Lindblad-driven recombination of the X(3872) tetraquark

TL;DR

The study investigates whether X(3872) is a compact tetraquark by modeling its production in heavy-ion collisions with a Lindblad open-quantum-system framework that captures both dissociation and regeneration from thermalized charm quarks. By deriving a coalescence rate and embedding it in a Bjorken-expanding medium, the authors find that recombination can dominate X(3872) production, yielding $R_{AA}$ values around or above unity in realistic LHC kinematics. A cross-check with a chemical-equilibrium picture supports the qualitative robustness of regeneration while highlighting that the result depends on the assumed internal size. The work proposes $R_{AA}$ as a powerful observable to distinguish a compact tetraquark from a hadronic molecule and outlines future extensions to more sophisticated medium dynamics and explicit molecular calculations.

Abstract

The internal structure of the exotic meson X(3872) remains an open question. We investigate its production in heavy-ion collisions under the hypothesis that it is a compact tetraquark. To this end, we derive a coalescence model from the Lindblad equation, assuming that unbound heavy quarks are thermalized within the quark-gluon plasma and that the adiabatic approximation holds. Using this model, we predict the nuclear modification factor of the X(3872) at LHC energies, with proton-proton baseline cross sections estimated from available experimental data. We also consider the effect of simplifying assumptions on the model, and a complementary approach based on chemical equilibration. Our results indicate that recombination is the dominant production mechanism for a tetraquark X(3872). It leads to a significant yield enhancement in heavy-ion collisions, suggesting that the nuclear modification factor is a powerful observable for probing the exotic nature of this state

Figures (4)

• Figure 1: Prediction for $R_{AA}$ of $X(3872)$ in Pb--Pb collisions at LHCb conditions. The dashed line considers only cold nuclear matter effects, following the model discussed in Escobedo:2021ifp.
• Figure 2: Midrapidity $p_T$ integrated $R_{AA}$ for $X(3872)$ for Pb-Pb collisions at $\sqrt{s_{NN}}=5.02~\mathrm{TeV}$ including suppression and recombination. The dotted lines represents the effect of shadowing modeled as in Escobedo:2021ifp, which is included in all next scenarios. The dashed line correspond to the suppression of the $X(3872)$ states that are initially present in the plasma. The contribution from recombined pairs is represented by stars. Finally, the solid line represents the full contribution to $R_{AA}$.
• Figure 3: Nuclear modification factor assuming a Gaussian wave function unaffected by the medium, for different values of $\langle r^2\rangle^{\frac{1}{2}}$.
• Figure 4: Nuclear modification factor in the limit $\sqrt{MT}\gg p_{bs}$, with $p_{bs}$ the momentum of the bound state.