Context : Theory and observations indicate that the distribution of stars along the horizontal branch of Galactic globular clusters mainly depends on the metal content .
However , the existence of globular clusters with similar metal content and absolute age but different horizontal branch morphologies , suggests the presence of another parameter affecting the star distribution along the branch .

Aims : To investigate the variation of the horizontal branch morphology in Galactic globular clusters , we define a new photometric horizontal branch morphology index , overcoming some of the limitations and degeneracies affecting similar indices available in the literature .

Methods : We took advantage of a sample of 64 Galactic globular clusters , with both space-based imaging data ( Advanced Camera for Surveys survey of Galactic globular clusters ) and homogeneous ground-based photometric catalogues in five different bands ( U , B , V , R , I ) .
The new index , \tau _ { HB } , is defined as the ratio between the areas subtended by the cumulative number distribution in magnitude ( I ) and in colour ( V–I ) of all stars along the horizontal branch .

Results : This new index shows a linear trend over the entire range in metallicity ( -2.35 \leq [ Fe/H ] \leq -0.12 ) covered by our Galactic globular cluster sample .
We found a linear relation between \tau _ { HB } and absolute cluster ages .
We also found a quadratic anti-correlation with [ Fe/H ] , becoming linear when we eliminate the age effect on \tau _ { HB } values .
Moreover , we identified a subsample of eight clusters that are peculiar according to their \tau _ { HB } values .
These clusters have bluer horizontal branch morphology when compared to typical ones of similar metallicity .
These findings allow us to define them as the ’ second parameter ’ clusters in the sample .
A comparison with synthetic horizontal branch models suggests that they can not be entirely explained with a spread in helium content .

Conclusions :