What is a proton made of?

We have published a new paper, which has quite a bold topic: That a proton has a bit more structure than what you usually hear about.

Usually, you hear a proton is made up out of three quarks, the so-called valence quarks. These quarks, two up-quarks and one down quark, are termed valence quarks. Valence particles provide the proton with its characteristic properties, like its electric charge and spin. In addition, every other particle can also appear inside the proton, as a so-called sea particle. But these are quantum fluctuations, which are only very short lived. There existence has been tested in experiments for gluons, strange quarks, charm quarks, and bottom quarks, as well as photons. We understand this relatively well. Their contribution gets smaller the larger their mass is. So what do we want to add?

Those people reading this blog longer have already seen that one of the central topics we are looking at in our research are the weak interactions and the Higgs. Especially, we figured out that this part of the standard model of particle physics is more involved than is usually assumed. Most importantly, it requires for mathematical consistency that most particles, which we usually call elementary, are more involved bound states, i.e. made up out of multiple particles. Such bound states are very different from elementary particles. E.g., they should have a size. And, in principle, this should show up in experiments.

Of course, mathematical consistency is not sufficient for nature to behave is a certain way. Though it is nice if it does. Therefore 'should' is not sufficient. If we are right, it *must* show up in experiments. Unfortunately, as all of this is associated with the Higgs, which is very heavy, this requires a lot of energy. Since there is currently only one powerful enough experiment available, the LHC at CERN, we need to figure out how to test our ideas with this one. Which, unfortunately, is not ideally suited. But you have to make do with what you have.

Already two years back we figured out that all of the mathematical consistency arguments had a surprising impact for our proton. You see, the proton is one of two very similar particles, the proton and the neutron, the so-called nucleons. They make up all atomic nuclei. The difference between proton and neutron are threefold. Two are their mass and electric charge. They are explained by the valence quarks. The third is the protoness and neutroness - a feature which is called flavor (or sometimes isospin). The aforementioned valence quarks can actually not be really responsible for this quantum number. The argument is very technical, and has a lot to do with gauge symmetry, and especially its more involved aspects. Those who are interested in all the technical details can find it in my review article. Ultimately, it boils down that this flavor cannot come from the valence quarks. Something else needs to provide it.

This something else should not upset those things which are explained by the valence quarks, the mass and spin. Thus, it needs to be spinless and chargeless. The Higgs is the only particle in the standard model, which fits the bill. And it indeed carries something, which can provide the difference between protons and neutrons. In technical terms, it is called the custodial quantum number. What only matters is that this quantity can have two different values, and one can be associated with being proton and the other with being neutron, mathematically completely consistent, if the Higgs is another valence particle.

As the Higgs is much heavier than the proton, the immediate question is, how can that be? But here the combination of quantum mechanics and relativity comes to the rescue. It allows a bound state to be lighter (or heavier) than the sum of the masses of their constituents. Actually, an hydrogen atom is, e.g., lighter than the mass of the constituent proton and electron. But only by an extremely small amount. In the proton, this now works in the same way, but hugely amplified. But we have examples that this is actually possible. So this is fine.

When we now smash two protons together, like at the LHC, we actually get its constituents to interact with each other. And we have now additional Higgs content, so these Higgs can interact as well. However, this will be suppressed by the large mass of the Higgs, as in this case the interaction is as 'if it was alone'. And then it is heavy. Thus, even at the LHC this will be rare.

What we did in the paper was to estimate how rare, and which processes could best be sensitive to this. We find that the LHC so far is not too sensitive to the valence Higgs beyond uncertainties, if the effect is really there. But we figure out that with the production of top quarks at the LHC we should have a sensitive handle for looking for the valence Higgs.

This is really just the first step in hunting the valence Higgs. And it may well be that we need a more powerful experiment in the future to really see the effect. Not to mention that our estimates a very crude, and a lot of calculations need still to be done much better. But it is the first time that the effect of the valence Higgs, as required from mathematical consistency of the standard model, is tested experimentally. And this is a big step into a completely unknown domain. Who knows what we will find along the way.

The size of the W

As discussed in an earlier entry we set out to measure the size of a particle: The W boson. We have now finished this, and published a paper about our results. I would like to discuss these results a bit in detail.

This project was motivated because we think that the W (and its sibling, the Z boson) are actually more complicated than usually assured. We think that they may have a self-similar structure. The bits and pieces of this is quite technical. But the outline is the following: What we see and measure as a W at, say, the LHC or earlier, is actually not a point-like particle. Although this is the currently most common view. But science has always been about changing the common ideas and replacing them with something new and better. So, our idea is that the W has a substructure. This substructure is a bit weird, because it is not made from additional elementary particles. It rather looks like a bubbling mess of quantum effects. Thus, we do not expect that we can isolate anything which resembles a physical particle within the W. And if we try to isolate something, we should not expect it to behave as a particle.

Thus, this scenario gives two predictions. One: Substructure needs to have space somewhere. Thus, the W should have a size. Two: Anything isolated from it should not behave like a particle. To test both ideas in the same way, we decided to look at the same quantity: The radius. Hence, we simulated a part of the standard model. Then we measured the size of the W in this simulation. Also, we tried to isolate the most particle-like object from the substructure, and also measured its size. Both of these measurements are very expensive in terms of computing time. Thus, our results are rather exploratory. Hence, we cannot yet regard what we found as final. But at least it gives us some idea of what is going on.

The first thing is the size of the W. Indeed, we find that it has a size, and one which is not too small either. The number itself, however, is far less accurate. The reason for this is twofold. On the one hand, we have only a part of the standard model in our simulations. On the other hand, we see artifacts. They come from the fact that our simulations can only describe some finite part of the world. The larger this part is, the more expensive the calculation. With what we had available, the part seems to be still so small that the W is big enough to 'bounce of the walls' fairly often. Thus, our results still show a dependence on the size of this part of the world. Though we try to accommodate for this, this still leaves a sizable uncertainty for the final result. Nonetheless, the qualitative feature that it has a significant size remains.

The other thing are the would-be constituents. We indeed can identify some kind of lumps of quantum fluctuations inside. But indeed, they do not behave like a particle, not even remotely. Especially, when trying to measure their size, we find that the square of their radius is negative! Even though the final value is still uncertain, this is nothing a real particle should have. Because when trying to take the square root of such a negative quantity to get the actual number yields an imaginary number. That is an abstract quantity, which, while not identifiable with anything in every day, has a well-defined mathematical meaning. In the present case, this means this lump is nonphysical, as if you would try to upend a hole. Thus, this mess is really not a particle at all, in any conventional sense of the word. Still, what we could get from this is that such lumps - even though they are not really lumps, 'live' only in areas of our W much smaller than the W size. So, at least they are contained. And let the W be the well-behaved particle it is.

