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

It is shown that the evaluation of the expectation value (EV) of topological charge density over theta 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 theta occurs to be equal to zero at least in the pure Yang-Mills (YM) and QCD in the chiral limit (QCD subchi) theories. As a consequence, topological susceptibilities of both YM and (known result) QCD subchi vacua defined in a Wick sense are equal to zero, whereas, when defined in a Dyson sense, they can differ from zero by the quantities proportional to the respective condensates of the chromomagnetic field. Thus, the usual Witten-Veneziano formula for the eta sup ' -meson mass is modifie