The nature of particles

I have written some time ago that most of the particles we know decay, i.e. after some time they fall apart into other particles. Probably that is not to surprising. After all, essentially everything we know tends to fall apart after a while. Hence, we can think of these particles being made out of the particles into which they decay. Such particles made up out of other particles are called bound states or composite particles. The particles into which it decays are called decay products, but here I will just use particles. Actually, even the particles into which the composite particle decays may in turn decay further. But for the things I want to write about in this entry, this will not matter. Thus, I will just talk about a composite particle and the particles it decays into.

But there is an important difference between usual things falling apart and particles falling apart.

Think about a tower made from wood logs, like a child's toy. You build it from the logs, and after some time it will break down again into the logs. Especially, when a child is around to kick it. But the logs themselves remain intact. So far, this is the same with composite particles. You start with a composite particle, it then decays into other particles. You can rebuild your tower from the logs. This is also possible with the particles. The decay products can be refused into the original composite particle.

But now there is a difference. When you build the tower, the logs keep there identity. If you look close enough at the tower, you can still see the individual logs you used to build the tower. That is not so simple with particles. This is best seen by a specific example. Start with two particles, and fuse them to a new composite particle. So far, nothing new. But then it may happen that this composite particle decays into entirely different other particles then the original ones, or it may decay into the original ones. The expression we use is that the composite particle has different decay channels. It is not that all the possible particles are stored in the original particle, it really changes its identity. It would be like the wood logs turn into plastic ones while being in the tower.

Describing such a spontaneous change is not simple. We have become quite expert in modeling the starting composite particle, and then perform at some point an explicit change into the different particles. But that is a little bit like taking the tower and, very nifty, exchanging each log while it is inside the tower from wood to plastic. What we would like to be able is to have this as a dynamical process. Without our interference, the structure of the composite particle changes, and thus decays differently as it has been formed.

We actually know how to simulate this. But there we can just observe that this happens. We also would like to know how this proceeds inside the structure of the composite particle itself, what governs this process in detail.

Learning this is another project which I now supervise as a PhD project. We will use the so-called equations of motion to dissect the process. For this, we will be looking at a very simple particle, the so-called (charged) pion. It is a composition of two quarks, but can also decay into an electron and a neutrino. Choosing this particular composite particle has a number of reasons. One is that it is very well studied both experimentally and theoretically. We can therefore concentrate on the new aspects, the change of identity of the constituents. The decay is also rather slow, ad therefore technically easier to control. And finally, quarks, electrons and neutrinos are very different particles. As theoreticians, we can use this fact by modifying their properties, and therefore switch on and off various features of the process. And finally, though the pion is made up (sometimes) of quarks, it can actually not really decay into them, due to confinement. Therefore, we need only to consider the change inside the pion, but not outside. This also reduces the technical challenges.

Solving this question, we will continue on to more interesting composite particles, like bound states of the Higgs. But this project is an enormously important first step on this road.

A model for a model

One of the more disturbing facts of modern theoretical particle physics is complexity. We can formulate the standard model on, more or less, two pages of paper. But to calculate most interesting quantities is so seriously challenging that even an approximate result takes many person-years, and often even much, much more.

Fortunately, the standard model is in one respect kind: For many interesting questions only a small part of it is relevant. This does not mean that the parts are really independent. But the influence of the other parts on the subject in question is so minor that the consequences are often much smaller than any reasonable theoretical or experimental accuracy could resolve. For example, many features of the strong interactions can be determined without ever considering the Higgs explicitly. In fact, it is even possible to learn much about the strong interactions just from looking at the gluons alone, neglecting the quarks. This reduced theory is called Yang-Mills theory. It is a very reduced model for the core features of the strong interactions.

Unfortunately, even this theory, which contains only a single of the particles of the standard model, is very complex. One of our lines of research is dealing with the resulting problems. One of these problems has to do with the properties of the local symmetry of this model, the so-called gauge symmetry. This feature leads to certain, technically necessary, redundancies. But when doing calculations, we need to do approximations. This may mess up the classification of what is redundant and what is not. Getting this straight is important, and this is the research topic I write about today.

And it is here where the title comes into play. Even if the theory of only gluons is much simpler than the original theory, it is still so complicated that the redundancies are pretty messed up. Therefore, we decided by now that it would be better to understand first a different case. A case, in which the same redundancies appear, but all the rest is simpler. A (simpler) model for a (more complicated) model.

