Consistent parameter fixing in the quark-meson model with vacuum fluctuations
Consistent parameter fixing in the quark-meson model with vacuum fluctuations
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DOI：
10.1103/physrevd.94.034023
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发表时间：
2016-06
影响因子：
5
通讯作者：
S. Carignano;M. Buballa;W. Elkamhawy
中科院分区：
文献类型：
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作者：
S. Carignano;M. Buballa;W. Elkamhawy
我们在扩展的平均场近似下重新讨论了夸克-介子模型的重整化公式，其中包含了真空夸克涨落。在给定的截止尺度下，模型参数通过拟合真空量来固定，通常包括σ介子质量${m}_{\ensuremath{\sigma}}$和π介子衰变常数${f}_{\ensuremath{\pi}}$。在大多数出版物中，后者被识别为sigma场的期望值，而对于${m}_{\ensuremath{\sigma}}$，则采用曲率质量。然而，当夸克环被包括在内时，这个规定是不一致的，正确的识别涉及重整化π衰变常数和σ极质量。本文研究了在有限温度和有限化学势下，参数固定方案对模型相结构的影响。尽管在两个方案的模型参数之间的差异很大，我们发现，在均匀的物质上的相图的影响是相对较小的。另一方面，对于非均匀相，选择合适的重整化公式是至关重要的。特别是，我们表明，如果不考虑重整化对π衰变常数的影响，该模型甚至没有提出一个定义良好的重整化极限时，截止发送到无穷大。
We revisit the renormalization prescription for the quark-meson model in an extended mean-field approximation, where vacuum quark fluctuations are included. At a given cutoff scale the model parameters are fixed by fitting vacuum quantities, typically including the sigma-meson mass ${m}_{\ensuremath{\sigma}}$ and the pion decay constant ${f}_{\ensuremath{\pi}}$. In most publications the latter is identified with the expectation value of the sigma field, while for ${m}_{\ensuremath{\sigma}}$ the curvature mass is taken. When quark loops are included, this prescription is however inconsistent, and the correct identification involves the renormalized pion decay constant and the sigma pole mass. In the present article we investigate the influence of the parameter-fixing scheme on the phase structure of the model at finite temperature and chemical potential. Despite large differences between the model parameters in the two schemes, we find that in homogeneous matter the effect on the phase diagram is relatively small. For inhomogeneous phases, on the other hand, the choice of the proper renormalization prescription is crucial. In particular, we show that if renormalization effects on the pion decay constant are not considered, the model does not even present a well-defined renormalized limit when the cutoff is sent to infinity.