[Paper Review] Sequential Coalescence with Charm Conservation in High Energy Nuclear Collisions

Jiaxing Zhao, Shuzhe Shi+2 more|arXiv (Cornell University)|May 28, 2018

High-Energy Particle Collisions Research21 citations

TL;DR

This paper proposes a sequential coalescence model with charm conservation to explain charmed hadron production in high-energy nuclear collisions. By solving the two-body Dirac equation with lattice QCD potentials and coupling it to hydrodynamic evolution, the model predicts earlier formation of $D_s^+$ mesons due to charm conservation, leading to a $D_s^+/D^0$ yield enhancement and $\Lambda_c^+/D^0$ suppression, consistent with RHIC and LHC data.

ABSTRACT

Heavy quarks are initially produced in nuclear collisions and the number is conserved during the evolution of the system. We establish a sequential coalescence model with charm conservation and apply it to charmed hadron production at RHIC and LHC energies. The charm conservation enhances the earlier formed hadrons and reduces the later formed ones, which leads to a $D_s/D^0$ enhancement and a $Λ_c/D^0$ suppression. The mass dependence of the sequential hadron formation provides us a new tool for studying the quark-gluon plasma hadronization in high energy nuclear collisions.

Motivation & Objective

• To address the impact of charm quark number conservation on charmed hadron production in quark-gluon plasma.
• To model sequential hadronization of heavy quarks by incorporating mass-dependent dissociation temperatures.
• To explain the observed $D_s^+/D^0$ enhancement and $\Lambda_c^+/D^0$ suppression in heavy-ion collisions at RHIC and LHC.
• To extend the framework to bottom quark hadronization and predict $\bar{B}_s^0/\bar{B}^0$ yields.
• To establish a mass-dependent sequential coalescence mechanism as a probe of QGP hadronization dynamics.

Proposed method

• Solve the two-body Dirac equation with lattice QCD-derived quark-antiquark potentials to determine binding energies and dissociation temperatures for charmed mesons.
• Use hydrodynamic equations to model the fireball evolution and extract coalescence times for different hadrons.
• Apply charm conservation by reducing the available charm fraction for later-formed hadrons, with $r = (N_c - N_{D_s^+})/N_c \approx 90\%$ for $D^0$.
• Incorporate strangeness enhancement via thermalization parameters $\alpha=0.3$, $\beta=0.7$ to model enhanced $D_s^+$ production.
• Calculate hadron spectra and yield ratios using sequential coalescence, comparing with simultaneous coalescence (fixed $r=1$) as a baseline.
• Extend the model to bottom hadrons using $m_b = 4.7$ GeV and similar dissociation temperature estimates.

Experimental results

Research questions

• RQ1 How does charm quark number conservation affect the relative yields of $D_s^+$ and $D^0$ mesons in heavy-ion collisions?
• RQ2 To what extent does sequential hadronization, driven by mass-dependent dissociation temperatures, explain the observed $D_s^+/D^0$ enhancement at RHIC and LHC?
• RQ3 How does the interplay between charm conservation and strangeness enhancement influence the $\Lambda_c^+/D^0$ yield ratio?
• RQ4 What is the predicted behavior of bottom hadron ratios $\bar{B}_s^0/\bar{B}^0$ under sequential coalescence with bottom conservation?
• RQ5 Can the mass dependence of hadron formation times serve as a probe of quark-gluon plasma hadronization dynamics?

Key findings

• The sequential coalescence model with charm conservation predicts a $D_s^+/D^0$ enhancement at intermediate $p_T$, consistent with experimental data from RHIC and LHC.
• The $D_s^+/D^0$ ratio is enhanced due to earlier formation of $D_s^+$ mesons (with $r=1$) and later formation of $D^0$ mesons (with $r \approx 90\%$) under charm conservation.
• The $\Lambda_c^+/D^0$ ratio is suppressed in the sequential model due to the lower charm fraction ($r \approx 0.6$) available for baryon formation compared to $D^0$ ($r \approx 0.9$).
• The model predicts $T_{D_s^+} = 1.2\, T_c$ and $T_{D^0} \simeq 1.15\, T_c$, indicating earlier hadronization of charm-strange mesons.
• For bottom hadrons, the model predicts $\bar{B}_s^0/\bar{B}^0 \simeq 1$ in central Pb+Pb collisions at LHC, with $T_{\bar{B}_s^0} \simeq T_{D_s^+}$ and $T_{\bar{B}^0} \simeq T_{D^0}$.
• The results demonstrate that the mass dependence of sequential hadron formation provides a unique probe of QGP hadronization dynamics, with stronger effects for heavier quarks.