum rules, valid separately for spin-flip and non-spin-flip amplitudes, are derived for the ${56}^{+}$ states. For the negative-parity states, a number of nontrivial sum rules connecting different $\mathrm{SU}\left(3\right)\mathrm{}$ multiplets are obtained.