[Paper Review] Holographic mesons in D4/D6 model revisited

Kwanghyun Jo, Youngman Kim+1 more|arXiv (Cornell University)|Apr 12, 2011

Black Holes and Theoretical Physics13 references3 citations

TL;DR

This paper revisits the D4/D6 holographic QCD model to study light vector mesons and heavy quarkonium properties in both confining and deconfining phases using a single compactification scale $M_{KK}$, enabling consistent treatment of light and heavy quarks. It finds that vector meson mass scales linearly with the square root of quark mass at high masses and observes a smooth transition of heavy quarkonium mass across the deconfinement phase, with a derived in-medium dispersion relation crucial for understanding screening and dissociation in quark-gluon plasma.

ABSTRACT

We revisit holographic mesons in the D4/D6 model to study holographic light vector mesons and the properties of heavy quarkonium in confining and deconfining phases. To treat the light mesons and heavy quarkonium on the same footing, we use the same compactification scale MKK in both systems. We observe that like scalar and pseudo-scalar mesons the vector meson mass is linearly proportional to the square root of the quark mass, when the quark mass is large. With a MKK fixed by light meson masses, we calculate the mass of heavy quarkonium in confining and deconfining phases. We also obtain the inmedium dispersion relation for heavy quarkonium, which is important to understand the dissociation and the screening mass of heavy quarkonium in quark-gluon plasma.

Motivation & Objective

• To study light vector mesons and heavy quarkonium on the same footing in the D4/D6 model using a single compactification scale $M_{KK}$.
• To investigate the behavior of heavy quarkonium mass and in-medium dispersion relation across the deconfinement phase transition.
• To compare results with bottom-up AdS/QCD models and other approaches, particularly regarding the smoothness of mass evolution.
• To assess the D4/D6 model's suitability for describing heavy quarkonium physics in quark-gluon plasma, including screening and dissociation.

Proposed method

• Uses the D4/D6 brane configuration with Nc D4 branes generating a confining background and Nf D6 branes as probes for meson states.
• Applies gauge/gravity duality to compute meson spectra via fluctuations of the D6 brane in the D4 background, using the induced metric and DBI action.
• Fixes the compactification scale $M_{KK}$ using light meson masses to ensure consistency across light and heavy quark systems.
• Derives the in-medium dispersion relation for heavy quarkonium by analyzing the D6 brane embedding in the high-temperature deconfining geometry.
• Computes meson masses in both confining and deconfining phases by solving the equations of motion for scalar, pseudo-scalar, and vector modes.
• Compares the smooth evolution of quarkonium mass across $T_c$ with previous studies based on bottom-up AdS/QCD, QCD sum rules, and holographic potentials.

Experimental results

Research questions

• RQ1 How does the mass of light vector mesons scale with quark mass in the D4/D6 model at high quark masses?
• RQ2 Can the same $M_{KK}$ scale describe both light mesons and heavy quarkonia in the D4/D6 model?
• RQ3 How does the mass of heavy quarkonium evolve smoothly across the deconfinement transition in the D4/D6 model?
• RQ4 What is the in-medium dispersion relation for heavy quarkonium in the deconfining phase, and how does it relate to screening and dissociation?
• RQ5 How does the D4/D6 model's prediction for quarkonium mass evolution compare with bottom-up AdS/QCD and QCD sum rule approaches?

Key findings

• The vector meson mass is linearly proportional to the square root of the quark mass for large quark masses, consistent with scalar and pseudo-scalar mesons.
• Using $M_{KK}$ fixed by light meson masses, the calculated charmonium mass in the confining phase matches phenomenological expectations.
• The mass of heavy quarkonium changes smoothly from confining to deconfining phase, in contrast to previous models that suggest discontinuous or abrupt shifts.
• The maximum shift in charmonium mass at $T = 1.05T_c$ is about 200 MeV, or roughly 6.7% of the $J/\psi$ mass, suggesting a small but measurable effect.
• The in-medium dispersion relation for heavy quarkonium is derived, providing a framework to study screening and dissociation in quark-gluon plasma.
• The D4/D6 model shows potential for describing heavy quarkonium physics due to its natural inclusion of quark mass and dual confining/deconfining phases.