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Stiff self-interacting string near QCD deconfinement point

We compare the predictions of Nambu-Goto effective string model at two loop-order for the Casimir energy and the width of the quantum delocalization of the string to the corresponding quark-antiquark potential and width profile of the color tube in pure SU (3) Yang-Mills LGT at 4-dimensions near the deconfinement point. Minor effects are returned, when considering NLO terms for both the $Q\bar{Q}$ potential and broadening of the color tube, at the temperature $T/T_c= 0.8$. At a closer temperature to the critical point $T/T_c$= 0.9, we found that the NLO contributions, from the expansion of the Nambu-Goto string, to have a significant effect in improving the match to lattice data in the intermediate distances scales. The string's self-interactions contribute towards the suppressed broadening of the string's width and the squeezed profile along the string at the intermediate color source separation distance.