Chiral Perturbation Theory vs. Linear Sigma Model in a Chiral Imbalance Medium

• Main Authors: Alexander Andrianov, Vladimir Andrianov, Domenec Espriu
• Format: Article
• Language: English
• Published: MDPI AG 2020-01-01
• Series: Particles
• Subjects: chiral imbalance; chiral perturbation theory; linear sigma model; charged pion decay in chiral medium; local parity breaking
• Online Access: https://www.mdpi.com/2571-712X/3/1/2
• ISSN: 2571-712X

We compare the chiral perturbation theory (ChPT) and the linear sigma model (LSM) as realizations of low energy quantum chromodynamics (QCD) for light mesons in a chirally-imbalanced medium. The relations between the low-energy constants of the chiral Lagrangian and the corresponding constants of the linear sigma model are established as well as the expressions for the decay constant of <inline-formula> <math display="inline"> <semantics> <mi>&#960;</mi> </semantics> </math> </inline-formula>-meson in the medium and for the mass of the <inline-formula> <math display="inline"> <semantics> <msub> <mi>a</mi> <mn>0</mn> </msub> </semantics> </math> </inline-formula>. In the large <inline-formula> <math display="inline"> <semantics> <msub> <mi>N</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> count taken from QCD the correspondence of ChPT and LSM is remarkably good and provides a solid ground for the search of chiral imbalance manifestations in pion physics. A possible experimental detection of chiral imbalance (and therefore a phase with local parity breaking) is outlined in the charged pion decays inside the fireball.