Extract Spectral Function With Deep Learning Method

Our goal is to extract hadron spectral functions at a finite temperature space.Theoretically,the spectral function of the hadron should contain all the thermody-namic properties of the hadron.Light hadrons will be dissociated due to the Debye screening effect,but heavy hadrons will survive even above the critical temperature.Therefore,the main goal of this paper is to extract the spectral function of heavy hadron.The spectral function cannot be computed directly,but it is included in the correlation function.Specifically,the correlation function is the integration with the spectral function multiplied by a integral kernel in the frequency space.On the other hand,the correlation function can be computed directly from lattice QCD.Therefore,we can extract the spectral function by solving the first type of integral equation.However,solving the first type of integral equation is an ill-posed problem.The mostly used methods are the Maximum Entropy Method and the stochastic Optimization Method.In this thesis,we will briefly review the Maximum Entropy Method.The Maximum Entropy Method is mainly based on Bayes's theorem and Maximum Likelihood Estimation.The shortcoming of Maximum Entropy Method is that its output depends on a priori information called default model.This thesis also propose a new approach based on neural network.The advantage of this method is that it can fit any function with high precisions,but the output depends on the training dataset.In order to ensure that the network's output results have physical meaning,we divide the spectral function into three parts:transport,resonance,continuum part.In addition,by studying the neural network's the output on mock correlat,ors,we.know the depe.ndence of the network's output on the training dataset.Finally,we apply the new neural network to the real correlator.In this study,we mainly focus on vector channel at 0.75Tc(N? = 96)and 1.5Tc(N?= 48).Comparing the results of the Maximum entropy method,we found that both methods can obtain the similar resonance peak and transport peak.