So, the bottom line is, our simulations agreed with our ideas. That is good. But it is not enough. After all, who can tell if what we simulate is actually the thing happening in nature? So, we will need an experimental test of this result. This is surprisingly complicated. After all, you cannot really get a measure stick to get the size of a particle. Rather, what you do is, you throw other particles at them, and then see how much they are deflected. At least in principle.

Can this be done for the W? Yes, it can be done, but is very indirect. Essentially, it could work as follows: Take the LHC, at which two protons are smashed in each other. In this smashing, it is possible that a Z boson is produced, which smashes of a W. So, you 'just' need to look at the W before and after. In practice, this is more complicated. Since we cannot send the W in there to hit the Z, we use that mathematically this process is related to another one. If we get one, we get the other for free. This process is that the produced Z, together with a lot of kinetic energy, decays into two W particles. These are then detected, and their directions measured.

As nice as this sounds, this is still horrendously complicated. The problem is that the Ws themselves decay into some leptons and neutrinos before they reach the actual detector. And because neutrinos escape essentially always undetected, one can only indirectly infer what has been going on. Especially the directions of the Ws cannot easily be reconstructed. Still, in principle it should be possible, and we discuss this in our paper. So we can actually measure this size in principle. It will be now up to the experimental experts if it can - and will - be done in practice.

Looking for something when no one knows how much is there

This time, I want to continue the discussion from some months ago. Back then, I was rather general on how we could test our most dramatic idea. This idea is connected to what we regard as elementary particles. So far, our idea is that those you have heard about, the electrons, the Higgs, and so on are truly the basic building blocks of nature. However, we have found a lot of evidence that indicate that we see in experiment, and call these names, are actually not the same as the elementary particles themselves. Rather, they are a kind of bound state of the elementary ones, which only look at first sight like they themselves would be the elementary ones. Sounds pretty weird, huh? And if it sounds weird, it means it needs to be tested. We did so with numerical simulations. They all agreed perfectly with the ideas. But, of course, its physics, and thus we need also an experiment. The only question is which one.

We had some ideas already a while back. One of them will be ready soon, and I will talk again about it in due time. But this will be rather indirect, and somewhat qualitative. The other, however, required a new experiment, which may need two more decades to build. Thus, both cannot be the answer alone, and we need something more.

And this more is what we are currently closing in. Because one has this kind of weird bound state structure to make the standard model consistent, not only exotic particles are more complicated than usually assumed. Ordinary ones are too. And most ordinary are protons, the nucleus of the hydrogen atom. More importantly, protons is what is smashed together at the LHC at CERN. So, we have a machine already, which may be able to test it. But this is involved, as protons are very messy. They are already in the conventional picture bound states of quarks and gluons. Our results just say there are more components. Thus, we have somehow to disentangle old and new components. So, we have to be very careful in what we do.

Fortunately, there is a trick. All of this revolves around the Higgs. The Higgs has the property that interacts stronger with particles the heavier they are. The heaviest particles we know are the top quark, followed by the W and Z bosons. And the CMS experiment (and other experiments) at CERN has a measurement campaign to look at the production of these particles together! That is exactly where we expect something interesting can happen. However, our ideas are not the only ones leading to top quarks and Z bosons. There are many known processes which produce them as well. So we cannot just check whether they are there. Rather, we need to understand if there are there as expected. E.g., if they fly away from the interaction in the expected direction and with the expected speeds.

So what a master student and myself do is the following. We use a program, called HERWIG, which simulates such events. One of the people who created this program helped us to modify this program, so that we can test our ideas with it. What we now do is rather simple. An input to such simulations is how the structure of the proton looks like. Based on this, it simulates how the top quarks and Z bosons produced in a collision are distributed. We now just add our conjectured additional contributions to the proton, essentially a little bit of Higgs. We then check, how the distributions change. By comparing the changes to what we get in experiment, we can then deduced how large the Higgs contribution in the proton is. Moreover, we can even indirectly deduce its shape, i.e. how in the proton the Higgs is located.

And this we now study. We iterate modifications of the proton structure with comparison to experimental results and predictions without this Higgs contribution. Thereby, we constraint the Higgs contribution in the proton bit by bit. At the current time, we know that the data is only sufficient to provide an upper bound to this amount inside the proton. Our first estimates show already that this bound is actually not that strong, and quite a lot of Higgs could be inside the proton. But on the other hand, this is good, because that means that the expected data in the next couple of years from the experiments will be able to actually either constraint the contribution further, or could even detect it, if it is large enough. At any rate, we now know that we have a sensitive leverage to understand this new contribution.

How to test an idea

As you may have guessed from reading through the blog, our work is centered around a change of paradigm: That there is a very intriguing structure of the Higgs and the W/Z bosons. And that what we observe in the experiments are actually more complicated than what we usually assume. That they are not just essentially point-like objects.

This is a very bold claim, as it touches upon very basic things in the standard model of particle physics. And the interpretation of experiments. However, it is at the same time a necessary consequence if one takes the underlying more formal theoretical foundation seriously. The reason that there is not a huge clash is that the standard model is very special. Because of this both pictures give almost the same prediction for experiments. This can also be understood quantitatively. That is where I have written a review about. It can be imagined in this way:

Thus, the actual particle, which we observe, and call the Higgs is actually a complicated object made from two Higgs particles. However, one of those is so much eclipsed by the other that it looks like just a single one. And a very tiny correction to it.

So far, this does not seem to be something where it is necessary to worry about.

However, there are many and good reasons to believe that the standard model is not the end of particle physics. There are many, many blogs out there, which explain the reasons for this much better than I do. However, our research provides hints that what works so nicely in the standard model, may work much less so in some extensions of the standard model. That there the composite nature makes huge differences for experiments. This was what came out of our numerical simulations. Of course, these are not perfect. And, after all, unfortunately we did not yet discover anything beyond the standard model in experiments. So we cannot test our ideas against actual experiments, which would be the best thing to do. And without experimental support such an enormous shift in paradigm seems to be a bit far fetched. Even if our numerical simulations, which are far from perfect, support the idea. Formal ideas supported by numerical simulations is just not as convincing as experimental confirmation.

So, is this hopeless? Do we have to wait for new physics to make its appearance?

Well, not yet. In the figure above, there was 'something'. So, the ideas make also a statement that even within the standard model there should be a difference. The only question is, what is really the value of a 'little bit'? So far, experiments did not show any deviations from the usual picture. So 'little bit' needs indeed to be really rather small. But we have a calculation prescription for this 'little bit' for the standard model. So, at the very least what we can do is to make a calculation for this 'little bit' in the standard model. We should then see if the value of 'little bit' may already be so large that the basic idea is ruled out, because we are in conflict with experiment. If this is the case, this would raise a lot of question on the basic theory, but well, experiment rules. And thus, we would need to go back to the drawing board, and get a better understanding of the theory.

