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The chiral imbalance defined as a difference between the numbers of RH and LH quarks may occur in the fireball after a heavy-ion collision at high energy. It can lead to the formation of a local parity breaking LPB in a quark-hadron medium and adiabatically characterized by a topological charge and, accordingly, a topological (chiral) chemical potential $\mu_5$. In the field theory, it can be considered as a time-like axial-vector $b_\mu$ coupled to a fermion field with its zero component associated with $\mu_5$. The consistent way for the construction of the Lagrangian in the presence of constant axial-vector background has been obtained in [1, 2] for QED theory.
In this report, for the description of the properties of light vector mesons in the presence of LPB in a fireball, the vector-meson dominance model is applied in the lightest SU(2) sector. Employing the approach, developed in [1, 2], to the vector $\rho$ and $\omega$ mesons, we obtain the mass spectrum as a function of momentum and chiral chemical potential $\mu_5$. We show that in addition to the Chern–Simons term [3], splitting the transverse polarisations of the mesons, there is an additional contribution that becomes important at momentum and $\mu_5$ around a few hundred MeV.
References:
[1] J. Alfaro, A. Andrianov, M. Cambiaso, P. Giacconi and R. Soldati, Phys. Lett. B 639, 586-590 (2006), arXiv:hep-th/0604164 [hep-th].
[2] J. Alfaro, A. Andrianov, M. Cambiaso, P. Giacconi and R. Soldati, Int. J. Mod. Phys. A 25, 3271-3306 (2010), arXiv:0904.3557 [hep-th].
[3] A. Andrianov, V. Andrianov, D. Espriu and X. Planells, Phys. Lett. B 710, 230-235 (2012), arXiv:1201.3485 [hep-ph].
