$DK$ and $BK$-like spectra from Laplace sum rule at NLO

Abstract

Encouraged by the agreement, with the recent LHCb data on the $D^{-}{K}^{+}$ invariant mass from $B\to D^{+}{D}^{-}{K}^{+}$ decay, of our results for the masses of the $0^{+}$ and $1^{-}$ open charm $(\bar{c}\bar{d})(us)$ tetraquarks and molecules states from QCD spectral sum rules within stability criteria, which we review here, we extend our analysis to the $b$-quark channel. We find, in the $0^{+}$ case the lowest mass $M_{BK}=5195(15)\mathrm{MeV}$ with $f_{BK}=8.3(2.4)\mathrm{keV}$ and three (almost) degenerate states having respectively the masses $M_{SS}=5702(60)\mathrm{MeV}$, $M_{AA}=5661(75)\mathrm{MeV}$ and $M_{B^{\ast }{K}^{\ast }}=5720(71)\mathrm{MeV}$ and couplings $f_{SS}=22.2(2.3)\mathrm{keV}$, $f_{AA}=30.1(3.1)\mathrm{keV}$ and $f_{B^{\ast }{K}^{\ast }}=26.5(2.8)\mathrm{keV}$, from which we can associate a scalar tetramole with $M_{{\mathcal{T}}_{{\mathcal{M}}_0}}=5694(69)\mathrm{MeV}\text{and}{f}_{{\mathcal{T}}_{{\mathcal{M}}_0}}=26.5(2.7)\mathrm{keV}$. In the spin 1 case, we find four (almost) degenerate states associated with a tetramole having $M_{{\mathcal{T}}_{{\mathcal{M}}_1}}=5700(81)\mathrm{MeV}\text{and}{f}_{{\mathcal{T}}_{{\mathcal{M}}_1}}=16.2(2.6)\mathrm{keV}$. For the first radial excitation of the $BK$ molecule, we have $M_{(BK{)}_1}=6265(146)\mathrm{MeV}$ and $f_{(BK{)}_1}=22.8(3.2)\mathrm{keV}$ . For the remaining states, we associate a scalar and vector tetramoles having respectively $M_{(T_{{\mathcal{M}}_0}{)}_1}=7439(314)\mathrm{MeV},f_{(T_{{\mathcal{M}}_0}{)}_1}=74.7(8.4)\mathrm{keV}$ and $M_{(T_{{\mathcal{M}}_1}{)}_1}=7544(345)\mathrm{MeV},f_{(T_{{\mathcal{M}}_1}{)}_1}=33.0(6.7)\mathrm{keV}$.

Comments: arXiv admin note: text overlap with arXiv:2008.13463