Extraction of parameters from final state interactions

It is argued that final state enhancements in production reactions at large momentum transfers, such as $pp\to K^{+}\mathrm{\Lambda }p$, are primarily sensitive to the position of a virtual bound state pole in the $\mathrm{\Lambda }p$ system rather than the $\mathrm{\Lambda }p$ scattering length and effective range. These arguments are supported by a study of the dispersion relation derived to describe such processes as a function of the cut-off energy. This shows that the position of the virtual bound state is independent of the cut-off energy.

Figure 1

Missing-mass spectrum of the reaction $pp\to K^{+}\{X=\mathrm{\Lambda }p\}$ measured at ${\theta }_K=0^{\circ }$ by the COSY-HIRES collaboration at $T_p=1.953$ GeV [4]. The (black) solid line represents the description of Eq. (1), including the $\mathrm{\Lambda }p$ FSI generated by the Jost function of Eq. (2). The experimental fit takes into account the missing-mass resolution with $\sigma =0.84$ MeV, but this is not important for the present discussion and is not shown. The (blue) dashed line represents the shape of the $pp\to K^{+}\mathrm{\Lambda }p$ phase space distribution, whereas the (red) chain curve is the shape of the Jost representation of the $\mathrm{\Lambda }p$ FSI. The arbitrarily normalized FSI function of Eq. (10) used in the analysis of the COSY-TOF experimental data [8] is shown by the less steep (green) chain curve.

Figure 2

Evaluations of the approximations to the scattering length and effective range for the Jost function of Eq. (2) as functions of $Q_{\max }$. The asymptotic parameters used in this study, $\alpha =-0.307{\mathrm{fm}}^{-1}$ and $\beta =1.212{\mathrm{fm}}^{-1}$, were those found by the COSY-HIRES collaboration [4].

Figure 3

Evaluations on the basis of the truncated effective range expansion of Eq. (4) of the approximations to the pole parameters for the Jost function of Eq. (2) as functions of $Q_{\max }$. The asymptotic parameters used in this exercise, $\alpha =-0.307{\mathrm{fm}}^{-1}$ and $\beta =1.212{\mathrm{fm}}^{-1}$, were those found by the COSY-HIRES collaboration [4].