无自旋Salpeter方程描述的四夸克态质量谱
Mass spectra of Tetraquark States from the Spinless Salpeter Equation
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中文总结 AI 辅助
本研究采用无自旋Salpeter方程结合Cornell势，构建双夸克-反双夸克模型，通过变分法等计算重四夸克质量，其结果与实验观测合理吻合，助力理解重四夸克结构与动力学。
中文摘要 AI 辅助
本研究采用无自旋Salpeter方程结合Cornell势，对四夸克态的质量谱展开研究。通过变分法推导得到解析波函数，进而得出束缚态的特定质量公式。在组分双夸克-反双夸克模型框架下，探究重四夸克态的质量谱，其中双夸克与反双夸克组分间的相互作用由Cornell势描述。为考虑相对论效应，采用一阶微扰理论纳入相对论动能算子展开产生的领头阶动能修正项；同时运用变分法确定基态质量，通过最小化系统能量得到最优变分参数β，再以此确定更高激发态的质量。我们在一系列强耦合常数取值范围内，系统计算了多个实验观测到及理论预言的四夸克候选态的质量。结果显示，计算得到的四夸克质量对模型参数具有敏感性，该模型给出的理论质量预测与这些奇特强子态的实验观测结果合理吻合，为深入理解重四夸克的内部结构与动力学提供了支撑。
英文摘要
The mass spectrum of tetraquark states is examined using the spinless Salpeter equation alongside the Cornell potential. Analytical wave functions are derived through a variational approach, resulting in a specific mass formula for the bound states. This study investigates the mass spectra of heavy tetraquark states within a constituent diquark-antidiquark model. We employ a spinless Salpeter equation framework, incorporating the Cornell potential to describe the interaction between the diquark and antidiquark constituents. To account for relativistic effects, we utilize first-order perturbation theory to include the leading-order kinetic energy corrections arising from the expansion of the relativistic kinetic energy operator. A variational approach is adopted to determine the ground state masses, where the optimal variational parameter $β$ is found by minimizing the system's energy and then for higher states. We systematically calculate the masses of several experimentally observed and predicted tetraquark candidates, across a range of strong coupling constant values. Our results demonstrate a sensitivity of the calculated tetraquark masses to, and the model provides theoretical mass predictions that are in reasonable agreement with experimental observations for these exotic hadronic states. This work contributes to a deeper understanding of the internal structure and dynamics of heavy tetraquarks.
