“…In the simplest model of structure formation involving a purely gravitational collapse of dark matter haloes, groups and clusters form a population of self-similar objects with simple relations between their total mass and other physical quantities (Kaiser 1986). Numerous works have explored and tried to fully characterize these links between mass and baryonic observables such as the ICM X-ray luminosity, temperature, pressure, or entropy from X-ray observations (Finoguenov et al 2001;Vikhlinin et al 2002;Ettori et al 2004;Arnaud 2005;Kotov & Vikhlinin 2005;Vikhlinin et al 2006;Hoekstra 2007;Rykoff et al 2008;Pratt et al 2009;Leauthaud et al 2010;Okabe et al 2010;Mahdavi et al 2013), the Compton parameters derived from Sunyaev-Zel'dovich (SZ) observations (McCarthy et al 2003;Morandi et al 2007;Bonamente et al 2008;Marrone et al 2009;Lancaster et al 2011;Planck Collaboration et al 2011c,b), or the galaxy velocity dispersions, richness and optical luminosity from optical observations (Lin et al 2003(Lin et al , 2004Popesso et al 2005Popesso et al , 2007Becker et al 2007;Johnston et al 2007;Reyes et al 2008;Mandelbaum et al 2008;Rozo et al 2009;Andreon & Hurn 2010;Foëx et al 2012). However, many observational results have found discrepancies between the theoretical predictions derived from the gravitationally driven model of structure formation (different slope and normalization, break of self-similarity at low mass, large intrinsic scatter, non-standard redshift evolution), thus revealing the combined influence of various non-gravitational physical processes that affect the properties of groups and clusters (e.g.…”