Or, we get something which is in agreement with current experiment, because it is smaller then the current experimental precision. But then we can make a statement how much better experimental precision needs to become to see the difference. Hopefully the answer will not be so much that it will not be possible within the next couple of decades. But this we will see at the end of the calculation. And then we can decide, whether we will get an experimental test.

Doing the calculations is actually not so simple. On the one hand, they are technically challenging, even though our method for it is rather well under control. But it will also not yield perfect results, but hopefully good enough. Also, it depends strongly on the type of experiment how simple the calculations are. We did a first few steps, though for a type of experiment not (yet) available, but hopefully in about twenty years. There we saw that not only the type of experiment, but also the type of measurement matters. For some measurements the effect will be much smaller than for others. But we are not yet able to predict this before doing the calculation. There, we need still much better understanding of the underlying mathematics. That we will hopefully gain by doing more of these calculations. This is a project I am currently pursuing with a number of master students for various measurements and at various levels. Hopefully, in the end we get a clear set of predictions. And then we can ask our colleagues at experiments to please check these predictions. So, stay tuned.

By the way: This is the standard cycle for testing new ideas and theories. Have an idea. Check that it fits with all existing experiments. And yes, this may be very, very many. If your idea passes this test: Great! There is actually a chance that it can be right. If not, you have to understand why it does not fit. If it can be fixed, fix it, and start again. Or have a new idea. And, at any rate, if it cannot be fixed, have a new idea. When you got an idea which works with everything we know, use it to make a prediction where you get a difference to our current theories. By this you provide an experimental test, which can decide whether your idea is the better one. If yes: Great! You just rewritten our understanding of nature. If not: Well, go back to fix it or have a new idea. Of course, it is best if we have already an experiment which does not fit with our current theories. But there we are at this stage a little short off. May change again. If your theory has no predictions which can be testable in any foreseeable future experimentally. Well, that is a good question how to deal with this, and there is not yet a consensus how to proceed.

How large is an elementary particle?

Recently, in the context of a master thesis, our group has begun to determine the size of the W boson. The natural questions on this project is: Why do you do that? Do we not know it already? And does elementary particles have a size at all?

It is best to answer these questions in reverse order.

So, do elementary particles have a size at all? Well, elementary particles are called elementary as they are the most basic constituents. In our theories today, they start out as pointlike. Only particles made from other particles, so-called bound states like a nucleus or a hadron, have a size. And now comes the but.

First of all, we do not yet know whether our elementary particles are really elementary. They may also be bound states of even more elementary particles. But in experiments we can only determine upper bounds to the size. Making better experiments will reduce this upper bound. Eventually, we may see that a particle previously thought of as point-like has a size. This has happened quite frequently over time. It always opened up a new level of elementary particle theories. Therefore measuring the size is important. But for us, as theoreticians, this type of question is only important if we have an idea about what could be the more elementary particles. And while some of our research is going into this direction, this project is not.

The other issue is that quantum effects give all elementary particles an 'apparent' size. This comes about by how we measure the size of a particle. We do this by shooting some other particle at it, and measure how strongly it becomes deflected. A truly pointlike particle has a very characteristic reflection profile. But quantum effects allow for additional particles to be created and destroyed in the vicinity of any particle. Especially, they allow for the existence of another particle of the same type, at least briefly. We cannot distinguish whether we hit the original particle or one of these. Since they are not at the same place as the original particle, their average distance looks like a size. This gives even a pointlike particle an apparent size, which we can measure. In this sense even an elementary particle has a size.

So, how can we then distinguish this size from an actual size of a bound state? We can do this by calculations. We determine the apparent size due to the quantum fluctuations and compare it to the measurement. Deviations indicate an actual size. This is because for a real bound state we can scatter somewhere in its structure, and not only in its core. This difference looks pictorially like this:

So, do we know the size already? Well, as said, we can only determine upper limits. Searching for them is difficult, and often goes via detours. One of such detours are so-called anomalous couplings. Measuring how they depend on energy provides indirect information on the size. There is an active program at CERN underway to do this experimentally. The results are so far say that the size of the W is below 0.0000000000000001 meter. This seems tiny, but in the world of particle physics this is not that strong a limit.

And now the interesting question: Why do we do this? As written, we do not want to make the W a bound state of something new. But one of our main research topics is driven by an interesting theoretical structure. If the standard model is taken seriously, the particle which we observe in an experiment and call the W is actually not the W of the underlying theory. Rather, it is a bound state, which is very, very similar to the elementary particle, but actually build from the elementary particles. The difference has been so small that identifying one with the other was a very good approximation up to today. But with better and better experiments may change. Thus, we need to test this.

Because then the thing we measure is a bound state it should have a, probably tiny, size. This would be a hallmark of this theoretical structure. And that we understood it. If the size is such that it could be actually measured at CERN, then this would be an important test of our theoretical understanding of the standard model.

However, this is not a simple quantity to calculate. Bound states are intrinsically complicated. Thus, we use simulations for this purpose. In fact, we actually go over the same detour as the experiments, and will determine an anomalous coupling. From this we then infer the size indirectly. In addition, the need to perform efficient simulations forces us to simplify the problem substantially. Hence, we will not get the perfect number. But we may get the order of magnitude, or be perhaps within a factor of two, or so. And this is all we need to currently say whether a measurement is possible, or whether this will have to wait for the next generation of experiments. And thus whether we will know whether we understood the theory within a few years or within a few decades.

Finding - and curing - disagreements

The topic of grand-unified theories came up in the blog several times, most recently last year in January. To briefly recap, such theories, called GUTs for short, predict that all three forces between elementary particles emerge from a single master force. That would explain a lot of unconnected observations we have in particle physics. For example, why atoms are electrically neutral. The latter we can describe, but not yet explain.

However, if such a GUT exists, then it must not only explain the forces, but also somehow why we see the numbers and kinds of elementary particles we observe in nature. And now things become complicated. As discussed in the last entry on GUTs there maybe a serious issue in how we determine which particles are actually described by such a theory.

To understand how this issue comes about, I need to put together many different things my research partners and I have worked on during the last couple of years. All of these issues are actually put into an expert language in the review of which I talked in the previous entry. It is now finished, and if your interested, you can get it free from here. But it is very technical.

So, let me explain it less technically.

