Precision calculations to test supersymmetry at colliders

After the introduction to supersymmetry posted last Monday, I discuss today my latest scientific publication on this topic. It appeared on the arXiv about a month ago, and it is currently undergoing peer review. In this article, collaborators and I achieved a precision calculation in a supersymmetric context, such a calculation being relevant for the upcoming runs of the Large Hadron Collider (the LHC) at CERN.

In this calculation, we computed state-of-the-art predictions for a specific process in which two supersymmetric particles are produced from the collision of two protons. In the context of the LHC, usually the focus is put on the production of a pair of identical supersymmetric particles. On the contrary we considered the simultaneous production of two different supersymmetric particles: one partner of the quarks (i.e. the elementary building blocks of atomic nuclei), and one partner of either the electroweak bosons (i.e. the weak or electromagnetic force carriers) or of the Higgs boson.

In this blog, I first summarise the outcome of the previous post to emphasise why supersymmetry is an interesting theory for phenomena beyond the Standard Model of particle physics. Next, I move on with searches for supersymmetry at the LHC and detail what is done experimentally. From the conclusions arising from data, we can naturally explain why processes such as those considered in my last article are important, despite of the fact that they have been a bit overlooked up to now. Finally, I discuss one plot illustrating the level of precision in the predictions that we achieved in our work.

For those pushed for time, feel free to go directly to the last section of this blog, which includes a TLDR version of it.

^{[Credits: Original image from darksouls1 (Pixabay)]}

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Why supersymmetry?

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Supersymmetry appears naturally when we try to build a generic theory of particle physics satisfying some symmetry principles.

To make it short, in our universe there are two classes of particles with very different properties, fermions and bosons. The difference between them comes from their spin quantum number, that indicates the amount of intrinsic angular momentum that they possess. This quantum number is a half-integer multiple of a fundamental quantity for a fermion, and an integer multiple of this fundamental quantity for a boson. All the structure of the world around us originates from this simple difference. Whereas all of this may sound confusing, feel free to check out the previous post for more information.

In supersymmetry, each fermion of the theory is linked to a bosonic partner, and each boson of the theory is linked to a fermionic partner. If we apply this to the Standard Model, we end up with a supersymmetrised version of the Standard Model in which the quarks and leptons are associated with bosonic partners called squarks and sleptons. In addition, the forcer carriers and the Higgs boson are paired with gauginos and higgsinos. Among those, we distinguish the gluinos (the partners of the gluons) and the electroweakinos (the partners of the photon, the W boson, the Z boson and the Higgs boson).

Doubling the particle content of the Standard Model has some interesting features. For instance, the theory gets equipped with a particle that can play the role of dark matter. In addition, other conceptual limitations of the Standard Model are cured, like its hierarchy problem (i.e. why the size of the Higgs field is what it is), and supersymmetry paves the way to the unification of the fundamental interactions at high energies.

As a consequence, supersymmetry is actively searched for, for instance, at CERN’s Large Hadron Collider.

^{[Credits: Pcharito (CC BY-SA 3.0)]}

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Supersymmetry at the LHC

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In order to search for supersymmetry at CERN’s Large Hadron Collider, we rely on the fact that in a supersymmetric model there is a dark matter particle, and that this particle is always the lightest of all superpartners.

When produced, dark matter leaves the detector invisibly. The only way to feel its presence is through the fact that some energy is missing. One of the golden rules of physics indeed tells us that energy and momentum are conserved quantities. Therefore, the energy and momentum available in the initial state of any process is equal to those available in the final state of the process. If dark matter is produced, then some energy and momentum are missing, carried away by the undetected dark matter. This is precisely how we reconstruct invisible stuff from what is visible.

Moreover, any heavy supersymmetric particle always decays into dark matter and particles of the Standard Model. This decay can be either a direct one, or a cascade decay. In the former case, the produced supersymmetric particle decays directly into dark mater and one particle of the Standard Model. For instance, a squark can decay into a quark and dark matter. In the latter case, the supersymmetric particle decays first into another lighter supersymmetric particle and one Standard Model particle; then the second supersymmetric particle decays itself, and so on. This cascade stops when we reach the lightest supersymmetric particle, namely dark matter, that is stable.

Consequently, a typical supersymmetric signal contains a copious amount of missing energy and some Standard Model particles. Among all options, we focus first on the simplest signals and on those that are expected to be produced more.

^{[Credits: CERN (CC BY 4.0]}

The strong interaction being the strongest of all fundamental interactions, then it is reasonable to consider the production of supersymmetric particles that are sensitive to this force. This leads to the production of two types of supersymmetric particles, squarks (the partners of the Standard Model quarks) and gluinos (the partners of the gluons).

In the simplest cases, those particles decay into dark matter a one or two quarks. Therefore, the corresponding signals are made of jets of collimated strongly-interacting particles (see here for more information) and missing energy carried away by the produced dark matter particles.

So far, there is however no sign for supersymmetry in data, and in particular no hint left by a squark or a gluino in a detector. As a consequence, if squarks and gluinos exist, then they must be very heavy. Their large mass consequently leads to a small production rate, despite of the strength of the strong interaction driving their production.

Another option to explain their non observation would be to consider more complex decays. There are experimental analyses targeting these, and the conclusions are the same: no sign of any phenomena beyond the Standard Model of particle physics in data.

^{[Credits: CERN]}

By being enforced to be heavy, squarks and gluinos are now associated with rare phenomena. In order to check out something potentially more frequent, we focus on the production of supersymmetric particles non sensitive to the strong interaction. In this case, the production rate is smaller than that of a pair of squarks or gluinos for a fixed mass. Therefore, we may have those particles around, being light, and still escaping observation (as yielding too rare events).

