Electromagnetic corrections to π−\pi ^-p scattering length from pionic hydrogen

We derive a closed, model space independent, expression for the electromagnetic correction factor $\delta$ to the scattering length $a$ extracted from a hydrogenic atom with an extended charge to order $\alpha ^2$ and $a^3$ in the limit of a short ranged hadronic interaction.Comment: 4 pages; PANIC02, XVIth Conference on Particles and Nuclei, Osaka, to appear in Nuclear Physics

The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules as probes of constraints from analyticity and chiral symmetry in dynamical models for pion-nucleon scattering

The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion-nucleon scattering using two different methods: 1) by evaluating the scattering amplitude at the corresponding low-energy kinematics and 2) by evaluating the sum-rule integrals with the calculated total cross section. The discrepancy between the results of the two methods provides a measure of the breaking of analyticity and chiral symmetry in the model. The contribution of the $\Delta$ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.Comment: 12 pages, 6 figures, using RevTEX4. References added, discussion extended, conclusions unchanged. To be published in Nuclear Physics

pi(-)p atom in ChPT: strong energy-level shift

The general formula of the pi(-)p atom strong energy-level shift in the 1s state is derived in the next-to-leading order in the isospin breaking, and in all orders in chiral expansion. Isospin-breaking corrections to the level shift are explicitly evaluated at order p^2 in ChPT. The results clearly demonstrate the necessity to critically reaccess the values of the piN scattering lengths, extracted from the energy-level shift measurement by means of the potential model-based theoretical analysis.Comment: 16 pages, LaTeX-file, 1 Figur

Chiral restoration from pionic atoms?

We evaluate widths and shifts of pionic atoms using a theoretical microscopical potential in which the pion decay constant $f_\pi$ is changed by an in--medium density dependent one ($f_\pi(\rho)$), predicted by different partial Chiral restoration calculations. We show that the results obtained for shifts and widths are worse than if this modification were not implemented. On the other hand, we argue that in microscopic many body approaches for the pion selfenergy, based on effective Lagrangians, the mechanisms responsible for the change of $f_\pi$ in the medium should be automatically incorporated. Therefore, the replacement of $f_\pi$ by $f_\pi(\rho)$ in the many body derivation of the microscopic potential would be inappropriate.Comment: 10 pages, new comments and references adde

Pion-nucleon amplitude near threshold: the sigma-term and scattering lengths beyond few loops

The pion-nucleon amplitude is considered in the vicinity of the elastic scattering threshold within a relativistic dynamical model dressing the pi N N and pi N Delta vertices self-consistently with an infinite number of meson loops. The dressing is formulated as solution of a system of coupled integral equations incorporating unitarity, crossing symmetry and analyticity constraints. The calculated scattering lengths and the sigma-term agree with recent data analyses. The dressing is important in this model both below and at threshold. The contribution of the Delta resonance is discussed, including effects of the consistent dressing of the pi N Delta vertex. A comparison with the approaches of chiral perturbation theory and the Bethe-Salpeter equation is outlined.Comment: 28 pages, 3 figures, using REVTeX. The influence of various model ingredients on the near-threshold parameters is discussed in more detail. To be published in Nucl.Phys.