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Notes on chiral hydrodynamics within effective theory approach

We address the issue of evaluating chiral effects (such as the newly discovered chiral separation) in hydrodynamic approximation. The main tool we use is effective theory which defines interaction in terms of chemical potentials $μ,μ_5$. In the lowest order in $μ,μ_5$ we reproduce recent results based on thermodynamic considerations. In higher orders the results depend on details of infrared cutoff. Another point of our interest is an alternative way of the anomaly matching through introduction of effective scalar fields arising in the hydrodynamic approximation.