Narrow Results

In this presentation, we briefly review recent investigations on pion and kaon structures from the instanton vacuum. Starting from the low-energy QCD partition function, we have computed the Gasser-Leutwyler low-energy constants, electromagnetic form factors of the pion and kaon, and semileptonic decay form factors of the kaon. The results are in good agreement with the experimental and empirical data.

In this talk, we report our recent work on the pion weak decay constant (F_π) and pion mass (m_π) using the nonlocal chiral quark model with the finite quark-number chemical potential (μ) taken into account. Considering the breakdown of Lorentz invariance at finite density, the time and space components are computed separately, and the corresponding results turn out to be: and at μ_c ≈ 320 MeV, respectively. Using the in-medium Gell-Mann-Oakes-Renner (GOR) relation, we show that the pion mass increases by about 15% at μ_c.

We investigate the thermal conductivity (κ) of the quark matter at finite quark chemical potential (μ) and temperature (T), employing the Green–Kubo formula, for the SU(2) light-flavor sector with the finite current-quark mass m = 5 MeV. As a theoretical framework, we construct an effective thermodynamic potential from the (μ, T)-modified liquid-instanton model (mLIM). Note that all the relevant model parameters are designated as functions of T, using the trivial-holonomy caloron solution. By solving the self-consistent equation of mLIM, we acquire the constituent-quark mass M₀ as a function of T and μ, satisfying the universal-class patterns of the chiral phase transition. From the numerical results for κ, we observe that there emerges a peak at μ≈200 MeV for the low-T region, i.e. T≲100 MeV. As T increase over T≈100 MeV, the curve for κ is almost saturated as a function of T in the order of ~ 10^-1GeV², and grows with respect to μ smoothly. At the normal nuclear-matter density ρ₀ = 0.17 fm^-3, κ shows its maximum 6.22 GeV² at T≈10 MeV, then decreases exponentially down to κ≈0.2 GeV². We also compute the ratio of κ and the entropy density, i.e. κ/s as a function of (μ, T) which is a monotonically decreasing function for a wide range of T, then approaches a lower bound at very high T: κ/s_min≳0.3 GeV^-1 in the vicinity of μ = 0.