2020/02/29 by D. Espriu, Domènec Espriu, A. Gómez Nicola +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Chiral anomaly #Chiral model #Chiral perturbation theory #Cosmology and Gravitation Theories #Lagrangian #Lattice (music) #Observable #Parity (physics) #Pion #Quantum Chromodynamics and Particle Interactions #Topological quantum number #hep-ph
paper · pdf · doi:10.1007/jhep06(2020)062
28 pages, 9 figures. Version accepted in JHEP. References, comments, section 5F and Figs.8,9 added
openalex created_date 2020/03/06 · arxiv created 2020/06/09 · openalex publication_date 2020/06/09 · arxiv updated 2020/07/15 · openalex updated_date 2026/08/05
A bstract We construct the most general low-energy effective lagrangian including local parity violating terms parametrized by an axial chemical potential or chiral imbalance μ 5 , up to O(p4) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mfenced> </mml:math> order in the chiral expansion for two light flavours. For that purpose, we work within the Chiral Perturbation Theory framework where only pseudo-NGB fields are included, following the external source method. The O(p2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mfenced> </mml:math> lagrangian is only modified by constant terms, while the O(p4) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mfenced> </mml:math> one includes new terms proportional to μ52 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>μ</mml:mi> <mml:mn>5</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> and new low-energy constants (LEC), which are renormalized and related to particular observables. In particular, we analyze the corrections to the pion dispersion relation and observables related to the vacuum energy density, namely the light quark condensate, the chiral and topological susceptibilities and the chiral charge density, providing numerical determinations of the new LEC when possible. In particular, we explore the dependence of the chiral restoration temperature T c with μ 5 . An increasing T c ( μ 5 ) is consistent with our fits to lattice data of the ChPT-based expressions. Although lattice uncertainties are still large and translate into the new LEC determination, a consistent physical description of those observables emerges from our present work, providing a theoretically robust model-independent framework for further study of physical systems where parity-breaking effects may be relevant, such as heavy-ion collisions.