Model for Thermal Relic Dark Matter of Strongly Interacting Massive Particles
7/8/2015
441 citations (397 excluding self-citations). The concrete model that turned the SIMP mechanism from a general framework into a calculable theory.
The Problem
The SIMP Miracle paper established that 3-to-2 annihilations could set the dark matter relic abundance and naturally produce sub-GeV dark matter with sizable self-interactions. But the mechanism needed a concrete realization: a specific theory where the 3-to-2 process arises naturally, the rates are calculable, and the predictions are sharp enough to test.
The Key Idea
The model uses a hidden-sector gauge theory that confines, exactly like QCD. The dark matter particles are the pseudo-Nambu-Goldstone bosons of the hidden chiral symmetry breaking, analogous to pions in QCD. The critical ingredient is the Wess-Zumino-Witten (WZW) term, a topological interaction that arises automatically in any theory with chiral symmetry breaking. The WZW term provides exactly the 3-to-2 vertex needed for the SIMP mechanism. It is not added by hand; it is a mathematical consequence of the symmetry structure.
The model predicts a preferred mass window where the relic abundance, self-interaction cross-section, and kinetic equilibrium with the Standard Model are all simultaneously satisfied. The 2-to-2 self-interaction rate, set by the same chiral Lagrangian that controls the 3-to-2 rate, falls in the range favored by astrophysical observations of galaxy cores and cluster collisions. Adding Hitoshi Murayama to the collaboration brought expertise in chiral perturbation theory that made the calculation precise.
Impact
The paper gave the SIMP program a concrete target for experimentalists. The preferred mass window and the relationship between the 3-to-2 and 2-to-2 cross-sections are specific enough to compare against direct detection experiments like SENSEI and DarkSide-50, astrophysical self-interaction constraints from galaxy clusters, and collider searches for dark photon mediators. Much of the subsequent SIMP literature uses this model, or close variants, as the benchmark. The LDMX experiment proposal (247 citations) cites the SIMP model as a headline theoretical target.
The model also opened an unexpected direction: Schwaller’s “Gravitational Waves from a Dark Phase Transition” (384 citations) showed that the strongly coupled hidden sector in the SIMP model undergoes a first-order phase transition in the early universe, producing gravitational wave signals potentially detectable by future experiments like LISA. The SIMP mechanism connected particle physics not just to dark matter detection but to gravitational wave astronomy.
Recollections
In late 2013, I visited the Institute for Physics and Mathematics of the Universe in Japan and gave a talk on the SIMP mechanism. Hitoshi Murayama was in the audience. Hitoshi is one of the great model builders in the world, and during the talk he immediately understood two things: how crappy our toy models were, and how to fix them. Right after I finished, Hitoshi proposed the solution: pions of a hidden non-Abelian gauge theory. The 5-point interaction comes from the Wess-Zumino-Witten term, which is topological and appears automatically in any theory with chiral symmetry breaking. The pions are completely stable. No model-building tricks required.
We wrote it up quickly, largely thanks to the heroic efforts of Eric Kuflik and Hitoshi. The paper made a huge difference in the perception of the SIMP mechanism. The original paper had established the mechanism but relied on schematic models that were, fairly described, “puke buckets” — every trick a model builder knows crammed together. Hitoshi’s model showed that nature might actually choose to realize the SIMP mechanism in a simple, beautiful way. The WZW interaction is, as far as I’m concerned, the coolest interaction in all of quantum field theory, and here it was doing exactly the job the SIMP miracle needed.