$2^{++}$ Tensor Di-Gluonium from Laplace Sum Rules at NLO

Abstract

We evaluate the next-to-leading (NLO) corrections to the perturbative (PT) and $<{\alpha }_s{G}^2>$ condensate and the LO constant term of the $<G^3>$ contributions to the $2^{++}$ tensor di-gluonium two-point correlator. Using these results into the inverse Laplace transform sum rules (LSR) moments and their ratio, we estimate the mass and coupling of the lowest ground state. We obtain\,: $M_T=3028(287)$ MeV and the renormalization group invariant (RGI) coupling ${\hat{f}}_T=224(33)$ MeV within a vacuum saturation estimate of the $D=8$ dimension gluon condensates ($k_G=1$). We study the effect of $k_G$ on the result and find: $M_T=3188(337)$ MeV and ${\hat{f}}_T$=245(32) MeV for $k_G=(3\pm 2)$. Our result does not favour the pure gluonia/glueball nature of the observed $f_2(2010,2300,2340)$ states.

7 pages, 9 figures, 1 Table