A hint of a new resonance at a mass of 750\,GeV has been observed in the
diphoton channel of LHC Run 2 at s=13 TeV. The signal rate is too
large to interpret it as a new Higgs boson in the context of weakly-coupled
renormalizable models. One way is to reduce its total decay rate, which is
possible if the CP-even heavy Higgs boson H0 in the aligned two Higgs
doublet model becomes top-phobic. To ensure sufficient gluon fusion production,
we introduce vector-like quarks (VLQ). The Higgs precision data as well as the
exclusion limits from no excesses in other 8 TeV LHC searches of Zγ,
bbˉ, τ+τ−, and jj channels are simultaneously included. In
Type I, top-phobic H0 cannot explain the 750\,GeV diphoton signal and the
Higgs precision data simultaneously since the universal Yukawa couplings of the
up-type and down-type VLQs always make more contribution to h0 than to
H0. In Type II, small Yukawa coupling of the up-type VLQ but sizable Yukawa
coupling for the down-type VLQ is shown to explain the signal while satisfying
other LHC exclusion limits.Comment: Errors in the Type I calculation are corrected, and references are
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