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 a0 and a 1 0 of K̄N scattering with isospin I = 0 and I = 1 satisfy the low–energy theorem a0 + 3a 1 0 = 0 valid to leading order in chiral expansion. In the model of strong low–energy K̄N interactions at threshold (EPJA 21,11 (2004)) we revisit the contribution of the Σ(1750) resonance, which does not saturate the low–energy theorem a0+3a 1 0 = 0, and replace it by the baryon background with properties of an SU(3) octet. We calculate the S–wave scattering amplitudes of KN and Kd scattering at threshold. We calculate the energy level displacements of the ground states of kaonic hydrogen and kaonic 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 Kp scattering for laboratory momenta of the incident K meson from the domain 70MeV/c < p K < 150MeV/c. The theoretical results agree with the available experimental data within two standard deviations. PACS: 11.10.Ef, 11.55.Ds, 13.75.Gx, 21.10.–k, 36.10.-k E–mail: [email protected], Tel.: +43–1–58801–14261, Fax: +43–1–58801–14299 Permanent Address: State Polytechnic University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation E–mail: [email protected] E–mail: [email protected], Tel.: +43–1–58801–14261, Fax: +43–1–58801–14299 E–mail: [email protected] E–mail: [email protected], State Polytechnic University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation E–mail: [email protected] State Polytechnic University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation E–mail: [email protected]