Search for Sphalerons: IceCube vs. LHC

We discuss the observability of neutrino-induced sphaleron transitions in the IceCube detector, encouraged by a recent paper by Tye and Wong (TW), which argued on the basis of a Bloch wave function in the periodic sphaleron potential that such transitions should be enhanced compared to most previous calculations. We calculate the dependence on neutrino energy of the sphaleron transition rate, comparing it to that for conventional neutrino interactions, and we discuss the observability of tau and multi-muon production in sphaleron-induced transitions. We use IceCube 4-year data to constrain the sphaleron rate, finding that it is comparable to the upper limit inferred previously from a recast of an ATLAS search for microscopic black holes at the LHC with $\sim 3$/fb of collisions at 13 TeV. The IceCube constraint is stronger for a sphaleron barrier height $E_{\rm Sph} \gtrsim 9$ TeV, and would be comparable with the prospective LHC sensitivity with 300/fb of data at 14 TeV if $E_{\rm Sph} \sim 11$ TeV.