Abstract
We investigate the implications of Nambu-Goto (NG), Lüscher Weisz (LW) and Polyakov-Kleinert (PK) effective string actions for the Casimir energy and the width of the quantum delocalization of the string in 4-dim pure SU(3) Yang-Mills lattice gauge theory. At a temperature closer to the critical point T/Tc=0.9, we found that the next to leading-order (NLO) contributions from the expansion of the NG string in addition to the boundary terms in LW action to decrease the deviations from the lattice data in the intermediate distance scales for both the quark-antiquark QQ̅ potential and broadening of the color tube compared to the free string approximation. We conjecture possible stiffness of the QCD string through studying the effects of extrinsic curvature term in PK action and find a good fitting behavior for the lattice Monte-Carlo data at both long and intermediate quark separations regions.
Highlights
The formulation of an effective bosonic string description for gluonic degrees of freedom binding the hadron has been an attractive picture in consistency with with the main infrared (IR) features of quantum chromodynamics (QCD)
The most simple choice relevant to the QCD string description is the NG string which is a bosonic string with an action taken proportional to the world-sheet area
In the leading order approximation of the NG string action, the quantum fluctuations of the string bring forth a universal quantum correction to the linearly rising potential well known as the Lüscher term [1]in the meson and entail geometrical Lüscher-like terms [2] in the baryonic configuration
Summary
The formulation of an effective bosonic string description for gluonic degrees of freedom binding the hadron has been an attractive picture in consistency with with the main infrared (IR) features of quantum chromodynamics (QCD). The simplified picture of the free bosonic string derived on the basis of the leading order formulation of NG action does not provide a good description of the numerical data in the intermediate distances and high temperatures. A comparison with the lattice Monte-Carlo data has shown the validity of the leading-order approximation at sources separation larger than R = 0.9 fm [12, 13] for both the quark–antiquark (QQ) potential and color-tube width profile. In the baryon [14, 15], we found a similar behavior [16] for the long Y-string among quarks In this proceeding, we summarize the results obtained by studying the effects of the extrinsic curvature of the PK string in addition to the next to leading order expansion of the NG string action with boundary terms and the corresponding match to the lattice data. The numerical data of the potential and width profile of the energy density distribution is compare to the Casimir energy and the mean-square width of the string fluctuations of both PK and NG string action
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