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 Z Q , X Q and T QQq 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 M S 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 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 Xc = 3876(44) MeV and M T Zc = 3900(42) MeV. In the 2nd part, we focus on the analysis of the four-quark nature of different T QQq q 1 + and 0 + states within the 3c 3 c interpolating currents. The final results from R and R ⊕ DRSR 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 1 + cc =3886(6) MeV. In a similar way, the DRSR for the(3) MeV. The SU3 breaking ratios M T 0 + ccss /M T 0 + cc lead to the improved mass predictions : 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 + bbq q (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 1 + ,0 + QQq q masses. Our combined LSR ⊕ DRSR results are confronted with the ones from some other approaches (lattices and quark models) in Fig. 25.

Tests of the Z_c-like Laplace Sum Rule (LSR) results using FESR at NLO

“…which has the same value as the one in our different analysis for the four-quark and molecule states [15][16][17][18][19].…”

An updated review of the new hadron states

“…In Refs. [435,436,437] the authors performed a comprehensive QCD sum rule analysis of the J P = 0 + and 1 − udsc tetraquark states using the interpolating currents given in Table 9. They considered the stability criteria by including the factorised perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE.…”