$σ$共振在手征微扰论收敛性中的作用
Role of the $σ$-resonance in determining the convergence of chiral perturbation theory
摘要：
无量纲参数$ξ= M_π^2/(16 π^2 F_π^2)$，其中$F_π$是π介子衰变常数，$M_π$是π介子质量，有望控制适用于QCD的手征微扰理论的收敛。在这里，我们证明了一个强耦合格点规范理论模型具有相同的对称性作为两味QCD，但与一个更轻的$σ$共振是不同的。我们的模型使我们能够有效地研究作为$ξ$函数的手征微扰理论的收敛性。我们首先确认，领先的低能量常数出现在手征拉格朗日是相同的计算时，从$p$ -政权和$ε$ -政权的预期。然而，$ξ\lesssim 0.002$是必要的1环手性微扰理论预测的数据在1%以内。对于$ξ> 0.0035$的数据开始显着偏离1环手性微扰理论的预测。我们认为，这种质的变化是由于存在的光$σ$共振在我们的模型。我们的研究结果可能对格点QCD研究有用。
英文摘要：
The dimensionless parameter $ξ= M_π^2/(16 π^2 F_π^2)$, where $F_π$ is the pion decay constant and $M_π$ is the pion mass, is expected to control the convergence of chiral perturbation theory applicable to QCD. Here we demonstrate that a strongly coupled lattice gauge theory model with the same symmetries as two-flavor QCD but with a much lighter $σ$-resonance is different. Our model allows us to study efficiently the convergence of chiral perturbation theory as a function of $ξ$. We first confirm that the leading low energy constants appearing in the chiral Lagrangian are the same when calculated from the $p$-regime and the $ε$-regime as expected. However, $ξ\lesssim 0.002$ is necessary before 1-loop chiral perturbation theory predicts the data within 1%. For $ξ> 0.0035$ the data begin to deviate dramatically from 1-loop chiral perturbation theory predictions. We argue that this qualitative change is due to the presence of a light $σ$-resonance in our model. Our findings may be useful for lattice QCD studies.
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