Fine Structure of the QCD String Spectrum

TL;DR

Three distinct scales are established in the excitation spectrum of the gluon field around a static quark-antiquark pair as the color source separation R is varied, providing important clues for developing an effective bosonic string description.

Abstract

Using advanced lattice methods in Quantum Chromodynamics, three distinct scales are established in the excitation spectrum of the gluon field around a static quark-antiquark pair as the color source separation R is varied. On the shortest length scale, the excitations are consistent with states created by local gluon field operators arising from a multipole operator product expansion. An intermediate crossover region below 2 fm is identified with a dramatic rearrangement of the level orderings. On the largest length scale of 2-3 fm, the spectrum agrees with that expected for string-like excitations. The energies nearly reproduce asymptotic pi/R string gaps, but exhibit a fine structure, providing important clues for developing an effective bosonic string description.

Figures (3)

• Figure 1: Energy gaps $\Delta E$ above $\Sigma^+_g$ are shown in string units for quantum numbers in continuum and lattice notation. The Nambu-Goto string is discussed in the text.
• Figure 2: Short-distance degeneracies and crossover in the spectrum. The solid curves are only shown for visualization. The dashed line marks a lower bound for the onset of mixing effects with glueball states which requires careful interpretation.
• Figure 3: The disorder profile of the vacuum and two excitations are shown with arrows indicating the $q\bar{q}$ axis.