  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.
