Spectrum of very excited $\Sigma_g^+$ flux tubes in SU(3) gauge theory

TL;DR

This study computes the excitation spectrum of $ ext{SU}(3)$ flux tubes in 3+1 dimensions, testing theoretical models and exploring high excitation levels using lattice QCD with various gauge actions.

Contribution

It provides the first comprehensive lattice QCD analysis of high-level excitations of $ ext{SU}(3)$ flux tubes, especially for the $ ext{Sigma}_g^+$ state, using advanced operator construction and eigenvalue techniques.

Findings

Spectrum of flux tubes up to high excitations obtained

Comparison of different lattice gauge actions conducted

Enhanced understanding of flux tube excitation structure

Abstract

Spectra with full towers of levels are expected due to the quantization of the string vibrations, however different theoretical models exist for the excitation spectra. First principle computations are important to test the different models and to search for novel phenomena, but so far only a few excited states of QCD flux tubes have been studied with pure gauge SU(3) lattice QCD in 3+1 dimensions. We thus aim to study a spectrum of flux tubes with static quark and antiquark sources up to a significant number of excitations. We specialize on the spectrum of the most symmetric case, namely $\Sigma_g^+$, where up to two levels are already published in the literature. To achieve the highest possible excitation level, we construct a large set of operators with the correct symmetry, solve the generalized eigenvalue problem and compare the results of different lattice QCD gauge actions with different lattice spacings and anisotropies.