Can Nonrelativistic QCD Explain the γγ* → ηc Transition Form Factor Data?

Unlike the bewildering situation in the gamma gamma* -> pi form factor, a widespread view is that perturbative QCDcan decently account for the recentBABAR measurement of the gamma gamma* ->eta(c) transition formfactor. The nextto- next-to-leading-order perturbative correction to the gamma gamma* ->eta(c,b) form factor, is investigated in the nonrelativistic QCD (NRQCD) factorization framework for the first time. As a byproduct, we obtain, by far, the most precise order-alpha(2)(s) NRQCD matching coefficient for the eta(c,b) -> gamma gamma process. After including the substantial negative order-alpha(2)(s) correction, the good agreement between NRQCD prediction and the measured gamma gamma* ->eta(c) form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of the NRQCD approach to hard exclusive reactions involving charmonium.