Tackling ambiguities

I have recently published a paper with a rather lengthy and abstract title. I wanted to enlighten in this entry a little bit what is going on.

The paper is actually on a problem which occupies me by now since more than a decade. And this is the problem how to really define what we mean when we talk about gluons. The reason for this problem is a certain ambiguity. This ambiguity arises because it is often much more convenient to have auxiliary additional stuff around to make calculations simple. But then you have to deal with this additional stuff. In a paper last year I noted that the amount of stuff is much larger than originally anticipated. So you have to deal with more stuff.

The aim of the research leading to the paper was to make progress with that.

So what did I do? To understand this, it is first necessary to say a few words about how we describe gluons. We describe them by mathematical functions. The simplest such mathematical functions makes, loosely speaking, a statement about how probable it is that a gluon moves from one point to another. Since a fancy word for moving is propagating, this function is called a propagator.

So the first question I posed was whether the ambiguity in dealing with the stuff affects this. You may ask whether this should happen at all. Is a gluon not a particle? Should this not be free of ambiguities? Well, yes and no. A particle which we actually detect should be free of ambiguities. But gluons are not detected. Gluons are, in fact, never seen directly. They are confined. This is a very peculiar feature of the strong force. And one which is not satisfactorily fully understood. But it is experimentally well established.

Since therefore something happens to gluons before we can observe them, there is now a way out. If the gluon is ambiguous, then this ambiguity has to be canceled by whatever happens to it. Then whatever we detect is not ambiguous. But cancellations are fickle things. If you are not careful in your calculations, something is left uncanceled. And then your results become ambiguous. This has to be avoided. Of course, this is purely a problem for us theoreticians. The experimentalists never have this problem. A long time ago I actually already wrote together with a few other people a paper on this, showing how it may proceed.

So, the natural first step is to figure out what you have to cancel. And therefore to map the ambiguity in its full extent. The possibilities discussed since decades look roughly like this:

As you see, at short distances there is (essentially) no ambiguity. This is actually quite well understood. It is a feature very deeply embedded in the strong interaction. It has to do with the fact that, despite its name, the strong interaction makes itself less known the shorter the distance. But for weak effects we have very precise tools, and we therefore understand it.

On the other hand at long distances - well, there we knew for a long time not even qualitatively what is going on for sure. But, finally, over the decades, we were able to constrain the behavior at least partly. Now, I tested a large part of the remaining range of ambiguities. In the end, it indeed mattered little. There is almost no effect left of the ambiguity on the behavior of the gluon. So, it seems we have this under control.

Or do we? One of the important things in research is that it is never sufficient to confirm your result just by looking at a single thing. Either your explanation fits everything we see and measure, or it cannot be the full story. Or may even be wrong and the agreement with part of the observations is just a lucky coincidence. Well, actually not lucky. Rather terrible, since this misguides you.

Of course, doing all in one go is a horrendous amount of work, and so you work on a few at the time. Preferably, you first work on those where the most problems are expected. It is just ultimately that you need to have covered everything. But you cannot stop and claim victory before you did.

So I did, and looked in the paper at a handful of other quantities. And indeed, in some of them there remain effects. Especially, if you look at how strong the strong interaction is, depending on the distance where you measure it, something remains:

The effects of the ambiguity are thus not qualitative. So it does not change our qualitative understanding of how the strong force works. But there remains some quantitative effect, which we need to take into account.

There is one more important side effect. When I calculated the effects of the ambiguity, I learned also to control how the ambiguity manifests. This does not alter that there is an ambiguity, nor that it has consequences. But it allows others to reproduce how I controlled the ambiguity. This is important because now two results from different sources can be put together, and when using the same control they will fit such that for experimental observables the ambiguity cancels. And thus we have achieved the goal.

To be fair, however, this is currently at the level of an operative control. It is not yet a mathematically well-defined and proven procedure. As with so many cases, this still needs to be developed. But having operative control allows to develop the rigorous control easier than starting without it. So, progress has been made.

