Vector and Axial - Vector Current Correlators within the Instanton Model of Qcd Vacuum

The pion electric polarizability, α E π ± , the leading order hadronic contribution to the muon anomalous magnetic moment, a hvp(1) µ , and the ratio of the difference to the sum of vector and axial-vector correlators, (V − A)/(V + A), are found within the instanton model of QCD vacuum. The results are compared with phenomenological estimates of these quantities following from the ALEPH and OPAL data on vector and axial-vector spectral densities. In the chiral limit, where the masses of u, d, s light quarks are set to zero, the vector (V) and axial-vector (A) current-current correlation functions in the momentum space (with −q 2 ≡ Q 2 ≥ 0) are defined as Π J,ab µν (q) = i d 4 x e iqx Π J,ab µν (x) = q µ q ν − g µν q 2 Π J (Q 2)δ ab , (1) Π J,ab µν (x) = 0 T J a µ (x)J b ν (0) † 0, where the QCD V and A currents are J a µ = qγ µ λ a √ 2 q, J 5a µ = qγ µ γ 5 λ a √ 2 q, and λ a are Gell-Mann matrices trλ a λ b = 2δ ab in flavor space. The momentum-space two-point correlation functions obey (suitably subtracted) dispersion relations, Π J (Q 2) = ∞ 0 ds s + Q 2 1 π ImΠ J (s), (2) where the imaginary parts of the correlators determine the spectral functions ρ J (s) = 4πImΠ J (s + i0) measured by ALEPH 1 and OPAL 2. In the instanton liquid model (ILM) gauged by interaction with external vector and axial-vector fields 3 the correlators in the chiral limit have