This strategy creates the bridge to my previous entry on supersymmetry.

Theories which have this supersymmetry are, in almost all cases, much simpler than theories without. As I wrote, there are different levels of supersymmetry. In its simplest form, supersymmetry relates the kinds of possible particles, and constrains a few interactions. In the maximum version, essentially the whole structure of the theory, and almost all details, are constrained. These constrains are so rigid and powerful that we can solve the theory almost exactly. Nonetheless, this theory has the same kind of redundancies as Yang-Mills theory, and even the full standard model. Thus, we can study what approximations do to these redundancies. Especially, using the exact knowledge, we can reverse engineer essentially everything we want.

In fact, we make a kind of theoretical experiment: We take the theory. We treat it with a method - in our case we use the so-called equations-of-motion. We know the results. Now, we perform the same type of approximations we do in the more complicated models, or even the full theory. We see how this modifies the results. Well, actually we will see, since we are still working on this bit. From the change of the results, we will learn a lot of things. One is which kind of approximations make a qualitative change. Since any qualitative difference compared to the exact result will be a wrong result, we should not do such approximations. Not in this theory, and especially not in more complicated theories. Just small quantitative changes are probably fine, though there is no guarantee. And we can explicitly see if the approximations start to mix redundant parts such that they are treated wrongly. From this we will (hopefully) learn more about how to correctly treat the redundancies in the more complicated models.

A partner for every particle?

A master student has started with me a thesis on a new topic, one on which I have not been working before. Therefore, before going into details about the thesis' topic itself, I would like to introduce the basic physics underlying it.

The topic is the rather famous concept of supersymmetry. What this means I will explain in a minute. Supersymmetry is related to two general topics we are working on. One is the quest for what comes after the standard model. It is with this respect that it has become famous. There are many quite excellent introductions to why it is relevant, and why it could be within the LHC's reach to discover it. I will not just point to any of these, but write nonetheless here a new text on it. Why? Because of the relation to the second research area involved in the master thesis, the ground work about theory. This gives our investigation a quite different perspective on the topic, and requires a different kind of introduction.

So what is supersymmetry all about? I have written about the fact that there are two very different types of particles we know of: Bosons and fermions. Both types have very distinct features. Any particle we know belong to either of these two types. E.g. the famous Higgs is a boson, while the electron is a fermion.

One question to pose is, whether these two categories are really distinct, or if there are just two sides of a single coin. Supersymmetry is what you get if you try to realize the latter option. Supersymmetry - or SUSY for short - introduces a relation between bosons and fermions. A consequence of SUSY is that for every boson there is a fermion partner, and for every fermion there is a boson partner.

A quick counting in the standard model shows that it cannot be supersymmetric. Moreover, SUSY also dictates that all other properties of a boson and a fermion partner must be the same. This includes the mass and the electric charge. Hence, if SUSY would be real, there should be a boson which acts otherwise like an electron. Experiments tell us that this is not the case. So is SUSY doomed? Well, not necessarily. There is a weaker version of SUSY where it only approximately true - a so-called broken symmetry. This allows to make the partners differently massive, and then they can escape detection. For now.

SUSY, even in its approximate form, has many neat features. It is therefore a possibility desired by many to be true. But only experiment (and nature) will tell eventually.

But the reason why we are interested in SUSY is quite different.

As you see, SUSY puts tight constraints on what kind of particles are in a theory. But it does even more. It also restricts the way how these particles can interact. The constraints on the interactions are a little bit more flexible than on the kind of particles. You can realize different amounts of SUSY by relaxing or enforcing relations between the interactions. What does 'more or less' SUSY mean? The details are somewhat subtle, but a hand-waving statement is that more SUSY not only relates bosons and fermions, but in addition also partner particles of different particles more and more. There is an ultimate limit to the amount of SUSY you can have, essentially when everything and everyone is related and every interaction is essentially of the same strength. That is what is called a maximal SUSY theory. A fancy name is N=4 SUSY for technical reason, if you should come across it somewhere on the web.

