Pseudo-ϵ expansion and critical exponents of superfluid helium

The pseudo-ϵ expansions (τ-series) for critical exponents of the three-dimensional XY model describing λ-transition in liquid helium are derived up to the τ6 terms. Numerical estimates extracted from the τ-series obtained using the Padé-Borel resummation technique, scaling relations and the seven-loop (τ7) estimate for the Fisher exponent η are presented including those for the exponents α and ν measured in experiments with a record accuracy. For the exponent α the procedure argued to be most reliable gives α=−0.0117, the number that is very close to the most accurate experimental values. It signals that the pseudo-ϵ expansion approach is a powerful tool robust enough to evaluate critical exponents with small absolute errors. The arguments in favor of such a robustness are presented.