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arXiv 2405.00525hep-ph
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$T_{cc}^{+}$ 态的同位旋破坏效应与三体衰变

Isospin violation effect and three-body decays of the $T_{cc}^{+}$ state

Zhi-Feng Sun, Ning Li, Xiang Liu

AI总结:

本研究基于介子交换方法探讨了 $T_{cc}^+$ 态的同位旋破坏效应与三体衰变,通过求解 Schrödinger 方程确定了其波函数和衰变宽度,结果支持 $T_{cc}^+$ 是 $D^*D$ 的强子分子。

摘要:

在本研究中,我们对 LHCb 合作组于 2021 年观测到的 $T_{cc}^+$ 态进行了研究。在使用 One-Boson-Exchange Potential Model 获取有效势时,我们采用了指数形状因子,并发现 $π$、$ρ$ 和 $ω$ 交换的贡献在短程和中程范围内相当,而在长程范围内 $π$ 交换的贡献占主导地位。基于 $T_{cc}^+$ 是 $D^*D$ 的弱束缚态的假设,我们使用介子交换方法研究了其三体衰变。考虑到 $D^{*+}D^0$ 和 $D^{*0}D^+$ 的阈值之间的差异甚至大于 $T_{cc}^+$ 的束缚能,同位旋破坏效应被 $T_{cc}^+$ 的小束缚能放大。通过显式地包含这种同位旋破坏效应,我们通过求解 Schrödinger 方程得到,对于 $T_{cc}^+$,同位旋标量分量的概率约为 $91\%$,而同位旋矢量分量的概率约为 $9\%$。使用 $T_{cc}^+$ 质量的实验值作为输入,我们获得了 $T_{cc}^+$ 的波函数,并进一步通过三体强子衰变和辐射衰变获得了其宽度。我们获得的总宽度与 LHCb 测量结果中的 unitarised Breit-Wigner profile 实验值一致。反之,当前结果支持 $T_{cc}^+$ 是 $D^*D$ 的强子分子的结论。

英文摘要:

In this work, we make a study of $T_{cc}^+$ state observed by the LHCb collaboration in 2021. In obtaining the effective potentials using the One-Boson-Exchange Potential Model we use an exponential form factor, and find that in the short and medium range, the contributions of the $π$, $ρ$ and $ω$ exchanges are comparable while in the long range the pion-exchange contribution is dominant. Based on the assumption that $T_{cc}^+$ is a loosely bound state of $D^*D$, we focus on its three-body decay using the meson-exchange method. Considering that the difference between the thresholds of $D^{*+}D^0$ and $D^{*0}D^+$ is even larger than the binding energy of $T_{cc}^+$, the isospin-breaking effect is amplified by the small binding energy of $T_{cc}^+$. Explicitly including such an isospin-breaking effect we obtain, by solving the Schrödinger equation, that the probability of the isoscalar component is about $91\%$ while that of the isovector component is around $9\%$ for $T_{cc}^+$. Using the experimental value of the mass of $T_{cc}^+$ as an input, we obtain the wave function of $T_{cc}^+$ and further obtain its width via the three-body hadronic as well as the radiative decays. The total width we obtain is in agreement with the experimental value of the LHCb measurement with a unitarised Breit-Wigner profile. Conversely, the current results support the conclusion that $T_{cc}^+$ is a hadronic molecule of $D^*D$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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