Christoph Ditsche

Electromagnetic corrections in η→3π decays

We re-evaluate the electromagnetic corrections to η→3π decays at next-to-leading order in the chiral expansion, arguing that effects of order e2(mu−md) disregarded so far are not negligible compared to other contributions of order e2 times a light-quark mass. Despite the appearance of the Coulomb pole in η→π+π−π0 and cusps in η→3π0, the overall corrections remain small.

Roy-Steiner equations for pion-nucleon scattering

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

Dispersive analysis of the scalar form factor of the nucleon

\pi \pi \to \overline N N

Rescattering effects in η → 3π decays

partial waves into the form of a Muskhelishvili-Omnès 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.

Improved dispersive analysis of the scalar form factor of the nucleon

A bstractBased on the recently proposed Roy-Steiner equations for pion-nucleon (πN) scattering [1], we derive a system of coupled integral equations for the

Roy–Steiner equations for πN scattering

\pi \pi \to \overline N N

RoyâSteiner equations for Ï N scattering

and

Rescattering effects in → 3 decays ∗

\overline K K \to \overline N N

Electromagnetic effects in

S-waves. These equations take the form of a two-channel Muskhelishvili-Omnès 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

\eta\rightarrow 3 \pi

\overline K K