Properties of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>3875</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mover accent="true"><mml:mi>c</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>c</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>3875</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math> and their heavy-quark spin partners in nuclear matter

Abstract

We discuss the modification of the properties of the tetraquark-like ${T}_{cc}{(3875)}^{+}$ and ${T}_{\overline{c}\overline{c}}{(3875)}^{\ensuremath{-}}$ states in dense nuclear matter. We consider the ${T}_{cc}^{+}$ and ${T}_{\overline{c}\overline{c}}^{\ensuremath{-}}$ in vacuum as purely isoscalar ${D}^{*}D$ and $\overline{D}{}^{*}\overline{D} S$-wave bound states, respectively, dynamically generated from a heavy-quark effective interaction between the charmed mesons. We compute the $D, \overline{D}, {D}^{*}$, and $\overline{D}{}^{*}$ spectral functions embedded in a nuclear medium and use them to determine the corresponding ${T}_{cc}^{+}$ and ${T}_{\overline{c}\overline{c}}^{\ensuremath{-}}$ self-energies and spectral functions. We find important modifications of the ${D}^{*}D$ and $\overline{D}{}^{*}\overline{D}$ scattering amplitudes and of the pole position of these exotic states already for ${\ensuremath{\rho}}_{0}/2$, with ${\ensuremath{\rho}}_{0}$ the normal nuclear density. We also discuss the dependence of these results on the ${D}^{*}D$ ($\overline{D}{}^{*}\overline{D}$) molecular component in the ${T}_{cc}^{+}$ (${T}_{\overline{c}\overline{c}}^{\ensuremath{-}}$) wave function. Owing to the different nature of the ${D}^{(*)}N$ and $\overline{D}{}^{(*)}N$ interactions, we find characteristic changes of the in-medium properties of the ${T}_{cc}{(3875)}^{+}$ and ${T}_{\overline{c}\overline{c}}{(3875)}^{\ensuremath{-}}$, which become increasingly visible as the density increases. The experimental confirmation of the found distinctive density pattern will give support to the existence of molecular components in these tetraquark-like states, since in the case they were mostly colorless compact quark structures ($cc\overline{\ensuremath{\ell}}\overline{\ensuremath{\ell}}$ and $\overline{c}\overline{c}\ensuremath{\ell}\ensuremath{\ell}$, with $\ensuremath{\ell}=u,d$), the density behaviors of the ${T}_{cc}{(3875)}^{+}$ and ${T}_{\overline{c}\overline{c}}{(3875)}^{\ensuremath{-}}$ nuclear medium spectral functions, though different, would not likely be the same as those found in this work for molecular scenarios. Finally, we perform similar analyses for the isoscalar ${J}^{P}={1}^{+}$ heavy-quark spin symmetry partners of the ${T}_{cc}^{+}$ (${T}_{cc}^{*+}$) and the ${T}_{\overline{c}\overline{c}}^{\ensuremath{-}}$ (${T}_{\overline{c}\overline{c}}^{*\ensuremath{-}}$) by considering the ${D}^{*0}{D}^{*+}$ and $\overline{D}{}^{*0}{D}^{*\ensuremath{-}}$ scattering $T$ matrices.

Topics & Concepts