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arXiv 2210.08051hep-lathep-phnucl-th
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利用格点量子色动力学研究$γ^\star γ^\star \to ππ$的前景

Prospects for $γ^\star γ^\star \to ππ$ via lattice QCD

Raúl A. Briceño, Andrew W. Jackura, Arkaitz Rodas, Juan V. Guerrero

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23 pages, 9 figures
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摘要：

$γ^\star γ^\star \to ππ$散射振幅在许多现象中起着关键作用，包括理解标量共振的内部结构以及约束强子对μ子异常磁矩的贡献。在这项工作中，我们解释了如何从有限体积欧氏相关函数的无限体积闵可夫斯基振幅可以限制。有限体积欧几里德相关函数和所需振幅之间的关系保持到$3π$态可以进入壳层的能量，并且精确到指数级小修正，如$\mathcal{O}(e^{-m_πL})$，其中$L$是立方体积的空间范围，$m_π$是π介子质量。为了实现这种形式并消除所有幂律有限体积误差，必须首先获得$ππ\to ππ$、$πγ^\star \to π$、$γ^\star \toππ$和$ππγ^\star \toππ$振幅;所有这些都可以通过晶格量子色动力学计算确定。

英文摘要：

The $γ^\star γ^\star \to ππ$ scattering amplitude plays a key role in a wide range of phenomena, including understanding the inner structure of scalar resonances as well as constraining the hadronic contributions to the anomalous magnetic moment of the muon. In this work, we explain how the infinite-volume Minkowski amplitude can be constrained from finite-volume Euclidean correlation functions. The relationship between the finite-volume Euclidean correlation functions and the desired amplitude holds up to energies where $3π$ states can go on shell, and is exact up to exponentially small corrections that scale like $\mathcal{O}(e^{-m_πL})$, where $L$ is the spatial extent of the cubic volume and $m_π$ is the pion mass. In order to implement this formalism and remove all power-law finite volume errors, it is necessary to first obtain $ππ\to ππ$, $πγ^\star \to π$, $γ^\star \toππ$, and $ππγ^\star \toππ$ amplitudes; all of which can be determined via lattice quantum chromodynamic calculations.

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