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arXiv 0801.3821nucl-thhep-ph
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关于光矢量和轴矢量介子的辐射衰变

On the radiative decays of light vector and axial-vector mesons

M. F. M. Lutz, S. Leupold

摘要:

我们研究了光矢量介子和轴矢量介子。根据强子发生猜想,这两类状态的性质是不同的。轴矢量介子是由耦合道相互作用动态生成的,其基础是用Goldstone玻色子和光矢量介子的形式写成的手征拉格朗日量。我们提出了一个新的计数方案,如果手征拉格朗日补充的约束下,从大N_c QCD的背景下的强子生成猜想。通过对矢量介子性质的系统研究,成功地检验了计数方案。利用Goldstone玻色子与矢量介子的首阶相互作用,并辅以唯象修正项,导出了轻轴矢量介子的谱。f_1(1282)、b_1(1230)、h_1(1386)、a_1(1230)和K_1(1272)介子被恢复为分子态。在此基础上,系统地计算了单圈效应对轴矢量分子到赝标或矢量介子的电磁衰变幅度的贡献。为了以透明的方式得到规范不变的结果,我们选择用反对称张量场来表示矢量粒子。它强调,有没有树级贡献的辐射衰减幅度的一个给定的状态,如果该状态是由耦合通道动力学产生的。将后者包括在内将是重复计算。目前,我们仅限于一个矢量和一个赝标介子耦合到轴矢量分子的环。我们认为,最终和预测的结果需要进一步的计算涉及中间状态与两个矢量介子。后者的相关性由我们的计数规则预测。

英文摘要:

We study the light vector and axial-vector mesons. According to the hadrogenesis conjecture the nature of the two types of states is distinct. The axial-vector mesons are generated dynamically by coupled-channel interactions based on the chiral Lagrangian written down in terms of the Goldstone bosons and the light vector mesons. We propose a novel counting scheme that arises if the chiral Lagrangian is supplemented by constraints from large-N_c QCD in the context of the hadrogenesis conjecture. The counting scheme is successfully tested by a systematic study of the properties of vector mesons. The spectrum of light axial-vector mesons is derived relying on the leading order interaction of the Goldstone bosons with the vector mesons supplemented by a phenomenology for correction terms. The f_1(1282), b_1(1230), h_1(1386), a_1(1230) and K_1(1272) mesons are recovered as molecular states. Based on those results the one-loop contributions to the electromagnetic decay amplitudes of axial-vector molecules into pseudo-scalar or vector mesons are evaluated systematically. In order to arrive at gauge invariant results in a transparent manner we choose to represent the vector particles by anti-symmetric tensor fields. It is emphasized that there are no tree-level contributions to a radiative decay amplitude of a given state if that state is generated by coupled-channel dynamics. The inclusion of the latter would be double counting. At present we restrict ourselves to loops where a vector and a pseudo-scalar meson couple to the axial-vector molecule. We argue that final and predictive results require further computations involving intermediate states with two vector mesons. The relevance of the latter is predicted by our counting rules.

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