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arXiv 1003.3827hep-ph
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Bethe-Salpeter方程框架下重量子态的谱及相关波函数的混合

Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation

Chao-Hsi Chang, Guo-Li Wang

摘要:

考虑到重夸克偶素的某些激发态(粲偶素和底偶素)在实验观测中仍然缺失以及束缚态相关波函数的潜在应用,我们在Bethe-Salpeter(B.S.)一个适当的QCD启发的内核方程。这种与非相对论夸克模型势有关的重夸克偶素核是瞬时的,因此我们称之为B. S。方程作为BS-In方程贯穿全文。特别是,一种新的方法来解决B.提出了一个不同于传统的方程,它不仅重新产生了已知的重夸克偶素谱,而且引入了一个重要的问题,即,所获得的方程的解“自动地”包括“精细”、“超精细”分裂和波函数混合,例如在$J^{PC}=1^{--}$状态中的$S-D$波混合,对粲偶素、底偶素等的$J^{PC}=2^{++}$态进行了$P-F$波混频实验,指出了测试混合波的最佳地点可能是$Z$工厂($e^+e^-$对撞机在$Z$ -玻色子极运行,光度极高)。

英文摘要:

Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) still missing in experimental observations and potential applications of the relevant wave functions of the bound states, we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to potential of non-relativistic quark model, is instantaneous, so we call the corresponding B.S. equation as BS-In equation throughout the paper. Particularly, a new way to solve the B.S. equation, which is different from the traditional ones, is proposed here, and with it not only the known spectrum for the heavy quarkonia is re-generated, but also an important issue is brought in, i.e., the obtained solutions of the equation `automatically' include the 'fine', 'hyperfine' splittings and the wave function mixture, such as $S-D$ wave mixing in $J^{PC}=1^{--}$ states, $P-F$ wave mixing in $J^{PC}=2^{++}$ states for charmonium and bottomonium etc. It is pointed out that the best place to test the wave mixture probably is at $Z$-factory ($e^+e^-$ collider running at $Z$-boson pole with extremely high luminosity).

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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