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arXiv 1201.2860nucl-thhep-ph
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在阿贝尔Nambu-Jona-Lasinio模型中冷密夸克物质的最佳微扰的类矢量贡献

Vector-like contributions from Optimized Perturbation in the Abelian Nambu--Jona-Lasinio model for cold and dense quark matter

Jean-Loic Kneur, Marcus Benghi Pinto, Rudnei O. Ramos, Ederson Staudt

备注：
9 pages, 5 figures. In press Int. J. Mod. Phys. E (2012)
发表信息：
Int. J. Mod. Phys. E 21, 1250017 (2012)
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摘要：

用优化微扰理论（OPT）方法对标准Abel Nambu-Jona-Lasinio模型进行了双圈修正。这些贡献改进了通常的平均场和Hartree-Fock的结果，产生了一个$1/N_c$抑制项，它只在有限的化学势的贡献。我们采取零温度极限观察，在OPT，手征对称性恢复在一个较高的化学势$μ$，而由此产生的状态方程是刚性比平均场时得到的标准版本的模型。为了理解这些有限的$N_c$贡献的物理性质，我们进行了数值分析，表明OPT量子校正模仿有效的排斥矢量-矢量相互作用的贡献。我们还推导出质量间隙的简单解析近似，在百分比水平上精确，与通过额外矢量通道扩展到OPT的平均场近似相匹配。对于$μ\gtrsim μ_c$，匹配OPT的有效矢量耦合在数值上接近（对于阿贝尔模型）Fierz诱导的Hartree-Fock值$G/(2N_c)$，其中$G$是标量耦合，然后以明确的方式随着$μ$而增加。

英文摘要：

Two-loop corrections for the standard Abelian Nambu-Jona-Lasinio model are obtained with the Optimized Perturbation Theory (OPT) method. These contributions improve the usual mean-field and Hartree-Fock results by generating a $1/N_c$ suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential $μ$, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite $N_c$ contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector-vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For $μ\gtrsim μ_c$ the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree-Fock value $G/(2N_c)$, where $G$ is the scalar coupling, and then increases with $μ$ in a well-determined manner.

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