Hadronic photon correction to ${\gamma }^{\ast }\gamma \to f_2(1270)$ at next-to-leading order

Abstract

Within the framework of light-cone sum rules, we calculate the hadronic photon corrections to the ${\gamma }^{\ast }\gamma \to f_2(1270)$ transition form factors induced by the leading-twist photon distribution amplitude of the real photon. We establish the factorization formula for the vacuum-to-photon correlation function at next-to-leading order in ${\alpha }_s$, and extract the perturbative hard matching coefficients by applying the method of regions. The parametrically large logarithms appearing in the hard functions are resummed to next-to-leading logarithmic accuracy by solving the two-loop evolution equation for the corresponding light-ray tensor operator. Combining the resulting light-cone sum rules with the known leading-power contributions from QCD collinear factorization, we provide updated theoretical predictions for the three helicity form factors $T_0(Q^2)$, $T_1(Q^2)$ and $T_2(Q^2)$, including an estimate of the theoretical uncertainties.