Extending light-front holographic QCD using the 't Hooft Equation

TL;DR

This paper combines the 't Hooft Equation with light-front holographic Schrödinger Equation to better understand meson confinement, accurately predicting meson spectra across different mass regimes and revealing a universal hadronic scale.

Contribution

It introduces a unified framework linking transverse and longitudinal confinement dynamics in mesons using these two equations, enhancing the predictive power of holographic QCD models.

Findings

Accurately predicts light, heavy-light, and heavy-heavy meson spectra.

Identifies a universal hadronic scale of approximately 0.5 GeV.

Shows the numerical coincidence of confinement scales in heavy-heavy mesons.

Abstract

We show the 't Hooft Equation and the light-front holographic Schr\"odinger Equation are complementary to each other in governing the transverse and longitudinal dynamics of colour confinement in quark-antiquark mesons. Together, they predict remarkably well the light, heavy-light and heavy-heavy meson spectroscopic data. The universal emerging hadronic scale of light-front holography, $\kappa \approx 0.5$ GeV, controls the transverse dynamics of confinement in all mesons. In heavy-heavy mesons, it also coincides numerically with the 't Hooft coupling which governs longitudinal confinement, thus reflecting the restoration of manifest 3-dimensional rotational symmetry