论文标题
仔细检查$ππ$根据最近的晶格相位移动
Scrutinizing $ππ$ scattering in light of recent lattice phase shifts
论文作者
论文摘要
在本文中，通过使用S-Matrix的新颖分散解决方案（即PKU表示）来分析$ IJ = 00、11、20 $部分波$π$π$π$π$π$π$π$π$π$π$ππ$ππ$ππ$ππ$ππ$约束状态，虚拟状态和共鸣。左手切割的贡献是由$ su（2）$手性扰动理论估计的，对$ \ Mathcal {o}（p^4）$。 Balanchandran-Nuyts-Roskies关系被认为是满足交叉对称要求的约束。据发现，Hadron Spectrum协作（HSC）以$m_π= 391 $ MEV获得的$ ij = 00 $ $ $π$π$散射相位移动揭示了有限状态极和在$ππ$阈值以下的虚拟状态极，而不仅仅是$σ$的一个绑定状态极。为了重现$m_π= 391 $ meV的晶格相移，发现$ ij = 20 $通道中的虚拟状态极是为了平衡手性振幅的左手切割效应所必需的。还对晶格结果进行了类似的讨论，并从HSC $M_π= 236 $ MEV进行了类似的讨论。极点方面的观察到的行为相对于倾斜质量的变化，可以为我们对$σ$共振的动态起源的理解提供深入的见解。
In this paper, the $IJ=00, 11, 20$ partial wave $ππ$ scattering phase shifts determined by the lattice QCD approach are analyzed by using a novel dispersive solution of the S-matrix, i.e. the PKU representation, in which the unitarity and analyticity of scattering amplitudes are automatically satisfied and the phase shifts are conveniently decomposed into the contributions of the cuts and various poles, including bound states, virtual states and resonances. The contribution of the left-hand cut is estimated by the $SU(2)$ chiral perturbation theory to $\mathcal{O}(p^4)$. The Balanchandran-Nuyts-Roskies relations are considered as constraints to meet the requirements of the crossing symmetry. It is found that the $IJ=00$ $ππ$ scattering phase shifts obtained at $m_π=391$ MeV by Hadron Spectrum Collaboration (HSC) reveal the presence of both a bound state pole and a virtual state pole below the $ππ$ threshold rather than only one bound state pole for the $σ$. To reproduce the lattice phase shifts at $m_π=391$ MeV, a virtual-state pole in the $IJ=20$ channel is found to be necessary in order to balance the left-hand cut effects from the chiral amplitudes. Similar discussions are also carried out for the lattice results with $m_π=236$ MeV from HSC. The observed behaviors of the pole positions with respect to the variation of the pion masses can provide deep insights into our understanding of the dynamical origin of $σ$ resonance.
