自旋-3/2重子的能量-动量张量横向分布
Transverse distributions of the energy-momentum tensor for a spin-$3/2$ baryon
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中文总结 AI 辅助
本研究针对自旋-3/2重子的能量-动量张量横向分布建立多极描述，通过弹性参考系插值，结合数值输入揭示了不同极化靶的能量、动量等分布特性。
中文摘要 AI 辅助
我们针对自旋-3/2重子的能量-动量张量横向分布，在通过纵向洛伦兹 boost 关联的参考系中建立了多极描述。在横向 Breit 参考系中，T^{00}、T^{03}和T^{33}矩阵元通过7个能量、角动量和应力的多极形状因子表示。在有限纵向动量下，我们将这三个分量的洛伦兹混合与外态的自旋-3/2 Wigner 旋转分离开来。所得弹性参考系矩阵元包含6个横向多极，其傅里叶变换定义了能量、纵向动量和纵向动量通量的分布。我们还通过光前 Rarita-Schwinger 旋量直接计算了T^{++}、T^{+-}和T^{--}。弹性参考系构造提供了从横向 Breit 参考系到无限动量参考系的连续插值。在该极限下，Wigner 旋转变为 Melosh 旋转，且主导弹性参考系矩阵元重现了对应的光前结果。以 Skyrme 模型得到的Δ重子引力形状因子作为代表性数值输入，我们发现能量分布由横向 Breit 参考系中定义的能量单极主导，且在纵向 boost 下仅微弱变化。通过 boost 混合，该单极在有限P_z时对纵向动量分布及其通量提供主导贡献。对于纵向极化的自旋-3/2靶，分布仅包含单极贡献；而横向极化靶的分布则呈现自旋相关的四极和八极形变，以及使峰值发生偏移的偶极项。
英文摘要
We develop a multipole description of transverse distributions of the energy-momentum tensor for a spin-$3/2$ baryon in frames connected by a longitudinal boost. In the transverse Breit frame, the $T^{00}$, $T^{03}$, and $T^{33}$ matrix elements are expressed through seven multipole form factors for energy, angular momentum, and stress. At finite longitudinal momentum, we factorize the Lorentz mixing of these three components from the spin-$3/2$ Wigner rotations of the external states. The resulting elastic-frame matrix elements contain six transverse multipoles, whose Fourier transforms define the distributions of energy, longitudinal momentum, and longitudinal momentum flux. We also calculate $T^{++}$, $T^{+-}$, and $T^{--}$ directly with light-front Rarita-Schwinger spinors. The elastic-frame construction provides a continuous interpolation from the transverse Breit frame to the infinite-momentum frame. In this limit, the Wigner rotation becomes the Melosh rotation, and the leading elastic-frame matrix elements reproduce the corresponding light-front results. Using the $Δ$-baryon gravitational form factors obtained in the Skyrme model as a representative numerical input, we find that the energy distribution is dominated by the energy monopole defined in the transverse Breit frame and changes only weakly under longitudinal boosts. Through boost mixing, this monopole provides the dominant contribution to the longitudinal momentum distribution and its flux at finite $P_z$. For a longitudinally polarized spin-$3/2$ target, the distributions contain only the monopole contributions, whereas those of a transversely polarized target exhibit spin-dependent quadrupole and octupole deformations and a dipole that shifts their maxima.
