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

TL;DR

This paper calculates twist-six power corrections to the transition form factors of eta and eta' mesons in QCD, revealing smaller coefficients than twist-four corrections and highlighting the importance of pseudoscalar quark densities.

Contribution

It provides the first calculation of twist-six corrections to eta and eta' transition form factors using collinear factorization, considering a specific subset of operators.

Findings

Power corrections start as 1/Q^4 with smaller coefficients than twist-four.

Pseudoscalar quark densities significantly influence the results.

Results agree with existing data when combined with lower-twist corrections.

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.