The order of the quantum chromodynamics transition predicted by the standard model of particle physics

Abstract

We determine the nature of the QCD transition using lattice calculations for physical quark masses. Susceptibilities are extrapolated to vanishing lattice spacing for three physical volumes, the smallest and largest of which differ by a factor of five. This ensures that a true transition should result in a dramatic increase of the susceptibilities.No such behaviour is observed: our finite-size scaling analysis shows that the finite-temperature QCD transition in the hot early Universe was not a real phase transition, but an analytic crossover (involving a rapid change, as opposed to a jump, as the temperature varied). As such, it will be difficult to find experimental evidence of this transition from astronomical observations.

Figures (4)

• Figure 1: Susceptibilities for the light quarks for $N_t$=4 (left panel) and for $N_t$=6 (right panel) as a function of $6/g^2$, where $g$ is the gauge coupling ($T$ grows with $6/g^2$). The largest volume is eight times bigger than the smallest one, so a first-order phase transition would predict a susceptibility peak that is eight times higher (for a second-order phase transition the increase would be somewhat less, but still dramatic). Instead of such a significant change we do not observe any volume dependence. Error bars are s.e.m.
• Figure 2: Normalised susceptibilities $T^4/(m^2\Delta\chi)$ for the light quarks for aspect ratios r=3 (left panel) r=4 (middle panel) and r=5 (right panel) as functions of the lattice spacing. Continuum extrapolations are carried out for all three physical volumes and the results are given by the leftmost blue diamonds. Error bars are s.e.m with systematic estimates.
• Figure 3: Continuum extrapolated susceptibilities $T^4/(m^2\Delta\chi)$ as a function of 1/$(T_c^3V)$. For true phase transitions the infinite volume extrapolation should be consistent with zero, whereas for an analytic crossover the infinite volume extrapolation gives a non-vanishing value. The continuum-extrapolated susceptibilities show no phase-transition-like volume dependence, though the volume changes by a factor of five. The V$\rightarrow$$\infty$ extrapolated value is 22(2) which is 11$\sigma$ away from zero. For illustration, we fit the expected asymptotic behaviour for first-order and O(4) (second order) phase transitions shown by dotted and dashed lines, which results in chance probabilities of $10^{-19}$ ($7\times10^{-13}$), respectively. Error bars are s.e.m with systematic estimates.
• Figure 4: The line of constant physics. We show our choice for $m_s$ (strange quark mass) and 20$m_{ud}$ (u,d quark masses) in lattice units as functions of $6/g^2$.