No‐Exotics‐NoGo Theorems and Inclusive Reactions

Abstract

The process $\mathrm{a}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\mathrm{E}\mathrm{\hspace{0.17em}\to \hspace{0.17em}}\mathrm{a}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\mathrm{E}$ , where $\mathrm{E}$ is an exotic baryon, is relevant to the inclusive reaction $\mathrm{a}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\mathrm{b}\mathrm{\hspace{0.17em}\to \hspace{0.17em}}\mathrm{c}\mathrm{\hspace{0.17em}+\hspace{0.17em}}\mathrm{X}$ , with $\mathrm{E}$ representing the (cb) system. The theorem proves that an amplitude which vanishes when (aE) is exotic and which also vanishes for exotic exchanges in the (aa) channel must vanish for any octet meson a, even when (aE) is not exotic. Thus in a kinematic region where the inclusive reaction is described by coupling the conventional Regge trajectories to the (aa) channel and exotic exchanges are forbidden, an amplitude which vanishes when (abc) is exotic will also vanish when (bc) is exotic and (abc) is not exotic; i.e. whenever the fragmentation vertex $\mathrm{b}\mathrm{\hspace{0.17em}\to \hspace{0.17em}}\mathrm{c}$ involves an exotic exchange. The assumption that certain “exotic” amplitudes vanish in inclusive reactions¹ has been shown to lead under certain reasonable assumptions to the conclusions that certain other amplitudes must also vanish, even though they are not normally considered exotic.² The exact implications and the validity of this result have been questioned. We present here a theorem which provides a concise and systematic statement of which nonexotic amplitudes must also vanish when the criterion of Chan et al is assumed.¹ We do not enter into the dynamical discussion of which criterion of exoticity is the proper one to use for inclusive reactions. This is a matter to be settled by experiment.