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In a recent work by some of us it was shown that the long-standingdiscrepancy between the QCD perturbation series for the inclusive hadronic taudecay rate computed in the CIPT and FOPT expansion approaches can be understoodfrom the fact that CIPT has an infrared (IR) sensitivity that it not compatiblewith the standard form of the operator production expansion (OPE). For concreteIR renormalon models for the QCD Adler function the resulting CIPT-FOPTdiscrepancy, the asymptotic separation, can be calculated analytically from theBorel representation of the CIPT series expansion. If the known perturbativecorrections for the QCD Adler function at the 5-loop level already have asizeable contribution from the asymptotic behavior related to the gluoncondensate (GC) renormalon, the asymptotic separation is dominated by thatrenormalon. This implies that the CIPT expansion can be reconciled with FOPT,when a renormalon-free scheme for the GC is adopted. In this talk we discusssuch a renormalon-free scheme for the GC, which involves perturbativesubtractions in analogy to using short-distance quark mass schemes instead ofthe pole mass. Using a concrete realistic high-order Borel model for the Adlerfunction consistent with the known corrections up to 5 loops and containing asizeable GC renormalon contribution, we show that the CIPT-FOPT discrepancy canbe avoided when switching to the renormalon-free GC scheme. At the same time,the perturbative convergence of $\tau$ hadronic spectral funtion momentsstrongly sensitive to the GC OPE corrections is considerably improved. We showthat these improvements may lead to higher precision for strong couplingdeterminations.

Inclusive $\tau$ Hadronic Decay Rate in a Renormalon-Free Gluon Condensate Scheme