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 high-energy coherent production of a dijet (treated as a $q\overline{q}$ moving at high relative transverse momentum, ${\ensuremath{\kappa}}_{t})$ from a nucleon and a nuclear target. The direct evaluation of the relevant Feynman diagrams shows that, in the target rest frame, the space-time evolution of this reaction is dominated by the process in which the high ${\ensuremath{\kappa}}_{t}$ $q\overline{q}$ component (point-like configuration) of the pion wave function is formed before reaching the target. This point-like configuration then interacts through a two-gluon exchange with the target. In the approximation of keeping the leading order in powers of ${\ensuremath{\alpha}}_{s}$ and in the leading logarithmic approximation in ${\ensuremath{\alpha}}_{s}\mathrm{ln}({\ensuremath{\kappa}}_{t}^{2}/{\ensuremath{\Lambda}}_{\mathrm{QCD}}^{2}),$ the amplitudes for other processes are shown to be smaller by at least a power of ${\ensuremath{\alpha}}_{s}$ and/or the powers of Sudakov-type form factors and the small probability, ${w}_{2},$ to find a $q\overline{q}$ pair with no gluons at an average separation between constituents. Thus the high ${\ensuremath{\kappa}}_{t}$ component of the pion wave function, including the contribution of Gegenbauer polynomials of rank $n>0,$ can be measured in principle at sufficiently large values of ${\ensuremath{\kappa}}_{t}^{2}.$ At large values of ${\ensuremath{\kappa}}_{t}^{2},$ the resulting dominant amplitude is proportional to $z(1\ensuremath{-}z){\ensuremath{\alpha}}_{s}{(k}_{t}^{2}){\ensuremath{\kappa}}_{t}^{\ensuremath{-}4}[\mathrm{ln}({\ensuremath{\kappa}}_{t}^{2}/{\ensuremath{\Lambda}}^{2}){]}^{{C}_{F}/\ensuremath{\beta}}$ $[z$ is the fraction light cone (+) momentum carried by the quark in the final state, $\ensuremath{\beta}$ is the coefficient in the running coupling constant] times the skewed gluon distribution of the target. For pion scattering by a nuclear target, this means that at fixed ${x}_{N}=2{\ensuremath{\kappa}}_{t}^{2}/s$ (but ${\ensuremath{\kappa}}_{t}^{2}\ensuremath{\rightarrow}\ensuremath{\infty})$ 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---initial and final state interaction effects are absent for sufficiently large values of ${\ensuremath{\kappa}}_{t}.$ These findings are in accord with the recent experiment performed at Fermilab. We also reexamine a potentially important nuclear multiple scattering correction which is positive and varies as the length of the nucleus divided by an extra factor of $1/{\ensuremath{\kappa}}_{t}^{4}.$ 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 ${\ensuremath{\kappa}}_{t}$ achieved at fixed target energies, dijet production by the electromagnetic field of the nucleus leads to an insignificant correction which gets more important as ${\ensuremath{\kappa}}_{t}$ increases. We explain also that the same regularities are valid for photoproduction of forward light quark dijets.