Formula omitted] and TQQ within QCD Laplace sum rules

Abstract

We present a review of our results for the masses and couplings of the scalar fully heavy four-quarks and TQQq¯q¯′(JP=0±,1±) tetraquarks states from (inverse) QCD Laplace sum rule (LSR), their ratios R and double ratio of sum rules (DRSR) within stability criteria and including Factorized Next-to-Leading Order (FNLO) Perturbative (PT) corrections. As the Operator Product Expansion (OPE) usually converges for d⩽6−8, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to 〈G3〉. Our results for the 0++ fully heavy four-quark states may explain the LHCb broad structure around (6.2−6.7)GeV which can be due to ηc‾ηc,χc1‾χc1 and J/ψ‾J/ψ molecules or/and their analogue ScSc,AcAc and VcVc tetraquarks. The peak at (6.8−6.9)GeV can be identified to the χc0‾χc0 molecule or/and the PcPc tetraquark state. Then, combining R and DRSR we focus on the analysis of the four-quark nature of Tccq¯q¯′1± and 0± states. We show that combining R and DRSR can provide more precise results: MTcc1+=3886(6)MeV and MTcc0+=3883(3)MeV. In a similar way, one obtain the improved mass predictions: MTccs¯u¯1+=3931(7)MeV, MTccs¯u¯0+=3983(7)MeV and MTccs¯s¯0+=3993(11)MeV. From our estimates of the masses of the Pseudoscalar and Vector Tccq¯q¯′ states, we observe that the interpolating currents lead to two classes: Class H (Heavy) states with masses around 6GeV and Class L (Light) states around (3.8−4.4)GeV where the pseudoscalar (resp. all vector states) are below the D‾D0,D‾sDs0 (resp. D‾D1,D‾sDs1) open charm thresholds. Finally, we extend the whole study to the bottom sector and confront our results with the ones from different LSR predictions and some other approaches (lattice, potential models, ⋯) in the literature.