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arXiv 0907.5084hep-phnucl-th
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矢量介子线性西格玛模型中核子手征伴子的真空唯象

Vacuum phenomenology of the chiral partner of the nucleon in a linear sigma model with vector mesons

Susanna Gallas, Francesco Giacosa, Dirk H. Rischke

备注：
16 pages, 2 figures. To appear in Phys. Rev. D
发表信息：
Phys.Rev.D82:014004,2010
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摘要：

研究了具有整体手征$U(2)_{R} \times U(2)_{L}$对称性的线性西格玛模型.介子的自由度是标准标量和赝标量介子以及矢量和轴矢量介子。重子的自由度是核子$N$和它的手征伙伴$N^{*}$，后者通常用N（1535）表示。手征合作伙伴被纳入所谓的镜像分配，其中核子质量不仅是由手征凝聚体，但也由手征不变的质量项，$m_{0}$。（轴向）矢量场的存在修改了核子$g_{A}^{N}$及其伙伴$g_{A}^{N^{*}}$的轴向耦合常数的表达式。使用衰变$N^{*} \to N π$和$a_{1} \toπγ$的实验数据，以及$g_{A}^{N^{*}}$的晶格结果，我们推断出$m_{0}\sim500$ MeV，即，相当数量的核子质量来自手征凝聚体以外的源。我们测试我们的模型通过评估衰变$N^{*} \to N η$和s波核子-π介子散射长度$a_{0}^{(\pm)}$。

英文摘要：

We investigate a linear sigma model with global chiral $U(2)_{R} \times U(2)_{L}$ symmetry. The mesonic degrees of freedom are the standard scalar and pseudoscalar mesons and the vector and axial-vector mesons. The baryonic degrees of freedom are the nucleon, $N$, and its chiral partner, $N^{*}$, which is usually identified with N(1535). The chiral partner is incorporated in the so-called mirror assignment, where the nucleon mass is not solely generated by the chiral condensate but also by a chirally invariant mass term, $m_{0}$. The presence of (axial-) vector fields modifies the expressions for the axial coupling constants of the nucleon, $g_{A}^{N}$, and its partner, $g_{A}^{N^{*}}$. Using experimental data for the decays $N^{*} \to N π$ and $a_{1} \toπγ$, as well as lattice results for $g_{A}^{N^{*}}$ we infer $m_{0}\sim500$ MeV, i.e., an appreciable amount of the nucleon mass originates from sources other than the chiral condensate. We test our model by evaluating the decay $N^{*} \to N η$ and the s-wave nucleon-pion scattering lengths $a_{0}^{(\pm)}$.

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