On kaonic hydrogen. Phenomenological quantum field theoretic model revisited

We argue that due to isospin and U-spin invariance of strong low-energy interactions the S-wave scattering lengths a00 and a10 of anti KN scattering with isospin I=0 and I=1 satisfy the low-energy theorem a00+3a10=0 valid to leading order in chiral expansion. In the model of strong low-energy anti KN interactions at threshold (Eur. Phys. J. A 21, 11 (2004)) we revisit the contribution of the Σ(1750) resonance, which does not saturate the low-energy theorem a00+3a10=0, and replace it by the baryon background with properties of an SU(3) octet. We calculate the S-wave scattering amplitudes of K-N and K-d scattering at threshold. We calculate the energy level displacements of the ground states of kaonic hydrogen and deuterium. The result obtained for kaonic hydrogen agrees well with recent experimental data by the DEAR Collaboration. We analyse the cross-sections for elastic and inelastic K-p scattering for laboratory momenta 70 MeV/c<pK< 150 MeV/c of the incident K--meson. The theoretical results agree with the available experimental data within two standard deviations. (orig.)