Asymptotic behavior of composite-particle form factors and the renormalization group

Composite-particle form factors are studied in the limit of large momentum transfer Q. It is shown that in models with spinor constituents and either scalar or guage vector gluons, the meson electromagnetic form factor factorizes at large Q² and is given by independent light-cone expansions on the initial and final meson legs. The coefficient functions are shown to satisfy a Callan-Symanzik equation. When specialized to quantum chromodynamics, this equation leads to the asymptotic formula of Brodsky and Lepage for the pion electromagnetic form factor. The nucleon form factors GM(Q²), GE(Q²) are also considered. It is shown that momentum flows which contribute to subdominant logarithms in GM(Q²) vitiate a conventional renormalization-group interpretation for this form factor. For large Q², the electric form factor GE(Q²) fails to factorize, so that a renormalization-group treatment seems even more unlikely in this case.