The 750 GeV Diphoton excess, Dark Matter and Constraints from the IceCube experiment

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 Zγ, 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.