Pion-Absorption Contribution to theπ-dScattering Length in a Simple Dispersion-Theoretic Approach

Abstract

The pion-absorption contribution to the $\pi$-$d$ scattering length ($a_{\pi d}^{}{}_{}{}^{\prime }$) is calculated in the Hulthén model in a simple dispersion-theoretic approach with Koltun-Reitan input modified through the introduction of the off-shell $S$-wave range parameter ${\alpha }_0$ with ${\alpha }_0=500\mathrm{}$ MeV/c. In this approach one finds the uncrossed result, $a_{\pi d}^{}{}_{}{}^{\prime }=-2.69\mathrm{}\times {10}^{-3\mathrm{}}m_{\pi }^{}{}_{}{}^{-1\mathrm{}}$, increased by $1.30\times {10}^{-3\mathrm{}}m_{\pi }^{}{}_{}{}^{-1\mathrm{}}$ with the inclusion of crossing.