Baryogenesis from cosmological CP breaking

TL;DR

This work addresses the origin of the baryon asymmetry by proposing that a cosmological CP-violating scalar tau, arising from either a spontaneously broken local U(1) or modular invariance, dynamically modulates CP-violating parameters in the Standard Model. Using a general effective field theory with tau-dependent Yukawas, theta terms, and current couplings, the authors derive a set of chemical-potential evolution equations that couple to tau dynamics and to baryon- and lepton-number-violating processes. They show that a CP-violating evolution of tau can generate the observed asymmetry, with viable realizations at $T \sim 10^{11}$ GeV (TeV-scale tau) and at higher temperatures (heavier tau) provided washout and entropy-dilution effects are appropriately managed; isocurvature constraints from inflation further bound $m_\tau$ and the decay constant. The mechanism links baryogenesis to high-energy CP violation encoded in modular invariance and spontaneous symmetry breaking, offering a string-motivated route to baryogenesis compatible with the strong CP problem and presenting concrete numerical benchmarks across cosmological histories.

Abstract

We show that baryogenesis can arise from the cosmological evolution of a scalar field that governs CP-violating parameters, such as the Yukawa couplings and the theta terms of the Standard Model. During the big bang, this scalar may reach a CP-violating minimum, where its mass can be comparable to the inflationary Hubble scale. Such dynamics can emerge in theories featuring either a spontaneously broken local U(1) symmetry or modular invariance. The latter arises naturally as the effective field theory capturing the geometric origin of CP violation in toroidal string compactifications. Modular baryogenesis is compatible with the modular approach to resolving the strong CP problem.

Figures (4)

• Figure 1: The shaded bands represent the range of temperatures where SM couplings equilibrate chemical potentials with rates fast enough to be in thermal equilibrium. The last column considers $\Delta L=2$ interaction from atmospheric Majorana neutrino masses: the upper band is the misleading result of the $(LH)^2$ effective operator approximation; while the vertical bands represent the range assuming a right-handed neutrino, depending on its unknown mass. Flavor effects undergo a qualitative change around the horizontal line: at lower temperatures enough Yukawa rates are fast enough to suppress quantum coherence.
• Figure 2: Sample evolution of the chemical potentials $\mu_P/T$ (left) and of rates $\gamma_I/H T^3$ (right). The CP-breaking scalar $\tau$ is relatively light, and both panels also include its evolution, in arbitrary units. Baryogenesis is sourced around $10^{11}\,{\rm GeV}$ by the varying phase of up Yukawa coupling, assumed to be proportional to $E_4(\tau)$. At this temperature all rates are in thermal equilibrium, except for the $\Delta L=2$ rate, so that eq. (\ref{['eq:evoB-L']}) for $\mu_{B-L}$ would be enough.
• Figure 3: Sample evolution of the chemical potentials $\mu_P/T$ (left) and of rates $\gamma_I/H T^3$ (right). The CP-breaking scalar is now heavier, $m_\tau=10^{11}\,{\rm GeV}$. Baryogenesis is sourced around $10^{14}\,{\rm GeV}$ by the varying phase of the charged lepton Yukawa coupling, assumed to be proportional to $E_4(\tau)$. Some rates are not in thermal equilibrium,
• Figure 4: Sample evolution of the chemical potentials $\mu_P/T$ (left) and of rates $\gamma_I/H T^3$ (right). In this example the too large baryon asymmetry generated around the mass of the heavier right-handed neutrino is later partially washed out by $\Delta L=2$ interactions mediated by the lighter right-handed neutrino.