Fine Structure of the QCD String Spectrum

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 stringlike 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.