µ ν q 1PI Figure 1.4: The vector current two-point function, Π$_{V}$ ( − q $^{2}$). The grey blob represents all possible one particle irreducible diagrams that can be inserted. f$_{π}$ in equation (1.35) is a measure of the extent of the chiral symmetry breaking. If there is no chiral symmetry breaking its value is zero. In QCD it can be determined from measuring the decay rate of π 0 particles [24]. It is found to be 92 MeV. It is not just the pion that has a decay constant associated with it. All pseudoscalar mesons, P, have a decay constant F$_{P}$ , defined by And the vector meson decay constants ¶ are defined as: where p and λ are the momentum and polarization state of the vector meson V ( p ; λ ). ϵ$_{µ}$ is the corresponding polarization vector. Experimentally, F$_{P}$ can be measured from leptonic decays of the ap- propriate meson [24]. F$_{V}$ can be measured from the decays of tau lep- $^{¶}$vector mesons have two decay constants: the transverse polarization decay constant, F T V , and the longitudinal polarization decay constant F$_{V}$ . Only the longitudinal decay constant can be determined experimentally. 21 Meson decay constants 〈 0 | A$_{µ}$ (0) | P ( q ) 〉 = iF$_{P}$ q$_{µ}$ (1.36) 〈 0 | ¯ Q (0) γ $^{µ}$Q (0) | V ( p ; λ ) 〉 = iF$_{V}$ m$_{V}$ ϵ µ λ (1.37)