Partial-wave analysis to determine the spin of \(\Xi (1690)^{-}\) and \(\Xi (1820)^{-}\) produced in \(\overline{p}p\) annihilation

Abstract

Recently (The PANDA collaboration, arXiv:2201.03852v2) the PANDA collaboration studied the feasibility of determining the spin and parity of the \(\Xi (1690)^{-}\) and \(\Xi (1820)^{-}\) resonances in the \(\Lambda K^-\) system produced in \(\bar{p}p\) collisions via the reaction channel \(\overline{p} p \rightarrow \bar{\Xi }^{+} \Lambda K^{-}\). The present paper aims to study these reactions using a model-independent irreducible tensor formalism developed earlier. This study leads us to identify the partial-wave amplitude and the observable, which would be zero if \(\Xi (1690)^{-}\) or \(\Xi (1820)^{-}\) had spin-1/2, provided these resonances are produced at threshold (s-wave production).