Hadronic Atoms

Abstract

We review the theory of hadronic atoms in QCD+QED. The non-relativistic effective Lagrangian approach, used to describe this type of bound states, is illustrated with the case of π + π − atoms. In addition, we discuss the evaluation of isospin-breaking corrections to hadronic atom observables by invoking chiral perturbation theory.

The role of nucleon recoil in low-energy antikaon-deuteron scattering

“…( 26) into Eq. ( 24) one obtains where we exploited the othogonality of the bound-and continuum-state wave functions and made use of the normalization of Ψ(p) according to d 3 p Ψ 2 (p) = (2π) 3 . Thus, at order ξ 1/2 there is a complete cancellation of the recoil corrections both for isoscalar and isovector types of KN interaction.…”

“…The non-vanishing recoil corrections to the static term appear at order ξ both for isoscalar and isovector KN interactions. In order to perform an analytic study of this and higher-order terms in the expansion we choose N N interaction in the separable form V (p, p ′ ) = λg(p)g(p ′ ), where 3 , and β = 1.4 fm −1 .…”

“…Recent combined analyses of pionic hydrogen and pionic deuterium have revealed a significant progress towards a precise extraction of the pion-nucleon interaction parameters at threshold, see Ref. [1] and also [2,3] for review articles. One might expect that the properties of the KN interaction can be investigated in a similar way using a combined analysis of kaonic hydrogen and kaonic deuterium.…”

Isospin breaking in the pion–nucleon scattering lengths

“…which, in addition to f 1 and c 1 , also includes a sizeable fixed shift (cf. the discussion in [41,42]). Finally, we point out that the remnants of the cusp effect contribute roughly one third to the difference a π 0 p − a π 0 n = (−3.4 ± 0.4) • 10 −3 M −1 π and hence modify Weinberg's prediction [1] significantly.…”

Isospin symmetry breaking

“…[44] the isospin-breaking corrections to the charge-exchange amplitude have been evaluated at o(p 2 ). For the recent review on the subject, see, e.g., [46,47].…”