γ*γ*→ηctransition form factor

Abstract

We study the ${\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}$ transition form factor, ${F}_{{\ensuremath{\eta}}_{c}\ensuremath{\gamma}\ensuremath{\gamma}}({Q}_{1}^{2},{Q}_{2}^{2})$, with the local-duality (LD) version of QCD sum rules. We analyze the extraction of this quantity from two different correlators, $⟨PVV⟩$ and $⟨AVV⟩$, with $P$, $A$, and $V$ being the pseudoscalar, axial-vector, and vector currents, respectively. The QCD factorization theorem for ${F}_{{\ensuremath{\eta}}_{c}\ensuremath{\gamma}\ensuremath{\gamma}}({Q}_{1}^{2},{Q}_{2}^{2})$ allows us to fix the effective continuum thresholds for the $⟨PVV⟩$ and $⟨AVV⟩$ correlators at large values of ${Q}^{2}={Q}_{2}^{2}$ and some fixed value of $\ensuremath{\beta}\ensuremath{\equiv}{Q}_{1}^{2}/{Q}_{2}^{2}$. We give arguments that, in the region ${Q}^{2}\ensuremath{\ge}10--15\text{ }\text{ }{\mathrm{GeV}}^{2}$, the effective threshold should be close to its asymptotic value such that the LD sum rule provides reliable predictions for ${F}_{{\ensuremath{\eta}}_{c}\ensuremath{\gamma}\ensuremath{\gamma}}({Q}_{1}^{2},{Q}_{2}^{2})$. We show that, for the experimentally relevant kinematics of one real and one virtual photon, the result of the LD sum rule for ${F}_{{\ensuremath{\eta}}_{c}\ensuremath{\gamma}}({Q}^{2})\ensuremath{\equiv}{F}_{{\ensuremath{\eta}}_{c}\ensuremath{\gamma}\ensuremath{\gamma}}(0,{Q}^{2})$ may be well approximated by the simple monopole formula ${F}_{{\ensuremath{\eta}}_{c}\ensuremath{\gamma}}({Q}^{2})=2{e}_{c}^{2}{N}_{c}{f}_{P}({M}_{V}^{2}+{Q}^{2}{)}^{\ensuremath{-}1}$, where ${f}_{P}$ is the ${\ensuremath{\eta}}_{c}$ decay constant, ${e}_{c}^{2}$ is the $c$-quark charge, and the parameter ${M}_{V}$ lies in the mass range of the lowest $\overline{c}c$ vector states.