Emergent spin polarization from ρ meson condensation in rotating hadronic matter

The behavior of vector mesons in extreme environments provides a unique probe of non-perturbative Quantum Chromodynamics. We investigate the conditions for Bose-Einstein condensation (BEC) of spin-1 ρ mesons in dense rotating hadronic matter, a regime relevant to the peripheral heavy-ion collisions and the interiors of rapidly rotating neutron stars. When the ρ meson chemical potential ( μ ρ ) approaches its effective mass ( m ρ * ), a phase transition to BEC occurs. We demonstrate that this transition is non-trivially influenced by global rotation, which couples to the spin of the ρ mesons, leading to a macroscopic spin alignment of the condensate along the axis of rotation. This interplay between condensation and rotation results in distinct polarization patterns, which can serve as a possible signature of a BEC in experiments. The results suggest that rapidly rotating neutron stars may harbor an anisotropic, spin-polarized ρ -condensed phase, which could impact their equation of state.