Axial anomaly and low energy tests for instanton vacuum models in QCD

Improved effective action for light quarks beyond the chiral limit

“…For these calculations we need an Improved Effective Action in the presence of an external electromagnetic field a and of a field κ coupled with the topological density g 2 GG. A similar problem was solved in our previous works [11,12] and we follow this method. The most essential part of the Improved Effective Action, w ψ , is transformed to Here gauged momentum isK =k − eQâ as usual, the matrices Φ ± , whose usual decomposition is The quark condensate and the pseudoscalar meson masses from Improved Effective Action.…”

“…This approach led to the DP Effective Action with a specific choice of these degrees of freedom. This Effective Action fulfilled some axial-anomaly low energy theorems in the chiral limit, but failed beyond this limit [10,11]. So this Action is hardly applicable to the strange quarks.…”

“…In our previous papers [10][11][12] we showed that the constituent quarks appear as effective degrees of freedom in the fermionic representation of det B. This approach led to the DP Effective Action with a specific choice of these degrees of freedom.…”

Magnetic susceptibility of the QCD vacuum

“…In the previous paper [17], it was demonstrated how to gauge the nonlocal effective chiral action in the presence of the external electromagnetic field. The gauged action was successfully tested by showing that the low-energy theorem of the axial anomaly related to the process G G → γγ (see also [18,19]) is satisfied.…”

A test of the instanton vacuum with low-energy theorems of the axial anomaly

“…Some years ago, one of the authors showed that the low-energy QCD effective chiral action from the instanton vacuum [5,9] satisfies the low energy theorems with an accuracy of about 17 % [10,11]. This discrepancy is due to the fact that the vector and axial-vector currents are not conserved because of the momentum-dependent dynamical quark mass in the effective action [12,13,14,15].…”