Particle physics is actually superinvolved. If we would like to write down a theory which describes what we see, and only what we see, it would be terribly complicated. It is much more simple to introduce redundancies in the description, so-called gauge symmetries. This makes life much easier, though still not easy. However, the most prominent feature is that we add auxiliary particles to the game. Of course, they cannot be really seen, as they are just auxiliary. Some of them are very obviously unphysical, called therefore ghosts. They can be taken care of comparatively simply. For others, this is less simple.

Now, it turns out that the weak interaction is a very special beast. In this case, there is a unique one-to-one identification between a really observable particle and an auxiliary particle. Thus, it is almost correct to identify both. But this is due to the very special structure of this part of particle physics.

Thus, a natural question is whether, even if it is special, it is justified to do the same for other theories. Well, in some cases, this seems to be the case. But we suspected that this may not be the case in general. And especially not in GUTs.

Now, recently we were going about this much more systematically. You can again access the (very, very technical) result for free here. There, we looked at a very generic class of such GUTs. Well, we actually looked at the most relevant part of them, and still by far not all of them. We also ignored a lot of stuff, e.g. what would become quarks and leptons, and concentrated only on the generalization of the weak interaction and the Higgs.

We then checked, based on our earlier experiences and methods, whether a one-to-one identification of experimentally accessible and auxiliary particles works. And it does essentially never. Visually, this result looks like

On the left, it is seen that everything works nicely with a one-to-one identification in the standard model. On the right, if one-to-one identification would work in a GUT, everything would still be nice. But a our more precise calculation shows that the actually situation, which would be seen in an experiment, is different. There is non one-to-one identification possible. And thus the prediction of the GUT differs from what we already see inn experiments. Thus, a previously good GUT candidate is no longer good.

Though more checks are needed, as always, this is a baffling, and at the same time very discomforting, result.

Baffling as we did originally expect to have problems under very special circumstances. It now appears that actually the standard model of particles is the very special case, and having problems is the standard.

It is discomforting because in the powerful method of perturbation theory the one-to-one identification is essentially always made. As this tool is widely used, this seems to question the validity of many predictions on GUTs. That could have far-reaching consequences. Is this the case? Do we need to forget everything about GUTs we learned so far?

Well, not really, for two reasons. One is that we also showed that methods almost as easily handleable as perturbation theory can be used to fix the problems. This is good, because more powerful methods, like the simulations we used before, are much more cumbersome. However, this leaves us with the problem of having made so far wrong predictions. Well, this we cannot change. But this is just normal scientific progress. You try, you check, you fail, you improve, and then you try again.

And, in fact, this does not mean that GUTs are wrong. Just that we need to consider somewhat different GUTs, and make the predictions more carefully next time. Which GUTs we need to look at we still need to figure out, and that will not be simple. But, fortunately, the improved methods mentioned beforehand can use much of what has been done so far, so most technical results are still unbelievable useful. This will help enormously in finding GUTs which are applicable, and yield a consistent picture, without the one-to-one identification. GUTs are not dead. They likely just need a bit of changing.

This is indeed a dramatic development. But one which fits logically and technically to the improved understanding of the theoretical structures underlying particle physics, which were developed over the last decades. Thus, we are confident that this is just the next logical step in our understanding of how particle physics works.

How to search for dark, unknown things: A bachelor thesis

Today, I would like to write about a recently finished bachelor thesis on the topic of dark matter and the Higgs. Though I will also present the results, the main aim of this entry is to describe an example of such a bachelor thesis in my group. I will try to follow up also in the future with such entries, to give those interested in working in particle physics an idea of what one can do already at a very early stage in one's studies.

The framework of the thesis is the idea that dark matter could interact with the Higgs particle. This is a serious possibility, as both objects are somehow related to mass. There is also not yet any substantial reason why this should not be the case. The unfortunate problem is only: how strong is this effect? Can we measure it, e.g. in the experiments at CERN?

We are looking in a master thesis in the dynamical features of this idea. This is ongoing, and something I will certainly write about later. Knowing the dynamics, however, is only the first step towards connecting the theory to experiment. To do so, we need the basic properties of the theory. This input will then be put through a simulation of what happens in the experiment. Only this result is the one really interesting for experimental physicists. They then look what any kind of imperfections of the experiments change and then they can conclude, whether they will be able to detect something. Or not.

In the thesis, we did not yet had the results from the master student's work, so we parametrized the possible outcomes. This meant mainly to have the mass and the strength of the interaction between the Higgs and the dark matter particle to play around. This gave us what we call an effective theory. Such a theory does not describe every detail, but it is sufficiently close to study a particular aspect of a theory. In this case how dark matter should interact with the Higgs at the CERN experiments.

With this effective theory, it was then possible to use simulations of what happens in the experiment. Since dark matter cannot, as the name says, be directly seen, we needed somehow a marker to say that it has been there. For that purpose we choose the so-called associate production mode.

We knew that the dark matter would escape the experiment undetected. In jargon, this is called missing energy, since we miss the energy of the dark matter particles, when we account for all we see. Since we knew what went in, and know that what goes in must come out, anything not accounted for must have been carried away by something we could not directly see. To make sure that this came from an interaction with the Higgs we needed a tracer that a Higgs had been involved. The simplest solution was to require that there is still a Higgs. Also, there are deeper reasons which require that dark matter in this theory should not only arrive with a Higgs particle, but should be obtained also from a Higgs particle before the emission of the dark matter particles. The simplest way to check for this is that there is besides the Higgs in the end also a so-called Z-boson, for technical reasons. Thus, we had what we called a signature: Look for a Higgs, a Z-boson, and missing energy.

There is, however, one unfortunate thing in known particle physics which makes this more complicated: neutrinos. These particles are also essentially undetectable for an experiment at the LHC. Thus, when produced, they will also escape undetected as missing energy. Since we do not detect either dark matter or neutrinos, we cannot decide, what actually escaped. Unfortunately, the tagging with the Higgs and the Z do not help, as neutrinos can also be produced together with them. This is what we call a background to our signal. Thus, it was necessary to account for this background.

Fortunately, there are experiments which can detect, with a lot of patience, neutrinos. They are very different from the one we at the LHC. But they gave us a lot of information on neutrinos. Hence, we knew how often neutrinos would be produced in the experiment. So, we would only need to remove this known background from what the simulation gives. Whatever is left would then be the signal of dark matter. If the remainder would be large enough, we would be able to see the dark matter in the experiment. Of course, there are many subtleties involved in this process, which I will skip.

So the student simulated both cases, and determined the signal strength. From that she could deduce that the signal grows quickly with the strength of the interaction. She also found that the signal became stronger if the dark matter particles become lighter. That is so because there is only a finite amount of energy available to produce them. But the more energy is left to make the dark matter particles move the easier it gets to produce them, an effect known in physics as phase space. In addition, she found that if the dark matter particles have half the mass of the Higgs their production became also very efficient. The reason is a resonance. Just like two noises amplify each other if they are at the same frequency, so such amplifications can happen in particle physics.

