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arXiv 1003.4934hep-phnucl-th
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具有矢量介子和整体手征不变性的线性西格玛模型中介子的真空性质

Vacuum Properties of Mesons in a Linear Sigma Model with Vector Mesons and Global Chiral Invariance

Denis Parganlija, Francesco Giacosa, Dirk H. Rischke

备注：
22 pages, 6 figures
发表信息：
Phys.Rev.D82:054024,2010
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摘要：

本文提出了一个具有整体手征对称性和矢量及轴矢量介子的双味线性西格玛模型。我们计算了标量、矢量和轴矢量介子的π-π散射长度和衰变宽度。它表明，矢量和轴矢量介子自由度在这些低能量过程中起着重要的作用，一个合理的理论描述，需要全局手征不变的矢量介子质量项以外的其他条款。介子真空现象学的一个重要问题是物理标量f0（600）和a0（980）介子的夸克含量。我们调查这个问题，通过分配夸克-反夸克σ和a0状态的我们的模型与这些物理介子。我们通过与实验数据的详细比较表明，这种情况下可以描述所有的真空特性研究这里除了衰减宽度的西格玛，这原来是太小了。我们还研究了标量介子的另一种指定f0（1370）和a0（1450）。在这种情况下，衰变宽度与实验值一致，但π-π散射长度$a_{0}^{0}$太小。这表明有必要通过额外的标量自由度来扩展我们的模型。

英文摘要：

We present a two-flavour linear sigma model with global chiral symmetry and vector and axial-vector mesons. We calculate pion-pion scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f0(600) and a0(980) mesons. We investigate this question by assigning the quark-antiquark sigma and a0 states of our model with these physical mesons. We show via a detailed comparison with experimental data that this scenario can describe all vacuum properties studied here except for the decay width of the sigma, which turns out to be too small. We also study the alternative assignment f0(1370) and a0(1450) for the scalar mesons. In this case the decay width agrees with the experimental value, but the pion-pion scattering length $a_{0}^{0}$ is too small. This indicates the necessity to extend our model by additional scalar degrees of freedom.

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