Using evolution for particle physics

(I will start to illustrate the entries with some simple sketches. I am not very experienced with it, and thus, they will be quite basic. But with making more of them I should gain experience, and they should become better eventually)

This entry will be on the recently started bachelor thesis of Raphael Wagner.

He is addressing the following problem. One of the mainstays of our research are computer simulations. But our computer simulations are not exact. They work by simulating a physical system many times with different starts. The final result is then an average over all the simulations. There is an (almost) infinite number of starts. Thus, we cannot include them all. As a consequence, our average is not the exact value we are looking for. Rather, it is an estimate. We can also estimate in which range around the real result should be.

This is sketched in the following picture

The black line is our estimate and the red lines give the range were the true value should be. From left to right some parameter runs. In the case of the thesis, the parameter is the time. The value is roughly the probability for a particle to survive this time. So we have an estimate for the survivability probability.

Fortunately, we know a little more. From quite basic principles we know that this survivability cannot depend in an arbitrary way on the time. Rather, it has a particular mathematical form. This function depends only on a very small set of numbers. The most important one is the mass of the particle.

What we then do is to start with some theory. We simulate it. And then we extract from such a survival probability the masses of the particles. Yes, we do not know them beforehand. This is because the masses of particles are changed in a quantum theory by quantum effects. These are which we simulate, to get a final value of the masses.

Up to now, we try to determine the mass in a very simple-minded way: We determined them by just looking for numbers for the mathematical functions which are closest to the data. That seems reasonable. Unfortunately, the function is not so simple. Thus, you can mathematically show that this does not give necessarily the best result. You can imagine this in the following way: Imagine you want to find the deepest valley in area. Surely, walking down hill will get you in a valley. But only walking down hill this will usually not be the deepest one:

But this is the way we determine the numbers so far. So there may be other options.

There is a different possibility. In the picture of the hills, you could rather deploy a number of ants, of which some prefer to walk up, some down, and some sometimes so and otherwise opposite. The ants live, die, and reproduce. Now, if you give the ants more to eat if they live in a deeper valley, at some time evolution will bring the population to live in the deepest valley:

And then you have what you want.

This is called a genetic algorithm. It is used in many areas of engineering. The processor of the computer or smartphone you use to read this has likely been optimized using such algorithms.

The bachelor thesis is now to apply the same idea to find better estimates for the masses of the particles in our simulations. This requires to understand what would be the equivalent to the deepness of the valley and the food for the ants. And how long we let evolution run its course. Then, we have only to monitor the (virtual) ants to find our prize.

A shift in perspective - or: what makes an electron an electron?

We have recently published a new paper. It is based partially on the master thesis of my student Larissa Egger, but involves also another scientist from a different university. In this paper, we look at a quite fundamental question: How do we distinguish the matter particles? What makes an electron an electron and a muon a muon?

In a standard treatment, this identity is just an integral part of the particle. However, results from the late 1970ies and early 1980ies as well as our own research point to a somewhat different direction. I have described the basic idea sometime back. The basic idea back then was that what we perceive as an electron is not really just an electron. It consists itself out of two particles. A Higgs and something I would call a constituent electron. Back then, we were just thinking about how to test this idea.

This took some time.

We thought this was an outrageous question, putting almost certain things into question.

Now we see: Oh, this was just the beginning. And things got more crazy in every step.

But, as a theoretician, if I determine the consequences of a theory, we should not stop because something sounds crazy. Almost everything what we take for granted today, like quantum physics, sounded crazy in the beginning. But if you have reason to believe that a theory is right, then you have to take it seriously. And then its consequences are what they are. Of course, we may just have made an error somewhere. But that remains to be checked, preferably by independent research groups. After all, at some point, it is hard to see the forest for the trees. But so far, we are convinced that we made at most quantitative errors, but no qualitative errors. So the concept appears to us sound. And therefore I keep on writing about it here.

The older works was just the beginning. And we just followed their suggestion to take the standard model of particle physics not only serious, but also literal.

