Topological charge and topological susceptibility in connection with translation and gauge invariance

Kotzinian, A. M.; Shevchenko, O. Yu.; Sissakian, A. N.

Topological charge and topological susceptibility in connection with translation and gauge invariance

Authors

Kotzinian, A. M.

Shevchenko, O. Yu.

Sissakian, A. N.

Description

It is shown that the evaluation of the expectation value (EV) of topological charge density over $θ$-vacuum is reduced to investigation of the Chern-Simons term EV. An equation for this quantity is established and solved. EV of the topological charge density at an arbitrary $θ$ occurs equal to zero and, as a consequence, topological susceptibility of both QCD and pure Yang-Mills vacua defined in a Wick sense is equal to zero, whereas when defined in a Dyson sense it differs from zero by the quantity proportional to the respective condensate of the chromomagnetic field. Thus, the usual Witten-Veneziano formula for the $η^{'}$ meson mass is modified.