Perturbative QCD and factorization of coherent pion photoproduction on the deuteron

We analyze the predictions of perturbative QCD for pion photoproduction on the deuteron γD⃗π⁰D 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 M_γD⃗π⁰D(u,t) factorizes as a product of three factors: (1) the nucleon photoproduction amplitude M_{γN1→π⁰N1}(u/4,t/4) at half of the overall momentum transfer, (2) a nucleon form factor F_N2(t/4) at half the overall momentum transfer, and (3) the reduced deuteron form factor f_d(t), which, according to perturbative QCD, has the same monopole falloff as a meson form factor. A comparison with the recent JLAB data for γD⃗π⁰D of Meekins et al. [Phys. Rev. C 60, 052201 (1999)] and the available γp⃗π⁰p 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 p_T¹¹M_γD⃗π⁰D→F(θ_c.m.) at large momentum transfer. This is found to be consistent with measurements for photon lab energies E_lab>3 GeV at θ_c.m.=90° and E_lab>10 GeV at 136°.