The ${\eta }^{\prime }{g}^{\ast }{g}^{\ast }$ vertex with arbitrary gluon virtualities in the perturbative QCD hard scattering approach

Abstract

We study the ${\eta }^{\prime }{g}^{\ast }{g}^{\ast }$ vertex for arbitrary gluon virtualities in the time-like and space-like regions, using the perturbative QCD hard scattering approach and an input wave-function of the ${\eta }^{\prime }$-meson consistent with the measured ${\eta }^{\prime }{\gamma }^{\ast }\gamma$ transition form factor. The contribution of the gluonic content of the ${\eta }^{\prime }$-meson is taken into account, enhancing the form factor over the entire virtuality considered. However, data on the electromagnetic transition form factor of the ${\eta }^{\prime }$-meson is not sufficient to quantify the gluonic enhancement. We also study the effect of the transverse momenta of the partons in the ${\eta }^{\prime }$-meson on the ${\eta }^{\prime }{g}^{\ast }{g}^{\ast }$ vertex, using the modified hard scattering approach based on Sudakov formalism. Analytic expressions for the ${\eta }^{\prime }{g}^{\ast }{g}^{\ast }$ vertex are presented in limiting kinematic regions and parametrizations are given satisfying the QCD anomaly, for real gluons, and perturbative QCD behavior for large gluon virtualities, in both the time-like and space-like regions. Our results have implications for the inclusive decay $B\to {\eta }^{\prime }X$ and exclusive decays, such as $B\to {\eta }^{\prime }(K,K^{\ast })$, and in hadronic production processes $N+N(\bar{N})\to {\eta }^{\prime }X$.

Comments: 23 pages, 19 figures (requires revtex4, amssymb, epsf); several typos corrected, this version now identical to the one accepted for publication in Phys. Rev. D