Energy and decay width of the πK atom

Abstract

The energy and the decay width of the πK atom are evaluated in the framework of the quasipotential-constraint theory approach. The main electromagnetic and isospin symmetry breaking corrections to the lowest-order formulas for the energy shift from the Coulomb binding energy and for the decay width are calculated. They are estimated to be of the order of a few per cent. We display formulas to extract the strong interaction S-wave πK scattering lengths from future experimental data concerning the πK atom.

QCD and strongly coupled gauge theories: challenges and perspectives

“…In the future, the DIRAC Collaboration also aims to measure the energy splitting, which would allow for the separate measurements of the two -wave scattering lengths. Another project of the collaboration is the study of the properties of the atom, in analogy with the pionium case, thus providing the -wave scattering lengths [ 541 , 542 ]. Preliminary tests of the experiment at CERN have already begun [ 543 ].…”

QCD and strongly coupled gauge theories: challenges and perspectives

“…From a sample of 21000 pionium atoms a 4% measurement of the difference of the ππ scattering lengths has been obtained [541]: In the future, the DIRAC Collaboration also aims to measure the 2s − 2p energy splitting, which would allow for the separate measurements of the two S-wave scattering lengths. Another project of the collaboration is the study of the properties of the πK atom, in analogy with the pionium case, thus providing the S-wave πK scattering lengths [542,543]. Preliminary tests of the experiment at CERN have already begun [544].…”

Hadronic Atoms

“…[ Because ChPT is the low-energy effective theory of QCD+QED, one might be tempted to start from this framework. However, describing bound states in ChPT by using standard techniques, based on the Bethe-Salpeter equation or on 3-dimensional reductions thereof (92,93,94,95,96,97), is a complicated enterprise, which makes it very difficult to reach the required precision. We do not, therefore, discuss this method here.…”