Can Nonrelativistic QCD Explain the γγ^{*}→η_{c} Transition Form Factor Data?

Abstract

Unlike the bewildering situation in the γγ^{*}→π form factor, a widespread view is that perturbative QCD can decently account for the recent BABAR measurement of the γγ^{*}→η_{c} transition form factor. The next-to-next-to-leading-order perturbative correction to the γγ^{*}→η_{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-α_{s}^{2} NRQCD matching coefficient for the η_{c,b}→γγ process. After including the substantial negative order-α_{s}^{2} correction, the good agreement between NRQCD prediction and the measured γγ^{*}→η_{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.