Consequences of aQQQ¯Model for Meson-Baryon Processes. II. Positive-Parity Mesons

Abstract

The consequences of a $\mathrm{QQ}\overline{Q}$ model of meson-baryon processes, proposed recently by Mitra, are examined in relation to production of positive-parity mesons in association with both the octet ($B$) and the decuplet (${B}^{*}$) of baryons. As Mitra showed, the basic amplitudes which represent the processes $\mathrm{PQ}\ensuremath{\rightarrow}\mathrm{TQ}$, $\mathrm{PQ}\ensuremath{\rightarrow}\mathrm{AQ}$, $\mathrm{PQ}\ensuremath{\rightarrow}\mathrm{SQ}$, and $\mathrm{PQ}\ensuremath{\rightarrow}{B}^{\ensuremath{'}}Q$ (where $P$ denotes a pseudoscalar meson and $T$, $A$, $S$, and ${B}^{\ensuremath{'}}$ denote $^{3}P_{2,1,0}$ and $^{1}P_{1}$ mesons, respectively) can be classified in terms of two sets: (+) amplitudes, which represent transitions between positive-parity $\mathrm{QQ}\overline{Q}$ states, and (-) amplitudes which represent those between negative-parity $\mathrm{QQ}\overline{Q}$ states. The analysis of the data for the processes $\mathrm{PB}\ensuremath{\rightarrow}^{3}P_{2}B$, made in terms of the density matrices, indicates a predominance of the (+) over the (-) amplitudes. A similar analysis for the processes $\mathrm{PB}\ensuremath{\rightarrow}^{1}P_{1}{B}^{*}$, under the assumption of domiance of one type of amplitude over the other, gives widely different answers for the ${B}^{*}$ and $^{1}P_{1}$ density matrices in the forward direction, so that an experimental test, which may not be too difficult, should be able to throw further light on the hypothesis of the dominance of the (+) amplitudes over the (-) amplitudes for positive-parity meson production. A sum rule of the form $\frac{4}{3}({\ensuremath{\rho}}_{3,3}+\sqrt{3}{\ensuremath{\rho}}_{3,\ensuremath{-}1})={\ensuremath{\rho}}_{1,1}+{\ensuremath{\rho}}_{1,\ensuremath{-}1}$, which has been derived by previous authors in different models for the reaction $\mathrm{PB}\ensuremath{\rightarrow}V{B}^{*}$, is found to be valid also for $\mathrm{PB}\ensuremath{\rightarrow}^{3}P_{1}{B}^{*}$. Some cross-section relations for various processes are also presented and compared with experiment. The agreement is fairly good. As to the possible dynamical significance of the results, they indicate the dominance of the $Q\overline{Q}$ force over $\mathrm{QQ}$, but the assumption of spin and unitary-spin independence of the quark forces does not yield any additional results, unlike the negative-parity meson production considered earlier. Finally, the general classification of the amplitudes in terms of (+) and (-) types, now indicates a dominance of the (+) over the (-) amplitudes, which is exactly the opposite of the conclusion for the production of vector and pseudoscalar mesons, but not necessarily in contradiction with the latter, since the $Q\overline{Q}$ structures of the respective states have opposite parities.