Abstract
Three-quark potentials are studied in great details in the three-dimensional SU(3) pure gauge theory at finite temperature, for the cases of static sources in the fundamental and adjoint representations. For this purpose, the corresponding Polyakov loop model in its simplest version is adopted. The potentials in question, as well as the conventional quark–anti-quark potentials, are calculated numerically both in the confinement and deconfinement phases. Results are compared to available analytical predictions at strong coupling and in the limit of large number of colours N. The three-quark potential is tested against the expected Δ and Y laws and the 3q string tension entering these laws is compared to the conventional qq¯ string tension. As a byproduct of this investigation, essential features of the critical behaviour across the deconfinement transition are elucidated.
Highlights
The interest in studying the interquark potential for a three-quark system is not a recent issue at all
First we studied the dependence of Γf3 on the geometry, considering ∆ and Y laws
The residual spread of the points can be at least partially explained by different triangle pairs having different R1 − R2 values, which are not distinguished on these plots. Another observation that supports the Y law is that the collapse line for the σqeqffq closely matches the line of σqeqff, which suggests that the sigma values entering the two- and the three-point correlation are the same if we consider the Y law, and that the parameters η are similar in these cases
Summary
The interest in studying the interquark potential for a three-quark system is not a recent issue at all. New results are somewhat contradictory, which could be reasonably explained by the difficulty of accurate measurements of the three-quark potential. From these discussions spanning many years, two main Ansatze emerged to describe the three-quark potential: the ∆ law and the Y law. In this paper we are going to study an SU (3) spin model which is an effective model for Polyakov loops and can be derived from the original gauge theory in the strong coupling region. The main tool of our analytical investigation is the large-N expansion Within this expansion we demonstrate that the fundamental three-point correlator is described by a sum of the Y and Λ laws.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
