THE DEPENDENCE OF OVERLAP INTEGRAL ON QUARK MASS IN BETHE-SALPETER THEORY

In the literature, the overlap integral of a transition (e.g. 1^-→0^-+γ) is usuallywritten asI = ∫d³xe^iσx/2φ_f^*(x')φ_i(x) Using Bethe-Salpeter equation with instantaneous approximation, we arrive at adifferent result which depends obviously on the mass of the quarks. Our result willapproximate the above expression only when the binding energy can be neglected.