Beyond the Zero-Binding Approximation in Quarkonium

Abstract

The hadronic decays of quarkonium and the B meson inclusive decay into J/Psi + X, if treated in the zero-binding approximation, suggest a value of the strong coupling constant much smaller than the value implied in the standard model by running from measurements at the Z. Thus, assuming the standard model is correct in the low energy region, there must be very substantial relativistic binding corrections to these processes. We discuss the wave function factor appearing in covariant treatments of quarkonium production and decay processes with special attention to the way in which the spin of the quarks carries over into the spin of the bound state. We find that Lorentz covariance requires that the bound state be a superposition of free quark and antiquark spinors notably different from the usual ones. We resolve a superficial apparent paradox suggesting that the relative momentum of the quarks should lie in a plane perpendicular to the spin quantization axis and we calculate the J/Psi binding corrections to lepton pair decay and to the inclusive B decay.