M13 at intermediate metallicity regime ($[Fe/H]\sim-1.5$; Ferraro et al. 1997) and M15 - M92 at low metallicities ($[Fe/H]\sim-2.3$).\
These noticeable exceptions have required the introduction of a second (Freeman & Norris 1981) and possibly a third parameter in order to explain the HB distributions in all GGCs. What we can call now the *[“i-th parameter problem”]{}* is still a hot topic, as stressed by several authors, we recall the reader to Catelan 2009 for a nice review (see also Dotter et al. 2010 and Gratton et al. 2010; hereafter D10 and G10 respectively).[^1]\
An accurate knowledge of the physical parameters playing a role in shaping the HB is extremely important also for an appropriate interpretation of distant unresolved stellar populations. In fact it is well known that the HB morphology can have a strong impact on the integrated light of stellar populations, affecting colours and line indices (Lee et al. 2002; Schiavon et al. 2004; Percival & Salaris 2011; Dalessandro et al. 2012).\
Despite the huge efforts made to address this problem, its solution is not obvious and still different scenarios are proposed. One of the reasons that complicates the identification of the mechanisms – other than metallicity – at 