We propose the sparse modeling method to estimate the spectral function from the smeared correlation functions. We give a description of how to obtain the shear viscosity from the correlation function of the renormalized energy-momentum tensor (EMT) measured by the gradient flow method ( C ( t, τ )) for the quenched QCD at finite temperature. The measurement of the renormalized EMT in the gradient flow method reduces a statistical uncertainty thanks to its property of the smearing. However, the smearing breaks the sum rule of the spectral function and the over-smeared data in the correlation function may have to be eliminated from the analyzing process of physical observables. In this work, we demonstrate the sparse modeling analysis in the intermediate-representation basis (IR basis), which connects between the Matsubara frequency data and real frequency data. It works well even using very limited data of C ( t, τ ) only in the fiducial window of the gradient flow. We utilize the ADMM algorithm which is useful to solve the LASSO problem under some constraints. We show that the obtained spectral function reproduces the input smeared correlation function at finite flow-time. Several systematic and statistical errors and the flow-time dependence are also discussed.

中文翻译：

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从涂抹相关函数获得剪切粘度的稀疏建模方法

我们提出了稀疏建模方法，以从模糊的相关函数中估计谱函数。我们描述了如何从有限温度下淬火 QCD 的梯度流法 (C ( t, τ )) 测量的重整化能量-动量张量 (EMT) 的相关函数获得剪切粘度。由于其拖尾特性，梯度流方法中重归一化 EMT 的测量降低了统计不确定性。然而，拖尾破坏了谱函数的求和规则，相关函数中的拖尾数据可能不得不从物理可观测量的分析过程中消除。在这项工作中，我们展示了中间表示基础（IR 基础）中的稀疏建模分析，连接松原频率数据和实际频率数据。即使仅在梯度流的基准窗口中使用非常有限的 C ( t, τ ) 数据，它也能很好地工作。我们利用 ADMM 算法来解决某些约束下的 LASSO 问题。我们表明，获得的谱函数在有限的流动时间内再现了输入的模糊相关函数。还讨论了几个系统和统计误差以及流动时间依赖性。