An example of those particles are electroweakinos (the partners of the photon, the W boson, the Z boson and the Higgs boson). The results of the corresponding searches are however negative: there is no signal of an electroweakino in data. Consequently bounds are imposed on their masses.

These bounds are however weaker than that set on squarks and gluinos. In all cases, the bounds are such that the resulting production rates are small enough to explain the non-observation of any signal. For particles subject to a very copious production rate (like squarks or gluinos), then the only way to make the rate small enough is to enforce the mass of these particles to be large. On the contrary, for particles subject to a naturally smaller rate (like for electroweakinos), then we can live with a smaller lower value for their mass.

This brings us to the topic of my last research article. Whereas we always consider the production of a pair of identical supersymmetric particles (two squarks, two gluinos or two electroweakinos), we can wonder what goes on when we consider the production of one strongly-interacting supersymmetric particle like a squark, together with one non-strongly-interacting supersymmetric particle like an electroweakino.

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Semi-strong supersymmetry production

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Today, limits on supersymmetry are pretty strong (especially for the strongly-interacting partners). However, future data is only expected to make them slightly stronger. The margin is indeed thin. It is thus important to think about new ways to get insight on supersymmetric phenomena. This is where my work starts to play a role.

Collaborators and I decided to focus on a process a bit more complicated than those currently investigated, namely the production of a pair of different supersymmetric particles. We considered the production of one squark and one electroweakino. The former is sensitive to the strong interaction and is thus constrained to be very heavy by the non-observation of any signal. The latter is not sensitive to the strong force and is thus subjected to weaker bounds.

We thus have a process that is both semi-strong and semi-non-strong, and that leads to the production of one particle that can be light and one particle that is heavy. The main advantage is that the production rate that is not small (as involving partly the strong force). However, the entire setup becomes more complicated when we try to have a simple view of what is going on. The reason is that there are more particles involved in the process than in the case of the production of pair of identical particles, which gives more free parameters to play with and more options that need to be tried out.

In my work, we achieved a new precision calculation for the production of one squark and one electroweakino, such a process being among those potentially useful in the upcoming runs of the LHC. This calculation will be useful to extract the best possible limits in the case of a non-observation, or to measure the relevant parameters in the case of a discovery. An example of results is shown on the figure below.

^{[Credits: arXiv]}

In this illustrative figure, we depict the production rate of a squark and an electroweakino as a function of the squark mass, and for a fixed electroweakino mass. The rate is displayed on the y-axis. The value 10^-3 pb corresponds to about 150 events in the currently recorded LHC dataset, or 4,000 events expected in future data. The squark mass is displayed on the x-axis and is given in GeV (1 GeV is the mass of a proton).

We display results for three calculations (in blue, orange and green), each being attached to a different level of precision that can be extracted from the shaded areas shown in the lower panel of the plot. A large band corresponds to a large error and a small one to a small error (and thus a precise calculation).

• The blue result is the most naive one and is known for decades. It can be obtained in 3 minutes with tools such as the one presented in this blog advertising a particle physics citizen science project on Hive. It however suffers from large uncertainties (the blue error bar is very large).
• The orange predictions are more complicated to obtain and are known for a few years only. In this calculation, sub-leading quantum corrections are included, which makes the result more reliable. More information on precision predictions are shared in this old blog.
• The green curve is our new result. We made use of state-of-the-art techniques to improve the predictive power by a significant amount, as testified by the size of the green error bar compared with that of the other bands.

The major improvement in our computation is that we identified and consistently included quantum corrections to all orders in perturbation theory, from the knowledge of older predictions (the orange curve). This resummation technique is well established and we applied it (this took us a year) to a process not considered so far. As a result, the size of the uncertainties is now within a few percents.

In our article we hence computed precision predictions for a supersymmetric process that has the potential to become very relevant in the near future, if squarks and gluinos are too heavy to be pair-produced.

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Summary - new precision predictions for supersymmetry

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Supersymmetry is one of the most studied frameworks for new phenomena beyond the Standard Model of particle physics. However, the absence of any signal at colliders such as CERN’s Large Hadron Collider implies strong constraints on the supersymmetric partners of the Standard Model particles.

The strongest bounds apply to squarks (the partners of the elementary building blocks of all atomic nuclei, the quarks) and gluinos (the partners of the mediators of the strong force, the gluons), as all these particles are sensitive to the strong force (so that large production rates are expected). Then come milder bounds on other supersymmetric particles, that are associated with smaller production rates.

As a consequence, whereas squarks must be heavy, electroweakinos (the partners of the Higgs boson, the photon, the W boson and the Z boson) can still be lighter.

In my last research article, we considered a process in which one squark is produced with one electroweakino. This processes is a semi-strong one, as only one of the two produced particles is sensitive to the strong force. The corresponding production rate is therefore of intermediate size, and this holds despite of the existing bounds. We indeed have here the possibility to produce one heavy particle (the squark) and one lighter particle (the electroweakino). This process is thus not too suppressed, and offers hence a good handle on supersymmetry for the up-coming years.

Collaborators and I achieved precision predictions for that process. This will offer the option to derive robust conclusions from data, both in case of a discovery or of a non-observation. With our work, the theoretical uncertainties inherent to the predictions are indeed reduced to a few percents.

I will stop here for today. However, feel free to share your questions, comments and feedbacks below, and of course to request clarifications wherever they may be needed. I am always glad to react to any form of engagement.

The current week being already super intense (much more than the previous one that was a true nightmare for me), I cannot guarantee any blog for the next Monday. I will however try. In the meantime, I wish you all a wonderful week!