$X(3872)$, $X(4014)$, and their bottom partners at finite temperature

The properties of the $X(3872)$ and its spin partner, the $X(4014)$, are studied both in vacuum and at finite temperature. Using an effective hadron theory based on the hidden-gauge Lagrangian, the $X(3872)$ is dynamically generated from the $s$-wave rescattering of a pair of pseudoscalar and vector charm mesons. By incorporating the thermal spectral functions of open charm mesons, the calculation is extended to finite temperature. Similarly, the properties of the $X(4014)$ are obtained out of the scattering of charm vector mesons. By applying heavy-quark flavor symmetry, the properties of their bottom counterparts in the axial-vector and tensor channels are also predicted. All the dynamically generated states show a decreasing mass and acquire an increasing decay width with temperature, following the trend observed in their meson constituents. These results are relevant in relativistic heavy-ion collisions at high energies, in analyses of the collective medium formed after hadronization or in femtoscopic studies, and can be tested in lattice-QCD calculations exploring the melting of heavy mesons at finite temperature.