How to find invisible particles in a collider

 You might have heard that one of the big things we are looking for in collider experiments are ever elusive dark matter particles. But given that dark matter particles are expected to interact very rarely with regular matter, how would you know if you happened to make some in a collision? The so called ‘direct detection’ experiments have to operate giant multi-ton detectors in extremely low-background environments in order to be sensitive to an occasional dark matter interaction. In the noisy environment of a particle collider like the LHC, in which collisions producing sprays of particles happen every 25 nanoseconds, the extremely rare interaction of the dark matter with our detector is likely to be missed. But instead of finding dark matter by seeing it in our detector, we can instead find it by not seeing it. That may sound paradoxical, but its how most collider based searches for dark matter work. 

The trick is based on every physicists favorite principle: the conservation of energy and momentum. We know that energy and momentum will be conserved in a collision, so if we know the initial momentum of the incoming particles, and measure everything that comes out, then any invisible particles produced will show up as an imbalance between the two. In a proton-proton collider like the LHC we don’t know the initial momentum of the particles along the beam axis, but we do that they were traveling along that axis. That means that the net momentum in the direction away from the beam axis (the ‘transverse’ direction) should be zero. So if we see a momentum imbalance going away from the beam axis, we know that there is some ‘invisible’ particle traveling in the opposite direction.

A sketch of what the signature of an invisible particle would like in a detector. Note this is a 2D cross section of the detector, with the beam axis traveling through the center of the diagram. There are two signals measured in the detector moving ‘up’ away from the beam pipe. Momentum conservation means there must have been some particle produced which is traveling ‘down’ and was not measured by the detector. Figure borrowed from here  

We normally refer to the amount of transverse momentum imbalance in an event as its ‘missing momentum’. Any collisions in which an invisible particle was produced will have missing momentum as tell-tale sign. But while it is a very interesting signature, missing momentum can actually be very difficult to measure. That’s because in order to tell if there is anything missing, you have to accurately measure the momentum of every particle in the collision. Our detectors aren’t perfect, any particles we miss, or mis-measure the momentum of, will show up as a ‘fake’ missing energy signature. 

A picture of a particularly noisy LHC collision, with a large number of tracks
Can you tell if there is any missing energy in this collision? Its not so easy… Figure borrowed from here

Even if you can measure the missing energy well, dark matter particles are not the only ones invisible to our detector. Neutrinos are notoriously difficult to detect and will not get picked up by our detectors, producing a ‘missing energy’ signature. This means that any search for new invisible particles, like dark matter, has to understand the background of neutrino production (often from the decay of a Z or W boson) very well. No one ever said finding the invisible would be easy!

However particle physicists have been studying these processes for a long time so we have gotten pretty good at measuring missing energy in our events and modeling the standard model backgrounds. Missing energy is a key tool that we use to search for dark matter, supersymmetry and other physics beyond the standard model.

Read More:

What happens when energy goes missing?” ATLAS blog post by Julia Gonski

How to look for supersymmetry at the LHC“, blog post by Matt Strassler

“Performance of missing transverse momentum reconstruction with the ATLAS detector using proton-proton collisions at √s = 13 TeV” Technical Paper by the ATLAS Collaboration

“Search for new physics in final states with an energetic jet or a hadronically decaying W or Z boson and transverse momentum imbalance at √s= 13 TeV” Search for dark matter by the CMS Collaboration

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