Ideal relativistic fluid limit for a medium with polarization

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQWe use Lagrangian effective field theory techniques to construct the equations of motion for an ideal relativistic fluid of which the constituent degrees of freedom have microscopic polarization. We discuss the meaning of such a system and argue that it is the first term in the Effective Field Theory ( EFT) appropriate for describing polarization observables in heavy ion collisions, such as final-state particle polarization and chiral magnetic and vortaic effects. We show that this system will generally require nondissipative dynamics at higher order in the gradient than second order, leading to potential stability issues known with such systems. We comment on the significance of this in the light of conjectured lower limits on viscosity.96519FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ2014/13120-7147435/2014-5301996/2014-8G.T. acknowledges support from FAPESP processo Grant No. 2014/13120-7 and CNPQ Bolsa de produtividade 301996/2014-8. L.T. was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Award No. DE-SC0004286 and Polish National Science Center Grant No. DEC-2012/06/A/ST2/00390. D.M. would like to acknowledge CNPQ graduate Fellowship No. 147435/2014-5. Parts of this work were done when L.T. visited Campinas on FAEPEX Fellowship No. 2020/16 as well as when G.T. participated in the INT workshop "Exploring the QCD Phase Diagram through Energy Scans." We thank FAEPEX and the INT organizers for the support provided. We wish to thank Miklos Gyulassy for enlightening discussions that posed the conceptual challenges that eventually led to this work and Mike Lisa for showing us experimental literature and useful discussions