The New Charm-Strange Resonances in the D−K+ Channel

Abstract

We evaluate the masses and decay constants of the 0+ and 1− open-charm (c¯d¯)(us) tetraquarks and molecular states from QCD spectral sum rules (QSSR) by using QCD Laplace sum rule (LSR). This method takes into account the stability criteria where the factorised perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE are included. We confront our results with the D−K+ invariant mass recently reported by LHCb from B+ → D+(D−K+) decays. We expect that the resonance near the D−K+ threshold can be originated from the 0++(D−K+) molecule and/or D−K+ scattering. The X0(2900) scalar state and the resonance XJ(3150) (if J = 0) can emerge from a minimal mixing model, with a tiny mixing angle θ0 ≃ (5.2 ± 1.9)0, between a scalar Tetramole (TM0) (superposition of nearly degenerated hypothetical molecules and compact tetraquarks states with the same quantum numbers), having a mass MTM0=2743(18)MeV, and the first radial excitation of the D−K+ molecule with mass M(DK)1 = 3678(310) MeV. In an analogous way, the X1(2900) and the XJ(3350) (if J = 1) could be a mixture between the vector Tetramole (TM1), with a mass MTM1=2656(20)MeV, and its first radial excitation having a mass MTM1=4592(141)MeV with an angle θ0 ≃ (9.1 ± 0.6)0. A (non)-confirmation of these statements requires experimental findings of the quantum numbers of the resonances at 3150 and 3350 MeV.