The curvature of the pseudo-critical line in the QCD phase diagram from mesonic lattice correlation functions

TL;DR

This paper advances the QCD phase diagram study by computing the curvature $\kappa$ of the pseudo-critical line $T_{\rm pc}(\mu_B)$ using hadronic observables derived from mesonic correlation functions. By expanding these correlators to $\mathcal{O}(\mu_B^2)$ and exploiting the approximate degeneracy of the vector and axial-vector channels, the authors extract $T_{\rm pc}(\mu_B)$ from lattice data with $N_f=2+1$ Wilson fermions on anisotropic FASTSUM ensembles. The resulting curvatures are $\kappa = 0.0131(23)(23)$ (Generation 2) and $\kappa = 0.034(14)$ (Generation 2L), in reasonable agreement with prior studies that used other observables, albeit without a continuum extrapolation and with heavier pions. Finite-volume effects are found negligible, while the noise from disconnected diagrams largely drives the uncertainties, particularly for the lighter-pion ensemble; future work will include spectral-function analyses to corroborate the findings.

Abstract

In the QCD phase diagram, the dependence of the pseudo-critical temperature, $T_{\rm{pc}}$, on the baryon chemical potential, $μ_B$, is of fundamental interest. The variation of $T_{\rm{pc}}$ with $μ_B$ is normally captured by $κ$, the coefficient of the leading (quadratic) term of the polynomial expansion of $T_{\rm{pc}}$ with $μ_B$. In this work, we present the first calculation of $κ$ using hadronic quantities. Simulating $N_f=2+1$ flavours of Wilson fermions on {\sc Fastsum} ensembles, we calculate the ${\cal O}(μ_B^2)$ correction to mesonic correlation functions. By demanding degeneracy in the vector and axial-vector channels we obtain $T_{\rm{pc}}(μ_B)$ and hence $κ$. While lacking a continuum extrapolation and being away from the physical point, our results are consistent with previous works using thermodynamic observables (renormalised chiral condensate, strange quark number susceptibility) from lattice QCD simulations with staggered fermions.

Figures (11)

• Figure 1: Generation 2 results for $R(\tau; \mu_q)$ as defined in Eq. (\ref{['eq:R-ratio']}) for several temperatures at $\mu_q=0$ (above) and $\mu_q=113$ MeV (below).
• Figure 2: Comparison between $R(\tau; 0)$ on the Generation 2 ensembles in the high-temperature phase (symbols) and for non-interacting lattice fermions, using the same parameters and lattice geometry (dashed lines).
• Figure 3: Averaged ratio $\overline{R}(\mu_q,T)$ as defined in Eq. (\ref{['eq:averaged_R']}), plotted against the temperature, for $\mu_q=0$ (above) and $\mu_q=56$ MeV (below). Blue (orange) symbols correspond to Generation 2 (2L) and the blue (orange) curves show the corresponding interpolating curves obtained using cubic splines. The dashed (dotted) vertical lines correspond to $T_{\rm pc}(\mu_q=0)$ obtained from the renormalised chiral condensate for Generation 2 (2L), including the error estimate, see Table \ref{['tab:ensembles']}. The $\mu_q$-dependent pseudo-critical temperature is determined by $\overline{R}(\mu_q, T_{\rm pc})=0$ and decreases with $\mu_q$.
• Figure 4: Pseudo-critical temperature as a function of $\mu_B$ from the Generation 2 (2L) ensembles shown by blue circles (orange squares). The blue (orange) curve is the fit of the data points to Eq. (\ref{['eq:kappa']}) for Generation 2 (2L). The $T_{pc}(0)$ values obtained from the renormalised chiral condensate are shown as grey (black) crosses for Generation 2 (2L), see Table \ref{['tab:ensembles']}. The dashed line is $\mu_q/T=1$ which sets a limit on the applicability of the Taylor expansion, Eq. (\ref{['eq:expansion']}).
• Figure 5: Final results for $\kappa$ obtained using Generation 2 (blue circle, $M_{\pi}=391(3)$$\mathrm{MeV}$) and Generation 2L (orange square, $M_{\pi}=239(1)$$\mathrm{MeV}$) compared with results from Refs. Bonati:2014rfaBellwied:2015rzaBonati:2018nutHotQCD:2018pdsBorsanyi:2020fev.