Universal effective coupling constant ratios of 3D scalar φ4 field theory and pseudo-ε expansion

The ratios R-2k = g(2k)/g(4)(k-1) of renormalized coupling constants g(2k) entering the small-field equation of state approach universal values R-2k* at criticality. They are calculated for the three-dimensional lambda phi(4) field theory within the pseudo-epsilon expansion approach. Pseudo-epsilon expansions for R-6*, R-8* and R-10* are derived in the five-loop approximation, numerical estimates are obtained with a help of the Pade-Borel-Leroy resummation technique. Its use gives R-6* = 1.6488, the number which perfectly agrees with the most recent lattice result R-6* = 1.649. For the octic coupling the pseudo-epsilon expansion is less favorable numerically. Nevertheless the Pade-Borel-Leroy resummation leads to the estimate R-8* = 0.890 close to the values R-8* = 0.871, R-8* = 0.857 extracted from the lattice and field-theoretical calculations. The pseudo-epsilon expansion for R-10* turns out to have big and rapidly increasing coefficients. This makes correspondent estimates strongly dependent on the Borel-Leroy shift parameter b and prevents proper evaluation of R-10*.