And it is this theory which is interesting to us. Having such very tight constraints enforces a very predetermined behavior. Many things are fixed. Thus, calculations are more simple. At the same time, many of there more subtle questions we are working on are nonetheless still there. Using the additional constraints, we hope to understand this stuff better. With these insights, we may have a better chance to understand the same stuff in a less rigid theory, like the standard model.

Can we tell when unification works?

Some time ago, I wrote about the idea that the three forces of the standard model, the electromagnetic force, the weak force, and the strong force, could all be just different parts of one unified force. In the group I am building I have now a PhD student working on such a theory, using simulations.

Together, we would like to answer a number of questions. The most important one is, whether such a theory is consistent with what we see around us. That is necessary to make such a theory relevant.

Now, there is almost an infinite number of versions of such unified theories. We could never hope to check each and every one of them. We could pick one. But hoping it would be the right one is somewhat too optimistic. We therefore take a different approach. We aim to get a general criterion such that we can check out many of the candidate theories at the same time.

For this reason, we ignore for the moment that we would like to reproduce experiments. Rather, we ask ourselves what are common traits of these theories. We have done that. What we are currently doing is to construct the simplest possible theory which has as many of these traits as possible. We have almost completed that. This reduced theory will become indeed very simple. Of known physics, it contains the weak force and the Higgs. As with every unified theory, it also contains a number of additional particles. But they are not dangerous, if they will be too heavy to be visible to us. At least, as long as we do not have more powerful experiments. The last ingredient are the interactions between the different particles. That is what we are working on now. Having the simplest possible theory has also another benefit - it demands small enough computer resources to be manageable.

After fixing the theory, how do the questions look like? One of the traits of such theories is that there are many new particles. What is there fate? How is it arranged that we cannot see them? If we think of the theory describing only rather small changes to the standard model, we can use perturbation theory. With this, we would just follow pretty old footsteps, and the answer can essentially be guessed form the experience of other people. The answer will be that all the surplus stuff is indeed very, very heavy. In fact, so heavy that our experiments will not be able to see it in any foreseeable future, except as very indirect effects. We get out what we put in.

But here comes the new stuff. As I have described earlier, there are many subtleties when it comes to the Higgs of the standard model. But in the end, everything collapses to a rather simple picture. Almost a miracle. Almost, but not quite. The reason is the structure of the standard model, which is very special in the number and properties of particles. The other one is that the parameters, things like masses, just fits.

The natural question is hence: Does the miracle repeats itself for this type of unified theory? Is the new stuff really heavy? Is the known stuff light enough? If the almost-miracle repeats itself, the answer is yes. Should it repeat itself? Well, we will test under which conditions it repeats itself, by playing around both with the number of particles, their structures, and the parameters. We assume right now that we can get it to work, but that we can also break it. And we would like to understand very precisely when it breaks and why it breaks. And finally, the most obvious question, do we want that it repeats itself? Probably the most obvious question, arguably the hardest to answer. If it does not repeat itself, a whole class of ideas becomes more problematic. Ideas, which are conceptually pretty attractive. So, in principle, we would like to see it repeating itself. But then, would it not be more interesting if we needed to start afresh? Probably also true. But in the end, our preference should not play a role. After all, nature decides, and we are just the spectators, trying to figuring out what goes on. And our preferences have nothing to do with it, and therefore we should keep them out of the game.

Take your theory seriously

I have published a new paper. This paper has a somewhat simple message, even if it is technical. This message is just: Take your theory seriously. This may seem obvious, but it is not necessarily so. The reason is that if a theory works spectacularly well, if you do not take it serious, why should you care? And if I mean spectacular, I mean an agreement with experimenter where any deviations are smaller than any background noise we could not yet eliminate. The theory which works so well is, of course, the standard model.

The paper is a follow-up of the proceeding I have discussed last year. The upshot of this proceeding is that we use perturbation theory to describe the physics we measure, e.g., at the LHC at CERN. However, perturbation theory is not taking the theory too seriously, but it works so very well. The reason for this can be understood: It is an almost miraculous coincidence that taking the theory seriously gives almost the same results. We have checked this in very great detail.

But understanding what is going on in the standard model is one thing. One of the big aims in modern particle physics is to understand what else there could be.

Now, comfortable with the success within the standard model, we have for a very long time assumed that taking the candidate theories for new physics also not seriously should work out. Of course, there have been some exceptions, where we knew it should not work. But by and large, the success with the standard model made us comfortable with using the same techniques.

