The Mass of the Baryon Junction: a lattice computation in 2 +1 dimensions

TL;DR

The paper determines the baryon junction mass $M$ in SU(3) Yang–Mills theory in $(2+1)$ dimensions by exploiting next-to-leading-order EST corrections to the three-point Polyakov-loop correlator, extracting $M/\,\sqrt{\sigma}=0.1355(36)$ from the open-string $1/R^2$ term. It simultaneously tests the high-temperature behavior via the Svetitsky–Yaffe mapping to the 2D three-state Potts model and conformal perturbation theory, finding excellent agreement between lattice results and Potts-model predictions. The results support a weakly coupled EST description for baryons and provide a nonperturbative benchmark for holographic models, while revealing a small ($\sim$3–4%) discrepancy in the string tension obtained from baryonic correlators. The authors outline future work to extend the analysis to $(3+1)$D and to full QCD to assess the universality of the junction mass and EST predictions in more realistic settings.

Abstract

We present a systematic study of baryonic flux tubes in SU(3) Yang-Mills theory in (2+1) dimensions. A recent next-to-leading-order derivation within the Effective String Theory framework has, for the first time, made explicit the corrections proportional to the mass of the baryon junction M, up to order $1/R^2$ (where $R$ is the length of the confining strings), opening the possibility of its non-perturbative determination. One of the main goals of this paper is, through high precision simulations of the three-point Polyakov loop correlator, to measure for the first time the baryon junction mass. By isolating the predicted $1/R^2$ term in the open string channel, we obtain the value $M/\sqrtσ = 0.1355(36)$, similar to the phenomenological value which is used to describe hadrons, although our computation was done in (2+1) dimensions. In addition, studying the high temperature behavior of the baryon, we present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions. Focusing on the high temperature regime, just below the deconfinement transition, we compare our lattice results for Polyakov loop correlators with the quantitative predictions obtained by applying conformal perturbation theory to the three-state Potts model in two dimensions and find excellent agreement.

Figures (8)

• Figure 1: Graphical representation of the baryon junction. The three blue arrows represent the quarks (or, on the lattice, the Polyakov loops); the worldsheets of the effective string are depicted as surfaces colored in three different shades of green; the wavy red line where the three worlsheets meet illustrates the baryon junction.
• Figure 2: Geometry of the three-point function on the lattice.
• Figure 3: Best fit of the data at $\beta=42.97$ according to the fit model in eq. \ref{['eq:threeptfitfunc']}.
• Figure 4: Combined best fits of the data across all four values of $\beta$ according to the fit model in eq. \ref{['eq:threeptfitfunc']}, performed under the assumption of a fixed same value of $M / \sqrt{\sigma}$. The correlator data points have been converted into the ground state energy level according to eq. \ref{['eqlowT']}, $E_0 = -\log \left(\braket{P(x_1) \, P(x_2) \, P(x_3)} / A_3 \right) / N_t$. This quantity does not show any correction due to the finite lattice spacing. The values of $A_3$ and $\sigma$, have been extracted from the combined fit (as independent parameters for each value of $\beta$). The red dash-dotted line represents the leading order expression for the ground state, assuming $M = 0$, i.e.$E_0 = 3 \sigma \, R$. The zoomed inset shows the points at the smallest distances, it is evident how the inclusion of the term proportional to $M$ is indispensable for an accurate description of the data.
• Figure 5: Fit of the three-point correlation function for $\beta = 46.29$ and $N_t = 15 \, a$ with the two models in eq. \ref{['eq:low-distance']} (short distance expansion, blue dashed line in the plot) and eq. \ref{['eq:long-distance']} (large distance expansion, red dashed-dotted). In this region ($24.12 \le R_Y / a \le 51.96$), they both fit accurately our data (blue circles) and show perfect agreement between each other.