[Paper Review] Bound state kinetics in high-energy nuclear collisions

Alberto Polleri|ArXiv.org|Mar 26, 2003

High-Energy Particle Collisions Research1 references3 citations

TL;DR

This paper presents a Lorentz-covariant kinetic equation for bound states in high-energy nuclear collisions, unifiedly describing formation and dissociation of quarkonia and (anti-)deuterons in strongly interacting matter. The exact closed-form solution reveals that final bound state yields scale proportionally with constituent particle numbers and inversely with dissociating medium particles, recovering the coalescence formula through dynamical evolution.

ABSTRACT

A Lorentz covariant kinetic equation for bound states and their constituents is presented and solved exactly in closed form. It describes in a unified way dynamical formation and dissociation of states such as quarkonia and (anti)-deuterons in the excited medium formed with a high-energy heavy-ion collision.

Motivation & Objective

• To develop a unified theoretical framework for describing bound state dynamics in the hot, dense medium formed in high-energy nuclear collisions.
• To model both tightly bound quarkonia (e.g., J/ψ, Υ) and loosely bound (anti-)deuterons within a single kinetic formalism.
• To provide an exact, closed-form solution of the kinetic equation for phase-space density of bound states, applicable to numerical simulations.
• To demonstrate how the final yield of bound states emerges from the interplay of formation and dissociation rates in evolving media.
• To recover the coalescence formula as a dynamical consequence of the kinetic evolution, rather than as an ad hoc assumption.

Proposed method

• Formulate a Lorentz-covariant kinetic equation for bound state phase-space density 𝒟_B(p,x), with drift and collision terms.
• Define the collision term as a sum of formation (C_F) and dissociation (C_D) rates, involving phase-space integrals over intermediate states and transition amplitudes.
• Use detailed balance to relate formation and dissociation transition probabilities W_{c1c2→Bn} = W_{Bn→c1c2}.
• Solve the kinetic equation exactly in closed form under two initial condition schemes: global time t₀ and proper time τ₀.
• Simplify the solution by neglecting spatial and momentum dependencies, focusing on time evolution of total yield N_B(τ).
• Assume time-dependent rates Λ_F(τ) ∝ N_{c1}N_{c2}/τ and Λ_D(τ) ∝ N_D/τ to derive a tractable analytical solution for the final yield.

Experimental results

Research questions

• RQ1 How can quarkonia and (anti-)deuterons, which form at vastly different stages of a heavy-ion collision, be described within a single kinetic framework?
• RQ2 What is the exact time evolution of bound state phase-space density in a dynamically evolving medium with both formation and dissociation processes?
• RQ3 Can the coalescence formula for (anti-)deuteron production be derived from first principles using a dynamical kinetic approach?
• RQ4 What determines the final yield of bound states in terms of constituent abundances and medium density?
• RQ5 How do formation and dissociation rates compete to shape the observed spectrum of bound states in high-energy nuclear collisions?

Key findings

• The exact solution of the kinetic equation is derived in closed form for both global and proper time initial conditions, enabling quantitative numerical studies.
• The simplified solution shows that the final yield of bound states scales as N_B^f ∝ (N_{c1}N_{c2}) / N_D, where N_D is the number of dissociating particles.
• When dissociation is strong (P_D N_D ≫ 1), the yield approaches a constant proportional to the product of constituent abundances and inversely proportional to the number of dissociating particles.
• The derived scaling law recovers the well-known coalescence formula CK86 as a dynamical outcome of the kinetic evolution, not a phenomenological input.
• The model supports the possibility of quarkonium formation in the quark-gluon plasma via medium-induced processes, consistent with experimental trends of inverse yield scaling with total hadron multiplicity.
• The framework provides a unified, covariant description of bound state kinetics applicable to both early-stage quarkonia and late-stage (anti-)deuterons in heavy-ion collisions.