Abstract:
We report the results of a phase-shift analysis (PSA) of the low-energy π^{±}p elastic-scattering data. Following the method which we had set forth in our previous PSA [1], we first investigate the self-consistency of the low-energy π^{±}p elastic-scattering databases, via two separate analyses of (first) the π^{+}p and (subsequently) the π^{-}p elastic-scattering data. There are two main differences to our previous PSA: 1) we now perform only one test for the acceptance of each data set (based on its contribution to the overall ^{2}) and 2) we adopt a more stringent acceptance criterion in the statistical tests. We show that it is possible to obtain self-consistent databases after removing a very small amount of the data (4.57% of the initial database). We subsequently fit the ETH model [38] to the truncatedπ^{±}p elastic-scattering databases. The model-parameter values show reasonable stability when subjected to different criteria for the rejection of single data points and entire data sets. Our result for the pseudovector πNN coupling constant is 0.0726±0.0014. We extract the scattering lengths and volumes, as well as the s- and p-wave hadronic phase shifts up to T = 100 MeV. Large differences in the s-wave part of the interaction can be seen when comparing our hadronic phase shifts with the current SAID solution (WI08); there is general agreement in the p waves, save for the ^{~1/2}_{1-} hadronic phase shift.

Abstract:
We give the modern derivation of Deser's formula using analytic continuation of the scattering amplitude as a function of momentum. The electromagnetic corrections to the pionium lifetime are given as evaluated in a potential model.

Abstract:
The hadronic properties of the pionium ion (Coulomb bound system of three charged pions) are estimated using the results for the positronium ion $P{s}^{-}$. It turns out that the hadronic shift of the ground state energy and the lifetime of the pionium ion are approximately the same as for pionium.

Abstract:
The value of $59 \pm 12$ MeV for the pion-nucleon ($\pi N$) $\Sigma$ 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 $\pi N$ 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 $\pi^+ p$ DCSs is not compatible in shape with the rest of the modern low-energy $\pi^+ p$ 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.

Abstract:
In a previous paper, we reported the results of a partial-wave analysis of the pion-nucleon ($\pi N$) differential cross sections (DCSs) of the CHAOS Collaboration and came to the conclusion that the angular distribution of their $\pi^+ p$ 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 $\pi N$ amplitude, and the inclusion of the effects of the variation of the $\sigma$-meson mass when fitting the ETH model of the $\pi N$ interaction to the experimental data. The new analysis of the CHAOS DCSs confirms our earlier conclusions and casts doubt on the value for the $\pi N$ $\Sigma$ term, which Stahov, Clement, and Wagner have extracted from these data.

Abstract:
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 ($\pi N$) 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.

Abstract:
We give a compact expression for the unpolarised differential cross section for muon-proton scattering in the one photon exchange approximation. The effect of adding the vacuum polarisation amplitude to the no-spin-flip amplitude for one photon exchange is calculated at small energies and scattering angles and is found to be negligible for present experiments.

Abstract:
The influence of the hadronic \pi\pi interaction on the wave functions of pionium (the Coulomb bound \pi^+\pi^- system) at distances less than 10 fm is calculated for s-states with principal quantum numbers n<5. Hadronic \pi\pi potentials are used that reproduce the scattering phase shifts of two-loop chiral perturbation theory. The pionium wave functions \psi_n (r) are obtained by integrating the coupled Schr\"odinger equations for the (\pi^+\pi^-,\pi^0\pi^0) system. We find that, for r<10 fm, n^{3/2} \psi_n (r) is practically independent of n. From this we conclude that the production rates of the s-states of pionium are proportional to n^{-3}, a result needed for the interpretation of the DIRAC experiment currently running at CERN.

Abstract:
We calculate the electromagnetic corrections needed to obtain isospin invariant hadronic pion-pion s-wave scattering lengths a^0, a^2 from the elements a_cc, a_0c of the s-wave scattering matrix for the (\pi^+ \pi^-, \pi^0 \pi^0) system at the \pi^+ \pi^- threshold. These elements can be extracted from experiments on pionium. Our calculation uses energy independent hadronic pion-pion potentials that satisfactorily reproduce the low-energy phase shifts given by two-loop chiral pertur- bation theory. We also take into account an important relativistic effect whose inclusion influences the corrections considerably.

Abstract:
Experimental values of the lifetime of the 1s level of pionium and of the difference between the energies of the 2s and 2p levels yield values of the a(0c) and a(cc) elements of the s-wave scattering matrix for the 2-channel (pi+ pi-, pi0 pi0) system at the pi+ pi- threshold. We develop a method for obtaining the isospin invariant quanties a20 - a00 and 2a00 + a20 from a(0c) and a(cc). We emphasize that the isospin invariant scattering lengths a00 and a20 universally used in the literature cannot be considered to be purely hadronic quantities.