A Pioneering Search for Jets-Of-Jets

Last week, when I wasn’t watching democracy bleed, I was participating in an international virtual workshop, attended by experts from many countries. This meeting of particle experimenters and particle theorists focused on the hypothetical possibility known as “hidden valleys” or “dark sectors”. (As shorthand I’ll refer to them as “HV/DS”). The idea of an HV/DS is that the known elementary particles and forces, which collectively form the Standard Model of particle physics, might be supplemented by additional undiscovered particles that don’t interact with the known forces (other than gravity), but have forces of their own. All sorts of interesting and subtle phenomena, such as this one or this one or this one, might arise if an HV/DS exists in nature.

Of course, according to certain self-appointed guardians of truth, the Standard Model is clearly all there is to be found at the Large Hadron Collider [LHC], all activities at CERN are now just a waste of money, and there’s no point in reading this blog post. Well, I freely admit that it is possible that these individuals have a direct line to God, and are privy to cosmic knowledge that I don’t have. But as far as I know, physics is still an experimental science; our world may be going backwards in many other ways, but I don’t think we should return to Medieval modes of thought, where the opinion of a theorist such as Aristotle was often far more important than actually checking whether that opinion was correct.

According to the methods of modern science, the views of any particular scientist, no matter how vocal, have little value. It doesn’t matter how smart they are; even Nobel Prize-winning theorists have often been wrong. For instance, Murray Gell-Mann said for years that quarks were just a mathematical organizing principle, not actual particles; Martinus Veltman insisted there would be no Higgs boson; Frank Wilczek was confident that supersymmetry would be found at the LHC; and we needn’t rehash all the things that Newton and Einstein were wrong about. In general, theorists who make confident proclamations about nature have a terrible track record, and only get it right very rarely.

The central question for modern science is not about theorists at all. It is this: “What do we know from experiments?”

And when it comes to the possibility of an HV/DS, the answer is “not much… not yet anyway.”

The good news is that we do not need to build another multibillion dollar experimental facility to search for this kind of physics. The existing LHC will do just fine for now; all we need to do is take full advantage of its data. But experimenters and theorists working together must develop the right strategies to search for the relevant clues in the LHC’s vast data sets. That requires completely understanding how an HV/DS might manifest itself, a matter which is far from simple.

Last week’s workshop covered many topics related to these issues. Today I’ll just discuss one: an example of a powerful, novel search strategy used by the ATLAS experiment. (It’s over a year old, but it appeared as my book was coming out, and I was too busy to cover it then.) I’ll explain why it is a good way to look for strong forces in a hidden valley/dark sector, and why it covers ground that, in the long history of particle physics, has never previously been explored.

Jets-of-Jets, and Why They’re Tricky

I already discussed topics relevant to today’s post in this one from 2022, where I wrote about a similar workshop, and you may well find reading that post useful as a complement to this one. There the focus was on something called “semi-visible jets”, and in the process of describing them I also wrote about similar “jets-of-jets”, which are today’s topic. So here is the second figure from that older post, showing ordinary jets from known particles, which are covered in this post, as well as the jets-of-jets and semi-visible jets that might arise from what is known as a “confining HV/DS.”

How does a jet-of-jets form? In a hidden valley with a “confining” force (a few examples of which were explored by Kathryn Zurek and myself in our first paper on this subject), some or all of the HV/DS particles are subject to a force that resembles one we are familiar with: the strong nuclear force that binds the known quarks and gluons into protons, neutrons, pions, and other hadrons. By analogy, a confining HV/DS may have “valley quarks” and “valley gluons” (also referred to as “dark quarks” and “dark gluons”) which are bound by their own strong force into dark hadrons.

The analogy often goes further. As shown at the left of Fig. 1, when a high-energy quark or gluon comes flying out of a collision of protons in the LHC, it manifests itself as a spray of hadrons, known as a jet. I’ll call this an “ordinary jet.” Most of the particles in that ordinary jet are ordinary pions, with a few other familiar particles, and they are observed by the LHC detectors. Images of these jets (not photographs, but precise reconstructions of what was observed in the detector) tend to look something like what is shown in Fig. 2. In this picture, the tracks from each jet have been given a particular color. You see that there are quite a lot of tracks in the highest-energy jets, whose tracks are colored green and red. [These tracks are mostly from the electrically charged pions. Electrically neutral pions turn immediately into photons, which are also detected but don’t leave tracks; they and instead are absorbed in the detector’s “calorimeters” (the red and green circular regions.) The energy from all the particles, with and without tracks, is depicted by the dark-green/yellow/dark-red bars drawn onto the calorimeters.]

