ar X iv : h ep - p h / 04 04 10 9 v 1 1 3 A pr 2 00 4 Transition to perturbative QCD in two - photon collisions

We propose that the different angular distributions in two-photon collisions observed at low and high center-of-mass energies Wγγ indicate the transition from nonperturbative to perturbative QCD. We calculate the differential cross sections of γγ → ππ, KK in the angle θ of one of the final-state mesons using QCD sum rules and the perturbative QCD approach based on kT factorization theorem. Our predictions from sum rules (perturbative QCD) decrease (increase) with | cos θ|, consistent with the Belle data of γγ → KK for Wγγ ≈ 1.5-1.7 (2.2-2.4) GeV. It has remained as a controversy whether perturbative QCD (PQCD) is applicable to exclusive processes at moderate energies [1]. This issue has been widely discussed in the literature, but general agreement is still not available. The discussion usually focused on the simplest case, hadronic form factors, which have been computed in nonperturbative frameworks, such as QCD sum rules (QSR) [2], and in the PQCD formalism [3, 4, 5, 6]. Within theoretical uncertainty, the predictions from both approaches were claimed to be consistent with experimental data [7]. The contradictory conclusions on the dominant dynamics, soft (Feynman mechanism [8]) or hard, in exclusive processes at moderate energies were drawn. We have explained this subtlety in [9], and argued that there is no contradiction, because the definitions of a soft contribution vary among different theoretical frameworks. With this subtlety, a hadronic form factor may not be the most appropriate quantity to discriminate the soft-dominance and hard-dominance pictures. In this work we shall propose that the angular distribution in two-photon collisions is an appropriate quantity for the purpose. We take the processes γγ → ππ, KK as an example, and calculate the pion and kaon angular distributions using nonperturbative QSR, which are reliable at a low center-of-mass energyWγγ , and the PQCD approach based on kT factorization theorem [10, 11, 12, 13, 14], which is reliable at a high Wγγ. It will be shown that QSR and PQCD give dramatically different predictions: the former decrease, while the latter increase with | cos θ|, where θ denotes the angle of one of the final-state mesons in the center-of-mass frame. In fact, this difference is a general feature of QSR and PQCD predictions for two-photon collisions, regardless the final states being baryons or mesons. It is thus important to measure the dependence of the angular distribution on Wγγ , and to see whether it evolves with Wγγ following the QSR and PQCD predictions. Such a transition has indeed been observed in the E-mail: [email protected] E-mail: [email protected]