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arXiv 2003.10974hep-lathep-phnucl-th
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将相对论量子化条件推广到所有三π介子的同位旋通道

Generalizing the relativistic quantization condition to include all three-pion isospin channels

Maxwell T. Hansen, Fernando Romero-López, Stephen R. Sharpe

备注：
46 pages, 4 figures. Updated to match erratum published in JHEP. Main conclusions and results unchanged
发表信息：
J. High Energ. Phys. 2020, 47 (2020)
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摘要：

本文推广了等对称QCD中非全同π介子的相对论性、有限体积、三粒子量子化条件。由此产生的形式主义允许一个使用离散的有限体积能量，确定使用晶格QCD，约束散射振幅的所有可能的值的2和3 π介子的同位旋。与前面考虑的相同π介子的情况一样，结果分为两步：第一步定义一个非微扰函数，其根等于允许能量$E_n(L)$，在给定的边长为$L$的立方体积中。这个函数依赖于一个中间的三体量，记为$\mathcal{K}_{\mathrm{df},3}$，因此可以从格点QCD输入约束。第二步是将$\mathcal{K}_{\mathrm{df},3}$与物理散射幅度$\mathcal M_3$相关联的一组积分方程。这两个关键的关系，$E_n(L) \leftrightarrow \mathcal{K}_{\mathrm{df},3}$和$\mathcal{K}_{\mathrm{df},3}\leftrightarrow \mathcal M_3$，被证明是块对角的基础上，明确的三π介子的同位旋，$I_{πππ}$，使一个实际上恢复四个独立的关系，对应于$I_{πππ}=0,1,2,3$。我们还提供了广义阈值扩展的$\mathcal{K}_{\mathrm{df},3}$的所有通道，以及参数化的所有三π介子共振存在的$I_{πππ}=0$和$I_{πππ}=1$。作为一个例子的效用的广义形式主义，我们提出了一个玩具实现的量子化条件$I_{πππ}=0$，专注于量子数的$ω$和$h_1$共振。

英文摘要：

We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: The first defines a non-perturbative function with roots equal to the allowed energies, $E_n(L)$, in a given cubic volume with side-length $L$. This function depends on an intermediate three-body quantity, denoted $\mathcal{K}_{\mathrm{df},3}$, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relating $\mathcal{K}_{\mathrm{df},3}$ to the physical scattering amplitude, $\mathcal M_3$. Both of the key relations, $E_n(L) \leftrightarrow \mathcal{K}_{\mathrm{df},3}$ and $\mathcal{K}_{\mathrm{df},3}\leftrightarrow \mathcal M_3$, are shown to be block-diagonal in the basis of definite three-pion isospin, $I_{πππ}$, so that one in fact recovers four independent relations, corresponding to $I_{πππ}=0,1,2,3$. We also provide the generalized threshold expansion of $\mathcal{K}_{\mathrm{df},3}$ for all channels, as well as parameterizations for all three-pion resonances present for $I_{πππ}=0$ and $I_{πππ}=1$. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for $I_{πππ}=0$, focusing on the quantum numbers of the $ω$ and $h_1$ resonances.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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