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

A. M. Kotzinian·O. Yu. Shevchenko·A. N. Sissakian
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Abstract

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.

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A. M. Kotzinian, O. Yu. Shevchenko, A. N. Sissakian. 2002-04-26. Topological charge and topological susceptibility in connection with translation and gauge invariance. https://arxiv.org/abs/hep-th/0204010

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