But what happens if a dark quark or dark gluon is produced in that collision? Well, as shown in the center panel of Fig. 1, a spray of dark hadrons results, in the form of a dark jet. The dark hadrons may be of various types; their precise nature depends on the details of the HV/DS. But one thing is certain: because they are hidden (dark), they can’t be affected by any of the Standard Model’s forces: electromagnetic, strong nuclear, or weak nuclear. As a result, dark hadrons interact with an LHC detector even less than neutrinos do, which means they sail right through it. And so there’s no hope of observing these objects unless they transform into something else that we can observe.

Fortunately [in fact this was the main point of my 2006 paper with Zurek], in many HV/DS examples, some or all of the dark particles

• will in fact decay to known, observable particles, and
• will do so fast enough that they can be observed in an LHC detector.

This is what makes the whole subject experimentally interesting.

For today, the main question is whether all or some of the dark hadrons decay faster than a trillionth of a second. If all of them do, then, as depicted in the central panel of Fig. 1, the dark jet of dark hadrons may turn into a jet-of-jets (or into something similar-looking, if a bit more complex to describe.) If only a fraction of the dark hadrons decay, while others pass unobserved through the detector, then the result is a semi-visible jet (or semi-visible jet-of-jets, really), shown in the right panel of Fig. 1.

Cool! Let’s go look through LHC data for jets-of-jets!

The Key Distinction Between Jets and Jets-Of-Jets

Not so fast. There’s a problem.

You see, ordinary jets come in such enormous numbers, and vary so greatly, that it’s not immediately obvious how to distinguish a somewhat unusual ordinary jet from a true jet-of-jets. How can this be done?

Theorists and especially experimenters have been looking into all sorts of complex approaches. Intricate measures of jet-weirdness invented by various physicists are being pumped en masse into machine learning algorithms (the sort of AI that particle physicists have been doing for over a decade). I’m all in favor of sophisticated strategies — go for it!

However, as I’ve emphasized again and again in these workshops, sometimes it’s worth doing the easy thing first. And in this context, the ATLAS experimental collaboration did just that. They used the simplest strategy you can think of — the one already suggested by the left and center panels of Figure 1. They exploit the fact that a jet-of-jets of energy E (or transverse momentum p_T) generally has more tracks than an ordinary jet with the same energy E (or p_T). [This fact, emphasized in Figs. 19 and 20 of this paper from 2008, follows from properties of confining forces; I’ll explain its origin in my next post on this subject.]

So at first glance, to look for this sign of an HV/DS, all one has to do is look for jets with an unusual number of tracks. Easy!

Well, no. Nothing’s ever quite that simple at the LHC. What complicates the search is that the number of LHC collisions with jets-of-jets might be just a handful — maybe two hundred? forty? a dozen? Making HV/DS particles is a very rare process. The number of LHC collisions with ordinary jets is gigantic by comparison! Collisions that make pairs of ordinary jets with energy above 1 TeV — a significant fraction of the energy of LHC’s proton-proton collisions — number in the many thousands. So this is a needles-in-a-haystack problem, where each of the needles, rather than being shiny metal, looks a lot like an unusual stalk of hay.

For example, look at the event in Fig. 3 (also from ATLAS). There are two spectacular jets, rather wide, with lots of tracks (and lots of energy, as indicated by the yellow rectangles on the detector’s outer regions.) Might this show two jets-of-jets?

Maybe. Or maybe not; more likely this collision produced two really unusual but ordinary jets. How are we to tell the difference?

In fact, we can’t easily tell, not without sophisticated methods. But with a simple strategy, we can tell statistically if the jets-of-jets are there, employing a trick of a sort commonly used at the LHC.

A Efficient, Simple, Broad Experimental Strategy

The key: both the ordinary jets and the jets-of-jets often come in pairs — for analogous reasons. It’s common for a high-energy quark to be made with a high-energy anti-quark going the opposite direction, giving two ordinary jets; and similarly it would be common for a dark quark to be made with a dark anti-quark, making two jets-of-jets. (Gluon pairs are also common, as would be pairs of dark gluons.)