In the proceeding, I already raised some doubt whether this would be justified when there should be a second Higgs. Under certain conditions, this may not be correct. In the full paper I now extend these doubts also to other theories, and even conclude it may be necessary to rethink even the cases where we thought we were careful.

What is the reason behind this departure? Why should it not work? Well, I do not state that it will not work, just that it might not work. In the standard model, we were in the comfortable situation that experiments told us that it does work. Now, in the absence of experimental results, we are left to theory to tell us where to look. So we do not know whether taking the theory not seriously works out, and may be misguided if it does not.

But why should it fail this time, when it works so well for the standard model? A legitimate question. It requires to understand why it does work for the standard model. Looking at it in detail shows that it requires two conditions to work. One is that the relative masses of the particles lie within a certain range. That is satisfied by the standard model. The second is that the relative number of particles is just right. Both conditions are or may not be met by the theories we have for new physics. In the paper, I give particular examples for several theories, and formulate requirements which have to be met for things to work out.

So is the paper now killing of models? No. At least not yet. I only formulate conditions and requirements. Whether a particular theory meets these is a question to the theory. I give some examples where the situation is very much on the borderline to have a starting point where to check. But what actually happens requires a calculation. A calculation in which we do take the theory very seriously. This will be very complicated, and in the end we may just figure out that it was unnecessary. But then we can be sure to be right, and the theory gives us the leeway to not take it too seriously. And being sure is a basic requirement when one ones to explain the unknown.

What is so important (to me) about the Higgs?

In a few weeks, I will give my inaugural lecture at the University of Graz. I have entitled it "The Higgs as a touchstone of theoretical particle physics". Of course, with this title I could easily give a lecture on many of the problems the Higgs present us with which are begging for new physics. I could write about how we have no idea why the Higgs has a mass of the size it has. How we do not understand why it does what it does. And so many other things.

But this is not what I want to write about. Nor is it what i want to talk about. It is rather something more mundane but also much more subtle. It is something for which I do not need any new physics to worry about. I can very well worry just about the known physics.

It has something to do with redundancy. In theoretical physics it is often very convenient - well, often indispensable - to add something redundant in our description. A redundancy is like writing instead of 2 2+0. Both statements have the same meaning. But adding zero to two is redundant. In this example, the zero is just redundant, but not useful. In particle physics, what we add is both redundant and useful.

It is this redundancy which helps us disentangling complicated problems. Of course, we are not allowed to change something by introducing the redundancy. But as long as we respect this requirement, we are pretty free what kind of redundancy we add. In the previous example, we could just write 2+0+0, and have another version of redundancy.

OK, so what has this to do with the Higgs? Well, if we measure something, it is of course independent of these redundancies - after all, they are man-made. And nothing made by us should influence what we measure. But if we look at the ordinary version of how we describe the Higgs, than there is a slight mismatch. In our theoretical description of the Higgs, there is some remainder of the redundancy still lingering. It is, like 2+0.001 pops up. Nonetheless, our theoretical description of the Higgs is spot on the experimental results. But how can this be if there is still redundancy polluting our result? It is this where the Higgs becomes a touchstone of understanding theoretical particle physics: In explaining why this is not correct and correct at the same time.

As always, the answer appears to be in the fine-print. In the standard way how we approach the Higgs, we are not doing it exactly. Well, to be honest, we could not do it exactly. We make some approximations. The consequences of these approximations is the appearance of the residual redundancy. Since our calculations are so spot on, these approximations appear to be good. However, after performing these approximations, we have now way short of experiment to confirm our approximations. That is highly unsatisfactory. We must be able to do it such that we can predict whether the approximations work. And understand why they work. It is in this sense that the Higgs is a touchstone. If we are not even able to answer these questions, how can we expect to solve the many outstanding questions?

This question has bugged people already 35 years ago, and some understanding of why it works was achieved. But not of when it works, at least not in the form of numbers. We have made some progress with this, especially recently. The amazing result was that it appears to work only in a very limited range of masses of the Higgs - with the observed Higgs mass essentially right in the middle of the possible range. This is even more surprising as already slight modifications of how many Higgs particles there are seem to change this. So, why is this so? Why is the Higgs mass just there? And what would happen otherwise? Understanding these questions will be very important to go beyond what is known. Without understanding, we may easily be fooled by our approximations, if we are not that lucky next time. This is the reason, why I think the Higgs is a touchstone for theoretical particle physics.

