Pion weak decay constant at finite density from the instanton vacuum

We investigate the pion weak decay constant (FπFπ) and pion mass (mπmπ) at finite density within the framework of the nonlocal chiral quark model from the instanton vacuum with the finite quark-number chemical potential (μ  ) taken into account. We mainly focus on the Nambu–Goldstone phase below the critical value of the chemical potential μc≈320 MeVμc≈320 MeV, which is determined consistently within the present framework. The breakdown of Lorentz invariance at finite density being considered, the time (Fπt) and space (Fπs) components are computed separately, and the corresponding results turn out to be: Fπt=82.96 MeV and Fπs=80.29 MeV at μcμc, respectively. Using the in-medium Gell-Mann–Oakes–Renner (GOR) relation, we show that the pion mass increases by about 15% at μcμc.