Primordial Magnetic Fields, Right Electrons, and the Abelian Anomaly

Abstract

In the standard model there are charges with Abelian anomaly only (e.g., right-handed electron number) which are effectively conserved in the early Universe until some time shortly before the electroweak scale. A state at finite chemical potential of such a charge, possibly arising due to asymmetries produced at the grand unified theory scale, is unstable to the generation of hypercharge magnetic field. Quite large magnetic fields (ϳ10 22 G at T ϳ 100 GeV with typical inhomogeneity scale ϳ 10 6 T ) can be generated. These fields may be of cosmological interest, potentially acting as seeds for amplification to larger scale magnetic fields through nonlinear mechanisms. Previously derived bounds on exotic B 2 L violating operators may also be evaded. [S0031-9007(97)03866-0] PACS numbers: 98.80. Cq, 11.10.Wx, 11.30.Fs, 98.62.En It is usually assumed that the early Universe at temperatures above the electroweak scale and below, say, 10 12 10 16 GeV (depending on the model of inflation) consists of an (almost) equilibrium primordial plasma of elementary particles, in which any long-range fields are absent. One exception is in the context of the problem of generating galactic magnetic fields, which may require the presence of primordial seed magnetic fields which are subsequently amplified by a galactic dynamo mechanism (see, e.g., [1]). The creation of long range magnetic fields requires that conformal invariance be broken in the coupling of the electromagnetic field to gravity [2], and a number of mechanisms based on different ideas about this breaking have been proposed to date [2,3]. In this Letter we argue that there may be a relation between the appearance of magnetic fields in the early Universe and two other, apparently completely unrelated, phenomena: (i) The smallness of the electron Yukawa coupling constant, and (ii) possible lepton asymmetry of the early Universe.In short, the logic goes as follows. There are three exact conservation laws in the standard electroweak theory. The associated conserved charges can be written aswhere L i is the lepton number of ith generation and B is the baryon number. The fourth possible combination, B 1 P i L i is not conserved because of electroweak anomalous processes, which are in thermal equilibrium in the range 100 , T , 10 12 GeV [4]. Now, if h e 0, where h e is the right electron Yukawa coupling constant, then the electroweak theory on the classical level shows a higher symmetry, associated with the chiral rotation of the right electron field. For the small actual value of the Yukawa coupling (h e 2.94 3 10 26 in the MSM), this symmetry has an approximate character. At temperatures higher than T R Ӎ 80 TeV perturbative processes with right electron chirality flip are slower than the expansion rate of the Universe [5], and therefore this symmetry may be considered as an exact one on the classical level at T . T R [6]. [The importance of this symmetry for the consideration of the washout of the grand unified theory (GUT) baryon asymmetry by anomalous electroweak B and...

Primordial Generation of Magnetic Fields

“…Further we have shown that the instability that can be present in a collisionless chiral plasma may not grow as fast as one found in presence of collision (in Ref. [12]) when δ << 1.…”

“…(4), we have defined m 2 D = e 2 p 2 dp 2π 2 df0 dp , c 2 D = e 2 pdp 2π 2 df0 dp , g 2 D = e 2 dp 2π 2 df0 dp & h 2 D = e 2 dp 2π 2 f 0 and f 0 = a f oi . Plasma with chirality imbalance are known to have instabilities that can generate magnetic fields in two different regimes: (i) for the case when k << ω << ν c [12] and (ii) in the quasi-static limit i.e. ω << k and ν c = 0 [7].…”

Intra-cone transition effect to magnetoconductivity in Dirac semimetal

“…The phenomena that the imbalance of the chemical potential between the left-and right-handed mode induces the electric current under the magnetic field is now called the chiral magnetic effect and is now getting a renewed interest in the quark gluon plasma [21], the electro-weak plasma in the early universe [22], and neutrinos in supernovae [23]. Our approach may also be extended to these systems.…”

Real-time Chern-Simons term for hypermagnetic fields

“…If they come with a non-vanishing net density, which can be described by a chemical potential, then a hypermagnetic Chern-Simons term gets induced. It has been argued that this leads to an instability and to the subsequent generation of large-scale hypermagnetic fields [6]. While it is believed that any length scales related to physics within the horizon of this epoch are too small to act as seeds for the currently observed galactic magnetic fields [7], such fields could have other physical consequences, for instance affecting the properties of the electroweak phase transition [8], the sphaleron energy [9], and electroweak baryogenesis [10] (in suitable extensions of the Standard Model).…”