Support, structure, and students

This time it will again be a behind-the-scenes entry. The reason is that we got just our graduate school prolonged. This is a great success. 'We' are in this case the professors doing particle physics here at the University of Graz, in total five. With this, we are now able to support nine new PhD students, i.e. give them a job during the time they are doing their PhD work, and giving them the opportunity to travel to conferences, or to invite people for them to talk to.

You may wonder what I mean by 'giving a job'. PhD students in physics are not only students. They are beginning researchers. Each and every PhD thesis contributes to our knowledge, and opens up new frontiers. In the course of doing this, the PhD students are guided and supported by us, their supervisors. The goal is, of course, that at the end of their thesis they have matured into equal partners in research. A goal, which is satisfyingly often achieved. And hence, they are not only studying but indeed contributing, and thus they also do a job, and should get paid for the work they are doing. And hence having PhD positions is not only nice - it is required already out of fairness. And therefore this success means that we can now accompany nine more young people on their way to become researchers.

But this is not everything a graduate school provides. A graduate school is also providing the infrastructure too provide advanced lectures by world-leading experts to the students. But here one has to walk a thin line. What we do not want is that they just soak up knowledge, and then reproduce it. This can never be how a PhD education should be. The aim of the PhD studies must always be that the students learn how to create, how to be creative, and how to think in directions nobody else did before. Especially not their supervisors. Providing a too much formalized education would quell much or all of this.

On the other hand, it cannot work without some formal education. While creativity is important, (particle) physics has become a vast field. As a consequence, almost every simple idea has already been found decades ago by someone else. Knowing what is known is therefore already important to avoid repeating the same things (and often the same mistakes) others did. At the same time, knowledge of general principles and structures is important such that one's own ideas can be embedded into the big picture. And in the course, checked for technical consistency. Without knowing about technical details, this would be hard to achieve. One could then easily loose oneself in pursuing a chain of technical points, leading one far astray. It is especially here where it shows that theoretical particle physics is nowadays an enormous collaborative and worldwide effort. None of the problems we are dealing with can be solved by one person alone. It requires the combined knowledge of many people to make progress.

Knowing what other people did - and do - is therefore of paramount importance. Here, the graduate school helps also in another way. It provides the PhD students with the possibility to travel themselves, meet people, and go to conferences. We also can make it possible for them to stay abroad for up to half a year at a different institution to work with different people on a different project. They can thereby substantially broaden their horizon, and learn how to cooperate with different people.

So, are there any downsides? Well, not for the students. Except that they may at times have to go a lecture or talk, which they otherwise would not go to. Most of the downsides are hitting us supervisors, because there is a lot of additional administrative work involved. However, this is easily outweighed by the possibility to have more PhD students to work with, and with their ambition achieve something new.

More on big blobs and little blobs

Two months ago, I have introduced you to what I called big blobs. In the end, just a big heap of particles, which act in unison. As announced there, I have meanwhile produced new results on this topic. So, what did I find?

In this investigation I tried to disentangle what relevance big blobs of gluons have for a single gluon. To do this, I somehow had to get my hands on blobs. To do this, I performed computer simulations of the strong force. Without any further modifications, this would deliver a mixture of small and large blobs, many, many individual gluons, and everything rather unorganized. This would not help much.

Fortunately, clever people have found a way how to isolate the blobs from this mixture. This is a method which is nowadays called smearing or cooling. The names are not quite accurate. What is actually done is to remove anything which even remotely resembles single gluons at high energies. This is really hand-waving, and nobody should take this too literal. But it gives a good idea, and avoids a lot of technicalities. In the end, the important thing is that this gave me a lot of blobs.

But the blobs alone were not interesting for me. Also, many people have studied them in the last forty years or so. I wanted something different. So I took the blobs, and then injected a single gluon into this heap of blobs. Then, I checked how the gluon behaved.

The first result was that at short distances, much shorter than the size of the blobs or the distance between them, the gluon did not feel anything. It just behaved as it would travel through empty space. This was not yet too surprising. After all, the big blobs are separated, and as long as the gluon did not crash into one, how should it know about it.

