Chiral magnetic effect in the presence of an external axial-vector field

Abstract

We study the excitation of the electric current of chiral fermions along the external magnetic field, known as the chiral magnetic effect, in the presence of the background axial-vector field. The calculation of the current is based on the exact solution of the Dirac equation for these fermions accounting for the external fields. First, this solution was obtained for massive particles and, then, we consider the chiral limit, which is used in the anomalous current computation. We obtain that, in this situation, the anomalous current does not contain the direct contribution of the axial-vector field. This result is compared with findings of other authors. * maxdvo@izmiran.ru

Gravitational and chiral anomalies in the running vacuum universe and matter-antimatter asymmetry

“…Notice that the chiral anomaly contributions to the KR background field are proportional to the Hubble parameter H(t) during the radiation era. If one considered the solution with C 0 = 0, then such corrections would contribute purely H 2 -running vacuum type corrections (71) to the energy density [8]. However, in view of the smallness of cosmic magnetic fields in the Universe, including possible primordial ones [60,62,63], we expect such terms to be suppressed compared to the a −3 (t) term in the early universe, when C 0 = 0, a case relevant for leptogenesis [38], as we shall discuss below.…”

“…21 We note, however, that there are important subtle physical differences between a bare µ 5 and the temporal component of an axial vector background (axial potential), such asḃ, coupled to the axial fermion current. The latter, unlike µ 5 , does not contribute [70,71] to the so-called chiral magnetic effect (CME) [72], that is the excitation of an electric current density in the presence of an external magnetic field, with a coefficient proportional to µ 5 , j CME = e 2 2π 2 µ 5 B, which is an effect associated with the chiral anomaly. Indeed, if one uses energy conservation arguments [70] or calculates the electric current density from first principles using, e.g., the relativistic quantum mechanics approach [71] in the presence of both a chiral chemical µ 5 and the axial potential, then only the µ 5 contributes to the current.…”

“…The latter, unlike µ 5 , does not contribute [70,71] to the so-called chiral magnetic effect (CME) [72], that is the excitation of an electric current density in the presence of an external magnetic field, with a coefficient proportional to µ 5 , j CME = e 2 2π 2 µ 5 B, which is an effect associated with the chiral anomaly. Indeed, if one uses energy conservation arguments [70] or calculates the electric current density from first principles using, e.g., the relativistic quantum mechanics approach [71] in the presence of both a chiral chemical µ 5 and the axial potential, then only the µ 5 contributes to the current. In our case, the non-contribution of the axial potential to the CME is consistent [38] with the fact that the contributions of the KR torsion (and thus the axial KR potentialḃ(x)) to the chiral anomaly can be removed by the addition of appropriate renormalisation group counterterms to the string effective action, order by order in perturbation theory [48,49].…”

Spontaneous CPT Violation and Quantum Anomalies in a Model for Matter–Antimatter Asymmetry in the Cosmos

“…However, as argued in [42,43], using different methods, the axial vector potential B 0 does not contribute to CME, and instead one has (28), even if B 0 = 0 is present 10 . The subtlety lies in the fact that, in the presence of a background field B 0 , as we have discussed in [26][27][28], the dispersion relations for the fermions are affected nontrivially by the presence of B 0 , which differentiates it from the chiral chemical potential case; moreover, there are subtleties related to the order of taking the massless limit m → 0.…”

“…The subtlety lies in the fact that, in the presence of a background field B 0 , as we have discussed in [26][27][28], the dispersion relations for the fermions are affected nontrivially by the presence of B 0 , which differentiates it from the chiral chemical potential case; moreover, there are subtleties related to the order of taking the massless limit m → 0. In the presence of a chiral chemical potential, an external constant magnetic field and a (generic, but constant) axial background (of which our (constant) B 0 is a special case) the CME was discussed in [43], within the framework of relativistic quantum mechanics [55]. It turns out to be important to take the massless (chiral fermion) limit m → 0 at the end of the computation: one should assume massive fermions, in the presence of a B 0 = 0, solve the corresponding Dirac equation, and only at the end take the limit m → 0.…”