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arXiv 1904.04136hep-lathep-ph
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格点量子色动力学中耦合$πω$、$πϕ$散射的$b_1$共振

The $b_1$ resonance in coupled $πω$, $πϕ$ scattering from lattice QCD

Antoni J. Woss, Christopher E. Thomas, Jozef J. Dudek, Robert G. Edwards, David J. Wilson

发表信息：
Phys. Rev. D 100, 054506 (2019)
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摘要：

本文首次采用格点量子色动力学计算了耦合$πω$和$πϕ$散射，将耦合$S$和$D$波$πω$合并到$J^P=1^+$中.通过对两点相关函数矩阵的变分分析，计算了三个体积中的夸克体积谱，这些函数使用类似于单介子、双介子和三介子结构的大基算子，轻夸克质量对应于$m_π\approx 391$ MeV的π介子质量。利用有限体积能量离散谱与无限体积散射振幅之间的关系，我们发现了一个窄轴矢量共振（$J^{PC}=1^{+-}$），它是$b_1$介子的类似物，质量为$m_{R}\approx1380$ MeV，宽度为$Γ_{R}\approx 91$ MeV.发现共振主要耦合到$S$波$πω$，与$D$波$πω$的耦合受到很大抑制，与$πϕ$的耦合可以忽略不计，与“OZI规则”一致。在$πϕ$中未观察到共振行为，表明不存在$πJ/ψ$中要求保护的$Z_c$的推定低质量$Z_s$类似物。为了最低限度地提出了一个单一的三通道散射矩阵的内容，我们介绍了传统的两通道Stapp参数化的$n$通道推广。

英文摘要：

We present the first lattice QCD calculation of coupled $πω$ and $πϕ$ scattering, incorporating coupled $S$ and $D$-wave $πω$ in $J^P=1^+$. Finite-volume spectra in three volumes are determined via a variational analysis of matrices of two-point correlation functions, computed using large bases of operators resembling single-meson, two-meson and three-meson structures, with the light-quark mass corresponding to a pion mass of $m_π\approx 391$ MeV. Utilizing the relationship between the discrete spectrum of finite-volume energies and infinite-volume scattering amplitudes, we find a narrow axial-vector resonance ($J^{PC}=1^{+-}$), the analogue of the $b_1$ meson, with mass $m_{R}\approx1380$ MeV and width $Γ_{R}\approx 91$ MeV. The resonance is found to couple dominantly to $S$-wave $πω$, with a much-suppressed coupling to $D$-wave $πω$, and a negligible coupling to $πϕ$ consistent with the `OZI rule'. No resonant behavior is observed in $πϕ$, indicating the absence of a putative low-mass $Z_s$ analogue of the $Z_c$ claimed in $πJ/ψ$. In order to minimally present the contents of a unitary three-channel scattering matrix, we introduce an $n$-channel generalization of the traditional two-channel Stapp parameterization.

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