The final outcome of the bachelor thesis was thus telling us for the values of the two parameters of the effective theory how strong our signal would be. Once we know these values from our microscopic theory in the master project, we know whether we have a chance to see these particles in this type of experiments.

Looking for one thing in another

One of the most powerful methods to learn about particle physics is to smash two particles against each other at high speed. This is what is currently done at the LHC, where two protons are used. Protons have the advantage that they are simple to handle on an engineering level, but since they are made up out of quarks andgluons, these collisions are rather messy.

An alternative are colliders using electrons and positrons. There have been many of these used successfully in the past. The reason is that the electrons and positrons appear at first sight to be elementary, but are technically much harder to use. Nonetheless, there are right now two large projects planned to use them, one in Japan and one in China. The decision is still out, whether either, or both, will be build, but they would both open up a new view on particle physics. These would start, hopefully, in the (late) 2020ies or early 2030ies.

However, they may be a little more messier than currently expected. I have written previously several times about our research on the structure of the Higgs particle. Especially that the Higgs may be much less simpler than just a singleparticle. We are currently working on possible consequences of this insight.

What has this to do with the collisions? Well, already 35 years ago people figured out that if the statements about the Higgs are true, then this has further implications. Especially, the electrons as we know them cannot be really elementary particles. Rather, they have to be bound states, a combination of what we usually call an electron and a Higgs.

This is confusing at first sight: An electron should consists out of an electron and something else? The reason is that a clear distinction is often not made. But one should be more precise. One should first think of an elementary 'proper' electron. Together with the Higgs this proper electron creates a bound state. This bound state is what we perceive and usually call an electron. But it is different from the proper electron. Thus, we should therefore call it rather an 'effective' electron. This chaos is not so much different as what you would get when you would call a hydrogen atom also proton, since the electron is such a small addition to the proton in the atom. That you do not do so has a historical origin, as it has in the reverse way for the (effective) electron. Yes, it is confusing.

Even after mastering this confusion, that seems to be a rather outrageous statement. The Higgs is so much heavier than the electron, how can that be? Well, field theory indeed allows to have a bound state of two particles which is much, much lighter than the two individual particles. This effect is called a mass defect. This has been measured for atoms and nuclei, but there this is a very small effect. So, it is in principle possible. Still, the enormous size of the effect makes this a very surprising statement.

What we want to do now is to find some way to confirm this picture using experiments. And confirm this extreme mass defect.

Unfortunately, we cannot disassemble the bound state. But the presence of the Higgs can be seen in a different way. When we collide such bound states hard enough, then we usually have the situation that we actually collide from each bound states just one of the elements, rather than the whole thing. In a simple picture, in most cases one of the parts will be in the front of the collision, and will take the larger part of the hit.

This means that sometimes we will collide the conventional part, the proper electron. Then everything looks as usually expected. But sometimes we will do something involving the Higgs from either or both bound states. We can estimate already that anything involving the Higgs will be very rare. In the simple picture above, the Higgs, being much heavier than the proper electron, mostly drags behind the proper electron. But 'rarer' is no quantitative enough in physics. Therefore we have to do now calculations. This is a project I intend to do now with a new master student.

We want to do this, since we want to predict whether the aforementioned next experiments we will be sensitive enough to see that some times we actually collide the Higgses. That would confirm the idea of bound states. Then, we would indeed find something else than people were originally been looking for. Or expecting.

Looking for something out of the ordinary

A few days ago, I was at a quite interesting workshop on "Anomalous quartic gauge couplings". Since the topic itself is quite interesting and has significant relevance to my own research on Higgs physics, I like to spend this entry on it. Let me start with describing what the workshop was about, and what is behind its rather obscure title.

At the experiments at the LHC what we do is smashing two protons into each other. Occasionally, either of two things may happen. The first possibility is that in the process each proton emits a W or Z boson, the carriers of the weak force. These two particles may collide themselves, but emerge without change. That is what we call an elastic scattering. Afterwards, these bosons are detected. Or rather, they are indirectly detected by their decay products. The second possibility is that either of the protons emits a very energetic W or Z, which then splits into three of these afterwards. These are then, again indirectly, observed. This is called an inelastic effect. Of course, much more usually goes on, but I will concentrate here on the most important part of the collision.

At first sight, both types of events may not have to do a lot with each other. But they have something important in common: In all cases four particles are involved. They may be any combination of Ws and Zs. To avoid further excessive use of 'W or Z', I will just call them all Ws. The details of which is which is not really important right now.

The fact that four are involved explains already the quartic in the name of the workshop. In the standard model of particle physics, that what happens can occur mainly in either of two ways. One is that two Ws form for some time another particle. This may either be another W or Z, or also a Higgs. Or they can all four interact with each other at the same time. That is then called a quartic gauge coupling, and thus the complete second half of the name of the workshop.

Now what is not right with this, as we talk about something anomalous? Actually, everything is all right with it in the standard model. But we are not only interested what there is in the standard model, but also whether there is something else. If there is something else, what we observe should not fit with what we calculate in the standard model alone. Such a difference would thus be anomalous. Hence, if we would measure that the quartic gauge coupling is different from the one we calculate in the standard model, we call it an anomalous quartic gauge coupling. And then we are happy, since we found something new. Hence, the workshop was about looking for such anomalous quartic gauge couplings. So far, we did not find anything, but we do not yet have seen many such situations. Far too few to make already any statements. But we will record many more in the future. Then we can make really a statement. At this workshop we were thus essentially preparing for the new data, which we expected to come in once the LHC is switched on again in early 2014.

What has this to do with my research? Well, I try to figure out whether two Higgs, or Ws, can form a bound state. If such bound states would exist, they would form exactly in such processes, for a very short time. Afterwards, they again decay into the final Ws. If they form, they would contribute to what we know. They are part of the standard model. So to see something new, we have to subtract their contributions, if they are there. Otherwise, they could be mistaken for a new, anomalous effect. Most important for me at the workshop was to understand, what is measured, and how they could contribute. It was also important to know what can be measured at all, since any experimental constraint I can get would help me in improving my calculations. This kind of connecting experiment and theory is very important for us, as we are yet far from the point where our results are perfect. The developments in this area remain therefore very important to my own research project.

Picking the right theory

One of the more annoying facts of modern particle physics is that our theories cannot stand purely alone. All of them have some parameters, which we are not able to predict (yet). The standard-model of particle physics has some thirty-odd parameters, which we cannot fathom by theoretical investigations alone. An example are the masses of the particles. We need to measure them in an experiment.

