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This is the revised version of Sect. I - IV of the paperhttps://doi.org/10.1103/PhysRevD.89.125022 originally published in 2014. Thething is that in https://doi.org/10.1103/PhysRevD.89.125022 the text wasinsufficiently clear and, in addition, it contained (through my fault) a fewtypos. This is the reason why I decided to offer a revised version.  Original abstract: This is the eighth paper in the series devoted to thesystematic study of effective theories. Below, I discuss the renormalization ofthe one-loop two-leg functions in multicomponent effective scalar theory. It isshown that only a part of numerous contributions that appear in the generalexpression for a two-leg graph can be considered as the true self-energyfunction. This part is completely fixed by the values of minimal couplingconstants; it is the only one that should be taken into account in theconventional process of the summation of Dyson's chain that results in explicitexpression for the full propagator. The other parts provide the well-definedfinite corrections for the graphs with the number of legs n > 2. It is alsoshown that there is no need to attract the renormalization prescriptions forthe higher derivatives of the two-leg function on the mass shell; therequirements of finiteness and diagonability turn out to be quite sufficient.

True self energy function and reducibility in effective scalar theories. (Revised)