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