Well, you may say that this is not too bad. If we just have to make a couple of measurements, and then can predict all the rest, this is acceptable. We just need to find as many independent quantities as there are parameters, and we are done. In principle, this is correct. But, once more, it is the gap between experiment and theory which makes live complicated. Usually, what we can easily measure is something which is very hard to compute theoretically. And, of course, something we ca calculate easily is hard to measure, if at all possible.

The only thing left is therefore to do our best, and get as close to each other as possible. As a consequence, we usually do not know the parameters exactly, but only within a certain error. This may still not seem too bad. But here enters something which we call theory space. This is an imaginary space in which every point corresponds to one particular set of parameters for a given theory.

In principle, when we change the parameters of our theory, we do not just change some quantitative values. We are really changing our theory. Even a very small change may produce a large effect. This is not only a hypothetical situation - we know explicit examples where this happens. Why is this so?

There are two main reasons for this.

One is that the theory depends very sensitively on its parameters. Thus, a slight change of the parameters will induce a significant change in everything we can measure. Finding then precisely the parameters which reproduce a certain set of measurements requires a very precise determination of the parameters, possibly with many digits of precision. This is a so-called fine-tuning problem. An example of this is the standard model itself. The mass of the Higgs is fine-tuned in the standard model, it depends strongly on the parameters. This was the reason why we were not able to fully predict its mass before we measured it, although we had many, many more measurements than the standard model has parameters. We could just not pinpoint it precisely enough, but only within a rough factor of ten.

A related problem is then the so-called hierarchy problem of modern particle physics. It is the question why the parameters are fine-tuned just to the value we measure in the experiment, and not slightly off and giving a completely different result. Especially this takes today the form of "Why is the Higgs particle rather light?"

But the standard model is not as worse as it can get. In so-called chaotic models the situation is far worse, and any de-tuning of the parameters leads to an exponential effect. That is the reason why these models are called chaotic - because everything is so sensitive, there is no structure at first sight. Of course, one can, at least in principle, calculate this dependency exactly. But any ever so slight imprecision is punished by an exponentially large effect. This makes chaotic models a persistent challenge to theoreticians. Fortunately, particle physics is not of this kind, but such models are known to be realized in nature nonetheless. E.g. some fluids behave like this, under certain conditions.

The other reason is that theory space can have separate regions. Inside these regions, so-called phases, the theory shows quite distinct behaviors. A simple example is water. If you take the temperature and pressure as parameters (though they are not really fundamental parameters of the theory of water, but this is just for the sake of the argument) then two such phases could be solid and liquid. In a similar manner theories in particle physics can show different phases.

If the parameters of a theory are very close by to the boundary between two phases, a slight change will push the theory from one phase to another. Thus, also here it is necessary to determine the parameters very precisely.

In the case of my research on Higgs physics, I am currently facing such a challenge. The problem is that the set of basic parameters are not unique - you can always exchange one set against another set, as log as the number is kept, and there is no trivial connection between two new parameters. Especially, depending on the methods used, particular set are more convenient. However, this implies that for every method it is necessary to redo the comparison to experiment. Since I work on Higgs physics, the dependence is strong, as I said above. It is thus highly challenging to make the right pick. And currently some for my results significantly depend on this determination.

So what can I do? Instead of pressing on, I have to make a step back, and improve my connection to experiment. Such a cycle is quite normal. First you make your calculation, getting some new and exciting result, but with large errors. To improve your errors, you have to go back, and make some groundwork, to improve the basis. Then you return back to the original result, and get an improved one. Then you do the next step, and repeat.

Right now, I am not only for the Higgs physics in such a process. Also our project on a neutron star's interior currently underoes such an improvement. This work is rarely very exciting or yields unexpected results. But it is very necessary, and one cannot get away without, once one wants to get reliable results. Also this is part of a researcher's (everyday) life.

(Almost) Nothing is forever: Decays

A truly remarkable fact is that most elementary particles do not live forever. Most of them exist only for a very brief moment in time. The only particles, for which we are reasonable sure that they live forever are photons. Then there are a number of particles, which live for almost forever. This means their life expectancy is much, much longer than the current age of the universe. The electron, the proton, and at least one neutrino belong to this group. And so do many nuclei. That is good, because almost all matter around us is made of these particles. It is rather reassuring that it will not disintegrate spontaneously anytime soon.

However, the vast majority of elementary particles has not a very long life expectancy. For some, their lifetime is still such that we can observe them directly. But for particles like the infamous Higgs, this is not the case.

If we want to learn something about such particles, we have to cope with this problem. A very important help is that a particle cannot just vanish without a trace. If a particle's life ends, it decays into other, lighter particles. For example, the Higgs can decay into two photons. Or into two light quarks. Or in some other particles, as long as the sum of their masses is lighter than the Higgs' mass. And these decays follow very specific rules. Take again the Higgs. If it is lying somewhere around, and then decays into an electron and a positron, these two particles are not completely free in their actions. Very basic rules of physics require them then to move away from the position of the Higgs in opposite directions, with the same speed. And this speed is also fixed.

These laws are what helps us. If we detect the electron and the positron, and measure their speed, we can reconstruct that they come from a Higgs. This is a bit indirect, and one has to measure things rather precisely. But it is possible. And it was exactly this approach with which we have detected (very likely) the Higgs last year.

Of course, there are a lot of subtleties involved. And not every decay can happen, which seems to be permitted at a first, superficial look. And so on. But all this follows very precise rules. And the experimental physicists have become very good at using these rules to their advantage.

And here enters my own research. One of my projects is about some particles which are build from Higgs particles and Ws and Zs. If I want to tell my experimental colleagues to check, whether my theory is right, I have to tell them for what to look. Since those complicated particles are not expected to live very long, they will decay. Hence, I should be able to tell how they decay, and into which particles with what speed. This will give what we call a signature: The traces a unstable particle leaves at the end of its life. Doing this is somewhat complicated, as you not only have to understand the structure of the particles, but also their dynamics. Fortunately, people have developed very sophisticated methods. I use them now in simulations. With them I start to obtain results how my complicated particles decay into two Ws. In addition, I learn how often and how effectively this will happen, and how long the original particle lived.

Of course, as always, my first results are not the final answer yet. But things look encouraging. And, what is best, I start to find hints that the complicated states may even live long enough that, just maybe, they could be seen by my experimental colleagues. This is important, because a particle which lives to short requires a precision to observe higher than what we have currently. But it is still a long road before anything is certain. As always.

Enthusiasm vs. Statistics

Being a theoretician permits one to speculate and make predictions what should be seen in experiments. How reality could, in fact, be. However, this is not always as simple as it looks. Not so much because of how to arrive at a prediction, but when it comes to judge whether a prediction is true.

