Perturbative QCD and factorization of coherent pion photoproduction on the deuteron

Abstract

We analyze the predictions of perturbative QCD for pion photoproduction on the deuteron $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{D}{\ensuremath{\pi}}^{0}D$ 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 ${\mathcal{M}}_{\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{D}{\ensuremath{\pi}}^{0}D}(u,t)$ factorizes as a product of three factors: (1) the nucleon photoproduction amplitude ${\mathcal{M}}_{\ensuremath{\gamma}{N}_{1}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{N}_{1}}(u/4,t/4)$ at half of the overall momentum transfer, (2) a nucleon form factor ${F}_{{N}_{2}}(t/4)$ 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 $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{D}{\ensuremath{\pi}}^{0}D$ of Meekins et al. [Phys. Rev. C 60, 052201 (1999)] and the available $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}{\ensuremath{\pi}}^{0}p$ 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 ${p}_{T}^{11}{\mathcal{M}}_{\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{D}{\ensuremath{\pi}}^{0}D}\ensuremath{\rightarrow}F({\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.})$ at large momentum transfer. This is found to be consistent with measurements for photon lab energies ${E}_{\mathrm{lab}}>3$ GeV at ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=90\ifmmode^\circ\else\textdegree\fi{}$ and ${E}_{\mathrm{lab}}>10$ GeV at $136\ifmmode^\circ\else\textdegree\fi{}.$