Recent LHC data show hints of a new resonance in the diphoton distribution at an invariant mass of 750 GeV. Interestingly, this new particle might be both CP odd and play the role of a portal into the dark matter sector. Under these assumptions and motivated by the fact that the requirement of $SU(2)_L$ invariance automatically implies the coupling of this alleged new resonance to $ZZ$ and $Zgamma$, we investigate the current and future constraints coming from the indirect searches performed through the neutrino telescope IceCube. We show that these constraints can be stronger than the ones from direct detection experiments if the dark matter mass is larger than a few hundred GeV. Furthermore, in the scenario in which the dark matter is a scalar particle, the IceCube data limit the cross section between the DM and the proton to values close to the predicted ones for natural values of the parameters.
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