The Weak Decay Constant of Positronium

The positronium, as the lightest, purely leptonic bound state, provides an ideal testing ground for the quantum field-theoretical description of composite systems. While its electromagnetic annihilation is well understood as the dominant decay channel, the weak interaction sector of the positronium is strongly suppressed. In this work, we extend the composite quantum field-theoretical framework developed earlier for the two-photon decay and introduce the concept of a weak decay constant for para-positronium. This constant, defined in analogy to those of pseudoscalar mesons, quantifies the coupling of the positronium field to the weak axial current and serves as a measure of its internal structure in the electroweak domain. Its numerical value fP ≃ α3/2 me/(2√π) = 89.8593 eV is, as expected, small. Nevertheless, the resulting expression and the related comparison with quarkonium systems allows us to determine the vertex function linking the positronium to its own constituents.