Pion Condensation by Rotation in a Magnetic Field

We show that the combined effects of a rotation plus a magnetic field can cause charged pion condensation. We suggest that this phenomenon may yield to observable effects in current heavy ion collisions at collider energies, where large magnetism and rotations are expected in off-central collisions.

Figure 1

Under the action of an external magnetic field $B$, the ${\pi }^{\pm }$ undergo opposite rotations in the lowest Landau level (LLL), which is degenerate. The action of a parallel rotation ($\overrightarrow{\mathrm{\Omega }}·\overrightarrow{B}>0$) lifts the degeneracy in the LLL. The energy of the ${\pi }^{+}$ shifts down and splits away from the energy of the ${\pi }^{-}$ that shifts up. The action of an antiparallel rotation ($\overrightarrow{\mathrm{\Omega }}·\overrightarrow{B}<0$) exchanges the roles of ${\pi }^{+}$ and ${\pi }^{-}$.

Figure 2

The mean number of condensed pions ${\mathbb{N}}_{{\pi }^{+}}={\mathbb{N}}_{{\pi }^{-}}$ in the range $0.04m_{\pi }\le \mathrm{\Omega }\le 0.06m_{\pi }$, for ${\mu }_f=0.86m_{\pi }$ and $0.5m_{\pi }\le T\le 1.5m_{\pi }$.