Vector interaction bounds in NJL-like models from LQCD estimated curvature of the chiral crossover line

TL;DR

This paper constrains vector-type interactions in a $2+1$ flavor NJL model by leveraging precise lattice QCD curvature data of the chiral crossover, focusing on $\kappa_2^{B}$ and $\kappa_4^{B}$. By comparing both flavor-independent ($G_V$) and flavor-dependent ($g_V$) vector couplings to lattice results, it derives allowed ranges and analyzes how the strangeness chemical potential $\mu_S$ modulates the curvature to disentangle vector-induced mixing from the $\;\text{t Hooft}$ flavor-mixing term. The study finds that lattice data permit both attractive and repulsive vector interactions, with $\kappa_4^{B}$ remaining near zero within uncertainties, and shows that $\mu_S$ dependence reveals distinct mixing contributions between the two vector channels. Within these constrained interactions, the model predicts shifts of the critical endpoint in the $T-\mu_B$ plane and emphasizes the potential of higher-order lattice susceptibilities to further sharpen these bounds, informing the QCD phase structure at finite density.

Abstract

We obtain improved bounds on both the flavor-independent and -dependent vector interactions in a $2+1$-flavor Nambu\textendash Jona-Lasinio (NJL) model using the latest precise LQCD results of the curvature coefficients of the chiral crossover line. We find that these lattice estimated curvature coefficients allow for both attractive and repulsive types of interactions in both the cases. With this constrained ranges of vector interactions, we further predict the behavior of the second $(κ_2^B)$ and fourth $(κ_4^B)$ order curvature coefficients as a function of the strangeness chemical potential $(μ_S)$. We observe that the flavor mixing effects, arising from the flavor-independent vector interaction as well as from the 't Hooft interaction, play an important role in $k_2^B$. We propose that the mixing effects due to the vector interaction can be separated from those arising from the 't Hooft interaction by analyzing the behavior of $k_2^B$ as a function of $μ_S$. Finally, we locate the critical endpoint in the $T-μ_B$ plane using the model-estimated ranges of vector interactions and find the model's predictions to be consistent with the latest LQCD bounds.

Figures (8)

• Figure 1: The curvature coefficient ($\kappa_2^B$) as a function of the strengths of vector interactions. Open squares (lines) are obtained using Parameter Set I (Set II), respectively. The bands represent the corresponding Lattice QCD estimations from Ref. HotQCD:2018pds.
• Figure 2: The curvature coefficient ($\kappa_2^B$) as a function of strangeness chemical potential ($\mu_S$). $[G_V^-, G_V^+]$ and $[g_V^-, g_V^+]$ are the allowed ranges of vector interaction found using LQCD data. Red data points are without the vector interaction i.e., $G_V=g_V=0$. Black point represents the LQCD estimations of the $\kappa^{B}_{2}$ at $\mu_S=0$HotQCD:2018pds.
• Figure 3: Curvature coefficient, $\kappa_2^B$ as a function of $\mu_{S}$ with $K=0$ for both Model-I and Model-II.
• Figure 4: The curvature coefficient for different values of $\mu_S$ in Model-II with the same parameter sets used in the above graph.
• Figure 5: Effect of the vector interactions on the QCD phase line for $\mu_S = 0$. Blue and magenta lines denote the estimation from the upper and lower bounds of the flavor-dependent vector interaction $g_V$, respectively. Soft blue and soft orange denote the same for flavor-independent scenario, i.e., with nonzero $G_V$. The red line denotes the limiting case with no vector interaction, $g_V = G_V = 0$.