Revisiting the Vector and Axial-vector Vacuum Susceptibilities
  We re-investigate the vector and axial-vector vacuum susceptibilities by taking advantage of the vector and axial-vector Ward-Takahashi identities. We show analytically that, in the chiral limit, the vector vacuum susceptibility is zero and the axial-vector vacuum susceptibility equals three fourths of the square of the pion decay constant. Besides, our analysis reproduces the Weinberg sum rule. 
Lei Chang, Yu-xin Liu, Wei-min Sun and Hong-shi Zong