We investigate models involving a vector-like quark X, which forms a 750 GeV bound state and reproduces the observed diphoton signals at the LHC, in connection with other excesses in the LHC data. An exotic hypercharge of -4/3 is required to fit the signal cross section, which indicates that there is additional particle(s) that mediates the decay of X in the full theory. We find that, introducing an SU(2) doublet vector-like quark of mass around 600 GeV in our UV-complete framework can accommodate not only the diphoton but also the on-Z excess (and potentially a slight excess in the monojet events). Our models also include a dark matter candidate. The most useful way to probe the models at the LHC is via monojet searches. The relic dark matter density is largely determined by coannihilation effects, and indirect detection of dark matter annihilation signals is the alternative and complementary probe of our models.
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