Chiral kinetic theory with small mass corrections and quantum coherent states

Abstract

We study the effect of a small fermion mass in the formulation of the on-shell effective field theory (OSEFT). This is our starting point to derive small mass corrections to the chiral kinetic theory. In the massless case, only four Wigner functions are needed to describe positive and negative energy fermions of left and right chirality, corresponding to the vectorial components of a fermionic two-point Green's function. As soon as mass correction are introduced, tensorial components are also needed, while the scalar components strictly vanish in the OSEFT. The tensorial components are conveniently parametrized in the so-called spin coherence function, which describe quantum coherent mixtures of left-right and right-left chiral fermions, of either positive or negative energy. We show that, up to second order in the energy expansion, vectorial and tensorial components are decoupled, and obey the same dispersion law and transport equation, depending on their respective chirality. We study the mass modifications of the reparametrization invariance of the OSEFT, and check that vector and tensorial components are related by the associated symmetry transformations. We study how the macroscopic properties of the system are described in terms of the whole set of Wigner functions, and check that our framework allows to account for the mass modifications to the chiral anomaly equation.

Version accepted for publication, typos corrected, and new section (VIIC) with explanations on the relation to other approaches. 38 pages, no figures

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• Spin Polarization Formula for Dirac Fermions at Local Equilibrium
• Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow
• Chiral Magnetic Effect in Heavy Ion Collisions: The Present and Future
• Lorentz-covariant kinetic theory for massive spin-1/2 particles
• Berry phase in the phase space worldline representation: the axial anomaly and classical kinetic theory
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• Mass corrections to the hard thermal/dense loops