$2^{++}$ Light Tensor Hybrid Meson from QCD Laplace Sum Rules

We present an analysis of the light tensor ($J^{PC}=2^{++}$) hybrid meson mass and coupling from QCD Laplace Sum Rules where the next-to-leading order (NLO) perturbative (PT) corrections and the contributions of the non-perturbative (NP) condensates up to dimension-six ($D=6$) are included. NLO leading-logarithms corrections due to the condensates which contribute in the chiral limit are considered. We obtain the mass $M_{2^{+}}=(2038\pm 190)$ MeV and a relatively small coupling $f_{2^{+}}=(10.5\pm 2.9)$ MeV normalized as $f_{\pi }=93$ MeV. Our results suggest that the $f_2(1950)$ or/and the $f_2^{\mathrm{\prime }}(2010)$ may have a sizeable $\bar{q}qg$ hybrid component. We also compute the tensor hybrid topological charge (value of the two-point function at zero momentum) and find (for the first time) at NLO: ${\mathrm{\Pi }}_{qg}(0)=(2.41\pm 0.43)\times {10}^{-4}{\mathrm{G}\mathrm{e}\mathrm{V}}^6$ which could be checked from some lattice QCD or/and low energy theorems (LET).