Baryogenesis from the Berry phase

Abstract

The spontaneous baryogenesis scenario explains how a baryon asymmetry can develop while baryon violating interactions are still in thermal equilibrium. However, generation of the chemical potential from the derivative coupling is dubious since the chemical potential may not appear after the Legendre transformation. The geometric phase (Pancharatnam-Berry phase) results from the geometrical properties of the parameter space of the Hamiltonian, which is calculated from the Berry connection. In this paper, using the formalism of the Berry phase, we show that the chemical potential defined by the Berry connection is consistent with the Legendre transformation. The framework of the Berry phase is useful in explaining the mathematical background of the spontaneous baryogenesis and also in calculating the asymmetry of the nonthermal particle production in time-dependent backgrounds. Using the formalism, we show that the mechanism can be extended to more complex situations. PACS numbers: 98.80Cq 4 See also Appendix B 5 Here, R in U (R) represents arbitrary parameters.

The exact WKB for cosmological particle production

“…The reader can compare these results with our earlier calculation [12,13] reviewed in appendix A. In our next paper, we are going to examine asymmetric particle formation (kinematic baryogenesis) using the results obtained in this paper [16].…”

“…In our future works, we are going to analyze in detail the conditions for asymmetric particle production [16,[29][30][31][32][33], using the ideas developed in this paper. Since baryogenesis requires B-violating interaction, and the interaction has to play a significant role in generating the asymmetry, the equations have to be multi-component (i.e, higher-order after decoupling).…”

“…While on the cosmological side, at least when compared with the mathematical developments of the same period, the discussions of particle production and baryogenesis have been quite ad-hoc. In our future works, we are going to solve the Stokes phenomena of multi-component equations when interactions (i.e, off-diagonal elements) are time-dependent, to show explicitly how the asymmetry appears in cosmological particle creation with time-dependent backgrounds [16]. The EWKB considered in this paper is useful for calculating the connection formulae of complicated differential equations, which cannot be solved simply using special functions, and such equations may often appear in the cosmological calculation of the baryon asymmetry.…”

The exact WKB and the Landau-Zener transition for asymmetry in cosmological particle production

“…16 In ref. [20], it has been shown for a single Dirac fermion that crucial cancellation disturbs asymmetry production. The reason is very simple.…”

“…(Note that in the lower panel the number densities are given for the log scale.) 20 In our numerical calculation, the wave functions u s k and v s k appeared in (2.4) are solved numerically, and they are interpreted into the distribution function. In appendix C we show how to calculate the distribution function by the wave functions.…”