arXiv subjects
Publications and source records attributed to Günther Rasche.
This paper presents the results of an updated phase-shift analysis of the low-energy (pion laboratory kinetic energy $T \leq 100$ MeV) pion-nucleon data; this solution will be referred to as `ZRH20'.
This work elaborates on former remarks of ours regarding two sets of predictions for the observables of the charge-exchange reaction $π^- p \to π^0 n$ at low energy (pion laboratory kinetic energy $T \leq 100$ MeV). The first prediction is obtained via the triangle identity from the results of fits to low-energy $π^\pm p$ elastic-scattering data, whereas the second is based on the same analysis of the combined low-energy $π^+ p$ and charge-exchange databases. Assuming the integrity of the data used in our fits (i.e., the absence of significant systematic effects in the determination of the absolute normalisation of the datasets) and the insignificance of residual effects in the electromagnetic corrections, a significant difference between these two sets of predictions may be interpreted as departure from the isospin invariance in the low-energy $πN$ interaction. We examine the sensitivity of the standard low-energy observables to the effect, and identify the kinematical regions which are promising for experimental survey. Accurate experiments under the suggested conditions will differentiate between the predictions, and thus provide an independent test of the isospin invariance in the low-energy $πN$ interaction.
In a previous paper, we reported the results of a partial-wave analysis of the pion-nucleon ($πN$) differential cross sections (DCSs) of the CHAOS Collaboration and came to the conclusion that the angular distribution of their $π^+ p$ data sets is incompatible with the rest of the modern (meson-factory) database. The present work, re-addressing this issue, has been instigated by a number of recent improvements in our analysis, namely regarding the inclusion of the theoretical uncertainties when investigating the reproduction of experimental data sets on the basis of a given `theoretical' solution, modifications in the parameterisation of the form factors of the proton and of the pion entering the electromagnetic part of the $πN$ amplitude, and the inclusion of the effects of the variation of the $σ$-meson mass when fitting the ETH model of the $πN$ interaction to the experimental data. The new analysis of the CHAOS DCSs confirms our earlier conclusions and casts doubt on the value for the $πN$ $Σ$ term, which Stahov, Clement, and Wagner have extracted from these data.
In the present paper, we investigate the propagation of a massive spin-$\frac{3}{2}$ field, aiming at a direct application in hadronic models of the pion-nucleon ($πN$) interaction. Suitable expressions for the contributions to the standard invariant amplitudes $A$ and $B$ are derived, applicable in the general case of isospin decomposition. We first deal with the details of the lengthy calculation involving the Rarita-Schwinger propagator and confirm the validity of the expressions which had appeared in the literature in the early 1970s. We subsequently derive the corresponding contributions when following two other approaches, one featuring the Williams propagator, the other being known as Pascalutsa's method.
The ETH model of the pion-nucleon ($πN$) interaction contains $t$-channel $σ$- and $ρ$-exchange graphs, as well as the $s$- and $u$-channel contributions with the well-established $s$ and $p$ baryon states with masses below $2$ GeV as virtual particles; the model amplitudes obey crossing symmetry and isospin invariance. In the present work, we give the analytical expressions for the model contributions to the $K$-matrix elements up to (and including) the $f$ waves. We also extract a new phase-shift solution after performing a partial-wave analysis of meson-factory $π^\pm p$ elastic-scattering data below $100$ MeV; included in our results now are also the effects of the variation of the $σ$-meson mass in the interval which is currently recommended by the Particle-Data Group. Finally, we revisit the subject of the $πN$ $Σ$ term and, using the model amplitudes, obtain $Σ= 72.4 \pm 3.1$ MeV. Our prediction agrees well with the result extracted with Olsson's method, after a few flaws in his paper [Phys. Lett. B 482 (2000) 50] were corrected.
The value of $59 \pm 12$ MeV for the pion-nucleon ($πN$) $Σ$ term, which Stahov, Clement, and Wagner recently extracted from the differential cross sections (DCSs) of the CHAOS Collaboration, does not match well the expectation of an enhanced (more positive) isoscalar component in the $πN$ interaction at low energies, which the rest of the modern (meson-factory) data favour. However, we have already demonstrated that the angular distribution of the CHAOS $π^+ p$ DCSs is not compatible in shape with the rest of the modern low-energy $π^+ p$ data. This problem must be addressed and resolved by the CHAOS Collaboration prior to the extrapolation of their partial-wave amplitudes into the unphysical region.