Eur. Phys. J. A (2005) 25: 329-338
https://doi.org/10.1140/epja/i2005-10128-9

Original Article

On kaonic hydrogen. Phenomenological quantum field theoretic model revisited

¹ Atominstitut der Österreichischen Universitäten, Arbeitsbereich Kernphysik und Nukleare Astrophysik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Österreich
² Stefan Meyer Institut für subatomare Physik, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, A-1090, Wien, Österreich

^* e-mail: ivanov@kph.tuwien.ac.at

Received: 4 May 2005
Accepted: 20 July 2005
Published online: 19 September 2005

Abstract

We argue that due to isospin and U-spin invariance of strong low-energy interactions the S-wave scattering lengths a ⁰ ₀ and a ¹ ₀ of ¯N scattering with isospin I = 0 and I = 1 satisfy the low-energy theorem a ⁰ ₀ +3a ¹ ₀ = 0 valid to leading order in chiral expansion. In the model of strong low-energy ¯N 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 a ⁰ ₀ +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 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 70MeV/c < p _K < 150MeV/c of the incident K^--meson. The theoretical results agree with the available experimental data within two standard deviations.