Revisiting \(KN\) Elastic and Charge Exchange Reactions in Search of the Pentaquark \({\mit \Theta }^+\) Baryon

In the search for the pentaquark \({\mit \Theta }^+\) baryon, the world data on \(K^+n\to K^+n\) and \(K^+n\to K^0p\) reactions on the deuteron target and \(K^0p\to K^+n\) and \(K^0_{\mathrm {L}}\,p\to K^0_{\mathrm {S}}\,p\) reactions on the hydrogen target are revisited to study the isoscalar component of the scattering amplitudes. The determination of the \(s\)- and \(p\)-wave phase shifts for the two former channels on the deuteron target is presented in the low-momentum region with the uncertainty due to the deuteron form factors at forward angles discussed. For the reactions on hydrogen targets, a similarity expected from time reversal between the charge exchange processes \(K^+n\to K^0p\) and \(K^0p\to K^+n\) is exploited, while we present the analysis of the \(K_{\mathrm {L}}^0\,p\to K_{\mathrm {S}}^0\,p\) scattering based on the \(s\)-wave phase shift for low momenta combined with the \(t\)-channel \(\rho ^0(775)+\omega (782)+\phi (1020)\) vector meson exchange at high momenta. With the mass of 1535 MeV and decay width of 5 MeV, the possibility of the \({\mit \Theta }^+\) in the Breit–Wigner (BW) form is tested in the differential cross section measured by Damerell <span class="it">et al.</span> [<span class="it">Nucl. Phys. B</span> <span class="bf">94</span>, 374 (1075)] at \({P_\mathrm {Lab}}=434\) MeV/\(c\) and polarization. Our analysis suggests measuring the polarization observable rather than the differential cross section, which has sufficient sensitivity to distinguish the \({\mit \Theta }^+\) baryon among all spin and parity states \(J^P = 1/2^\pm \) and \(3/2^\pm \). Abstract Published by the Jagiellonian University 2025 authors