Absorptive Part of Meson–baryon Scattering Amplitude and Baryon Polarization in Chiral Perturbation Theory

Abstract

We compute the spin asymmetry and polarization of the final-state baryon in its rest frame in twobody meson-baryon low-energy scattering with unpolarized initial state, to lowest non-trivial order in BChPT. The required absorptive amplitudes are obtained analytically at one-loop level. We discuss the polarization results numerically for several meson-baryon processes. Even at low energies above threshold, where BChPT can reasonably be expected to be applicable, sizable values of polarization are found for some processes. *

Baryon polarization in low-energy unpolarized meson-baryon scattering

“…We use tree-level BChPT partial waves unitarized with the method of [10,11,12], and determine their free parameters by fitting total and differential cross-section data (and spin-asymmetry or polarization data if available) for pK − , pK + and pπ + scattering. We also compare our results with those of a previous leading-order BChPT calculation [15], with the aim of further probing its domain of applicability.…”

“…The meson-baryon Lagrangian L MB has been given to O(q 3 ) in the three-flavor case in [20,21,22], and in [23] for two flavors. The tree-level amplitudes from L for mesonbaryon scattering have been given in [11] (see also [12,15]). We discuss here the associated partial waves, as used below to fit data.…”

Polarized pK- scattering in Unitary Baryon Chiral Perturbation Theory

“…The meson-baryon Lagrangian L MB has been given to O(q 3 ) in the three-flavor case in [36] (see also [37][38][39]), and in [40] for two flavors. The tree-level amplitudes from L for meson-baryon scattering have been given in [16] (see also [20,41]). The associated CM-frame partial waves have been given in full detail in [23], so there is no need to repeat them here.…”

“…with the function ω defined in (A.1) and x = p ′ · p in the CMF. If we denote P ′ the polarization of the final baryon in the CMF, the CMF spin asymmetry is given by [41],…”

“…If we denote P ′ the polarization of the final baryon in the CMF, the CMF spin asymmetry is given by [41],…”