This suggests the following simple strategy:

• Gather all collisions that exhibit two energetic jets (we’ll call them “dijet events”) and that satisfy a certain criterion that I’ll explain in the next section.
• Count the tracks in each jet; let’s call the number of tracks in the two jets n₁ and n₂.
• Suppose that we consider 75 tracks or more to be unusual — more typical of a jet-of-jets than of an ordinary jet. Then we can separate the events into four classes:
  • Class A: Those events where n₁ and n₂ are both less than 75;
  • Class B: Those events where n₁ < 75 ≤ n₂ ;
  • Class C: Those events where n₂ < 75 ≤ n₁ ;
  • Class D: Those events where n₁ and n₂ are both 75 or greater.
• Importantly, the two ordinary jets in a typical dijet event form largely independent of one another (with some caveats that we’ll ignore), so we can apply simple probability. If the probability that an ordinary jet has 75 tracks or more is p, then (see Fig. 4 below)
  • the number of events N_A in class A is proportional to (1-p)²,
  • the number of events N_B in class B and N_C in class C are both proportional to p(1-p), and
  • the number of events N_D in class D is proportional to p².

These proportions are just those of the areas of the corresponding regions of the divided square in Fig. 4.

As suggested by Fig. 4, because the two jets are of the same type, N_B ≈ N_C (where “≈“ means “approximately equal” — they differ only due to random fluctuations.) Furthermore, because the probability p of having more than 75 tracks in an ordinary jet is really small, we can write a few relations that are approximately true both of the numbers in each class and of the corresponding areas of the square in Fig. 4.

• N_total ≈ N_A
  • (i.e. almost all the events are in Class A)
• N_B / N_A ≈ N_C / N_A ≈ p(1-p) / (1-p)² = p / (1+p) ≈ p
  • (i.e. the fraction of events in class B or C is nearly p)
• N_D / N_total ≈ p² ≈ (N_B / N_A)² ≈ N_B N_C / ( N_total )²
  • (i.e therefore by measuring N_B , N_C , and N_total , we can predict the number of events in class D. )

Would you believe this strategy and others like it are actually called the “ABCD method” by experimental particle physicists? That name is more than a little embarrassing. But the method is indeed simple, and whatever we call it, it works. Specifically, it allows us to predict the number N_D before we actually count the number of events in class D. And when the count is made, two things may happen:

• If the measured N_D is roughly the same as the prediction, we know that most of the events in Class D — the dijet events where both jets have an extreme number of tracks — are probably pairs of unusual ordinary jets, and there’s no sign of anything unexpected.
• If the measured N_D is significantly larger than the prediction, then we have discovered a new source of dijet events where both jets have an extreme number of tracks, one that is not expected in the Standard Model. Maybe they are from an HV/DS, or maybe from something else — but that’s a detail to be figured out later, when we’re done drinking all the champagne in France.

[Note: I chose the number 75 for simplicity. The experimenters make their choice in a more complicated way, but this is a detail which doesn’t change the basic logic of the search.]

No similar search for jets-of-jets had ever previously been performed, so I’m sure the experimenters were quite excited when they finally unblinded their results and took a look at the data. But nothing unusual was seen. (If it had been, you would have already heard about it in the press, and France would have run out of bubbly.) Still, even though a null result isn’t nearly as revolutionarily important as a discovery, it is still evolutionarily important, representing an important increase in our knowledge.

What exactly we learn from this null result depends on the individual HV/DS example. Basically, if a specific HV/DS produces a lot of jets-of-jets, and those jets-of-jets have lots of tracks, then it would have been observed, so we can now forget about it. HV/DS models that produce fewer or less active jets-of-jets are still viable. What’s nice about this search is that its elegant simplicity allows a theorist like me to quickly check whether any particular HV/DS is now excluded by this data. That task won’t be so easy for the more sophisticated approaches that are being considered for other search strategies, even though they will be even more powerful, and necessary for some purposes.

One More Criterion in the Strategy

As I began to outline the strategy, I mentioned a criterion that was added when the dijet events were initially selected. Here’s what it is.

