Dark Forces Revisited

I have a new paper out with Sonny Mantry and Michael Ramsey-Musolf, following up on our earlier paper with Chris Stubbs. The original idea was to imagine a new long-range force that couples directly to dark matter, but not to ordinary visible matter. (A simple scalar force, which is universally attractive between any two objects, as opposed to all the messy complications of a dark electromagnetic force.) Due to the magic of quantum mechanics, such a force will couple indirectly to ordinary matter via virtual particles. So in the first paper we studied how you could use fifth-force searches in ordinary matter to look for such dark forces.

In this paper we are a little more systematic, and we follow Jo Bovy and Glennys Farrar in also considering consequences for direct dark matter detection experiments, as well as dark matter searches at colliders. Here is the (somewhat lengthy) abstract:

Implications of a Scalar Dark Force for Terrestrial Experiments
Authors: Sean M. Carroll, Sonny Mantry, Michael J. Ramsey-Musolf

Abstract: A long range Weak Equivalence Principle (WEP) violating force between Dark Matter (DM) particles, mediated by an ultralight scalar, is tightly constrained by galactic dynamics and large scale structure formation. We examine the implications of such a “dark force” for several terrestrial experiments, including Eotvos tests of the WEP, direct-detection DM searches, and collider studies. The presence of a dark force implies a non-vanishing effect in Eotvos tests that could be probed by current and future experiments depending on the DM model. For scalar singlet DM scenarios, a dark force of astrophysically relevant magnitude is ruled out in large regions of parameter space by the DM relic density and WEP constraints. WEP tests also imply constraints on the Higgs-exchange contributions to the spin-independent (SI) DM-nucleus direct detection cross-section. For WIMP scenarios, these considerations constrain Higgs-exchange contributions to the SI cross-section to be subleading compared to gauge-boson mediated contributions. In multicomponent DM scenarios, a dark force would preclude large shifts in the rate for Higgs decay to two photons associated with DM-multiplet loops that might otherwise lead to measurable deviations at the LHC or a future linear collider. The combination of observations from galactic dynamics, large scale structure formation, Eotvos experiments, DM-direct-detection experiments, and colliders can further constrain the size of new long range forces in the dark sector.

The looming problem with this whole game is that a long-range scalar force is unnatural. A scalar field should, by all rights, have a large mass, and that kind of mass drastically limits the range of the corresponding force. (That’s why the weak interactions are negligible compared to electromagnetism for everyday purposes; the W and Z bosons have a large mass, while the photon is massless.) You can keep scalar fields light by imposing symmetries, but that also tends to squelch any interesting interactions. But okay, it’s also unnatural for the Higgs boson to have a mass less than the Planck scale, or for the cosmological constant to be much less than the Planck scale. Unnatural things happen in the real world, so it’s not crazy to try to understand how they would manifest themselves.

The question is, once you’ve allowed yourself some unnaturalness, where do you stop? In this paper we’ve tried hard to minimize the number of parameters we unnaturally tuned to small values. We’ve tuned things to keep the scalar field light while not messing up the mass of the ordinary Higgs field, but tried not to tune anything else. In that case there should be mixing of the new scalar with the Higgs, and that mixing plays an important role in the phenomenology. In particular, there are implications for ground-based experiments; thus the title! It’s a long paper, but if you read one paper on the implications of a scalar dark force for terrestrial experiments this week, it should definitely be this one.