Doubly heavy tetraquarks: heavy quark bindings and chromomagnetically mixings

Abstract

We introduce an enhanced binding energy $B_{QQ}$ between heavy-heavy quarks $QQ$ and a flux-tube correction into the chromomagnetic interaction model to study nonstrange doubly-heavy tetraquarks $T_{QQ}$ ($Q=c,b)$. A simple relation in terms of baryon masses is proposed to estimate the binding energies $B_{QQ}$ and thereby map the flux-tube corrections in doubly-heavy tetraquarks $T_{cc}$, $T_{bb}$ and $T_{bc}$. Our computation via diagonalization of chromomagnetic interaction predicts the doubly charmed tetraquark $T_{cc}$ (in color rep. $\bar{3}_{c}\otimes 3_{c}$) and $T_{cc}^{\ast }$ (in $6_{c}\otimes \bar{6}_{c}$) with $IJ^{P}=01^{+}$ to have masses of $3879.2$ MeV and $4287.6$ MeV, respectively, with the former being in consistent with the measured mass $3874.7\pm 0.05$ MeV of the doubly charmed tetraquark $T_{cc}(1^{+})=cc\bar{u}\bar{d}$ discovered by LHCb. Further mass predictions are given of the doubly bottom tetraquarks $T_{bb}$ and the bottom-charmed tetraquarks $T_{bc}$ with $J^{P}=0^{+},1^{+},2^{+}$ and $I=0,1$. A chromomagnetical mixing between the color configurations $\bar{3}_{c}\otimes 3_{c}$ and $6_{c}\otimes \bar{6}_{c}$ is noted for the bottom-charmed states $T_{bc}$ with $IJ^{P}=01^{+}$ and $IJ^{P}=1(0^{+},1^{+})$.