Melting down a tetraquark: $D^{\ast}D^{(\ast)}$ interactions and $T_{cc}(3875)^+$ in a hot environment

TL;DR

This paper investigates how the tetraquark-like states $T_{cc}(3875)^+$ and its heavy-quark spin partner $T_{cc}(4016)^{*+}$ behave in a hot pion bath by modeling them as isoscalar $DD^*$ and $D^*D^*$ bound states with HQSS. The authors employ a Bethe-Salpeter framework with two energy-dependent potentials, fix the low-energy constants to reproduce vacuum properties, and include finite-temperature effects through the Imaginary-Time Formalism using thermal spectral functions for $D$ and $D^*$ to obtain temperature-dependent scattering amplitudes and spectral functions. They find that thermal dressing shifts the unitary cut to lower energies and broadens the spectral peaks, with stronger temperature dependence for larger molecular content $P_0$, leading to melting above about $80$–$100$ MeV when $P_0$ is large. The results propose that finite-temperature scattering measurements could reveal the molecular content of these exotics and connect to lattice QCD via Euclidean correlators, while providing input for heavy-ion collision simulations. The study also addresses uncertainties from neglected coupled-channel dynamics and possible temperature dependence of the interaction kernel.

Abstract

We discuss the modification of the properties of the tetraquark-like $T_{cc}(3875)^+$ and its heavy quark spin partner, $T_{cc}(4016)^{*+}$ immersed in a hot bath of pions. We consider these exotic states as purely isoscalar $DD^\ast$ and $D^\ast D^\ast$ $S$-wave bound states, respectively. Finite temperature effects are incorporated through the $D$ and $D^\ast$ state-of-the-art thermal spectral functions calculated in [G. Montana et al., Phys. Rev. D, 102 (2020) 096020], using the imaginary-time formalism. We find important modifications of the $DD^\ast$ and $D^\ast D^\ast$ scattering amplitudes already for $T=80$ MeV, and show that the hot-bath lineshapes of these tetraquark-like states strongly depend on their Weinberg molecular content. We find that the thermal $T_{cc}(3875)^+$ and $T_{cc}(4016)^{*+}$ spectral functions change more rapidly with temperature for high molecular probabilities $P_0$. For large values of $P_0$, the widths significantly increase with temperature, leading to the melting of these exotic states for temperatures larger than 80 MeV. For small molecular components, the changes in the spectral functions of these states due to temperature become significantly less important. All these results show that any future experimental determination of the $D^{(\ast)}D^*$ scattering amplitudes at finite temperature will provide valuable insights into the molecular content of the $T_{cc}(3875)^+$ and $T_{cc}(4016)^{*+}$ exotics.

Figures (6)

• Figure 1: Real (solid) and imaginary (dashed) parts of the $DD^\ast$ loop function at several temperatures, ranging from $T=0$ MeV to $T=$150 MeV.
• Figure 2: $T_{cc}(3875)$ spectral functions as a function of energy for different temperatures, computed using $V_A$ [top row, cf. Eq. \ref{['eq:VA']}] and $V_B$ [bottom row, cf. Eq. \ref{['eq:VB']}], for two values of the molecular probability (left and right panels, respectively).
• Figure 3: Real (solid) and imaginary (dashed) parts of the $D^\ast D^\ast$ loop function at several temperatures, ranging from $T=0$ MeV to $T=$150 MeV.
• Figure 4: $T_{cc}(4016)^{\ast+}$ spectral functions as a function of energy for different temperatures, computed using and $V_B$, for two values of the molecular probability (left and right panels, respectively). The shaded bands correspond to considering the $T_{cc}^\ast$ binding energy w.r.t. the $D^\ast D^\ast$ threshold in the interval $[0.8, 2.0]$ MeV.
• Figure 5: Illustration of the coupled-channel effects on the temperature-dependent $T_{cc}$ (left panel) and $T_{cc}^\ast$ (right panel) spectral functions, for different strengths of the coupling-channel potential parameter $\xi$, defined in Eq. \ref{['e:CoupledChannelsPotential']}.