Electromagnetic Corrections for π^±p Scattering

Hadronic potentials from effective field theories

“…Again, as in the one-channel case, we have truncated all terms which do not contribute to the quantity of interest (the decay width) at the accuracy we are working. In order to bring our framework in conformity with the relativized potential model which have been used for the study of pionium decay [7][8][9], below we include the relativistic corrections contained in L D , in the unperturbed Lagrangian. Diagrammatically, this corresponds to summing up all mass insertions in the free non-relativistic pion propagator (see Fig.…”

“…iv) The reason why the results of calculations for the observables of hadronic atoms carried out within the potential approach [7][8][9][10] generally differ from those obtained in ChPT, is now crystal clear. In order to agree with the latter, the potentials should be matched to QCD in the isospin-breaking phase.…”

“…In a result of these investigations, a systematic discrepancy between the results obtained within the potential scattering theory approach and the field-theoretical approach, has been discovered for the case of the π + π − atom decay width and the π − p atom ground-state energy. In particular, the prediction for the π + π − atom decay width [7][8][9] depends on the potential used, and on the choice of the free Green function in the Schrödinger equation. Earlier calculations [7] have predicted the isospin-breaking corrections with the opposite sign and with the same order of magnitude as in ChPT.…”

Electromagnetic corrections for the analysis of low energy scattering data

“…In the previous paper [1] we described the calculation of the electromagnetic corrections to the three hadronic phase shifts with l = 0, 1 for π + p elastic scattering at pion laboratory kinetic energy T π ≤ 100 MeV, using relativised Schrödinger equations (RSEs) containing the sum of an electromagnetic potential and an effective hadronic potential. In Section 1 of Ref.…”

“…In Section 1 of Ref. [1] we gave our reasons for using such a potential model rather than the dispersion theory model of the NORDITA group [2,3]. Our aim in this paper is to describe the corresponding calculations for the two-channel (π − p, π 0 n) system in the same energy region.…”