Thermal Modifications Of Quarkonia From Quenched Lattice QCD

We present our lattice study on the transport properties of the QCD medium and in-medium hadron properties.These properties can be obtained from the hadron spectral functions and screening masses,which are related with the lattice computable quanti-ties correlation functions.To this aim we calculated both the spatial and the tempo-ral correlation functions of charmonia and bottomonia at zero and nonzero momenta in quenched QCD.We performed simulations on fine,isotropic lattices at beta values ??7.192,7.394,7.544,7.793 corresponding to lattice spacings a-1 = 11.19,14.24,17.01,22.78 GeV,respectively.Currently we only focus on the finest lattice where the heavy quarks are accommodated on 1923 x 32,1923 x 48,1923 x 56,1923 x 64 and 1923 x 96 lattices.These lattices correspond to temperatures of 2.25Tc,1.50Tc,1.25Tc,1.10Tc and 0.75Tc,respectively.We used Wilson gauge action and clover-improved Wilson fermions in the simulations.To increase the signal to noise ratio in the axial-vector and scalar channels we used multi-sources for the measurement of spatial correlation functions.The extraction of spectral function from the temporal correlation functions is an ill-posed problem.To tackle this problem we introduced two stochastic approaches,S-tochastic Optimization Method(SOM)and Stochastic Analytical Inference(SAI).SOM has the advantage that it does not require prior information.On the other hand,SAI is a more generalized method based on Bayesian inference.Under mean field approximation SAI reduces to the often-used Maximum Entropy Method(MEM),and for a specific choice of the prior SAI becomes equivalent to SOM.In this work we present a detailed study of the applications of these two stochastic approaches.To test the applicability of these two stochastic methods to lattice QCD,firstly,we apply these methods to various reasonably chosen model correlation functions,and present detailed comparisons of the reconstructed spectral functions obtained from SOM,SAI and MEM.We also applied these methods to charmonium.correlation functions in the pseudo-scalar and vector channels computed on the large quenched lattice using clover-improved Wilson fermions at 0.75Tc with N?=96 and at 1.5Tc with N?=48.Even in these cases,we found consistent results using all three methods.While the location of the first resonance peak at T<Tc is correctly reproduced,the location of the first bump at 1.5Tc is shifted to higher frequency region by around 30-40%.However,given the fact that all three methods fail to satisfactorily reproduce the 0.75Tc spectral function extracted from the reconstructed correlation function,we cannot come to a definite conclusion on whether ?c and J/? exist as bound states in a gluon.plasma at 1.5Tc.We also studied the thermal modifications of charmonia and bottomonia via spatial correlation functions.By investigating on the temperature dependence of screening masses we discussed the thermal effects in different channels of heavy quarkonium states.Besides this the dispersion relation of the screening mass at different momenta was also discussed.we find that the screening masses of S-wave states for both bottomonia and charmonia increase monotonically in temperature.For bottomonia,Esc?,(2.25Tc)/Esc?(0.75Tc)-1 is 5.6%while for charmonia 54%.The screening masses of P-wave states for both bottomonia and charmonia increase non-monotonically in temperature.Our quenched calculations and 2+1 flavor HISQ calculations show the similar change tendency of the screening masses.At non-zero momenta we find that the dispersion relation in our quenched simulations seems to be not modified in the medium.The reason could be that the momentum of the quarkonium state is less than its mass at rest.