For example, I am working on interesting new phenomena in connection with the Higgs. Recently, I found some rather interesting results, which lead to some predictions. And now the ATLAS experiment  at the LHC continues to find that the Higgs properties are not exactly what they are expected to be in the standard model. What is actually not completely off from what I would expect because of my own calculations.

Should I now get excited, and cry that I have the explanation? I better not. Why? Why should I not be enthusiastic about these results?

Well, here comes the detective part in particle physics.

First, no calculation we can make today in any theory attempting to describe nature is exact. We always have to make some kind of approximations. For some of them we can make a firm statement how large the error, we are making, is at most. But in many cases, we cannot even reliably estimate the maximum size of the error. Do not get me wrong. It is not that most things are completely uncontrolled. In many cases we just cannot proof how large the error can be at most. But we have experience, experiments, and other kinds of approximations to which we can compare. This gives us a rather good idea of the size of the errors. But still, we cannot be absolutely sure about the true size. We then prefer to be better safe than sorry.

This is one of the reasons why I am not immediately enthusiastic. The approximations are yet too crude to be sure that what ATLAS sees must be unequivocally what my calculations give.

But there is more. It is not only theory which has errors. Experiments have errors as well. The reason is that nature is not strictly consequential. Because of quantum physics we cannot make the firm prediction that if A happens then B has to happen. We can just make a statement how probable B happens if A happens. As a consequence, modern particle physics experiments have, even if the machine itself is perfectly understood and perfectly build, an intrinsic error. Like any error for a probability it becomes smaller when we make more measurements.

Right now, this error for the consistency problems found by ATLAS is large. Not large in the sense of huge, but so large that there is a fair chance that the inconsistencies will go away, and we just see a random glitch of nature.

That sounds a bit odd at first. What should a glitch of nature be? Take a dice. If you throw it often enough, and just note the number of times a number comes up, then for very many throws every number will be there the same number of times. Try it. You will see that this will take a large number of throws before it happens, but it will happen eventually.

However, it may happen that you throw it ten times, and you will never get a one. Would you now conclude that there is no one on the dice? No, you would know that there is a one, just by looking at it. But you may need to throw some more times to get it at last once. But what if you get just told the numbers and never are allowed to look at the dice? Would you know that there is a one? Or could just somebody use a non-standard dice? What you would not expect is that nature just avoids ones, right?

In a particle physics experiment, it is like this. We cannot see the dice. We just get the counts. And like the case without ones, the current results of ATLAS could be a similar glitch. It just came up like this, and we have to go on, and count more.

Fortunately, you can make a statement how improbable it is not to get a one, if you throw the dice often enough. That is a number which quickly becomes small the larger the number of throws is.

Is particle physics, we can do the same thing. For the ATLAS experiment right now, there is a very good chance that things will turn out to be what they should be, and it is jut the good, old Higgs. What do I mean by good? Well, that is something like a one in a hundred chance, or so. That seems to be a far cry. But we physicists made the bitter experience that a one-in-a-hundred chance will turn against you in some cases. We make so many hundred measurements that at least some will turn out against the chances. That led in the past to false claims of discoveries, and nowadays we have become very careful, rather waiting long to reduce it to a one-in-a-million chance then to be premature.

Thus, I currently also think that the glitches seen by ATLAS are more likely not more than just such an effect. And I stay my enthusiasm for other occasions. But if the results of ATLAS should stay even with more data, well, then there may be finally the point reached to be enthusiastic. In spite of the potential problems lurking in my own calculations. Because then there is something new to be explained. And this may still be my own solution.

Using E=m*c*c

The last time I gave you a first, brief glimpse of special relativity. Special relativity has one property on which all modern experiments at accelerators like the LHC are based on. It is encoded in Einstein's most famous equation E=m*c*c, where E stands for energy, m for mass, and c is the speed of light. But what does this equation, which is already part of pop culture, really mean?

Let us have a look at its part. The symbol c denotes the speed of light. As discussed last time, the speed of light is always and everywhere constant. It is thus a constant of proportionality, without any dynamical meaning. In fact, its value is no longer measured anymore. In the international most used system of physical units it is defined to have a certain value, roughly 300000 km/s. Since it is so devoid of meaning, most particle physicist have decided that you do not need it, really, and replaced it with one. Ok, this may sound pretty strange to you, since one is not even a speed, it is just a number. But all such things like physical units are man-made. Nature knows only what a distance is, but not what a kilometer is. Thus, you must be able to formulate all laws of nature without such man-made things like a second or a kilometer.

Indeed, this is possible. However, we are just human, and thus working only with numbers turned out to be inconvenient for the mind. Thus, we usually set only so much irrelevant constants to one until we are left with just one single physical unit. Depending on the circumstances, for a particle physicist this is either the so called femtometer (short fm) or fermi, 0.000000000000001 meter, what is roughly the size of a proton. Or we use energy, measured in giga-electron volt (short GeV), or 100000000 electron volt. An electron volt is the amount of kinetic energy an electron gains when it is accelerated by one volt of voltage. That is roughly the voltage of an ordinary battery. Both units are very convenient when you do particle physics. If you are an astrophysicist, this would not be the case. They measure distances, e.g., in megaparsec, which is roughly 3261567 light years.

Anyway, lets get back to the equation. If we set c to one, it reads E=m. Much simpler. The left hand side now denotes an energy E, and the right-hand side a mass m. This is actually not what you can read off a scale. This is called weight, and depends on the planet you are on. Mass is a unique property of a body, form which one can derive the weight, once you chose a planet.

Since the left-hand side is an energy, measured in GeV, so is the right-hand side. Thus, we measure mass not in kilogram, but in energy. A proton has then roughly the mass of 1 GeV, while an electron has a mass of about 0.005 GeV.

But this equation is not just about units. It has a much deeper meaning. As it stands, it says that mass is equal energy. What does this mean? You know that you have to invest energy to get an object moving, again the kinetic energy. But the right-hand side does not contain a speed, so the energy on the left-hand side seems not to be a kinetic energy. This is correct. The reason is that this formula is actually a special case of a more general one, which only applies if you consider something which does not move. It makes the explicit statement that a body with a mass m at rest has an energy E. Thus, the energy has nothing to do with moving, and is therefore called a rest energy. If the particle should start to move, this energy is increased by the kinetic energy, but never decreased. This means that every body has a minimum energy equal to its rest energy, which in turn is equal to its mass.

Why is this so? The first answer is that it necessarily comes out of the mathematics, once you set up special relativity. That is a bit unsatisfactory. In quantum field theory, mass comes out as an arbitrary label that every body has, and which can take on any value. Only by experiment we can decide what particles of which mass do exist. We cannot yet predict the mass a particle has. That is one of the unsolved mysteries of physics. Note that the Higgs effect or the strong force seem to create mass. Thus, it seems we can predict mass. But this is a bit imprecise. Both of them do not really create mass, but add more to Einstein's equation. This makes particles behave as if they have a certain mass. But it is not quite the same.

