$2^{++}$ Di-gluonium from LSR at higher order

TL;DR

This paper refines the mass and coupling estimates of the $2^{++}$ di-gluonium state using advanced QCD sum rules, including higher-order corrections, and discusses implications for observed tensor mesons.

Contribution

It provides improved QCD sum rule calculations for $2^{++}$ di-gluonium, incorporating NLO corrections and analyzing the impact of gluon condensate factorization violations.

Findings

Estimated mass of di-gluonium: ~3 GeV

Estimated coupling: ~224 MeV

Results do not support observed tensor mesons as pure glueballs

Abstract

We improve the determination of the mass and coupling of the $2^{++}$ tensor di-gluonium by using relativistic QCD Laplace sum rules (LSR). In so doing, we evaluate the next-to-leading order (NLO) corrections to the perturbative (PT) and $\langle \alpha_s G^2 \rangle$ condensate and the lowest order (LO) $\langle G^3 \rangle$ contributions to the $2^{++}$ di-gluonium two-point correlator. Within a vacuum saturation estimate ($k_G=1$) of the dimension-eight gluon condensates, we obtain: $M_{T}=3028(287)\mbox{MeV}$ and the renormalization group invariant (RGI) coupling $\hat{f}_T=224(33)\mbox{MeV}$. Assuming that the factorization hypothesis can be violated, we study the effect of the violation factor $k_G$ on the results and obtain: $M_T=3188(337)\mbox{MeV}$ and $\hat{f}_T=245(32)\mbox{MeV}$ for $k_G=(3\pm 2)$. Our estimation does not favour the interpretation of the observed $f_2(2010)$, $f_2(2300)$ and $f_2(2340)$ as pure glueball state.