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We combine techniques previously utilized to study flux tube field density profiles and to study the excited spectrum of the gluonic fields produced by a static quark-antiquark pair. Working with pure gauge SU(3) fields discretized in a lattice, we utilize Wilson loops with a large basis of gluonic spacelike Wilson lines to include different excitations of the quark-antiquark flux tube. To increase the signal over noise ratio, we use the multihit technique in the temporal Wilson lines and the APE smearing in spatial Wilson lines. The number of gluonic operators combined with the space points where we compute the flux tube densities turns out to be very large, and we resort to GPUs and to CUDA codes. Computing the effective mass plot from the diagonalized correlation matrix, we separate the excitations with different two-dimensional angular momentum, parity, and radial quantum numbers. We then compute the color field density profiles for all the components of the colour electric and colour magnetic fields. We analyze our results for the first excitations of the flux tube and search for signals of novel phenomena beyond the Nambu-Goto string model, such as a longitudinal mode or an explicit gluon.
Bicudo et al. (Tue,) studied this question.