Lattice Determination of the Baryon Junction Mass in $(2+1)$ Dimensions

Abstract

This contribution investigates baryonic flux tube configurations in $SU(3)$ Yang--Mills theory in $(2+1)$ dimensions. Leveraging recent next-to-leading-order results within the Effective String Theory (EST) framework, which explicitly include corrections proportional to the baryon junction mass $M$ up to order $1/R^2$, we carry out a non-perturbative determination of this parameter, through high-precision simulations of the three-point Polyakov-loop in the open string channel. In addition, the high-temperature regime of the baryonic system is examined in order to test the Svetitsky--Yaffe conjecture. Close to the deconfinement transition, the lattice results for the correlators show close agreement with the predictions of the two-dimensional three-state Potts model.

Figures (3)

• Figure 1: Geometry of the three-point function on the lattice.
• Figure 2: Global best fits of the data at the four considered values of $\beta$, obtained using the fit ansatz of eq. \ref{['eqlowT']} and imposing a common value of $M/\sqrt{\sigma}$. No lattice-spacing dependence is observed for $E_0$. The parameters $A_3$ and $\sigma$ are determined from the combined fit, treating them as independent for each $\beta$. The red dash-dotted curve corresponds to the leading-order ground-state contribution with $M=0$, i.e.$E_0 = 3 \sigma, R$. The inset focuses on the small-distance regime, where the inclusion of the $M$-dependent term is essential for an accurate data description.
• Figure 3: Estimates of $E_0$ in the high-temperature regime derived from large-distance fits using eq. \ref{['eq:long-distance']}. Both axes are scaled by low-temperature $\sigma$ values at the same lattice spacings. In these units, the models described by eq. \ref{['eq5']} and eq. \ref{['eq9']} have no free parameters, and are indicated by the red dash-dotted and black dashed lines, respectively. The data show good agreement with the latter, this suggest the string tension remains consistent between the closed (high-temperature) and open (low-temperature) channels, and that the square-root functional form provides a finer approximation of the ground state energy.