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 $\gamma \gamma$, $Z\gamma$, and $W\gamma$. These decays are most phenomenologically interesting for the fermiophobic custodial fiveplet states $H_5^0$ and $H_5^{\pm }$ 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.