I will start out with the leptons, i.e. electrons, muons, and tauons as well as the three neutrinos. I come back to the quarks later.

The first thing we established was that it is indeed possible to think of particles like the electron as a kind of bound state of other particles, without upsetting what we have measured in experiment. We also gave an estimate what would be necessary to test this statement in an experiment. Though really exact numbers are as always complicated, we believe that the next generation of experiments which use electrons and positrons and collide them could be able to detect difference between the conventional picture and our results. In fact, the way they are currently designed makes them ideally suited to do so. However, they will not provide a measurement before, roughly, 2035 or so. We also understand quite well, why we would need these machines to see the effect. So right now, we will have to sit and wait for this. Keep your fingers crossed that they will be build, if you are interested in the answer.

Naturally, we therefore asked ourselves if there is no alternative. The unfortunate thing is that you will need at least enough energy to copiously produce the Higgs to test this. The only existing machine being able to do so is the LHC at CERN. However, to do so they collide protons. So we had to discuss whether the same effect also occurs for protons. Now a proton is much more complicated than any lepton, because it is already build from quarks and gluons. Still, what we found is the following: If we take the standard model serious as a theory, then a proton cannot be a theoretically well-defined entity if it is only made out of three quarks. Rather, it needs to have some kind of Higgs component. And this should be felt somehow. However, for the same reason as with the lepton, only the LHC could test it. And here comes the problem. Because the proton is made up out of three quarks, it has already a very complicated structure. Furthermore, even at the LHC, the effect of the additional Higgs component will likely be tiny. In fact, the probably best chance to probe it will be if this Higgs component can be linked to the production of the heaviest known quark, the top quark The reason is that the the top quark is so very sensitive to the Higgs. While the LHC indeed produces a lot of top quarks, producing a top quark linked to a Higgs is much harder. Even just the strongest effect has not yet been seen above doubt. And what we find will only be a (likely small) correction to it. There is still a chance, but this will need much more data. But the LHC will keep on running for a long time. So maybe, it will be enough. We will see.

So, this is what we did. In fact, this will all be part of the review I am writing. So, more will be told about this.

If you are still reading, I want to give you some more of the really weird stuff, which came out.

The first is that live is actually even more complicated. Even without all of what I have written about above, there are actually two types of electrons in the standard model. One which is affected by the weak interaction, and one which is not. Other than that, they are the same. They have the same mass, and they are electromagnetically the same. The same is actually true for all leptons and quarks. The matter all around us is actually a mixture of both types. However, the subtle effects I have been talking so far about only affect those which are affected by the weak interaction. There is a technical reason for this (the weak interaction is a so-called gauge symmetry). However, it makes detecting everything more harder, because it only works if we get the 'right' type of an electron.

The second is that electrons and quarks come in three sets of four particles each, the so-called generations or families. The only difference between these copies is the mass. Other than that, there is no difference that we know of. Though we cannot exclude it, but we have no experiment saying otherwise with sufficient confidence. This is one of the central mysteries. It occupies, and keeps occupying, many physicist. Now, we had the following idea: If we provide internal structure to the members of the family - could it be that the different generations are just different arrangements of the internal structure? That such things are in principle possible is known already from atoms. Here, the problem is even more involved, because of the two types of each of the quarks and leptons. This was just a speculation. However, we found that this is, at least logically, possible. Unfortunately, it is yet too complicated to provide definite quantitative prediction how this can be tested. But, at least, it seems to be not at odds with what we know already. If this would be true, this would be a major step in understanding particle physics. But we are still far, far away from this. Still, we are motivated to continue this road.

Making connections inside dead stars

Last time I wrote about our research on neutron stars. In that case we were concerned with the properties of neutron stars - its mass and size. But these are determined by the particles inside the star, the quarks and gluons and how they influence each other by the strong force.

However, a neutron star is much more than just quarks and gluons bound by gravity and the strong force.

