The $\gamma {\gamma }^{*}\to {\eta }_{c,b}$ transition form factors are computed using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory, and thereby unified with equivalent calculations of electromagnetic pion elastic and transition form factors. The resulting $\gamma {\gamma }^{*}\to {\eta }_c$ form factor, $G_{{\eta }_c}(Q^2)$, is consistent with available data; significantly, at accessible momentum transfers, $Q^2{G}_{{\eta }_c}(Q^2)$ lies well below its conformal limit. These observations confirm that the leading-twist parton distribution amplitudes of heavy-heavy bound states are compressed relative to the conformal limit. A clear understanding of the distribution of valence quarks within mesons thus emerges, a picture which connects Goldstone modes, built from the lightest quarks in nature, with systems containing the heaviest valence quarks that can now be studied experimentally, and highlights basic facts about manifestations of mass within the Standard Model.

• Received 23 October 2016

DOI:https://doi.org/10.1103/PhysRevD.95.074014