We re-evaluate the electromagnetic corrections to η → 3π decays at next-to-leading order in the chiral expansion, arguing that effects of order e 2 (mu − m d ) disregarded so far are not negligible compared to other contributions of order e 2 times a light-quark mass. Despite the appearance of the Coulomb pole in η → π + π − π 0 and cusps in η → 3π 0 , the overall corrections remain small. .Jx Decays of other mesons -13.40.Ks Electromagnetic corrections to strong-and weak-interaction processes PACS

The isospin-breaking decay η → 3π is an ideal tool to extract information on light quark mass ratios from experiment. For a precise determination, however, a detailed description of the Dalitz plot distribution is necessary. In that respect, in particular the slope parameter α of the neutral decay channel causes some concern, since the one-loop prediction from chiral perturbation theory misses the experimental value substantially. We use the modified non-relativistic effective field-theory, a dedicated framework to analyze final-state interactions beyond one loop including isospin-breaking corrections, to extract charged and neutral Dalitz plot parameters. Matching to chiral perturbation theory at next-to-leading order, we find α = −0.025 ± 0.005, in marginal agreement with experimental findings. We derive a relation between charged and neutral decay parameters that points towards a significant tension between the most recent KLOE measurements of these observables.

Based on the recently proposed Roy-Steiner equations for pion-nucleon scattering, we derive a system of coupled integral equations for the pi pi --> N-bar N and K-bar K --> N-bar N S-waves. These equations take the form of a two-channel Muskhelishvili-Omnes problem, whose solution in the presence of a finite matching point is discussed. We use these results to update the dispersive analysis of the scalar form factor of the nucleon fully including K-bar K intermediate states. In particular, we determine the correction Delta_sigma=sigma(2M_pi^2)-sigma_{pi N}, which is needed for the extraction of the pion-nucleon sigma term from pi N scattering, as a function of pion-nucleon subthreshold parameters and the pi N coupling constant.Comment: 24 pages, 6 figures; version published in JHE

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high-energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the $\pi\pi\to\bar NN$ partial waves into the form of a Muskhelishvili-Omn\`es problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.Comment: 106 pages, 18 figures; version published in JHE

Starting from hyperbolic dispersion relations for the invariant amplitudes of pion-nucleon scattering together with crossing symmetry and unitarity, one can derive a closed system of integral equations for the partial waves of both the s-channel (πN → πN) and the t-channel (ππ →NN) reaction, called Roy-Steiner equations. After giving a brief overview of the Roy-Steiner system for πN scattering, we demonstrate that the solution of the t-channel subsystem, which represents the first step in solving the full system, can be achieved by means of Muskhelishvili-Omnès techniques. In particular, we present results for the P-waves featuring in the dispersive analysis of the electromagnetic form factors of the nucleon.