  The present paper continues the series [V. V. Vereshagin, True self-energy
function and reducibility in effective scalar theories, Phys. Rev. D 89, 125022
(2014); A. Vereshagin and V. Vereshagin, Resultant parameters of effective
theory, Phys. Rev. D 69, 025002 (2004); K. Semenov-Tian-Shansky, A. Vereshagin,
and V. Vereshagin, S-matrix renormalization in effective theories, Phys. Rev. D
73, 025020 (2006)] devoted to the systematic study of effective scattering
theories. We consider matrix elements of the effective Lagrangian monomials (in
the interaction picture) of arbitrary high dimension D and show that the full
set of corresponding coupling constants contains parameters of both kinds:
essential and redundant. Since it would be pointless to formulate
renormalization prescriptions for redundant parameters, it is necessary to
select the full set of the essential ones. This is done in the present paper
for the case of the single scalar field.
