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Abstract
We calculate the rate of collisional decay of the axial charge in an ultrarelativistic electron-positron plasma, also known as the chirality flipping rate. We find that contrary to the existing estimates, the chirality flipping rate appears already in the first order in the fine-structure constant $\ensuremath{\alpha}$ and is therefore orders of magnitude greater than previously believed. The main channels for the rapid relaxation of the axial charge are the collinear emission of a weakly damped photon and the Compton scattering. The latter contributes to the $\mathcal{O}(\ensuremath{\alpha})$ result because of the infrared divergence in its cross section, which is regularized on the soft scale $\ensuremath{\sim}eT$ due to the thermal corrections. Our results are important for the description of the early Universe processes (such as leptogenesis or magnetogenesis) that affect differently left- and right-chiral fermions of the Standard Model, as discussed in more details in the companion Letter.
Highlights
An axially-charged electron-positron plasma coupled to a large-scale magnetic field provides a remarkable example of a system whose macroscopic collective motion evinces a purely quantum phenomenon, the axial gauge anomaly
Our results are important for the description of the early Universe processes that affect differently left- and right-chiral fermions of the Standard Model, as discussed in more details in the companion Letter
Due to the presence of the anomaly, the hydrodynamics of such a plasma contains an unusual collective degree of freedom, which is not locally connected to the thermodynamic variables characterizing the local equilibrium [1,2,3,4,5]. Such a deformation of the equations of hydrodynamics gives rise to new types of macroscopic behavior such as the chiral magnetic effect or the inverse magnetic cascade [1,2,6,7,8,9,10,11]. These phenomena can play an important role in the context of leptogenesis and cosmic magnetogenesis [1,2,6,8,9,12,13,14,15,16,17,18,19,20,21,22,23], for magnetic field evolution in primordial plasma [1,2,6,8,9,10,11], as well as in the heavy-ion collisions and quark-gluon plasma [7,24,25] and in the neutron stars [26,27,28,29,30,31]
Summary
An axially-charged electron-positron plasma coupled to a large-scale magnetic field provides a remarkable example of a system whose macroscopic collective motion evinces a purely quantum phenomenon, the axial gauge anomaly. Due to the presence of the anomaly, the hydrodynamics of such a plasma contains an unusual collective degree of freedom, which is not locally connected to the thermodynamic variables characterizing the local equilibrium [1,2,3,4,5] Such a deformation of the equations of hydrodynamics gives rise to new types of macroscopic behavior such as the chiral magnetic effect or the inverse magnetic cascade [1,2,6,7,8,9,10,11]. We demonstrate the existence of scattering channels which contribute to the chirality flipping rate in the first order of the fine-structure constant α, despite their nominal perturbative order being α2.
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