T. Hatsuda

Maximum entropy analysis of the spectral functions in lattice QCD

Abstract First principle calculation of the QCD spectral functions (SPFs) based on the lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian inference theory and the Maximum Entropy Method (MEM), which is a useful tool to extract SPFs from the imaginary-time correlation functions numerically obtained by the Monte Carlo method. Three important aspects of MEM are (i) it does not require a priori assumptions or parametrizations of SPFs, (ii) for given data, a unique solution is obtained if it exists, and (iii) the statistical significance of the solution can be quantitatively analyzed. The ability of MEM is explicitly demonstrated by using mock data as well as lattice QCD data. When applied to lattice data, MEM correctly reproduces the low-energy resonances and shows the existence of high-energy continuum in hadronic correlation functions. This opens up various possibilities for studying hadronic properties in QCD beyond the conventional way of analyzing the lattice data. Future problems to be studied by MEM in lattice QCD are also summarized.

Precursor of chiral symmetry restoration in the nuclear medium

Spectral enhancement near the

Hadronic spectral functions in lattice QCD

{2m}_{\ensuremath{\pi}}

Optimized perturbation theory at finite temperature

threshold in the

Possible critical phenomena associated with the chiral symmetry breaking

I\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

Structural change of Cooper pairs and momentum dependent gap in color superconductivity

channel in nuclei is shown to be a distinct signal of the partial restoration of chiral symmetry. The relevance of this phenomenon with the possible detection of

Chiral-symmetry realization for even- and odd-parity baryon resonances

2{\ensuremath{\pi}}^{0}

Spectral change of hadrons and chiral symmetry

and

Color molecular dynamics for high density matter

2\ensuremath{\gamma}

Effects of Finite Density on Chiral Domain-Wall in Neutron and Quark Matter

in hadron-nucleus and photon-nucleus reactions is discussed.