\(2^{++}\) Light tensor hybrid meson from QCD Laplace sum rules

Abstract

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) $ MeV and a relatively small coupling \(f_{2^+} = \left(10.5\pm2.9\right)\) MeV normalized as \(f_\pi = 93\) MeV. Our results suggest that the \(f_2\left(1950\right)\) or/and the \(f'_2\left(2010\right)\) 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: \(\Pi_{qg}(0) = \left(2.41\pm0.43\right)\times 10^{-4}\,\mathrm{GeV^6}\) which could be checked from some lattice QCD or/and low energy theorems (LET).