@Karshenboim:2014tka].

The range in mediator mass is chosen to span from the KT87 constraint to those near the weak scale, focusing on the mass range that has been of particular interest in recent work, e.g., Refs. [@Aarssen:2012fx; @Dasgupta:2013zpn; @Bringmann:2013vra]. Coincidentally, this is where the IceCube sensitivity is greatest, as we show below. The range in coupling is chosen from the boundary of the non-perturbative regime to where IceCube loses sensitivity. It would be possible to extend the figure to smaller masses and couplings, showing interesting features in some of the limits, but that would detract from our focus, so we just describe those features in the text.

There are three kinematic regimes in which constraints can be derived, depending on how the mediator mass, $M$, compares to the interaction energy in the center of momentum frame, $\sqrt{s}$. These are where the mediator mass is small (i.e., like a Majoron, where the mediator mass is zero or negligible), comparable to the interaction energy (i.e., where the energy dependence of the cross section depends on the mediator mass, possibly through a resonance), or large (i.e., an effective theory where the mediator mass has been integrated out). Constraints derived assuming extremely small or 