Improved XTZ masses and mass ratios from Laplace sum rules at NLO

We present improved estimates of the couplings, masses and mass ratios of the Z(Q), X-Q and T-QQ (q) over bar(q) over bar' states (Q = c, b; q, q' = u, d, s) using (inverse) QCD Laplace sum rules (LSR), their ratios Rand double ratios DRSR within stability criteria, where the NLO factorized PT QCD corrections are included which is important for giving a meaning on the running (MS) over bar heavy quark mass used in the analysis. We show that combined Rand DRSR can provide more precise results. In the 1st part of the paper, we conclude that the observed X-c(3872) and Z(c)(3900) are tetramolesstates (superposition of quasi-degenerated molecule and a tetraquark states having (almost) the same coupling to the currents) with the predicted masses: M-TXc = 3876(44) MeVand M-TZc = 3900(42) MeV. In the 2nd part, we focus on the analysis of the four-quark nature of different T-QQ (q) over bar(q) over bar' 1(+) and 0(+) states within the (3) over bar (c)3(c) interpolating currents. The final results from Rand R-circle plus DRSR are summarized in Table7. Combined Rand DRSR calibrated to the observed X-c(3872) lead to a precise prediction of e.g. MTcc1+ = 3886(6) MeV. In a similar way, the DRSR for the MTcc0+/MTcc1+ calibrated to MTcc1+ gives MTcc0+ = 3883(3) MeV. The SU3 breaking ratios MTcc (s) over bar(s) over bar0+/MTcc0+ cclead to the improved mass predictions: MTcc (s) over bar(s) over bar0+ = 3988(12) MeV. In the 3rd part, the analysis is extended to the beauty mesons, where we find the tetramole masses: M-TZb = 10579(99) MeVand M-Xb = 10545(131) MeV. We also observe that the T-bb (q) over bar(q) over bar'(1+,0+) (q, q' = u, d, s) states are (almost) stable (within the errors) against strong interactions. In the 4th part, we (critically) review and correct some recent LSR estimates of the T-QQ (q) over bar(q) over bar'(1+,0+) masses. Our combined LSR circle plus DRSR results are confronted with the ones from some other approaches (lattices and quark models) in Fig. 26. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, improved estimates of the couplings, masses, and mass ratios of different states are presented using various methods. The study includes the inclusion of NLO factorized PT QCD corrections and focuses on the tetramole states and four-quark nature of the particles. The results show the importance of combined Rand DRSR in providing precise predictions.