On the Contributions to the ${\mathbf{U}}_{\mathbf{Y}}(1)$ Chern-Simons Term and the Evolution of Fermionic Asymmetries and Hypermagnetic Fields

Abstract

We study simultaneous evolution of electron, neutrino and quark asymmetries, and large scale hypermagnetic fields in the symmetric phase of the electroweak plasma in the temperature range $100$GeV$\le T\le 10$TeV, taking into account the chirality flip processes via inverse Higgs decays and fermion number violation due to Abelian anomalies. We present a derivation of the coefficient of the Chern-Simons term for the hypercharge gauge field, showing that the left-handed and right-handed components of each fermion species contribute with opposite sign. This is in contrast to the results presented in some of the previous works. The ${\text{U}}_{\text{Y}}(1)$ Chern-Simons term affects the resulting anomalous magnetohydrodynamic (AMHD) equations. We solve the resulting coupled evolution equations for the lepton and baryon asymmetries, as well as the hypermagnetic field to obtain their time evolution along with their values at the electroweak phase transition ($T_{EW}\sim 100$GeV) for a variety of critical ranges for their initial values at $T=10$TeV. We first investigate the results of this sign change, by directly comparing our results with those obtained in one of the previous works and find that matter asymmetry generation increases considerably in the presence of a strong hypermagnetic field. Furthermore, we find that a strong hypermagnetic field can generate matter asymmetry starting from absolutely zero asymmetry, while matter asymmetry can generate a hypermagnetic field provided the initial value of the latter is nonzero.

29 pages, 4 figures

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• The effects of the U${}_{\text{Y}}$(1) Chern-Simons term and its baryonic contribution on matter asymmetries and hypermagnetic fields
• Contribution of the chiral vortical effect to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the early Universe
• Electroweak baryogenesis via chiral gravitational waves
• A Minimal System Including Weak Sphalerons for Investigating the Evolution of Matter Asymmetries and Hypermagnetic Fields
• Flavon Magneto-Baryogenesis
• The generation of matter-antimatter asymmetries and hypermagnetic fields by the chiral vortical effect of transient fluctuations
• The effects of non-helical component of hypermagnetic field on the evolution of the matter-antimatter asymmetry, vorticity, and hypermagnetic field
• Dyson-Schwinger equation approach to Lorentz Symmetry Breaking with finite temperature and chemical potential
• Magnetogenesis From Baryon Asymmetry During an Early Matter Dominated Era
• Thermal leptogenesis in the presence of helical hypermagnetic fields