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

Abstract

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 ${Q}^{2}$ 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 ${G}_{M}({Q}^{2})$, ${G}_{E}({Q}^{2})$ are also considered. It is shown that momentum flows which contribute to subdominant logarithms in ${G}_{M}({Q}^{2})$ vitiate a conventional renormalization-group interpretation for this form factor. For large ${Q}^{2}$, the electric form factor ${G}_{E}({Q}^{2})$ fails to factorize, so that a renormalization-group treatment seems even more unlikely in this case.