Two-Parameter Statistical Model

Abstract

A statistical model is described which empirically relates the volume (characterized by ${\lambda }_i$) associated with each particle to its mass ($m_i$). The functional dependence used in ${{\mathrm{m}}_i}^{\alpha }{\lambda }_i=\mathrm{const}$, where $\alpha$ is some constant. The two parameters ${\lambda }_{\pi }$ and $\alpha$, in addition to the masses $m_i$, determine all the other ${\lambda }_i$. The model is applied to antiproton-proton annihilation at low and moderate energies. The annihilation is assumed to proceed through all possible intermediate states consisting of all combinations of the five mesons, $\pi$, $K$ (or $\overline{K}$), $K^{*}$ (or ${\overline{K}}^{*}$), $\rho$, and $\omega$. The experimental multiplicities and fraction of $K\overline{K}m\pi$ ($m=0, 1, 2,\dots$) states determine the two parameters ${\lambda }_{\pi }$ and $\alpha$ to be 4.0±0.4 and 1.94±0.06, respectively. These values of ${\lambda }_{\pi }$ and $\alpha$ predict the extent to which the $K^{*}$ (or ${\overline{K}}^{*}$), $\rho$, and $\omega$ take part in the annihilation. These predictions are found to be in reasonable agreement with recent experimental data on the role of the $K^{*}$ (or ${\overline{K}}^{*}$), $\rho$, and $\omega$ in $\overline{p}p$ annihilation. The $\eta$ meson is also considered.