The second result was also not too surprising. If I let the gluon travel very far, it behaved essentially as if I would not have filtered everything out but the blobs. It was just plain normal. Also this makes sense. If the distances become much longer than the blob's size and their separation, the gluon just gets an average picture. And this picture should, and seems to be, not too different from the real thing.

But then came something, which surprised me at first. Though I later learned that somebody else has anticipated it long ago. If the gluon travels distances roughly of the size of the blobs, it behaved substantially different than normal. This behavior was actually what one would expect in the first place for something which is so strongly interacting as gluons do. That would be quite reassuring, as it was exactly this behavior which has been looked for in gluons since a long time. This would mean that just all the stuff which I have filtered out to get to the blobs would normally obscure it.

Since this sounds to good to be true, it probably is. Hence, a necessary next step must be to check this result, in some way. In the manuscript, I have developed some ideas, but none of them will be easy. They are thus part of future research. But it must be checked. After all, its science, and one should always check and try to falsify the results. And this one certainly deserves to be checked.

Challenging subtleties

I have just published a conference proceeding in which I return to an idea of how the standard model of particle physics could be extended. It is an idea I have already briefly written about: The idea is concerned with the question what would happen if there would be twice as many Higgs particles as there are in nature. The model describing this idea is therefore called 2-Higgs(-doublet)-model, or for short 2HDM. The word doublet in the official name is rather technical. It has something to do with how the second Higgs connects to the weak interaction.

As fascinating as the model itself may be, I do not want to write about its general properties. Given its popularity, you will find many things about it already on the web. No, here I want to write about what I want to learn about this theory in particular. And this is a peculiar subtlety. It connects to the research I am doing on the situation with just the single Higgs.

To understand what is going on, I have to dig deep into the theory stuff, but I will try to keep it not too technical.

The basic question is: What can we observe, and what can we not observe. One of the things a theoretician learns early on that it may be quite helpful to have some dummies. This means that he adds something in a calculation just for the sake of making the calculation simpler. Of course, she or he has to make very sure that this is not affecting the result. But if done properly, this can be of great help. The technical term for this trick is an auxiliary quantity.

Now, when we talk about the weak interactions, something amazing happens. If we assume that everything is indeed very weak, we can calculate results using so-called perturbation theory. And now an amazing thing happens: It appears, like the auxiliary quantities are real, and we can observe them. It is, and can only be, some kind of illusion. This is indeed true, something I have been working on since a long time, and others before me. It just comes out that the true thing and the auxiliary quantities have the same properties, and therefore it does not matter, which we take for our calculation. This is far from obvious, and pretty hard to explain without very much technical stuff. But since this is not the point I would like to make in this entry, let me skip these details.

That this is the case is actually a consequence of a number of 'lucky' coincidences in the standard model. Some particles have just the right mass. Some particles appear just in the right ratio of numbers. Some particles are just inert enough. Of course, as a theoretician, my experience is that there is no such thing as 'lucky'. But that is a different story (I know, I say this quite often this time).

Now, I finally return to the starting point: The 2HDM. In this theory, one can do the same kind of tricks with auxiliary quantities and perturbation theory and so on. If you assume that everything is just like in the standard model, this is fine. But is this really so? In the proceedings, I look at this question. Especially, I check whether perturbation theory should work. And what I find is: This may be possible, but it is very unlikely to happen in all the circumstances where one would like this to be true. Especially, in several scenarios in which one would like to have this property, it could indeed be failing. E.g., in some scenarios this theory could have twice as many weak gauge bosons, so-called W and Z bosons, as we see in experiment. That would be bad, as this would contradict experiment, and therefore invalidate these scenarios.

This is not the final word, of course not - proceedings are just status reports, not final answers. But that there may be, just may be, a difference. This is enough to require us (and, in this case, me) to make sure what is going on. That will be challenging. But this time such a subtly may make a huge difference.

Big blobs

One of the things I have discussed in my blog is how particles arise in quantum theories. Putting it into one (hand-waving) sentence, then particles are just isolated peaks in the quantum fields which fill up the universe. But is this all that there is possible?

The answer is no, and I had to do with the alternatives several times in my own research. But what are these alternatives?

