Novel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>cs</mml:mi></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi mathvariant="normal">c</mml:mi><mml:mover accent="true"><mml:mi mathvariant="normal">s</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow></mml:msub></mml:math> candidates in a constituent-quark-model-based meson-meson coupled-channels calculation

Abstract

Using proton-proton collisions at center-of-mass energies 7, 8, and 13 TeV, with a total integrated luminosity of $9\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, the LHCb collaboration has performed amplitude analyses of the ${B}^{+}\ensuremath{\rightarrow}{D}^{+}{D}^{\ensuremath{-}}{K}^{+}$, ${B}^{+}\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{D}_{s}^{+}{\ensuremath{\pi}}^{+}$, and ${B}^{0}\ensuremath{\rightarrow}{\overline{D}}^{0}{D}_{s}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays, observing that new ${T}_{cs}$ and ${T}_{c\overline{s}}$ resonances are required in order to explain the experimental data. These signals could be the first observation of tetraquark candidates that do not contain a heavy quark-antiquark pair; in fact, they consist of four different flavors of quarks, one of which is a doubly charged open-charm state. We present herein an analysis of the ${T}_{cs}$ and ${T}_{c\overline{s}}$ states, which is an extension of our recently published study of similar ${T}_{cc}^{+}$ exotic candidates. Our theoretical framework is a constituent-quark-model-based coupled-channels calculation of $q{q}^{\ensuremath{'}}\overline{s}\overline{c}$ and $cq\overline{s}{\overline{q}}^{\ensuremath{'}}$ tetraquark sectors for ${T}_{cs}$ and ${T}_{c\overline{s}}$ structures, respectively. We explore the nature, and pole position, of the singularities that appear in the scattering matrix with spin-parity quantum numbers: ${J}^{P}={0}^{\ifmmode\pm\else\textpm\fi{}}$, ${1}^{\ensuremath{\mp}}$, and ${2}^{\ifmmode\pm\else\textpm\fi{}}$. The constituent quark model has been widely used in the heavy quark sector, and thus all model parameters are already constrained from previous works. This makes our predictions robust and parameter-free. We find many singularities in the solution of various scattering-matrix problems which are either virtual states or resonances, but not bound states. Some of them fit reasonably well with the experimental observations of the spin-parity, mass, and width of ${T}_{cs}$ and ${T}_{c\overline{s}}$ candidates, and thus tentative assignments are made.

Topics & Concepts