Perturbative QCD and Factorization of Coherent Pion Photoproduction on the Deuteron

We analyze the predictions of perturbative QCD for pion photoproduction on the deuteron γD → π0D at large momentum transfer using the reduced amplitude formalism. The cluster decomposition of the deuteron wave function at small binding only allows the nuclear coherent process to proceed if each nucleon absorbs an equal fraction of the overall momentum transfer. Furthermore, each nucleon must scatter while remaining close to its mass shell. Thus the nuclear photoproduction amplitude MγD→π0D(u, t) factorizes as a product of three factors: (1) the nucleon photoproduction amplitude MγN1→π0N1(u/4, t/4) at half of the overall momentum transfer, (2) a nucleon form factor FN2(t/4) at half the overall momentum transfer, and (3) the reduced deuteron form factor fd(t), which according to perturbative QCD, has the same monopole fall-off as a meson form factor. A comparison with the recent JLAB data for γD → π0D of Meekins et al. and the available γp→ π0p shows good agreement between the perturbative QCD prediction and experiment over a large range of momentum transfers and center of mass angles. The reduced amplitude prediction is consistent with the constituent counting rule p11 T MγD→π0D → F (θcm) at large momentum transfer. This is found to be consistent with measurements for photon lab energies Eγ > 3 GeV at θcm = 90◦ and 136◦.