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arXiv 0904.4344hep-ph
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么正手征动力学中ρ和σ介子的性质

Properties of the rho and sigma Mesons from Unitary Chiral Dynamics

J. Nieves, E. Ruiz Arriola

摘要:

讨论了ρ和σ质量和宽度的手征极限。我们在SU(2)ChPT中的一个回路的逆振幅方法内工作,并分析所有手征共振在ρ通道中抵消的后果,而它们在sigma情况下不抵消,以及它们如何强烈影响后者共振的性质。我们的研究结果证实和解释的不同行为的西格玛和ρ极NC不远3,但我们扩展到非常大的NC,这两个共振的行为进行了重新分析的分析。我们注意到,共振饱和和么正化之间的一致性的相当自然的要求施加了有用的约束。通过只看ρ通道,在单共振近似下,我们发现,第一矢量和标量介子九重态的质量,在单共振近似下调用,原来是在大NC极限退化。相反,我们表明,对于足够大的NC,标量介子的演化超出了单圈反振幅方法的适用范围,如果标量通道也纳入分析,它可能会导致,在某些情况下,现象学上不一致的结果。

英文摘要:

The chiral limit of the rho and sigma masses and widths is discussed. We work within the inverse amplitude method to one loop in SU(2) ChPT and analyze the consequences that all chiral logarithms cancel out in the rho-channel, while they do not cancel for the sigma case, and how they strongly influence the properties of this latter resonance. Our results confirm and explain the different behavior of the sigma and rho poles for NC not far from 3, but we extend the analysis to very large NC, where the behavior of these two resonances is re-analyzed. We note that the rather natural requirement of consistency between resonance saturation and unitarization imposes useful constraints. By looking only at the rho-channel, and within the single resonance approximation, we find that the masses of the first vector and scalar meson nonets, invoked in the single resonance approximation, turn out to be degenerated in the large NC limit. On the contrary we show that, for sufficiently large NC, the scalar meson evolution lies beyond the applicability reach of the one-loop inverse amplitude method and if the scalar channel is also incorporated in the analysis, it may lead, in some cases, to phenomenologically inconsistent results.

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