Kaonic hydrogen and deuterium in Hamiltonian effective field theory

Abstract

The anti-kaon nucleon scattering lengths resulting from a Hamiltonian effective field theory analysis of experimental data and lattice QCD studies are presented. The same Hamiltonian is then used to compute the scattering length for the system, taking careful account of the effects of recoil on the energy at which the KNT-matrices are evaluated. These results are then used to estimate the shift and width of the 1S levels of anti-kaonic hydrogen and deuterium. The K¯p result is in excellent agreement with the SIDDHARTA measurement. In the K¯d case the imaginary part of the scattering length and consequently the width of the 1S state are considerably larger than found in earlier work. This is a consequence of the effect of recoil on the energy of the KN energy, which enhances the role of the Λ (1405) resonance.