<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mi>Q</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover><mml:mover accent="true"><mml:mrow><mml:mi>q</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mi>u</mml:mi></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:math>; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mi>c</mml:mi></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:math>) tetraquarks in the chiral quark model
Gang Yang, Jialun Ping, Jorge Segovia
Abstract
The low-lying $sQ\overline{q}\overline{q}$ ($q=u$, $d$, $Q=c$, $b$) tetraquark states with ${J}^{P}={0}^{+}$, ${1}^{+}$, and ${2}^{+}$, and in the isoscalar and isovector sectors, are systematically investigated in the framework of the real- and complex-scaling range of a chiral quark model, whose parameters are fixed in advance describing hadron, hadron-hadron, and multiquark phenomenology, and thus, all results presented here are pure predictions. Each tetraquark configuration compatible with the quantum numbers studied is taken into account; this includes meson-meson, diquark-antidiquark, and K-type arrangements of quarks with all possible color wave functions in the four-body sector. Among the different numerical techniques to solve the Schr\"odinger-like four-body bound-state equation, we use a variational method in which the trial wave function is expanded in complex-range Gaussian basis functions because of its simplicity and flexibility. Several compact bound states and narrow resonances are found in both charm-strange $cs\overline{q}\overline{q}$ and bottom-strange $bs\overline{q}\overline{q}$ tetraquark sectors, most of them as a product of the strong coupling between the different channels. In regard to the so-called ${X}_{0,1}(2900)$ structures recently discovered with good statistical significance by the LHCb Collaboration, whose properties point out to be $cs\overline{u}\overline{d}$ tetraquarks, we find that they are unstable in our formalism with several candidates in the single-channel computations. We distinguish four cases with $I({J}^{P})=0({0}^{+})$ quantum numbers: three K-type configurations with masses at 2.89, 2.96, and 2.97 GeV, and one hidden-color coupled-channel calculation delivering a mass 2.86 GeV. With quantum numbers $I({J}^{P})=0({1}^{+})$, only one candidate can be found in the hidden-color coupled-channel calculation with mass 2.94 GeV.