Recent precise determinations of the primordial He-abundance (Y_p) from cosmic microwave background (CMB) analyses and cosmological nucleosynthesis computations, provide Y_p=0.248$pm$0.001. On the other hand, recent works on the initial He-abundance of Galactic globular cluster (GGC) stars, making use of the R parameter as He-indicator, have consistently obtained $Y_{GGC}sim$0.20. In light of this serious discrepancy that casts doubt on the adequacy of low mass He-burning stellar models, we have rederived the initial He-abundance for stars in two large samples of GGCs, by employing theoretical models computed using new and more accurate determinations of the Equation of State for the stellar matter, and of the uncertain $^{12}$C$(alpha,gamma)^{16}$O reaction rate. Our models include semiconvection during the central convective He-burning phase, while the breathing pulses are suppressed, in agreement with the observational constraints coming from the measurements of the R_2 parameter in a sample of clusters. By taking into account the observational errors on the individual R-parameter values, as well as uncertainties in the GGC [Fe/H] scale, treatment of convection and $^{12}$C$(alpha,gamma)^{16}$O reaction rate, we have obtained, respectively, a mean $Y_{GGC}$=0.243$pm$0.006 and $Y_{GGC}$=0.244$pm$0.006 for the two studied GGC samples. These estimates are now fully consistent with Y_p obtained from CMB studies. Moreover, the trend of the individual He-abundances with respect to [Fe/H] is consistent with no appreciable He-enrichment along the GGC metallicity range.
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