Existence of a QCD critical point at finite baryon chemical potential

Determine whether a quantum chromodynamics (QCD) critical point exists at baryon chemical potentials greater than zero, at which the hadron–to–quark–gluon plasma transition changes from a smooth crossover at μ_B=0 to a first-order phase transition.

Background

The QCD phase diagram describes the phases of strongly interacting matter as a function of temperature and baryon chemical potential. Lattice QCD establishes that at μ_B=0 the transition from hadronic matter to quark–gluon plasma is a smooth crossover, but the fermion sign problem prevents direct lattice calculations at μ_B>0, leaving the global structure of the phase diagram uncertain.

A central question for both theory and experiment is whether a true critical point exists at higher μ_B where the crossover ends and a first-order transition begins. This motivates heavy-ion collision programs and analysis methods, such as finite-size scaling, aimed at detecting signatures of critical behavior and, if present, locating the critical point.

References

For example, although lattice calculations show that the hadron to quark-gluon plasma phase transition at μB=0 is a smooth crossover, it is not yet known whether a critical point exists at higher μB where the smooth crossover transition would change to a first-order phase transition.

— Locating the critical point for the hadron to quark-gluon plasma phase transition from finite-size scaling of proton cumulants in heavy-ion collisions  (2405.10278 - Sorensen et al., 2024) in Section 1, Introduction

In particular, it is not known whether, as $\mu_B$ is increased from zero, the crossover between hadronic matter and the QGP eventually turns into a first-order phase transition and, consequently, whether the QCD phase diagram contains a critical point~(CP).

— QCD phase structure at high baryon density  (2609.17363 - Sorensen, 15 Sep 2026) in Section 1, Introduction

Net-proton cumulants in the Beam Energy Scan region of heavy-ion collisions are widely used to probe critical fluctuations associated with the conjectured critical endpoint of Quantum Chromodynamics (QCD).

— Hadronic rescattering effects on net-proton cumulants from functional renormalization group calculations  (2608.28299 - Lin et al., 28 Aug 2026) in Abstract; Section 1, Introduction

At finite baryon chemical potential, the crossover may turn into a first-order transition via a critical endpoint; whether and where such an endpoint occurs remains a central open problem in QCD thermodynamics.

— Bias-Corrected Machine-Learning Estimation of Chiral Condensate Cumulants: A Retrospective Lattice QCD Case Study  (2608.30416 - Choi et al., 31 Aug 2026) in Section 1, Introduction

At finite baryon chemical potential ($\mu_B$), lattice QCD predicts a smooth crossover between hadronic and partonic matter, whereas at larger $\mu_B$, beyond the conjectured critical end point, the transition becomes first order.

— Charmonium production in p+A collisions at SPS and FAIR energies  (2608.30560 - Song et al., 31 Aug 2026) in Section 1, Introduction

The STAR fixed-target (FXT) program extends this reach to very high baryon chemical potential, up to \mu_{B}\approx 760~MeV, overlapping the region of interest for the conjectured QCD critical point.

— Non-Monotonicity of $p_{\rm T}$ Correlations in Au + Au Collisions at RHIC  (2609.26449 - Manikandhan, 22 Sep 2026) in Section 1, Introduction

Whether this crossover ends at a potential critical point (CP) is still an open question.

— Four-dimensional QCD equation of state with a critical surface from contours of constant entropy density  (2610.20806 - Gyure et al., 14 Oct 2026) in Section 1, Introduction