Sparse modeling study of extracting charmonium spectral functions from lattice QCD at finite temperature

We present charmonium spectral functions extracted from Euclidean-time correlation functions using sparse modeling (SpM). SpM solves inverse problems by considering only the sparsity of the target solution. To assess the applicability of the method, we first test it with mock data designed to mimic charmonium correlation functions. We demonstrate that while resonance peaks in the spectral functions can be reconstructed using this method, transport peaks are difficult to resolve without introducing further assumptions beyond sparsity. We then apply the method to charmonium correlation functions obtained from lattice quantum chromodynamics (QCD) at temperatures below and above the critical temperature. The results are found to be qualitatively consistent with those obtained using the maximum entropy method, although the transport peak is not clearly resolved. This indicates that, even when relying solely on the assumption of sparsity, the method can capture some relevant features of the underlying physics.