Studies in Pionium

Pionium is a bound state of a positive pion and a negative pion. Its existence was first considered in the literature more than sixty years ago and it was first detected in 1993 at the Serpukhov proton synchrotron. The DIRAC collaboration at CERN provided the first precise measurements of the pionium lifetime in the early 2000s. The dominant decay is to a pair of neutral pions. The state and its decay provide a convenient opportunity to investigate certain aspects of relativistic quantum mechanics. We use it to study the two-body Klein-Gordon equation with constraint dynamics. We also consider the decay in a wave-function formalism in which the decay is mediated by strong-interaction pair annihilation and creation graphs. The parameters used are those of an established potential model for quark-antiquark systems. Finally, we investigate the strong-interaction contribution to the bound-state energy. The pedagogical value of the calculations for advanced undergraduates is emphasized.