Nonrelativistic bound states in a moving thermal bath

Abstract

We study the propagation of nonrelativistic bound states moving at constant velocity across a homogeneous thermal bath and we develop the effective field theory which is relevant in various dynamical regimes. We consider values of the velocity of the bound state ranging from moderate to highly relativistic and temperatures at all relevant scales smaller than the mass of the particles that form the bound state. In particular, we consider two distinct temperature regimes, corresponding to temperatures smaller or higher than the typical momentum transfer in the bound state. For temperatures smaller or of the order of the typical momentum transfer, we restrict our analysis to the simplest system, a hydrogenlike atom. We build the effective theory for this system first considering moderate values of the velocity and then the relativistic case. For large values of the velocity of the bound state, the separation of scales is such that the corresponding effective theory resembles the soft collinear effective theory (SCET). For temperatures larger than the typical momentum transfer we also consider muonic hydrogen propagating in a plasma which contains photons and massless electrons and positrons, so that the system resembles very much a heavy quarkonium in a thermal medium of deconfined quarks and gluons. We study the behavior of the real and imaginary part of the static two-body potential, for various velocities of the bound state, in the hard thermal loop approximation. We find that Landau damping ceases to be the relevant mechanism for dissociation from a certain critical velocity on, in favor of screening. Our results are relevant for understanding how the properties of heavy quarkonia states produced in the initial fusion of partons in the relativistic collision of heavy ions are affected by the presence of an equilibrated quark-gluon plasma.

Dissociation of quarkonium in a complex potential

“…Earlier it was thought that a quarkonium state is dissociated when the Debye screening becomes so strong that it inhibits the formation of bound states but nowadays a quarkonium is dissociated at a lower temperature [16,35] even though its binding energy is nonvanishing, rather is overtaken by the Landau-damping induced thermal width [36], obtained from the imaginary part of the potential. Its consequences on heavy quarkonium spectral functions [35,37], perturbative thermal widths [36,38] quarkonia at finite velocity [39], in a T-matrix approach [40,41,42,43,44], and in stochastic real-time dynamics [45] have been studied. Recently the dynamical evolution of the plasma was combined with the real and imaginary parts of the binding energies to estimate the suppression of quarkonium [46] in RHIC and LHC energies.…”

Heavy quarkonium suppression in a fireball

“…With the above functions, we can write the evolution equations (38) and (39) in the Lindblad form (46). In addition to the Hermitian Lindblad operator H,…”

“…Eventually, the momentum dependence of the quark-antiquark pairs should also be addressed. This requires enlarging the Hilbert space of the density matrices and incorporating the effects of the relative motion of the pair with respect to the medium; see, for instance [46,47].…”

“…The result suggests that there may exist values of κ, γ, and δ that reproduce the present data. The fact that a value of κ lower than the lattice prediction is needed may be explained if most of the quark-antiquark pairs are moving with respect to the plasma [46,47], at least in the weak-coupling case. As mentioned before, the lattice results of [39] also seem to point to a lower value of kappa at higher temperatures.…”

Survival of charmonia in a hot environment

“…The transverse momentum of J/ψ detected at LHC ranges up to 100 GeV and its mean momentum squared varies with the collision energy between 7 and 10 GeV 2 [6]. However, the effects of melting has been calculated so far either assuming charmonium being at rest relative to the medium [1,7], or embedded into a moving homogeneous plasma in a thermal bath of a constant temperature [8][9][10], which limits applicability of such a description to heavy ion collisions.…”