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arXiv 1507.02541hep-phhep-exhep-lat
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物理点上格点量子色动力学的$ρ$共振剖析

Anatomy of the $ρ$ resonance from lattice QCD at the physical point

Wei Sun, Andrei Alexandru, Ying Chen, Terrence Draper, Zhaofeng Liu, Yi-Bo Yang

备注：
7 pages, 4 figures. Considerably modified, more discussions, matching to the published version
发表信息：
Chinese Physics C 42, 063102 (2018)
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摘要：

我们提出了一种策略，以访问的$ρ$共振格点量子色动力学的$q\bar{q}$组件。通过混合作用量形式（畴壁上的重叠价），导出了不同价夸克质量下的$q\bar{q}$分量的能量，并显示出与$m_π^2$的线性关系.确定斜率为$c_1=0.505(3)\,{\rm GeV}^{-1}$，使用Feynman-Hellman定理从其提取价$πρ$ σ项为$σ_{πρ}^{(\rm val)}=9.82(6)$ MeV。在物理π介子质量下，$q\bar{q}$分量的质量被内插为$m_ρ=775.9\pm 6.0\pm 1.8$ MeV，其接近于$ρ$共振质量。我们还得到了$q\bar{q}$分量的轻子衰变常数为$f_{ρ^-}=208.5\pm 5.5\pm 0.9$ MeV，它可以通过关系式$f_ρ^{\rm exp}=\sqrt{Z_ρ}f_{ρ^\pm} $与实验值$f_ρ^{\rm exp}\approx 221$ MeV进行比较，其中$Z_ρ\approx 1.13$是由于$ρ-π$相互作用而引起的$ρ$的壳层波函数重整化.我们强调，在以$ρ$为基本自由度的有效场论研究中，首次从QCD中得到的$q\bar{q}$分量的$m_ρ$和$f_ρ$可以作为$ρ$的输入参数.

英文摘要：

We propose a strategy to access the $q\bar{q}$ component of the $ρ$ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the $q\bar{q}$ component is derived at different valence quark masses, and shows a linear dependence on $m_π^2$. The slope is determined to be $c_1=0.505(3)\,{\rm GeV}^{-1}$, from which the valence $πρ$ sigma term is extracted to be $σ_{πρ}^{(\rm val)}=9.82(6)$ MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the $q\bar{q}$ component is interpolated to be $m_ρ=775.9\pm 6.0\pm 1.8$ MeV, which is close to the $ρ$ resonance mass. We also obtain the leptonic decay constant of the $q\bar{q}$ component to be $f_{ρ^-}=208.5\pm 5.5\pm 0.9$ MeV, which can be compared with the experimental value $f_ρ^{\rm exp}\approx 221$ MeV through the relation $f_ρ^{\rm exp}=\sqrt{Z_ρ}f_{ρ^\pm} $ with $Z_ρ\approx 1.13$ being the on-shell wavefunction renormalization of $ρ$ owing to the $ρ-π$ interaction. We emphasize that $m_ρ$ and $f_ρ$ of the $q\bar{q}$ component, which are obtained for the first time from QCD, can be taken as the input parameters of $ρ$ in effective field theory studies where $ρ$ acts as a fundamental degree of freedom.

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