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

We review the concept and properties of finite field-dependent BRST and BRST-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. Exact rules for calculating the Jacobian of a corresponding change of variables in the partition function are presented. Infrared peculiarities under $R_\xi$-gauges in the Yang--Mills theory and Standard Model are examined in a gauge-invariant way with an appropriate horizon functional and unaffected local $N=1,2$ BRST symmetries.