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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 ($A^t_{FB}$) 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 $1σ$ level. Also, we examined the Higgs decay $h\to Zγ$ and displayed its correlation with $h\to γγ$. We found that unlike other models, this model predicts a special correlation between $h\to Zγ$ and $h\to γγ$, i.e., the $Zγ$ rate is highly suppressed while the $γγ$ rate is enhanced. This behavior may help to distinguish this model in the future high luminosity run of the LHC.