Neutron stars are also affected by the weak force. This happens in a quite subtle way. The weak force can transform a neutron into a proton, an electron and an (anti)neutrino, and back. In a neutron star, this happens all the time. Still, the neutron are neutrons most of the time, hence the name neutron stars. Looking into this process more microscopically, the protons and neutrons consist out of quarks. The proton out of two up quarks and a down quark, and the neutron out of one up quark and two down quarks. Thus, what really happens is that a down quark changes into an up quark and an electron and an (anti)neutrino and back.

As noted, this does not happen too often. But this is actually only true for a neutron star just hanging around. When neutron stars are created in a supernova, this happens very often. In particular, the star which becomes a supernova is mostly protons, which have to be converted to neutrons for the neutron star. Another case is when two neutron stars collide. Then this process becomes much more important, and more rapid. The latter is quite exciting, as the consequences maybe observable in astronomy in the next few years.

So, how can the process be described? Usually, the weak force is weak, as the name says. Thus, it is usually possible to consider it a small effect. Such small effects are well described by perturbation theory. This is OK, if the neutron star just hangs around. But for collisions, or forming, the effect is no longer small. And then other methods are necessary. For the same reasons as in the case of inert neutron stars we cannot use simulations to do so. But our third possibility, the so-called equations of motion, work.

Therefore Walid Mian, a PhD student of mine, and myself used these equations to study how quarks behave, if we offer to them a background of electrons and (anti)neutrinos. We have published a paper about our results, and I would like to outline what we found.

Unfortunately, we still cannot do the calculations exactly. So, in a sense, we cannot independently vary the amount of electrons and (anti)neutrinos, and the strength of their coupling to the quarks. Thus, we can only estimate what a more intense combination of both together means. Since this is qualitatively what we expect to happen during the collision of two neutron stars, this should be a reasonable approximation.

For a very small intensity we do not see anything but what we expect in perturbation theory. But the first surprise was already when we cranked up the intensity. Much earlier than expected new effects which showed up. In fact, they started to be there at intensities some factor 10-1000 smaller than expected. Thus, the weak interaction could play a much larger role in such environments than usually assumed. That was the first insight.

The second was that the type of quarks - whether it is an up or a down quark is more relevant than expected. In particular, whether they have a different mass, like it is in nature, or the same mass makes a big difference. If the mass is different qualitatively new effects arise, which was not expected in this form.

The observed effects themselves are actually quite interesting: They make the quarks, depending on their type, either more sensitive or less sensitive to the weak force. This is important. When neutron stars are created or collide, they become very hot. The main way to get cooler is by dumping (anti)neutrinos into space. This becomes more efficient if the quarks react less to the weak force. Thus, our findings could have consequences on how quickly neutron stars could become colder.

We also saw that these effects only start to play a role if the quark can move inside the neutron star over a sufficiently large distance. Where sufficiently large is here about the size of a neutron. Thus the environment of a neutron star shows itself already when the quarks start to feel that they do not live in a single neutron, but rather in a neutron star, where there neutrons touch each other. All of the qualitative new effects then started to appear.

Unfortunately, to estimate how important these new effects for the neutron star really are, we first have to understand what it means for the neutrons. Essentially, we have to somehow pull our results on a larger scale - what does this mean for the whole neutron - before we can recreate our investigation of the full neutron star with these effects included. Not even to mention the impact for a collision, which is even more complicated.

Thus, our current next step is to understand what the weak interaction implies for hadrons, i.e. states of multiple quarks like the neutron. The first step is to understand how the hadron can decay and reform by the weak force, as I described earlier. The decay itself can be described already quite well using perturbation theory. But decay and reforming, or even an endless chain of these processes, cannot yet. To become able to do so is where we head next.

Building a dead star

I have written previously about how we investigate QCD to learn about neutron stars. Neutron stars are the extremely dense and small objects left over after a medium-sized star became a supernova.

