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 .