Fully and Doubly-heavy four-quarks within QCD Laplace sum rule

TL;DR

This paper reviews QCD Laplace sum rule calculations for fully heavy four-quark and tetraquark states, providing mass and coupling estimates that may explain observed structures at LHCb and exploring their nature across charm and bottom sectors.

Contribution

The paper introduces a comprehensive QCD sum rule analysis of heavy four-quark states, including NLO corrections and double ratios, offering new mass predictions and interpretations of experimental signals.

Findings

Mass estimates for fully heavy four-quark states around 6.2-6.9 GeV.

Identification of possible molecular and tetraquark structures corresponding to LHCb observations.

Predictions of $T_{ccar{q}ar{q}'}$ states with precise mass values and classification into heavy and light states.

Abstract

We present a review of our results for the masses and couplings of the scalar fully heavy four-quarks and $T_{QQ\bar{q}\bar{q}'}\, (J^P=0^\pm , 1^\pm)$ tetraquarks states from QCD Laplace sum rule (LSR), their ratios ${\cal R}$ 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 $d\leqslant 6-8$, we evaluated the QCD spectral functions at Lowest Order of PT QCD and up to $\langle G^3 \rangle$. 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 $\overline{\eta_c} \eta_c,~~ \overline{\chi_{c1}}\chi_{c1}$ and $\overline{J/\psi}J/\psi$ molecules or/and their analogue $S_c S_c,~~ A_cA_c$ and $V_cV_c$ tetraquarks. The peak at (6.8-6.9)GeV can be identified to the $\overline{\chi_{c0}}\chi_{c0}$ molecule or/and the $P_c P_c$ tetraquark state. Then, combining ${\cal R}$ and DRSR we focus on the analysis of the four-quark nature of $T_{cc\bar{q}\bar{q}'}$ $1^{\pm}$ and $0^{\pm}$ states. We show that combining ${\cal R}$ and DRSR can provide more precise results: $M_{T^{1^+}_{cc}}=3886(6)$MeV and $M_{T^{0^+}_{cc}}=3883(3)$MeV. From our estimates of the masses of the Pseudoscalar and Vector $T_{cc\bar{q}\bar{q}'}$ 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 $\overline{D}D_0,~~ overline{D}_s D_{s0}$ (resp. $\overline{D}D_1,~~ \overline{D}_s D_{s1}$) 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 in the literature.