Scalar decays to $\gamma\gamma$, $Z\gamma$, and $W\gamma$ in the Georgi-Machacek model

We compute the decay widths for the neutral and singly-charged Higgs bosons in the Georgi-Machacek model into the final states γγ, Zγ, and Wγ. These decays are most phenomenologically interesting for the fermiophobic custodial fiveplet states H50 and H5± when their masses are below threshold for decays into WW, ZZ, or WZ. We study the allowed branching ratios into these final states using scans over the allowed parameter space, and show how the model can be constrained by LEP searches for a fermiophobic Higgs boson decaying to two photons. The calculation involves evaluating one-loop diagrams in which the loop contains particles with two different masses, some of which do not appear in the existing literature. We give results for these diagrams in a form convenient for numerical implementation using the looptools package.