Sub-leading power corrections to transition form factors of $\eta$ and ${\eta }^{\prime }$ mesons from twist-six contributions

Abstract

Using collinear factorization, we have calculated twist-six corrections to $\eta \gamma$ and ${\eta }^{\prime }\gamma$ transition form factors in QCD. Only a sub-set of light-cone operators of twist-six which can be factorized as a product of two gauge invariant operators has been considered. Resulting power corrections start as $1/Q^4$ but coefficients are smaller compared to their counterparts for twist-four operators. Matrix element of pseudoscalar quark densities for $u$- and $d$-quarks between vacuum and meson state, $h_q$, has considerable influence on the result. Results obtained by superimposing our results on those obtained in literature for leading and sub-leading power corrections for lower twists have been plotted and compared with data.

Comments: 18 pages, 9 figures, 2 tables