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arXiv 0707.2402hep-lat
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晶格交错费米子的标量介子谱

Scalar Meson Spectroscopy with Lattice Staggered Fermions

Claude Bernard, Carleton DeTar, Ziwen Fu, Sasa Prelovsek

摘要:

当上夸克和下夸克足够轻时,等矢量($a_0$)和等单线态($f_0$)标量介子传播子在大距离处由两介子态支配。在格子量子色动力学的交错费米子公式中,味道对称性破缺导致了双介子态的扩散,这使得对这些通道的分析更加复杂。它们中的许多是晶格近似的非物理工件。预计它们将在连续极限消失。交错费米子第四根过程在有根交错手征微扰理论(rSXPT)中有其对应的理论。幸运的是,有根理论提供了一个严格的框架,允许分析的标量介子的耦合,只有少量的低能耦合。因此,在这种情况下的点对点标量介子的分析给出了一个有用的一致性检查的四次根程序和它的手征实现建议。通过数值模拟,我们已经测量了$a_0$和$f_0$通道中的“Asqtad”改进的交错费米子配方在晶格系综与晶格间距$a = 0.12$ fm。我们分析了这些fractionators的上下文中的rSXPT和获得的低能量的手性耦合的值是合理的一致与以前的测定。

英文摘要:

With sufficiently light up and down quarks the isovector ($a_0$) and isosinglet ($f_0$) scalar meson propagators are dominated at large distance by two-meson states. In the staggered fermion formulation of lattice quantum chromodynamics, taste-symmetry breaking causes a proliferation of two-meson states that further complicates the analysis of these channels. Many of them are unphysical artifacts of the lattice approximation. They are expected to disappear in the continuum limit. The staggered-fermion fourth-root procedure has its purported counterpart in rooted staggered chiral perturbation theory (rSXPT). Fortunately, the rooted theory provides a strict framework that permits the analysis of scalar meson correlators in terms of only a small number of low energy couplings. Thus the analysis of the point-to-point scalar meson correlators in this context gives a useful consistency check of the fourth-root procedure and its proposed chiral realization. Through numerical simulation we have measured correlators for both the $a_0$ and $f_0$ channels in the ``Asqtad'' improved staggered fermion formulation in a lattice ensemble with lattice spacing $a = 0.12$ fm. We analyze those correlators in the context of rSXPT and obtain values of the low energy chiral couplings that are reasonably consistent with previous determinations.

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