Regions of the H5 plane benchmark [35] of the Georgi-Machacek model [47,48] excluded via direct searches for new, heavy, neutral or charged Higgs bosons. Expected limits are quoted at 95% CL and are indicated for the expectation from the background model assuming only SM processes (dashed lines). The coloured areas indicate the expected excluded regions in this parameter space. The Higgs bosons that are searched for are produced via VBF for all searches shown here apart from pp&rarr; H<sup>&plusmn;&plusmn;</sup>H<sup>&#8723;&#8723;</sup> production that proceeds via the Drell-Yan mechanism. The vector-boson fusion calculations are performed with the VBF@NNLO code [51,52], whereas the Drell-Yan calculation follows Ref. [54]. The branching ratios and the natural widths of the Higgs bosons in the Georgi-Machacek model are calculated using GMCALC [53]. Because the heavy scalar search, H&rarr; ZZ&rarr; 4l+ll&nu;&nu;, is valid only for relatively narrow Higgs bosons, dotted lines at 0.5% denotes the reach of the validity of the exclusion areas. Thus for the H&rarr; ZZ&rarr; 4l+ll&nu;&nu; search, the limit on the H5 plane is valid up to about a Higgs boson mass of 500 GeV. The red dashed line correspond to the expected exclusion limit, is still shown in the large width region where the limit is invalid. The gray region indicates H boson widths larger than 10%, for which the experimental limits for heavy H boson searches are invalid.