# How do you distinguish between missing momentum from a neutrino and from dark matter?

I thought googling this would give me an answer quite quickly, but actually couldn't find much, so maybe it's a silly question. But I read that dark matter searches rely on measuring missing momentum in collisions, and wondered how would you know this was due to dark matter and not neutrinos? Would you look for missing energy in processes that shouldn't produce neutrinos?

• – Qmechanic Aug 6 '19 at 10:02
• In general you can’t ever be sure what a given event contained. You can only look at the statistics, i.e. if a given event type occurs more often than the SK would expect. – knzhou Aug 6 '19 at 15:40
• Events with neutrinos can be an irreducible background in DM searches – innisfree Aug 7 '19 at 15:15

The answer is more complicated than you bargained for, since we have to distinguish between different species of neutrinos:

1. The left-handed neutrinos: There are three flavors of left-handed neutrinos, namely electron/muon/tau neutrinos. They are the canonical massless neutrinos described in the text books as ingredients of the standard model. As the up town/isospin sister of the left-handed-neutrino-electron $$SU(2)$$ twin, they are involved in the weak interaction. This is the typical context where “missing momentum in collisions” is discussed by particle physicists.

2. The mostly-left-handed neutrinos: After the revelation that neutrinos can oscillate between flavors, we realize that neutrinos are not massless after all. Neutrino mass could be either Dirac mass (which means there are right-handed partners of the left-handed neutrinos, contrary to the claim of the original standard model) or Majorana mass. More likely they are the lighter Eigenvectors of the type I seesaw model, which implies that they are mostly left-handed with a bit right-handed non-pedigree. Given the tiny seesaw mass of these mostly-left-handed neutrinos, they are not clumpy and thus could only be hot (thus false) dark matter guarded by the Knights Who Say “Ni!”, different from the bona fide cold dark matter which is the Holy Grail of cosmology.

3. The mostly-right-handed neutrinos: They are the heavier Eigenvectors of the type I seesaw model, as opposed to the mostly-left-handed neutrinos which are the lighter Eigenvectors. The masses of the mostly-right-handed neutrinos are of Majorana origin, which are not constrained by the standard model symmetries and thus they could be very heavy (all the way up to the grand unification scale, which is not far from the Planck scale). In light of the humongous Majorana masses, they could be genuine cold dark matter candidates, the real McCoy which looms large in either early cosmos formation or galactic rotation curves. The catch is that you will not find them in the routine weak processes, since they (I am hereafter talking about the purely right-handed portion) are standard model singlets! They could potentially interact via the beyond-standard-model $$Z'$$ gauge field though, which are presumably suppressed by the tremendous Majorana mass scale (the other) “Higgs” mechanism. You could observe “missing momentum in collisions” of this sort, if you are willing to cough up more money than “building the wall” for such an almost unachievable large collider.

There is a nice summary of the search strategies in the paper Overview of searches for dark matter at the LHC by Vasiliki A Mitsou.

The strategy is to choose events with a large missing transverse momentum then reconstruct the scattering event using the observed particles. Since the interactions of neutrinos with standard model particles are well understood it is generally clear whether or not the missing momentum is consistent with neutrinos produced in the scattering.

• This is kind of vague. What property is it that differentiates one particle from the other? Are they reconstructing the mass? – Ben Crowell Aug 6 '19 at 13:15
• @BenCrowell If you have an event with a boosted centre-of-mass, then something invisible went off to the side. If the event conserves everything except lepton-number, the something is probably a neutrino. If the event did actually conserve everything (baryons and leptons), you might have something unusual. – Oscar Bravo Aug 7 '19 at 15:17