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 K − d system, taking careful account of the effects of recoil on the energy at which the KN T-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.