Investigation of meson loop effects in the Nambu-Jona-Lasinio model
Investigation of meson loop effects in the Nambu-Jona-Lasinio model
复制标题
Nambu-Jona-Lasinio 模型中介子环效应的研究
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
M. Oertel
中科院分区：
文献类型：
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作者：
M. Oertel
研究了介子涨落对Nambu-Jona-Lasinio模型中量的影响。为此，引入了不同的近似方案，以保证与手征对称性所导出的几个关系的一致性。特别是，这指的是戈德斯通定理，该定理指出，如果拉格朗日的对称性自发破缺，就存在无质量玻色子，在我们的例子中是介子。Gell-Mann-Okers-Renner关系描述了小电流夸克质量时的介子质量行为，它显式破坏了手征对称性。提出了三种不同的方案。它们是将环和包含在所谓的“Phi可导数方法”中，将1/nC的幂展开，并在有效作用量形式中展开至单介子回路。由于后两种格式是用来显式计算的，因此明确地证明了Goldstone定理和Gell-Mann-Okers-Renner关系在这两种格式中成立。研究了介子圈效应对夸克凝聚态、介子质量、介子衰变常数以及Rho介子和Sigma介子性质的影响。首先，我们专注于确定一组一致的参数。在1/Nc展开方案中，可以找到一组参数，它允许同时描述介子扇区中的量和与Rho介子有关的量，但在有效作用的展开中，这是不可能的。文中还讨论了Sigma介子的结果。在这里，与Rho介子类似，介子中间态是必不可少的。此外，还讨论了我们的模型与强子模型的关系。在本文的最后部分，我们研究了非零温度下夸克凝聚体的行为。在低温区，可以得到与模型一致的低阶独立手征微扰理论结果。微扰1/NC展开方案不允许在较高温度下考察手征相变，而这在介子环近似方案中是可能的。发现了一级相变。
The influence of mesonic fluctuations on quantities in the Nambu--Jona-Lasinio model are examined. To that end different approximation schemes are introduced which guarantee the consistency with several relations following from chiral symmetry. In particular this refers to the Goldstone theorem, which states the existence of massless bosons, in our case pions, if the symmetry of the Lagrangian is spontaneously broken. The Gell-Mann--Oakes--Renner relation describes the behavior of the pion mass for small current quark masses, which explicitly break chiral symmetry. Three different schemes are presented. These are the inclusion of the ring sum in a so-called ``Phi-derivable-method'', an expansion in powers of 1/Nc and an expansion up to one-meson loop in the effective action formalism. Since the two latter schemes are used for explicit calculations, it is explicitely proved that the Goldstone theorem as well as the Gell-Mann--Oakes--Renner relation hold within those schemes. The influence of meson-loop effects on the quark condensate, the pion mass, the pion decay constant and properties of rho- and sigma-meson are investigated. First we focus on the determination of a consistent set of parameters. In the 1/Nc-expansion scheme it is possible to find a set of parameters which allows to simultaneously describe the quantities in the pion sector and those related to the rho-meson, whereas this turns out to be not possible within the expansion of the effective action. Results for the sigma-meson are also discussed. Here, similarly to the rho-meson, mesonic intermediate states are essential. Besides, the relation of our model to hadronic models is discussed. In the last part of this thesis the behavior of the quark condensate at nonzero temperature is studied. In the low-temperature region agreement with the model independent chiral perturbation theory result in lowest order can be obtained. The perturbative 1/Nc-expansion scheme does not allow for an examination of the chiral phase transition at higher temperatures, whereas this is possible within the meson-loop approximation scheme. A first order phase transition is found.