# Recent Paper: Constraining the Strength and CP Structure of Dark Production at the LHC: the Associated Top-Pair Channel

I'm going to describe my most recent paper, written with my now-frequent collaborator, Dorival Gonçalves, postdoc at the IPPP at Durham University. As per the norm in particle physics, this is the arxiv version, to be followed up with a journal version once we get around to the peer review process.

This paper is closely related to Dorival and my previous paper together, which I wrote about here. In fact, this was the project we were working on when we realized what we were doing had application to Higgs physics. When that happened, we decided to drop what we were currently working on and rush out the Higgs-related paper. Then we returned to the original idea, which was to find ways to study dark matter production at the LHC.

As I say often in what I write on this website, we don't know what dark matter is, as a particle. We don't know how it interacts, what its quantum numbers are, its mass, or really anything about it. We have a pretty extensive knowledge of what it does do (have mass, be seen, for the most part), but that's about it.

As physicists, that's not a very satisfying answer, and as theorists, one way to approach the problem is to write down "reasonable" models of what dark matter could be, and ask how do we find those versions of dark matter. If dark matter has interactions vaguely on the order of the weak nuclear force, than we have a reasonable theoretical story of how it could have been produced in the early Universe, which is nice, and then a bunch of predictions for experiments, which is even better.

In particular, if dark matter has “significant” interactions (where “significant” means interactions vaguely as big as the most elusive of non-gravitational forces of Nature, so pretty insignificant in the big picture), then we might be able to produce it at the Large Hadron Collider. If we are producing it at the LHC, then dark matter would zip off invisibly through the detector.

Invisible things are hard to see, so what the LHC experiments (ATLAS and CMS) actual do is look for something invisible recoiling against something they can see. By conservation of momentum, if a visible particle moves very fast in one direction, something must be moving in the other, even if I can’t see it.

Of course, there are many ways this could go wrong. Neutrinos are regular, non-dark matter particles that also are invisible at the LHC, so they’ll be a background to our dark matter searches. If particles that should be visible instead slip through cracks in the detector, that will result in a momentum imbalance that will look like dark matter. If the detector elements that measure momentum in visible particles report too much, or too little, that will look like dark matter. Joe Lykken from Fermilab once called these dark matter searches at the LHC the “garbage collection,” since everything that can go wrong can end up looking like dark matter. You have to really know and trust your model of the detectors to be able to do these searches.

Fortunately, the ATLAS and CMS experimentalists are very good at their job. Good enough that our dark matter searches at the LHC are very advanced. We’ve gotten to the point where, if the LHC can make dark matter at rates high enough for us to see, then not only are we able to produce the dark matter, we’d likely be able to start producing whatever the particle that mediates the interaction between dark matter and the regular matter.

See, for dark matter to interact with regular matter, some particle has to be able to “talk” to both dark matter and regular stuff. It is possible that this is some particle we already know about: a $Z$ boson or the Higgs boson. Or it could be something completely new, just like dark matter itself. In principle, that particle could be heavy enough that we wouldn’t see it directly; its only effect at the LHC would be to allow dark matter to be produced (this is similar to the behavior of the $Z$ and $W$ bosons in previous colliders before we had enough energy to produce them directly. We didn’t make the particles themselves, but we could see that they were mediating new interactions). However, a lot of theoretical work recently has shown that the sensitivity of the LHC is high enough that we have a good shot of seeing not only the dark matter, but some other new thing as well. Caveats exist, but in theoretical physics, working on models that may or may not be the right model of the Universe, caveats always exist. You work with what you have, and what seems most likely.

This is very exciting, because it opens the prospect of studying the Dark Sector: the physics behind dark matter.

So in this paper, Dorival and I considered one particular version of the Dark Sector physics. We work with what’s called a Simplified Model: rather than trying to flesh out everything that might be going on with dark matter, you just add the bare minimum: dark matter, and one new particle that allows dark matter to talk to regular matter. Once you decide what the quantum numbers of this mediator are, you’ve locked in the range of possible interactions with normal matter, and you can start asking more detailed questions about how to look for that particular Simplified Model.