Click here for the details

The ATLAS experimenters assumed a simple and common scenario. They imagined that the jets-of-jets are produced when a new particle X with a high mass m_X is produced, and then the X immediately decays to two jets-of-jets. Simple examples of what X might be are

• a heavy version of a Z boson made in a collision of a quark and an anti-quark, or
• a heavy version of a Higgs-like boson created in the collision of two gluons.

An example of the former, in which the heavy Z-like particle is called a “Z-prime”, is shown in Fig. 5.

If the X particle were stationary, then its total energy would be given by Einstein’s formula E=m_Xc². If such a particle were subsequently to decay into two jets-of-jets, then the total energy of the two jet-of-jets would then also be E=m_Xc² (by energy conservation.) In such a situation, all the events from X particles would have the same total energy, and we could use that to separate possible jets-of-jets events from pairs of ordinary jets, whose energy would be far more random.

Typically, however, the X particle made in a proton-proton collision will not be stationary. Fortunately, a similar strategy can be applied, using something know as the invariant mass of the two jets-of-jets, which will always be m_X. [Well, nothing is simple at the LHC; these statements are approximately true, for various reasons we needn’t get into now.]

And so, when carrying out the strategy, the experimenters

• Pick a possible value of m_X ;
• Select all dijet events where the two jets together are measured to have an invariant mass approximately equal to m_X ;
• Carry out an ABCD search only within that selected set of events, to see if the number of Class D events exceeds the prediction;
• Repeat for a new value of m_X .

Missed Opportunity?

I have only one critique of this search, one of omission. It’s rather unfair, since we must give the experimenters considerable credit for doing something that had never been tried before. But here it is: a (temporarily) lost opportunity.

Click here for the details

For very large classes of HV/DS examples, the resulting jets-of-jets not only have many tracks but also have one or more of the following properties that are very unusual in ordinary jets:

• If their dark hadrons very often produce bottom quarks, which travel a tiny but measurable distance before they themselves decay to the hadrons we measure, a large fraction of the many tracks in the jet-of-jets will be “displaced”, meaning that they will not trace back precisely to the location of the proton-proton collision. [This too, is shown in Figure 19-20 of this paper.] Such a thing almost never happens in ordinary jets.
• If their dark hadrons themselves travel a tiny but measurable distance before they decay to ordinary hadrons or other Standard Model particles, then again a large fraction of the many tracks in the jet-of-jets will be displaced.
• If the dark hadrons in the dark jet very often decay to muons, or to bottom quarks and taus (which often subsequently decay to muons), then it will be common for a jet-of-jets to have three or more muons embedded within it. [This is observed in Table II of this paper, though in many HV/DS models the effect is even more dramatic.] While this is certainly not unheard of in ordinary jets, it is not at all typical.

And so, if one were to require not only many tracks but also many displaced tracks and/or several muons in each observed jet, then the fraction p of ordinary jets that would satisfy all these criteria would be substantially lower than it is in ATLAS’s current search, and the expected N_D would be much smaller. This would then allow ATLAS to discover an even larger class of HV/DS models, ones whose jets-of-jets are significantly rarer or that produce somewhat fewer tracks, but make up for it with one of these other unusual features.

I hope that the experimenters at ATLAS (or CMS, if they try the same thing) will include these additional strategies the next time this method is attempted. Displaced tracks and embedded muons are very common in HV/DS jets-of-jets, and adding these requirements to the existing search will neither complicate it greatly nor make it more difficult for theorists to interpret. The benefit of much smaller background from ordinary jets, and the possibility of a discovery that the current search would have missed, seems motivation enough to me.

Congrats to ATLAS, and a Look Ahead

Let me conclude with a final congratulations to my ATLAS colleagues. Some physicists seem to think that if the LHC were creating particles not found in the Standard Model, we would know by now. But this search is a clear demonstration that such a viewpoint is wrong. Marked by simplicity and power, and easy to understand and interpret, it has reached deep into uncharted HV/DS territory using a strategy never previously tried — and it had the potential to make a discovery that all previous LHC searches would have missed.

Nor is this the end of the story; many more searches of the wide range of HV/DS models remain to be done. And they must be done; to fail to fully explore the LHC’s giant piles of data would be a travesty, a tremendous waste of a fantastic machine. Until that exploration is complete, using as many innovations as we can muster, the LHC’s day is not over.