J-PARC, the Japan Proton Accelerator Research Complex, is an accelerator, which provides a
high-intensity proton beam. Recently as a very attractive project, the acceleration of heavy ions produced by supplementary ion sources, called J-PARC-HI, is seriously contemplated by domestic as well as international communities. The planned facility would accelerate heavy ions up to U92+ with a beam energy 20 AGeV ([see formula in PDF] of 6.2 AGeV). The highlight of the J-PARC-HI project is its very high beam rate up to ~1011 Hz, which will enable the study of very rare events. Taking advantage of this high intensity, J-PARC-HI will carry out frontier studies of new and rare observables in this energy region: (i) nuclear medium modification of chiral property of vector mesons through low-mass di-lepton signal, (ii) QCD critical pointcharacterization through event-by-event fluctuation signals of particle production, (iii) systematic measurements related to the equation of state through collective flow signal or two-particle momentum correlation signal, or (iv) the search of hyper nuclei with multi strangeness including or exceeding S = 3. The current plan of J-PARC-HI aims to carrying out the first experimental measurements in 2025.