Emergent spin polarization from $ρ$ meson condensation in rotating hadronic matter

TL;DR

This work addresses whether a spin-1 $ρ$ meson gas in dense, rotating hadronic matter can undergo Bose-Einstein condensation and how rotation affects spin polarization. The authors formulate a rotating relativistic Bose-Einstein framework in a cylindrical volume with energy shifts $ε_l = \\sqrt{k_r^2 + k_z^2 + m^2} - (l+s)ω$, define $n_{tot}$, $n_{ex}$, $n_{cond}$ and the BEC condition $μ=ε_{min}$ via $n_{ex}(T_c, μ=ε_{min}) = n_{tot}$, and compute spin-resolved densities and polarization $P_ρ=(n_{↑} - n_{↓})/(n_{↑} + n_{↓})$. They find that rotation lowers the effective chemical potential, increases the BEC transition temperature $T_c$ (with a non-monotonic dependence on $ω$ due to centrifugal terms), and induces strong spin alignment in both the condensate and thermal components, with polarization growing as the condensate fraction grows. The results imply potential experimental signatures in heavy-ion collisions (dilepton angular distributions) and astrophysical consequences for rotating neutron stars, such as anisotropic pressure and a softened equation of state. The study uses a non-interacting model as a baseline and suggests extensions to include medium effects and spatial inhomogeneity.

Abstract

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.

Figures (3)

• Figure 1: (Colour Online) The left panel shows the condensate fraction as a function of temperature, and the right panel demonstrates the temperature dependence of chemical potential for the three distinct values of $\omega$.
• Figure 2: (Colour Online) The variation of BEC transition temperature (left panel) and transition chemical potential (right panel) with rotation ($\omega$) for a constant rho meson density.
• Figure 3: (Colour Online) In the upper panels, the spin polarization of thermal (left) and condensate rho mesons (right) as a function of temperature is shown for different values of $\omega$. In the lower panel, the same is shown as a function of the condensate fraction.