Lepton asymmetry and the cosmic QCD transition

TL;DR

The paper investigates how a potentially large lepton asymmetry $l$ in the early Universe can influence the QCD epoch by coupling leptonic, baryonic, and electromagnetic conserved quantities. Using a thermodynamic framework with conserved charges $B$, $L_f$, and $Q$, the authors derive how chemical potentials $\mu_B$, $\mu_Q$, and $\mu_{L_f}$ depend on temperature and on $l$ and $b$, across the quark and hadron phases. They show that nonzero $l$ can drive substantial $\mu_B$ and $\mu_Q$ around the QCD transition, altering the cosmic trajectory in the $\mu_B$-$T$ plane and potentially turning the transition into first order if $|l|$ is sufficiently large, depending on the QCD phase diagram. These results imply that leptogenesis scenarios yielding sizable lepton asymmetries could leave observable imprints in the early Universe and motivate lattice QCD studies that include nonzero $\mu_B$ and $\mu_Q$ to quantify the effect on the cosmic QCD transition.

Abstract

We study the influence of lepton asymmetry on the evolution of the early Universe. The lepton asymmetry $l$ is poorly constrained by observations and might be orders of magnitude larger than the baryon asymmetry $b$, $|l|/b \leq 2\times 10^8$. We find that lepton asymmetries that are large compared to the tiny baryon asymmetry, can influence the dynamics of the QCD phase transition significantly. The cosmic trajectory in the $μ_B-T$ phase diagram of strongly interacting matter becomes a function of lepton (flavour) asymmetry. Large lepton asymmetry could lead to a cosmic QCD phase transition of first order.

Figures (11)

• Figure 1: Sketch of the phase diagram for physical QCD, based on findings from nuclear physics, lattice QCD and perturbative calculations. Solid lines indicate a first-order phase transition, while the dashed line indicates a crossover. The exact phase diagram with or without a critical end point ($T_{\rm e},\mu_{\rm e}$) is still under debate. So is also the (pseudo-)critical temperature $T_{\rm c} = 192(7)(4)$ MeV Cheng:2006qkKarsch:2007zza, which differs from $T_{\rm c} = 164\pm 2$ MeV, the value found in Aoki:2006br. While de Forcrand:2007zz argue that it is still an open question if a critical end point exists at all, Fodor:2004nz find $\mu_{\rm e} = 360 \pm 40$ MeV and $T_{\rm e} = 162 \pm 2$ MeV. The calculations and methods leading to these different results are discussed and compared in Karsch:2007zzaAoki:2006brde Forcrand:2007zzStephanov:2007fk.
• Figure 2: Evolution of net lepton densities $n_i$ in the quark phase for $l=-b$. We plot them with respect to the entropy density $s(T).$
• Figure 4: Evolution of net lepton densities in the quark phase for $l=3\times 10^{-4}$. The order of magnitudes is very different from the case $l = - b$ and the sign is reversed.
• Figure 6: Evolution of net particle densities in the hadron phase for $l= - b$. Mesons are included in the calculations but not shown.
• Figure 8: Trajectory of the quark phase in the $\mu_B-T$ plane for the $l=-b$ scenario. We compare several approximations to the exact result (black line). At high temperatures all particles can be assumed to be massless (blue line), while below $\sim 5$ GeV mass thresholds are important. Below 1 GeV the universe is well described by three quark (up, down, strange) and two lepton (electron, muon) flavours only (magenta line).