Pion weak decay constant at finite density from the instanton vacuum
  We investigate the pion weak decay constant (F_pi) and pion mass (m_pi) at finite density within the framework of the nonlocal chiral quark model from the instanton vacuum with the finite quark-number chemical potential (mu) taken into account. We mainly focus on the Nambu-Goldstone phase below the critical value of the chemical potential mu_c ~ 320 MeV, which is determined consistently within the present framework. The breakdown of Lorentz invariance at finite density being considered, the time (F^t_pi) and space (F^s_pi) components are computed separately, and the corresponding results turn out to be: F^t_pi = 82.96 MeV and F^s_pi = 80.29 MeV at mu_c, respectively. Using the in-medium Gell-Mann-Oakes-Renner (GOR) relation, we show that the pion mass increases by about 15% at mu_c. 
Seung-il Nam, Hyun-Chul Kim