Particles, I said, are isolated peaks. They are, what we call localized - existing at a single place. A single, and very slender, peak on a background of (nearly) nothing else. Of course, there are also bound states, like the hydrogen atom, and other such objects. These are two, or more particles, being close to each other, and which move in the same direction. However, in this case the individual particles are still, more or less, distinct.

Here, I want to introduce another concept. It arises, when one takes many particles, and puts them very close together. Then the peaks start to overlap, until it is impossible to say where one starts, and where another ends. In many cases such a bunch of particles is just unstable, and the particles fly apart pretty quickly. But several theories, most notably the strong interactions, provide another option. When carefully balancing how the particles are together, they form a super-particle, and the whole bunch behaves almost like one big particle. This is different from the bound states, because the particles are no longer individually detectable inside, it is just one big blob. Of course, it is possible to disassemble this blob, and the original particles come out. Hence, such blobs are not called particles, but pseudo-particles. A more fancy name for them is 'topological excitations'. This name has been given to them because of certain properties linked to the mathematical field of 'topology'. One of the particularly important features of these blobs is that they are, without external disturbance, extremely stable. The reason is, pictorially speaking, the way the particles are interwoven makes knots, which do not open.

So aside from the fascinating fact that these things exist, what is their use for physics? They play especially a role in theories where everything interacts strongly with each other, like the strong force. It is hypothesized that in such theories blobs emerge easily, and may even play the most important role. This would mean that effectively not the original particles, but the blobs are the usually encountered objects. And how they interact makes up the phenomena we see in experiments. Single particles are then just some minor disturbance to the game of the big blobs. The blobs become what physicists call the 'effective degrees of freedom', meaning the important players.

Is this true, especially in the strong interactions? It depends. We do not have an equivalent formulation of the theory in terms of blobs instead of particles, so we do not know for sure. We do know that several features, like mass generation, can be very simply explained just by using the blobs. There, it helped us a lot in understanding what is going on. Other features, like the famous confinement, turn out to be a much tougher cookie. We still are not sure, whether it is really possible.

Finally, what are my stakes in the blobs? One of the questions to be posed is, whether the properties of remaining individual particles are determined by the what the blobs do. Is their movement constrained by them? Are their interactions mainly with a blob involved, rather then directly between the particles? I am trying to answer these questions by simulations. Some preliminary findings are already available, but there will be more to come.

Triviality is not trivial

OK, starting with a pun is probably not the wisest course of action, but there is truth in it as well.

When you followed the various public discussiosn on the Higgs then you will probably have noticed the following: Though finding it, most physicists are not really satisfied with it. Some are even repelled by it. In fact, most of us are convinced that the Higgs is only a first step towards something bigger. Why is this so? Well, there are a number of reasons, from purely aesthetic ones to deeply troubling ones. As the latter also affect my own research, I will write about a particular annoying nuisance: The triviality referred to in the title.

To really understand this problem, I have to paint a somewhat bigger picture, before coming back to the Higgs. Let me start: As a theoretician, I can (artificially) distinguish between something I call classical physics, and something I call quantum physics.

Classical physics is any kind of physics which is fully predictive: If I know the start conditions with sufficient precision, I can predict the outcome as precisely as desired. Newton's law of gravity, and even the famous general theory of relativity belong to this class of classical physics.

Quantum physics is different. Quantum phenomena introduce a fundamental element of chance into physics. We do not know why this is so, but it is very well established experimentally. In fact, the computer you use to read this would not work without it. As a consequence, in quantum physics we cannot predict what will happen, even if we know the start as good as possible. The only thing we can do is make very reliable statements of how probable a certain outcome is.

All kinds of known particle physics are quantum physics, and have this element of chance. This is also experimentally very well established.

The connection between classical physics and quantum physics is the following: I can turn any kind of classical system into a quantum system by adding the element of chance, which we also call quantum fluctuations. This does not necessarily go the other way around. We know theories where quantum effects are so deeply ingrained that we cannot remove them without destroying the theory entirely.

Let me return to the Higgs. For the Higgs part in the standard model, we can write down a classical system. When we then want to analyze what happens at a particle physics experiment, we have to add the quantum fluctuations. And here enters the concept of triviality.

