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 corrections 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 coherent functions, 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.

Highlights

  • In this manuscript we study how small mass corrections affect the chiral transport theory derived from the on-shell effective field theory (OSEFT), following our previous studies on the subject [1,2,3]

  • As there are several parallelisms between OSEFT and soft-collinear effective theory (SCET) that were already discussed in Ref. [2], we find again the same sort of mass modifications here

  • We show explicitly how several of the macroscopic quantities are described in terms of both the vectorial and tensorial components, and check that the chiral quantum anomaly, with small mass corrections, is properly described in our framework

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Summary

INTRODUCTION

In this manuscript we study how small mass corrections affect the chiral transport theory derived from the on-shell effective field theory (OSEFT), following our previous studies on the subject [1,2,3]. Up to the second order in the energy expansion considered in this manuscript, the vectorial and tensorial components are decoupled We derive their corresponding collisionless transport equations, which turn out to be identical. In the transport framework, the Wigner function associated to vectorial and tensorial components are related after carrying out these combined transformations This means that both components are needed to respect the Lorentz symmetry in this slightly modified CKT. We show explicitly how several of the macroscopic quantities are described in terms of both the vectorial and tensorial components, and check that the chiral quantum anomaly, with small mass corrections, is properly described in our framework

A SMALL MASS TERM IN OSEFT
FERMION WIGNER FUNCTION
DISPERSION RELATION AND VALIDITY OF THE APPROACH
DERIVATION OF THE COLLISIONLESS TRANSPORT EQUATIONS WITH SMALL
REPARAMETRIZATION INVARIANCE OF OSEFT WITH A SMALL MASS
MACROSCOPIC VARIABLES OF THE SYSTEM
QED scalar and pseudoscalar densities in terms of the OSEFT components
E3q ð96Þ
Vector and axial currents
VIII. CHIRAL ANOMALY IN THE PRESENCE OF A SMALL MASS TERM
OUTLOOK
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