The Simplified Model we’re interested in in this paper is one where the dark matter talks to regular matter through a spin-0 particle: a particle similar to the Higgs. Indeed, this similarity to the Higgs is one of the reasons this type of Simplified Model is interesting: the mediator could be the Higgs discovered at the LHC, or it could be part of a larger Higgs sector (which is pretty common in theoretical models; there is no reason that the Higgs we found is the only Higgs boson). Connecting dark matter to the Higgs is an attractive idea, and such models are often called “Higgs Portal” mediators.

As I’ve talked about before , when you have a spin-0 particle, you can ask about its CP properties: how does the physics of that particle respect the inversion of charge and parity. One way to say this is: would the laws of physics be exactly the same here as compared to a universe made of antimatter… in a mirror. If something is CP-even, then turning matter to antimatter and switching left and right changes nothing, if something is CP-odd, then this transformation introduces a number of minus signs.

Spin-0 CP-even particles are called “scalars,” while the CP-odd particles are “pseudoscalars.” So if we want to think about Simplified Models of spin-0 mediators, we can think about either of these two options. This one difference results in a number of predictions: CP-even mediators could induce signals of dark matter from the Galactic Halo scattering in nuclei — searches for this are called “direct detection.” Pseudoscalar mediators don’t cause such interactions, but can allow annihilation of dark matter in the Universe today — this is called “indirect detection.”

So, one could imagine that, if you found a signal of dark matter at the LHC, you might want to know if it was mediated by a CP-even or CP-odd mediator, and then compare that with signals or lack of signals from our other types of dark matter experiments. In Dorival and my previous paper, we had found a way to directly measure the CP properties of the Higgs boson when it gets produced along with a pair of top quarks.

Azimuthal Angle for scalar mediators (black) and pseudoscalar mediators (red) after cut on large transverse momentum. Note the significant difference in angular distribution near 0.

So, one could imagine that, if you found a signal of dark matter at the LHC, you might want to know if it was mediated by a CP-even or CP-odd mediator, and then compare that with signals or lack of signals from our other types of dark matter experiments. In Dorival and my previous paper , we had found a way to directly measure the CP properties of the Higgs boson when it gets produced along with a pair of top quarks. Interestingly, the variable we found ($\Delta \phi_{\ell\ell}$) works better when the mediator gets a large size-ways momentum kick, recoiling against the top quarks and sending them flying with higher-than-average momentum. This is exactly the sort of event that you would need to find dark matter.

So we calculated how well we'd be able to look for dark matter assuming either a scalar or pseudoscalar mediator (we parameterized this in terms of the strength of the interaction with regular matter $g_v$ as a function of mediator mass. Heavier mediators are harder to produce, and thus require a bigger $g_v$). We had done an earlier analysis of this in a previous paper, and in fact that paper was a bit more general than some of the assumptions we made here, because here we were more interested in demonstrating that we could measure the CP properties.

We then did something completely new, which was to see how much data we’d need to distinguish between a CP-even and CP-odd mediator, assuming we found dark matter at the LHC (and assuming that it was this sort of Simplified Model, rather than the other options out there). It’s a fair amount of data (measured in inverse femtobarns as we are wont to do in particle physics), but it’s not bonkers-impossible levels of data. A decade of LHC running, not 100 years.

Amount of data required to distinguish CP-even and CP-odd mediators with 95% confidence.

So, this paper is about only one possible type of dark matter, with one possible interaction with the stuff that the LHC can probe directly. But it’s a fairly well-motivated model. The idea would be, if we’re fortunate enough to see dark matter, to start building variables like the one we propose, and then cross-correlate with signals (or lack of signals) from other experiments. If, for example, we find that our mediator should be CP-even but we’re not seeing direct detection signals, than that’d be a mystery.

And we physicists like those.