Stability of strings binding heavy-quark mesons

TL;DR

This work analyzes the linear stability of quarkonium-strings in $AdS_5$-Schwarzschild, modeling a moving heavy quarknti-quark pair and exploring how small deformations evolve. Using a boosted metric and NambuGoto dynamics, the authors show that for $\ell<\ell_{max}$ there are two static string branches parameterized by $\sigma_m$, of which the branch with $\sigma_m<\sigma_{max}$ is linearly stable ($\omega^2>0$) and the branch with $\sigma_m>\sigma_{max}$ is unstable ($\omega^2<0$). Transverse perturbations are always stable, while in-plane perturbations determine the stability threshold. The paper concludes that the no-drag propagation scenario is compatible with stability, and it discusses a speculative energy-dissipation mechanism via emission of massive string states, which could inform holographic descriptions of meson formation and dissipation in a quark-gluon plasma.

Abstract

We investigate the stability against small deformations of strings dangling into AdS_5-Schwarzschild from a moving heavy quark-anti-quark pair. We speculate that emission of massive string states may be an important part of the evolution of certain unstable configurations.

Figures (4)

• Figure 1: A) The separation $\ell$ as a function of $\sigma_m$ for $v = 0.9$. (See (\ref{['separation']}).) As explained below (\ref{['x2Equilibrium']}), $\sigma_m$ is the maximum value of $z$ along the string. The solid part of the plot corresponds to stable configurations; the dashed part corresponds to unstable configurations; and the red dot corresponds to $\sigma = \sigma_{\rm max}$, where the separation between the quark and anti-quark is maximized. B) A cartoon of string configurations corresponding to three points on the curve from A. For any separation of quark and anti-quark less than the maximum (corresponding to the red curve), there is a stable string configuration (solid) and an unstable one (dashed).
• Figure 2: Eigenfunctions for $v=0.9$ and $\sigma_m=0.6z_H$. The derivatives $\delta X_\parallel'(\sigma_m)$ and $\delta Z'(\sigma_m)$ are finite, which means that the perturbed string configuration is smooth at $\sigma=\sigma_m$: see the discussion following \ref{['sigmamBCs']}.
• Figure 3: $\Omega^2$ as a function of $\sigma_m$ for $v = 0.9$.
• Figure 4: A string (purple) and anti-string (green) trailing from a heavy quark and anti-quark, pictured here as $c$ and $\bar{c}$. The string and anti-string attract, and we propose that configurations where they come together and self-annihilate are an important aspect of the dynamics. The annihilation process of the string-anti-string pair produces highly excited closed strings, also pictured, which then fall into the horizon. Note that the closed strings (light blue) may be of a different type from the string-anti-string pair: see the discussion in point B below.