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

Abstract

We present improved estimates of the couplings, masses and mass ratios of the ZQ,XQ and TQQq¯q¯′ states (Q≡c,b;q,q′≡u,d,s) using (inverse) 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. In the 1st part of the paper, we conclude that the observed Xc(3872) and Zc(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: MTXc=3876(44)MeV and MTZc=3900(42)MeV. In the 2nd part, we focus on the analysis of the four-quark nature of different TQQq¯q¯′ 1+ and 0+ states within the 3¯c3c interpolating currents. The final results from R and R⊕ DRSR are summarized in Table 7. Combined R and DRSR calibrated to the observed Xc(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 MTccs¯s¯0+/MTcc0+ lead to the improved mass predictions: MTccs¯s¯0+=3988(12)MeV. In the 3rd part, the analysis is extended to the beauty mesons, where we find the tetramole masses: MTZb=10579(99)MeV and MXb=10545(131)MeV. We also observe that the Tbbq¯q¯′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 TQQq¯q¯′1+,0+ masses. Our combined LSR ⊕ DRSR results are confronted with the ones from some other approaches (lattices and quark models) in Fig. 26.