Let me get back to where I started. Why is this equation so important? Well, as I said, the energy gets only bigger by moving. Now, think of a single particle, which moves very fast. Thus, it has a lot of energy. At the LHC, the protons have currently 4000 times more energy than they have at rest. If you stop the proton by a hard wall, than most of this energy will go on and move the wall. But since a wall is usually pretty heavy, and even 4000 times the proton rest mass is not much on the scale of such walls, they do not move in a way that we would notice.

But now, let us collide this proton with another such proton. What will happen? We have a lot of energy and a head-on collision. One thing Einstein's equation permits, if you formulate it for more than one particle, is the following: You are permitted to convert all of this energy into new particles. At least, as long as the sum of kinetic and rest energy does not exceed the total energy of the two protons before-hand. By this, you can create new particles. And this is what makes this equation so important for modern experiments. You can create new particles, and observe them, if you just put enough energy into the system. And that is, why we use big accelerators like the LHC: To make new particles by converting the energy of the protons.

Unfortunately, we cannot predict to what the energy is converted, as already noted earlier. But well, at least we can create particles.

Oh, and there is a subtlety with the wall: If we are good, and hit a single particle inside the wall, then the same happens as when we collide just two protons. But in most cases, we do not hit a single particle, but it is more like the first shot of billiard, giving just a bit of energy to every particle in the wall. And then the wall as a whole is affected, and not a single particle. Just when you wonder if you ever hear of fixed-target experiment, instead of a collider. This it, how this works: Shot at a wall, and hope to hit just a single particle.

Two worlds: Theory and experiment

You will probably have heard that we have found the Higgs boson - or something similar to it. We are not quite sure yet. You may also have heard that we found it in an experiment, and that this was a triumph for theory, which predicted it long ago. This seems to be a wonderful combination, theory and experiment. But, as always, nothing is just as simple as it seems.

Let us undertake the journey and accompany a theoretical idea from its inception until its experimental test, to see what is going on.

Having an idea of how physics beyond the standard model could look like is essentially simple. Though, of course, many ideas have already found by some of the people thinking about it since the early 1970ies. The interesting question after having an idea is, how to check, whether it is actually describing nature, or is just an interesting mathematical toy.

To do this, two things are necessary. The first is to check whether the idea is compatible with what we know so far about nature. The second is to use the idea to predict something which is different from the standard model. That is necessary, so that we can distinguish both, and decide how nature can be described. To do both we have to to somehow compare to an experiment.

Unfortunately, experiments cannot directly work with the mathematical stuff a theoretician writes down. Modern particle experiments work in the following way: You send something into a box and then detect what comes out of the box. In case of the suspected Higgs, we send in protons. The box is an empty space where these protons hit each other. Because the encounter is violent enough, everything comes apart, and out of the box come a lot of other (known) particles. These are then detected. Actually, we can pretty well by now not only say that there is a particle, but also what particle it is, and where it is headed with which speed. The set of detected particles is what we call an event. We then do many collisions and collect many events. The reason for this is that quantum physics forbids us to know precisely what is going on, but only what happens on the average. And to get an average, we have to average over many events.

At any rate, we end up with such information. That is what modern experiments do.

Now, the theoretician has to somehow convert his idea to something which can be compared to this experimental outcome.

In most cases, things roughly proceed as follows:

What we actually collide are not protons, but the quarks and gluons inside the proton. Thus, the theoretician first computes how quarks and gluons become converted into a new particle. Unfortunately, the experiment can only talk about the protons going into the box. So we have to first compute how we find quarks inside the proton. This is actually very complicated, and so far only partially solved. Nonetheless, we can do it sufficiently well for our purpose, though it is a challenging calculation.

The next problem is that the new particles lives usually only for a very short time. Too short to escape the box. It will decay into other particles before it can leave the box. In fact, it will often decay into particles, which in turn still do not live long enough to escape the box, but also decay first. So you have to calculate the whole chain of decays, until you reach particles, which are so stable that they will escape the box, and can be detected in the detector.

Once you have this, you have what we call a cross section. This is a number, which tells you how often two colliding protons will end up being a certain set of particles, which come from the decay chain of the new particle. Usually, you also know how often these particles go with which speed into which direction.

Unfortunately, we cannot yet compare to experiment, for two reasons.

The first is that the detector is not perfect. For example, the detector has to have a hole where the protons enter. Also, we cannot suspend the detector in thin air, and the holding devices produce blind spots. In addition, we are actually not able to measure all the speeds and directions perfectly. And it can happen that we mistake one particle for a particle of a different species. All of this is part of the so-called detector efficiency. An experimentalist can determine this with a great amount of work for a given detector. As a theoretician, we have to combine our prediction with this detector efficiency, to make a reliable prediction. Just think what would happen if our idea produces a signal which would escape preferentially along the way the protons came in. If we would not take the detector efficiency into account, we would just see nothing, and would decide our idea is wrong. But knowing the detector efficiency, we can figure out what is going on.

The second problem is what we call background. This background has two origins.

One is that the remainder quarks and gluons of the protons usually do not go away nicely, but will produce many other particles in other collisions. At LHC we even have that usually more than two protons collide. This produces a lot of debris in the detector. To find the new particle then means to separate all the debris from the particles into which the new particle has decayed.

The second problem is that other processes may mimic the searched for particle to some extent. For example, by having similar decay products. Then we have to distinguish both cases.

Because of the detector efficiency, we are not able to resole both types of background perfectly. And neither can we resolve the signal perfectly. We just get a big pileup, and have to find the signal in it. To do this, theoreticians have to calculate all this background. By comparing than what one gets from background alone and from background plus the desired signal, we have reached our goal: We know, how our searched for new particle appears in the detector. And how the experiment will look like, if we were incorrect, and just the known bunch of things is there.

All of this is quite laborious, and a lot of groundwork. And all too often it comes out that for a given detector efficiency we will not be able to get the signal out of the background. Or that the number of times we have to try is so large that we cannot afford it - we would just have to get too many events to get a reasonable reliable average.

But well, this is life. Your options are then either to wait for a better experiment (which will usually take a couple of decades to build), or to go back to the drawing board. And find a new signal, which the present experiment can find. And then it may still happen that they find nothing, and this means you idea was incorrect from the very beginning. And then you can go back to step one. In case of the Higgs, it appears likely that it turned out be correct. But there the process was so complicated that it took 48 years to have good enough experiments and reliably enough theory. Physics beyond the standard model may require even more, if we are unlucky. If we are lucky, we may have something in a few months.