双夸克 - 三夸克图景中四夸克重五夸克态\(bb\bar{u}cc\)的\(λ\)、\(ρ\)和\(σ\)雷吉轨迹
$λ$, $ρ$, and $σ$ Regge trajectories for the quadruply heavy pentaquark $bb\bar{u}cc$ in the diquark-triquark picture
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中文总结 AI 辅助
研究四夸克重五夸克态\(bb\bar{u}cc\)的雷吉轨迹，利用双夸克和三夸克轨迹关系提出其轨迹关系，研究了四组轨迹，表明考虑内部结构对构建轨迹很关键，给出了不同轨迹行为及对激发态质量的粗略估计。
中文摘要 AI 辅助
目前仍缺乏对四夸克重五夸克态的四组雷吉轨迹的系统研究。利用双夸克和三夸克雷吉轨迹关系，我们提出了四夸克重五夸克态\({bb\bar{u}cc}\)的雷吉轨迹关系。研究了四组雷吉轨迹，即\(\lambda\)、\(\rho_1\)、\(\rho_2\)和\(\sigma\)轨迹。结果表明，考虑五夸克态的内部结构和子结构对于构建\(\rho_1\)、\(\rho_2\)和\(\sigma\)轨迹是必不可少的。此外，双夸克1、三夸克和双夸克2（嵌入在三夸克中）的雷吉轨迹与\(\rho_1\)、\(\rho_2\)和\(\sigma\)轨迹并非一一对应，但它们支配着各自轨迹的行为。对于两种构型\((bb)(\bar{u}(cc))\)和\((cc)(\bar{u}(bb))\)，\(\lambda\)、\(\rho_1\)和\(\sigma\)轨迹表现出\(M{\sim}x^{2/3}\)的行为，而\(\rho_2\)轨迹表现出\(M{\sim}\sqrt{x}\)的行为。双夸克和三夸克雷吉轨迹的函数行为为拟合五夸克雷吉轨迹提供了指导。此外，我们还对\(\lambda\)、\(\rho_1\)、\(\rho_2\)和\(\sigma\)激发态的自旋平均质量进行了粗略估计。
英文摘要
Systematic investigations of four series of Regge trajectories for quadruply heavy pentaquarks are still lacking. Using the diquark and triquark Regge trajectory relations, we propose the Regge trajectory relations for the quadruply heavy pentaquark ${bb\bar{u}cc}$: $M=2m_{b}+2m_{c}+m_{u}+5C/2 +β_{x_λ}(x_λ+c_{0x_λ})^{2/3} +β_{x_{ρ_1}}(x_{ρ_1}+c_{0x_{ρ_1}})^{2/3}+β_{x_{ρ_2}}\sqrt{x_{ρ_2}+c_{0x_{ρ_2}}} +β_{x_σ}(x_σ+c_{0x_σ})^{2/3}$. Four series of Regge trajectories, namely the $λ$-, $ρ_1$-, $ρ_2$-, and $σ$-trajectories, are investigated. We demonstrate that accounting for the internal structure and substructure of pentaquarks is indispensable for constructing the $ρ_1$-, $ρ_2$-, and $σ$-trajectories; without such structural considerations, functional form and trajectory parameters can only be obtained via pure fitting against theoretical or experimental data. We further prove that the Regge trajectories of diquark 1, triquark, and diquark 2 (embedded within the triquark) do not correspond one-to-one to the $ρ_1$-, $ρ_2$-, and $σ$-trajectories. Nevertheless, these trajectories govern the behaviors of the respective $ρ_1$-, $ρ_2$-, and $σ$-trajectories. For both configurations $(bb)(\bar{u}(cc))$ and $(cc)(\bar{u}(bb))$, the $λ$-, $ρ_1$-, and $σ$-trajectories exhibit behavior of $M{\sim}x^{2/3}$ ($x=n_{r_1},n_{r_3},l_1,l_3,N_{r},L$), whereas the $ρ_2$-trajectories exhibit behavior of $M{\sim}\sqrt{x}$ ($x=n_{r_2},\,l_2$). The functional behavior of Regge trajectories for diquarks and triquark offers guidance for fitting the pentaquark Regge trajectories. Additionally, we provide rough estimates for spin-averaged masses of the $λ$-, $ρ_1$-, $ρ_2$-, and $σ$-excited states.
发表机构
- School of Physics and Electronic Engineering, Shanxi Normal University（山西师范大学物理与电子工程学院）
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