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We review the concept and properties of finite field-dependent BRST andBRST-antiBRST transformations introduced in our recent study (A. Reshetnyak,IJMPA 29 (2014) 1450128, P. Moshin, A. Reshetnyak, Nucl. Phys. B 888 (2014) 92,Phys. Lett B 739 (2014) 110, IJMPA 29 (2014) 1450159, IJMPA 30 (2015) 1550021,IJMPA 31 (2016) 1650111, [arxiv:1604.03027 [hep-th]]) for gauge theories. Exactrules for calculating the Jacobian of a corresponding change of variables inthe partition function are presented. Infrared peculiarities under$R_\xi$-gauges in the Yang--Mills theory and Standard Model are examined in agauge-invariant way with an appropriate horizon functional and unaffected local$N=1,2$ BRST symmetries.

On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon