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arXiv 2011.10987hep-phnucl-th
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转动下矢量介子的质量分裂和自发自旋极化

Mass splitting of vector meson and spontaneous spin polarization under rotation

Minghua Wei, Yin Jiang, Mei Huang

摘要:

本文在2味Nambu-Jona-Lasinio模型的框架下研究了转动对标量介子和矢量介子质量的影响。转动的存在导致了一个冗长的夸克传播子和相应的极化函数。应用无规相近似,数值计算了介子质量。结果表明,在角速度$ω$下,标量和赝标介子质量的行为与有限化学势下的行为相似,都依赖于组分夸克质量的行为,反映了与手征对称性有关的性质.而矢量介子$ρ$的质量与转动有更深层次的关系。经过繁琐的计算,发现在低温和小化学势下,转动矢量介子的自旋分量$s_z=0,\pm 1$的质量表现出非常简单的质量分裂关系$m_ρ^{s_z}(ω)=m_ρ(ω=0)-ωs_z$,类似于带电介子在磁场下的塞曼分裂.特别注意到自旋分量$s_z=1$矢量介子$ρ$的质量随$ω$线性减小,在$ω_c=m_ρ(ω=0)$处质量为零,这表明系统将发生$s_z=1$矢量介子凝聚,系统在旋转作用下将自发自旋极化.

英文摘要:

In the present paper, we study the effect of the rotation on the masses of scalar meson as well as vector meson in the framework of 2-flavor Nambu--Jona-Lasinio model. The existence of rotation causes a tedious quark propagator and corresponding polarization function. Applying the random phase approximation, the meson mass is calculated numerically. It is found that the behavior of scalar and pseudoscalar meson masses under the angular velocity $ω$ is similar to that at finite chemical potential, both rely on the behavior of constituent quark mass and reflect the property related to the chiral symmetry. However, masses of vector meson $ρ$ have more profound relation with rotation. After tedious calculation, it turns out that at low temperature and small chemical potenial, the mass for spin component $s_z=0,\pm 1$ of vector meson under rotation shows very simple mass splitting relation $m_ρ^{s_z}(ω)=m_ρ(ω=0)-ωs_z$, similar to the Zeeman splitting of charged meson under magnetic fields. Especially it is noticed that the mass of spin component $s_z=1$ vector meson $ρ$ decreases linearly with $ω$ and reaches zero at $ω_c=m_ρ(ω=0)$, this indicates the system will develop $s_z=1$ vector meson condensation and the system will be spontaneously spin polarized under rotation.

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