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

Abstract: We present 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 that mimic charmonium correlation functions. We show that, while resonance peaks in the spectral functions can be reconstructed using this method, it is difficult to reconstruct transport peaks without further assumptions beyond SpM. Then we extract charmonium spectral functions from correlation functions obtained from lattice QCD at temperatures below and above the critical temperature. We show that this method yields results qualitatively consistent with those obtained using the maximum entropy method, although the transport peak is not obtained clearly. This suggests that the results solely from the assumption of the sparse solution can partially reflect underlying physics.