Special relativity in decays of hybrids

Abstract

A decay of a heavy hybrid is expected to produce light mesons flying out with speeds comparable to the speed of light and phenomenological models of the decay must respect symmetries of special relativity. We study consequences of this requirement in a class of simple constituent models with spin. Our models respect boost symmetry because they conform to the rules of a boost-invariant renormalization group procedure for effective particles in light-front QCD. But rotational symmetry of the decay amplitude is not guaranteed and the parameters in the model wave functions must take special values in order to obtain the symmetry. When the effective interaction Hamiltonian responsible for a hybrid decay has the same structure as the gluon-quark-antiquark interaction term obtained by solving the renormalization group equations for Hamiltonians in first order perturbation theory, the non-relativistic image of a hybrid as built from a quark and an antiquark and a heavy gluon that typically resides between the quarks, cannot produce rotationally symmetric amplitude. However, there exists an alternative generic picture in the model that does satisfy the requirements of special relativity. Namely, the distance between the quark and antiquark must be much smaller than the distance between the gluon and the pair of quarks, as if a hybrid were similar to a gluonium in which one gluon is replaced by a quark-antiquark pair.