Exclusive heavy-meson pair production at large recoil

The Brodsky-Lepage (BL) formalism in perturbative QCD is applied to estimate the validity of the heavy-quark effective theory and the high energy scaling laws to the exclusive heavy-meson pair production in two-photon collisions as well as e+e- annihilation. In addition to the ordinary heavy mesons such as B and D, the heavy mesons of which both quark masses are larger than the typical strong interaction scale ΛQCD are considered. Explicit forms of transition amplitudes are presented for the heavy mesons with two heavy quarks in the peaking approximation and the modifications for the ordinary heavy-meson production are described. The result in the heavy-quark limit is consistent with the heavy-quark effective theory only in a certain range of center of mass energy. In the high energy limit, the transition amplitudes turn out to comply with the high energy scaling laws. The common features and different points of the e+e- and γγ cases are described in detail. The limitation of the BL formalism and the heavy-quark effective theory is discussed.