Recommendations for the interpretation of LHC searches for $H_5^0$, $H_5^{\pm}$, and $H_5^{\pm\pm}$ in vector boson fusion with decays to vector boson pairs

We provide theory input for the interpretation of the LHC searches for the production of Higgs bosons $H_5^0$, $H_5^{\pm}$, and $H_5^{\pm\pm}$ that transform as a fiveplet under the custodial symmetry. We choose as a benchmark the Georgi-Machacek model, in which isospin-triplet scalars are added to the Standard Model Higgs sector in such a way as to preserve custodial SU(2) symmetry. This leads to several interesting features, including a tree-level $H_5^{\pm} W^{\mp} Z$ interaction, $H_5^{\pm\pm}$ decays to like-sign $W$ bosons, and $H_5^0$ decays to $W^+W^-$ and $ZZ$ in a different ratio than appears in the Standard Model, while still satisfying experimental constraints on the electroweak $\rho$ parameter. We provide cross sections for single production of all five scalars in vector boson fusion up to next-to-next-to-leading order in QCD for masses in the range 200-1000 GeV (200-2000 GeV) at the 8 TeV (13 TeV) LHC. We also provide tree-level decay widths for $H_5^0 \to W^+W^-$ and $ZZ$, $H_5^{\pm} \to W^{\pm}Z$, and $H_5^{\pm\pm} \to W^{\pm} W^{\pm}$ for masses in the range 200-2000 GeV.