Finite density QCD study by the lattice QCD simulation. How to work on the sign problem

Finite density lattice QCD study is reviewed. The main three means i.e., Taylor expansion method, imaginary chemical potential one and reweighting one used in the finite quark density system analyses are explained. The importance of the sign problem is illustrated by showing the phase fluctuation. Typical approaches to cope with the sign problem encountered in those methods are taken up and the consideration concerning the problems is illustrated. In the case of Taylor expansion, the second and the fourth order Taylor coefficients are playing main roles. In the case of imaginary chemical potentials, the phase boundary lines of the confine/non-confinement are shown and lattice QCD simulation results are plotted on them. Another way to avoid the sign problem is to use the Reweighting (RW) method considering the small change of the Gauge configuration. Example and caution to use RW are commented and multi-parameter reweighting (MPR) calculation is introduced. Equation of state, number density, the Taylor expansion of the number density susceptibility and the result of MPR are shown to compare their results. (S. Funahashi)