Relativistic form factors for clusters with nonrelativistic wave functions

Abstract

Using a simple variant of an argument employed by Licht and Pagnamenta (LP) on the effect of Lorentz contraction on the elastic form factors of clusters with nonrelativistic wave functions, it is shown how their result can be generalized to inelastic form factors so as to produce (i) a symmetrical appearance of Lorentz contraction effects in the initial and final states, and (ii) asymptotic behavior in accord with dimensional scaling theories. A comparison of this result with a closely analogous parametric form obtained by Brodsky and Chertok from a propagator chain model leads, with plausible arguments, to the conclusion of an effective mass M for the cluster, with M² varying as the number n of the quark constituents, instead of as n². A further generalization of the LP formula is obtained for an arbitrary duality-diagram vertex, again with asymptotic behavior in conformity with dimensina scaling. The practical usefulness of this approach is emphasized as a complementary tool to those of high-energy physics for phenomenological fits to data up to moderate values of q².