$$X(3872)$$transport in heavy-ion collisions

Biaogang Wu,Matthew Sibila,Xiaojian Du,Ralf Rapp

doi:10.1140/epja/s10050-021-00435-6

Abstract

AbstractThe production of the $$X(3872)$$ X ( 3872 ) particle in heavy-ion collisions has been contemplated as an alternative probe of its internal structure. To investigate this conjecture, we perform transport calculations of the $$X(3872)$$ X ( 3872 ) through the fireball formed in nuclear collisions at the LHC. Within a kinetic-rate equation approach as previously used for charmonia, the formation and dissociation of the $$X(3872)$$ X ( 3872 ) is controlled by two transport parameters, i.e., its inelastic reaction rate and thermal-equilibrium limit in the evolving hot QCD medium. While the equilibrium limit is controlled by the charm production cross section in primordial nucleon-nucleon collisions (together with the spectra of charm states in the medium), the structure information is encoded in the reaction rate. We study how different scenarios for the rate affect the centrality dependence and transverse-momentum ($$p_T$$ p T ) spectra of the $$X(3872)$$ X ( 3872 ) . Larger reaction rates associated with the loosely bound molecule structure imply that it is formed later in the fireball evolution than the tetraquark and thus its final yields are generally smaller by around a factor of two, which is qualitatively different from most coalescence model calculations to date. The $$p_T$$ p T spectra provide further information as the later decoupling time within the molecular scenario leads to harder spectra caused by the blue-shift from the expanding fireball.

Highlights

The X (3872) mass to the threshold of a D and D∗ meson is suggestive for a weakly bound molecular state [3,4]; on the other hand, its small decay width appears to suggest that its wave function has little overlap with D D∗ configurations, favoring a bound state of a color-antitriplet diquark and an antidiquark [5,6]
In the statistical hadronization model (SHM) [13], which is based on the assumption of thermal equilibrium, the X (3872) yields only depend on its mass, i.e., they are independent of internal structure that does not affect the mass
Due to the weak binding of the X (3872), we focus on the effects of the interacting hadronic medium which makes up nearly half of the fireball lifetime in central Pb-Pb collisions

Summary

Introduction

The problem of X (3872) production in HICs has mainly been addressed using instantaneous coalescence models (ICMs) [8–11], by calculating its yield at the hadronization transition with a suitable wave function in coordinate space to encode the different structure information. A (2021) 57:122 port parameters: the equilibrium limit and the inelastic reaction rate The former provides an important benchmark as the long-time limit of the transport equation, while the latter encodes the structure effects through its coupling to the medium. Aside from focusing on Pb-Pb collisions at LHC, differs from previous works in several aspects: our initial conditions vary between zero and the equilibrium limit (motivated by our previous transport results for charmonia), our reaction rates are generally larger (as suggested by recent literature), and the (temperature-dependent) equilibrium limit includes a large number of charm-hadron states which largely affects the evaluation of the charm-quark fugacity (which figures squared for states containing cc). 3 we present and discuss our results for the time evolution of the X (3872) equilibrium limit and the solutions of the rate equation for its yield in a molecular vs a tetraquark scenario.

Transport approach

Time evolution

65 MeV and mol 0

Findings

Conclusions