Recently, QCD at finite temperature and density attracts renewed interests, stimulated by advances in lattice QCD technique for finite density system and a beam energy scan (BES) program, which is an on-going experiment at RHIC to investigate the QCD phase diagram.

Towards the understanding of QCD at finite density, we employ a canonical approach, which is based on a fundamental equation describing the relation between canonical and grand canonical partition functions. I will talk about its applications both to BES experiment and lattice QCD simulations.

First, we introduce the framework and explain possible applications, such as moments of the probability distribution and Lee-Yang zeros. Then, we apply the technique to data obtained in BES experiments. We show that the canonical approach enables us to investigate a wide range of QCD phase diagram using data obtained at a certain point (chemical freeze-out point).

Next, we study canonical partition functions and Lee-Yang zeros in lattice QCD simulations. They show a drastic change from the confinement to deconfinement phases. In addition, we analytically solve canonical partition functions and Lee-Yang zeros for high temperature QCD using a saddle point approximation. We find that the analytic result of Lee-Yang zeros explain a gross feature of those obtained from lattice QCD simulations. We discuss its implications to experimental data.

References
1. Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
K. Nagata, K. Kashiwa, A. Nakamura, S. M. Nishigaki arXiv:1410.0783
2. Probing QCD Phase Structure by Baryon Multiplicity Distribution A. Nakamura, K. Nagata [arXiv:1305.0760]
3. Towards extremely dense matter on the lattice K. Nagata, S. Motoki, Y. Nakagawa, A. Nakamura, T.Saito [PTEP01A103(2012), arXiv:1204.1412]