Order of the chiral transition for massless light quarks
In plain words
If the up and down quarks had zero mass, QCD would have an exact symmetry that breaks as matter cools, and the transition would be either sudden or continuous. The answer constrains where a critical point can lie in the real phase diagram.
Precise statement
For $N_{f}=2$ massless flavors (and $2+1$ with physical strange mass) at $\mu_{B}=0$, determine whether the chiral transition is first or second order and, if second order, whether it is in the $O(4)$ universality class or a larger one because the anomalous $U(1)_{A}$ symmetry is effectively restored at $T_{c}$ (Pisarski and Wilczek, 1984). Answer: order and universality class from continuum-extrapolated lattice QCD, with $T_{c}$ in the chiral limit.
What would settle it
Lattice QCD with chirally symmetric fermions at several light-quark masses approaching zero, with continuum extrapolation, scaling analysis and $U(1)_{A}$-breaking susceptibilities.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Lattice studies found evidence consistent with a second-order transition in the continuum chiral limit for $N_f$ up to 6 (Cuteri, Philipsen, Sciarra, JHEP 11 (2021) 141), while the universality class and the fate of $\mathrm{U}(1)_A$ remained debated as of 2026.
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