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.
Highlights
Understanding the confinement of color remains a main theoretical problem of modern physics
An important evidence of confinement, where we may search for relevant details to understand it, is in the QCD flux tubes [1], computed in lattice QCD
We succeeded in obtaining the spectrum of several new excited flux tubes, using a large basis of operators, employing the computational techniques with graphics processing units (GPUs) of Ref. [40], and utilizing different actions with smearing and anisotropy
Summary
Understanding the confinement of color remains a main theoretical problem of modern physics. The subsequent opepraffitffior Oð1; 1Þ has its straight z direction line at distance l 1⁄4 2 from the charge axis, but for it to be invariant for the two-dimensional rotation around the charge axis and invariant for the parity inversion about the median point, we need to have a sum of all nop 1⁄4 8 of these possible Wilson curves to get a fully symmetric operator. Oð1; 0Þ, which azimuthal directions in the xy plane are φ 1⁄4 0; π=2; π; 3π=2, and Oð1; 1Þ, which azimuthal directions in the xy plane are φ 1⁄4 π=4; 3π=4; 5π=4; 7π=4, may be combined with an opposite phase, for instance, Oð1; 0Þ − Oð1; 1Þ in the case they are both properly normalized, which would correspond to a Γg state If these Oðl; l2Þ operators are all included in a correlation matrix, its diagonalization will pick up Σþg states and states with large angular momentum Λ 1⁄4 4 about the charge axis. It is interesting that using a smaller operator basis and less dense in the space of the flux tube lead to clearer results for the spectrum of excited states as we found out in our computation
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