Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Strangeness neutrality and the QCD phase diagram

Wei-jie Fu, Chuang Huang, Jan M. Pawlowski, Fabian Rennecke, Rui Wen, Shi Yin

Abstract

We map out the phase structure of $N_f=2+1$ flavour QCD at strangeness neutrality with functional QCD. We find a critical end point at $(T_{\rm CEP},μ_{B,{\rm CEP}})|_{n_S=0} = (92, 696)$\,MeV. The computation is done with the functional renormalisation group, and we systematically improve on previous works, hence reducing the systematic error significantly. Our results pass relevant QCD benchmarks: they agree well with and corroborate the QCD phase structure from functional QCD results at vanishing strangeness chemical potential. Moreover, they agree well with lattice QCD results at vanishing chemical potential. Specifically, the ratio of the second order curvature coefficient $κ_2$ agrees with that obtained from lattice computations, $κ_2(n_S=0)/κ_2(μ_S=0)=0.897(20)$.

Strangeness neutrality and the QCD phase diagram

Abstract

We map out the phase structure of flavour QCD at strangeness neutrality with functional QCD. We find a critical end point at \,MeV. The computation is done with the functional renormalisation group, and we systematically improve on previous works, hence reducing the systematic error significantly. Our results pass relevant QCD benchmarks: they agree well with and corroborate the QCD phase structure from functional QCD results at vanishing strangeness chemical potential. Moreover, they agree well with lattice QCD results at vanishing chemical potential. Specifically, the ratio of the second order curvature coefficient agrees with that obtained from lattice computations, .
Paper Structure (18 sections, 94 equations, 9 figures, 3 tables)

This paper contains 18 sections, 94 equations, 9 figures, 3 tables.

Table of Contents

  1. Effective action and approximation scheme
  2. Effective action
  3. Matter sector of $N_f=2+1$ flavour QCD
  4. Meson and quark masses and scatterings
  5. Functional RG approach to QCD with emergent composites
  6. Glue sector and quark-gluon interface
  7. Meson sector
  8. Quark Sector
  9. Quark-meson interface and emergent composites
  10. Physics Parameters at the initial cutoff scale
  11. QCD parameters at the initial cutoff scale
  12. Phenomenological parameters
  13. Infrared enhancement of the quark-gluon coupling
  14. 't Hooft determinant
  15. Polyakov loop potential
  16. ...and 3 more sections

Figures (9)

  • Figure 1: Left: Strangeness chemical potential $\mu_{S0}$ at strangeness neutrality, \ref{['eq:muS0']}, as a function of the baryon chemical potential $\mu_{B}$. The free quark gas limit $\mu_B/\mu_{S}=3$ is also plotted for comparison (black dashed line). Right: Heat map of the ratio $\mu_{S0}/\mu_B$ in the $T - \mu_B$ plane. We also show the the contours of constant $\mu_{S0}/\mu_{B}(T,\mu_B)$ for $T(\mu_B=0)=(150, 160, 170)$ MeV in comparison with the lattice QCD results Borsanyi:2025kiv.
  • Figure 2: Renormalised light quark chiral condensate $\Delta_{l,R}$ (left panel) and the reduced condensate $\Delta_{l,s}$ (right panel) as functions of temperature. We also show functional QCD results from Fu:2019hdw, and lattice QCD results from the Wuppertal-Budapest collaboration Borsanyi:2010bp at vanishing chemical potential.
  • Figure 3: QCD phase diagram in comparison to the previous fRG Fu:2019hdwPawlowski:2025jpg, DSE Gao:2020fblGunkel:2021oya and lattice QCD results HotQCD:2018pdsBorsanyi:2020fev. Freeze-out points STAR:2017salAlba:2014ebaAndronic:2017pugBecattini:2016xctVovchenko:2015idtSagun:2017eye are also plotted for comparison. The moat regions are only plotted in the area where $\mu_B<{\mu_{B}}_{_\text{CEP}}$.
  • Figure 4: Meson masses as functions of the chemical potential at the pseudo-critical temperature at strangeness neutrality.
  • Figure 5: Light and strange quark Yukawa couplings (left panel) and quark wave functions (right panel) as functions of the RG scale $k$ for various temperatures.
  • ...and 4 more figures