Coherent QCD phenomena in the Coherent Pion-Nucleon and Pion-Nucleus Production of Two Jets at High Relative Momenta

Abstract

We use QCD to compute the cross section for coherent production of a di-jet (treated as a $q\bar q$ moving at high relative transverse momentum,$\kappa_t$). In the target rest frame,the space-time evolution of this reaction is dominated by the process in which the high $\kappa_t$ $q\bar q$ component of the pion wave function is formed before reaching the target. It then interacts through two gluon exchange. In the approximation of keeping the leading order in powers of $\alpha_s$ and all orders in $\alpha_{s}\ln(\kappa_{t}^2/k_{0}^2),$ the amplitudes for other processes are shown to be smaller at least by a power of $\alpha_{s}$. The resulting dominant amplitude is proportional to $z(1-z) \kappa_t^{-4}$ ($z$ is the fraction light-cone(+)momentum carried by the quark in the final state) times the skewed gluon distribution of the target. For the pion scattering by a nuclear target, this means that at fixed $x_{N}= 2\kappa_{t}^2/s$ (but $\kappa_{t}^2\to \infty$) the nuclear process in which there is only a single interaction is the most important one to contribute to the reaction. Thus in this limit color transparency phenomena should occur.These findings are in accord with E971 experiment at FNAL. We also re-examine a potentially important nuclear multiple scattering correction which is positive and $\propto A^{1/3}/\kappa_t^4$. The meaning of the signal obtained from the experimental measurement of pion diffraction into two jets is also critically examined and significant corrections are identified.We show also that for values of $\kappa_t$ achieved at fixed target energies, di-jet production by the e.m. field of the nucleus leads to an insignificant correction which gets more important as $\kappa_t$ increases.Comment: 23 pages, 9 figure