Spectrum and decays of kaonic hydrogen

Abstract

By using the non-relativistic effective Lagrangian approach to bound states, a complete expression for the isospin-breaking corrections to the energy levels and the decay widths of kaonic hydrogen is obtained up-to-and-including O(alpha,m_d-m_u) in QCD. It is demonstrated that, although the leading-order corrections at O(alpha^{1/2},(m_d-m_u)^{1/2}) emerging due to the unitarity cusp, are huge, they can be expressed solely in terms of the KN S-wave scattering lengths. Consequently, at leading order, it is possible to derive parameter-free modified Deser-type relations, which can be used to extract the scattering lengths from the hadronic atom data.