Doubly hidden $0^{++}$ molecules and tetraquarks states from QCD at NLO

Abstract

Motivated by the LHCb-group discovery of exotic hadrons in the range (6.2 $\sim$ 6.9) GeV, we present new results for the masses and couplings of $0^{++}$ fully heavy $(\bar{Q}Q)(Q\bar{Q})$ molecules and $(QQ)(\overline{QQ})$ tetraquaks states from relativistic QCD Laplace Sum Rule (LSR) within stability criteria where Next-to-Leading Order (NLO) Factorized (F) Perturbative (PT) corrections is included. As the Operator Product Expansion (OPE) usually converges for $d\leqslant 6-8$, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to $\langle G^3 \rangle$. We also emphasize the importance of PT radiative corrections for heavy quark sum rules in order to justify the use of the running heavy quark mass value in the analysis. We compare our predictions in Table 3 with the ones from ratio of Moments (MOM). The broad structure arround (6.2 $\sim$ 6.9) GeV can be described by the $\overline{\eta}_c\eta_c$, $\overline{J/\psi}J/\psi$ and $\overline{\chi}_{c1}\chi_{c1}$ molecules or/and $\overline{S}_c S_c$, $\overline{A}_c A_c$ and $\overline{V}_c V_c$ tetraquarks lowest mass ground states. The narrow structure at (6.8 $\sim$ 6.9) GeV if it is a $0^{++}$ state can be a $\overline{\chi}_{c0}\chi_{c0}$ molecules or/and its analogue $\overline{P}_c P_c$ tetraquark. The $\overline{\chi}_{c1}\chi_{c1}$ predicted mass is found to be below the $\chi_{c1}\chi_{c1}$ threshold while for the beauty states, all of the estimated masses are above the $\eta_b \eta_b$ and $\Upsilon(1S)\Upsilon(1S)$ threshold.