Heavy- and light-flavor symmetry partners of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>3875</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3960</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> from light-meson exchange saturation

Abstract

The spectrum of the charmed meson-(anti)meson system is a fundamental tool for disentangling the nature of a few exotic hadrons, including the recently discovered ${T}_{cc}^{+}(3875)$ tetraquark, the $X(3960)$, or the $X(3872)$, the nature of which is still not clear after almost two decades of its discovery. Here we consider that the charmed meson-(anti)meson short-range interaction is described by the exchange of light mesons ($\ensuremath{\sigma}$, $\ensuremath{\rho}$, $\ensuremath{\omega}$). The effects of light-meson exchanges are recast into a simple contact-range theory by means of a saturation procedure, resulting in a compact description of the two-hadron interaction. From this, if the ${T}_{cc}^{+}$ were to be an isoscalar ${D}^{*}D$ molecule, then there should exist an isoscalar $J=1$ ${D}^{*}{D}^{*}$ partner, as constrained by heavy-quark spin symmetry. Yet, within our model, the most attractive two charmed meson configurations are the isovector $J=0$ ${D}^{*}{D}^{*}$ molecule and its sextet ${D}_{s}^{*}{D}^{*}$ and ${D}_{s}^{*}{D}_{s}^{*}$ flavor partners. Finally, we find a tension between the molecular descriptions of the ${T}_{cc}^{+}$ and that of the $X(3872)$ and $X(3960)$, where most parameter choices suggest that if the ${T}_{cc}^{+}$ is purely molecular then the $X(3872)$ overbinds [or conversely, if the $X(3872)$ is a molecule the ${T}_{cc}^{+}$ does not bind]. This might be consequential for determining the nature of these states.

Topics & Concepts