Two-Higgs-doublet model with a color-triplet scalar: a joint explanation for top quark forward-backward asymmetry and Higgs decay to diphoton

The excess of top quark forward-backward asymmetry ($A_{FB}^t$) reported by the Tevatron and the enhancement of the Higgs decay to diphoton observed by the LHC may point to a same origin of new physics. In this note we examined such anomalies in the two-Higgs-doublet model with a color-triplet scalar. We found that under current experimental constraints this model can simultaneously explain both anomalies at $1\sigma$ level. Also, we examined the Higgs decay $h\to Z\gamma$ and displayed its correlation with $h\to \gamma \gamma$. We found that unlike other models, this model predicts a special correlation between $h\to Z\gamma$ and $h\to \gamma \gamma$, i.e., the $Z\gamma$ rate is highly suppressed while the $\gamma \gamma$ rate is enhanced. This behavior may help to distinguish this model in the future high luminosity run of the LHC.