Erratum: Relativistic effects in the pionium lifetime [Phys. Rev. D 58, 014011 (1998)]

Abstract

The pionium decay width is evaluated in the framework of chiral perturbation theory and the relativistic bound state formalism of constraint theory. Corrections of order O(α) are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses.Strong interaction corrections from second-order perturbation theory of the bound state wave equation are found to be of the order of 0.4%. Electromagnetic radiative corrections, due to pion-photon interactions, are estimated to be of the order of −0.1%. Electromagnetic mass shift insertions in internal propagators produce a correction of the order of 0.3%. The correction due to the passage from the strong interaction scattering amplitude evaluated with the mass parameter fixed at the charged pion mass to the amplitude evaluated with the mass parameter fixed at the neutral pion mass is found to be of the order of 6.4%.

The rare decay $K_{\mathrm{L}} \rightarrow\pi^{0} \mu^{ + } \mu^{-}$ within the SM

“…Theoretical investigations on the spectrum and the decay of pionium have been performed beyond leading order in several settings. Potential scattering has been used [12,13,14] as well as field-theoretical methods [15,16,17,18,19,20]. In particular, the lifetime of pionium was studied by the use of the Bethe-Salpeter equation [19] and in the framework of the quasipotential-constraint theory approach [20].…”

Hadronic potentials from effective field theories

“…Recently, the problem of isospin-breaking corrections in hadronic atom observables has been addressed in the framework of ChPT [17][18][19][20][21][22] (see Ref. [20] for the comparison of different approaches).…”

Energy and decay width of the πK atom

“…Let us assume that the kernel V can be separated into two parts, 15) so that the solutions corresponding to V 1 are known. Let G 1 be the Green function associated with V 1 :…”

“…When the hadronic constituents are pseudoscalar mesons, then the probe concerns the properties of spontaneous chiral symmetry breaking in QCD. The simplest representative in that case is the ππ atom (pionium), which was produced and studied in the DIRAC experiment at CERN [7] and to which many theoretical studies were devoted [8,9,10,11,12,13,14,15,16,17,18,19,20]. At the next level in that category one finds the πK atom, the properties of which are tightly related to those of the SU(3) × SU(3) chiral symmetry breaking.…”

“…The present work is devoted to the study of the properties of the πK atom using the quasipotential-constraint theory approach [24,25,26,27,28] which was also applied to the pionium case [15] and which consists of a relativistic and covariant three-dimensional formulation of the bound state problem. Our aim is to calculate the O(α) corrections to the lowest-order formulas for the energy shift and decay width of the πK atom, where α is the fine structure constant, and to provide the means of extracting with sufficient precision the values of the strong interaction S-wave πK scattering lengths from future experimental data.…”