Holographic Meson Melting

TL;DR

This work presents a holographic framework for late-stage meson melting in a strongly coupled quark-gluon plasma using D7-branes in an AdS$_5$-Schwarzschild background. By analyzing fluctuations on Minkowski and black-hole embeddings, the authors compute quasinormal modes that encode meson lifetimes in the deconfined phase, solving the massless case analytically via a Heun equation and continued fractions and the massive case numerically with two robust strategies. They find that melting occurs for light enough quarks with $m_q \lesssim 0.92\,\Delta m(T)$, while heavier quarks form stable mesons, and the decay widths scale with temperature; this provides a holographic lens on quarkonium suppression and dissipative dynamics in the plasma. The results offer a quantitative route to compare holographic predictions with real-time QCD phenomena and motivate extensions to more QCD-like models and momentum-dependent studies.

Abstract

The plasma phase at high temperatures of a strongly coupled gauge theory can be holographically modelled by an AdS black hole. Matter in the fundamental representation and in the quenched approximation is introduced through embedding D7-branes in the AdS-Schwarzschild background. Low spin mesons correspond to the fluctuations of the D7-brane world volume. As is well known by now, there are two different kinds of embeddings, either reaching down to the black hole horizon or staying outside of it. In the latter case the fluctuations of the D7-brane world volume represent stable low spin mesons. In the plasma phase we do not expect mesons to be stable but to melt at sufficiently high temperature. We model the late stages of this meson melting by the quasinormal modes of D7-brane fluctuations for the embeddings that do reach down to the horizon. The inverse of the imaginary part of the quasinormal frequency gives the typical relaxation time back to equilibrium of the meson perturbation in the hot plasma. We briefly comment on the possible application of our model to quarkonium suppression.

Figures (2)

• Figure 1: Schrödinger potential close to the horizon for different horizon embeddings, corresponding to $\theta_0(1)=0.1, 0.5, 0.83, 0.9, 1.0, 1.2, 1.3$ and $1.5$. As $\theta_0(1)$ increases, the potential develops a negative-valued well.
• Figure 2: (Left) Quasinormal masses in temperature units for the first three modes as a function of the bare quark masses, and (right) quasinormal widths in temperature units for the first three modes as a function of the bare quark masses.