Adding quantum fluctuations is not necessarily a small effect. Indeed, quantum fluctuations can profoundly and completely alter the nature of a theory. One possible outcome of adding quantum fluctuations is that the theory becomes trivial. This technical term means the following: If I add quantum fluctuations to a theory, the resulting theory will describe particles which do not interact, no matter how complicated they do in the classical version. Hence, a trivial quantum theory describes nothing interesting. What is really driving this phenomena depends on the theory at hand. The important thing is that it can happen.

For the Higgs part of the standard model, there is the strong suspicion that it is trivial, though we do not have a full proof for (or against) it. Since we cannot solve the theory entirely, we cannot (yet) be sure. The only thing we can say is that if we add only a part of the quantum fluctuations, only a part of the so-called radiative corrections, the theory makes still sense. Hence it is not trivial to decide whether the theory is trivial, to reiterate the pun.

Assuming that the theory is trivial, can we escape it? Yes, this is possible: Adding something to a trivial theory can always make a theory non-trivial. So, if we knew for sure that the Higgs theory is trivial, we would know for sure that there is something else. On the other hand, trivial theories are annoying for a theoretician, because you either have nothing or have to remove artificially part of the quantum fluctuations. This is what annoys me right now with the Higgs. Especially as I have to deal with it in my own research.

Thus, this is one out of the many reasons people would prefer to discover soon more than 'just' the Higgs.

Why continue into the beyond?

I have just returned from a very excellent 37th International Conference on High-Energy Physics. However, as splendid as the event itself was, it was in a sense bad news: No results which hint at anything substantial beyond the standard model, except for the usual suspect statistical fluctuations. This does not mean that there is nothing - we know there is more for many reasons. But in an increasingly frustrating sequence of years all our observational and experimental results keep pushing it beyond our reach. Even for me as a theorist there is just not enough substantial information to be able to do more than just vague speculation of what could be.

Nonetheless, I just wrote that I want to venture into this unknown beyond, and in force. Hence it is reasonable - in fact necessary - to pose the question: Why? If I do not know and have too little information, is there any chance to hit the right answer? The answer to this: Probably not. But...

Actually, there are two buts. One is simply curiosity. I am a theorist, and I can always pose the question how does something work, even without having a special application or situation in mind. Though this may just end up as nothing, it would not be the first time that the answer to a question has been discovered long before the question. In fact, the single most important building block of the standard-model, so-called Yang-Mills theory, has been discovered by theorists almost a decade before it was recognized to be the key to explain the experimental results.

But this is not the main reason for me to venture into this direction. The main reason has to do with the experience I made with Higgs physics - that despite appearance there is often a second layer to the theory. Such a second layer has in this case shifted the perception of how things we describe in theory correlate with the things we see in experiment. Since many proposed theories beyond the standard model, especially such as have caught my interest, are extensions of the Higgs of the standard model. It thus stands to reason that similar statements hold true in their cases. However, whether they hold true, and how they work cannot be fathomed without looking at theses theories. And that is what I want to do.

Why should one do this? Such subtle questions seem to be at first not really related to experiment. But understanding how a theory really works should also give us a better idea of what kind of observations such a theory can actually deliver. And now it becomes very interesting for an experiment. Since we do at the current time not know what to expect, we need to think about what we could expect. This is especially important as to look in every corner requires much more resources than available to us in the foreseeable future. Hence, any insights into what kind of experimental results a theory can yield is very important to select where to focus.

Of course, my research alone will not be sufficient to do this. Since it easily can be that I am looking at the 'wrong' theory, it would not be a good idea to put too much effort in it. But, when there are many theoreticians working on many theories, and many theories all say that it is a good idea to look into a particular direction: Then we have a guidance for where to look. Then there seems to be something special in this direction. And if not, then we have excluded a lot of theories in one go.

As one person in a discussion session (I could not figure out who precisely) has put it aptly at the conference: "The time of guaranteed discoveries is over.". This means that now that we have all pieces of the standard model, we cannot expect to find a new piece any time soon. All our indirect results even tell us that the next piece will be much harder to find. Hence, we are facing a situation as was last seen in physics in the second half of the 19th century and beginning 20th century: There are only some hints that something does not fit. And now we have to go looking, without knowing in advance how far we will have to walk. Or in which direction. This is probably more of an adventure than the last decades, where things where essentially happening on schedule. But is also requires more courage, since there will be much more dead ends (or worse) available.