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We study the effect of a small fermion mass in the formulation of theon-shell effective field theory (OSEFT). This is our starting point to derivesmall mass corrections to the chiral kinetic theory. In the massless case, onlyfour Wigner functions are needed to describe positive and negative energyfermions of left and right chirality, corresponding to the vectorial componentsof a fermionic two-point Green's function. As soon as mass correction areintroduced, tensorial components are also needed, while the scalar componentsstrictly vanish in the OSEFT. The tensorial components are convenientlyparametrized in the so-called spin coherence function, which describe quantumcoherent mixtures of left-right and right-left chiral fermions, of eitherpositive or negative energy. We show that, up to second order in the energyexpansion, vectorial and tensorial components are decoupled, and obey the samedispersion law and transport equation, depending on their respective chirality.We study the mass modifications of the reparametrization invariance of theOSEFT, and check that vector and tensorial components are related by theassociated symmetry transformations. We study how the macroscopic properties ofthe system are described in terms of the whole set of Wigner functions, andcheck that our framework allows to account for the mass modifications to thechiral anomaly equation.

Chiral kinetic theory with small mass corrections and quantum coherent states