Improved XTZ masses and mass ratios from Laplace Sum Rules at NLO

TL;DR

This paper improves estimates of heavy tetraquark and molecule state masses using advanced QCD sum rules, providing more precise predictions and insights into their nature, including stability and composition, with comparisons to other models.

Contribution

It introduces refined NLO QCD Laplace sum rule techniques with combined ratios for more accurate mass and coupling predictions of exotic states.

Findings

X_c(3872) and Z_c(3900) are tetramole states with predicted masses around 3876 and 3900 MeV.

Predicted masses for T_{cc}^{1^+} and T_{cc}^{0^+} are 3886(6) MeV and 3883(3) MeV respectively.

Some T_{bbqq'} states are nearly stable against strong decays.

Abstract

We present improved estimates of the couplings, masses and mass ratios of the Z_Q,X_Q and T_{QQqq} states using QCD Laplace sum rules (LSR), their ratios R and 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 heavy quark mass used in the analysis. We show that combined R and DRSR can provide more precise results. First, we conclude that the observed X_c(3872) and Z_c(3900) are tetramoles states (superposition of quasi-degenerated molecule and a tetraquark states having (almost) the same coupling to the currents) with the predicted masses: M_{T_{X_c}}=3876(44) MeV and M_{ T_{Z_c}}=3900(42) MeV. In the 2nd part, we focus on the analysis of the four-quark nature of different T_{QQqq'} 1^+ and 0^+ states within the 3_c3_c interpolating currents. The final results are summarized in Table 7. Combined R and DRSR calibrated to the observed X_c(3872) lead to a precise prediction of e.g. M_{T_{cc}^{1^+}}=3886(6) MeV. In a similar way, the DRSR for M_{T_{cc}^{0^+}}/M_{T_{cc}^{1^+}} calibrated to M_{T_{cc}^{1^+}} gives M_{T_{cc}^{0^+}}= 3883(3) MeV. The SU3 breaking ratios M_{T_{ccss}^{0^+}}/ M_{T_{cc}^{0^+}} lead to the improved mass predictions: M_{T_{ccss}^{0^+}}=3988(12) MeV. In the 3rd part, the analysis is extended to the beauty mesons, where we find the tetramole masses : M_{ T_{Z_b}}=10579(99) MeV and M_{X_b}=10545(131) MeV. We also observe that the T^{1^+,0^+}_{bbqq'} 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^{1^+,0^+}_{QQqq'} masses. Our results from LSR+DRSR are confronted with the ones from some other approaches (lattices and quark models) in Fig. 25.