For that, we have decided to take a detour. To do so, we have slightly modified the strong interactions. The reason for this modification was to do numerical simulations. In the original version of the theory, this is yet impossible. Mainly, because we have not yet been able to develop an algorithm, which is fast enough to get a result within our lifetime. With the small changes we did to our theory, this changes. And therefore, we have now a (rough) idea of how this theory behaves at densities relevant for neutron stars.

Now Ouraman Hajizadeh, a PhD student of mine, and I went all the way. We used these results to construct a neutron star from it. What we found is written up in a paper. And I will describe here what we learned.

The first insight is that we needed a baseline. Of course, we could compare to what we have on neutron star from astrophysics. But we do not yet know too much about their internal structure. This may change with the newly established gravitational wave astronomy, but this will take a few years. Thus, we decided to use neutrons, which do not interact with each other, as the baseline. A neutron star of such particles is only held together by the gravitational pull and the so-called Pauli principle. This principle forbids certain types of particles, so-called fermions, to occupy the same spots. Neutrons are such fermions. Any difference from such a neutron star has therefore to be attributed to interactions.

The observed neutron stars show the existence of interactions. This is exemplified by their mass. A neutron star made out of non-interacting neutrons can have only masses which are somewhat below the mass of our sun. The heaviest neutron stars we have observed so far are more than twice the mass of our sun. The heaviest possible neutron stars could be a little bit heavier than three times our sun. Everything which is heavier would collapse further, either to a different object unknown to us, or to a black hole.

Now, the theory we investigated is different from the true strong-interactions by two effects. One is that we had only one type of quarks, rather than the real number. Also, our quarks was heavier than the lightest quark in nature. Finally, we have more colors and also more gluons than in nature. Thus, our neutron has a somewhat different structure than the real one. But we used this modified version of the neutron to create our baseline, so that we can still see the effect of interactions.

Then, we cranked the machinery. This machinery is a little bit of general relativity, and thermodynamics. The prior is not modified, but our theory determines the latter. What we got was a quite interesting result. First, our heaviest neutron star was much heavier than our baseline. Roughly 20 to 50 percent heaver than our sun, depending on details and uncertainties. Also, a typical neutron star of this mass had much less variation of its size than the baseline. For non-interacting neutrons, changing the maximum mass by ten percent changes the radius by a kilometer, or so. In our case, this changed the radius almost not at all. So, our heaviest neutron stars are much more reluctant to change. So interactions indeed change the structure of a neutron star considerably.

Another long-standing question is, what the internal structure of a neutron star is. Especially, whether they are a, more or less, monolithic block, except for a a very thin layer close to the surface. Or whether they are composed of many different layers, like our earth. In our case, we find indeed a layered structure. There is an outer surface, a kilometer or so thick, and then a different state of matter down to the core. However, the change appears to be quite soft, and there is no hard distinction. Still, our results signal that there a light neutron stars, which only consist out of the 'surface' material, and only heavier neutron stars have such a core of different stuff. Thus, there could be two classes of neutron stars, with different properties. However, the single-type class is lighter than those which have been observed so far. Such light neutron stars, while apparently stable, seem not, or rarely, be formed during the supernovas giving birth to neutron stars.

Of course, the question is, to which extent such qualitative features can be translated to the real case. We can learn more about this by doing the same in other theories. If features turn out to be generic, this points at something which may also happen for the real case. But even our case, which in a certain sense is the simplest possibility, was not trivial. It may take some time to repeat it for other theories.

Can we tell when unification works? - Some answers.

This time, the following is a guest entry by one of my PhD students, Pascal Törek, writing about the most recent results of his research, especially our paper.

Some time ago the editor of this blog, offered me to write about my PhD research here. Since now I gained some insight and collected first results, I think this is the best time to do so.

In a previous blog entry, Axel explained what I am working on and which questions we try to answer. The most important one was: “Does the miracle repeat itself for a unified theory?”. Before I answer this question and explain what is meant by “miracle”, I want to recap some things.

The first thing I want to clarify is, what a unified or a grand unified theory is. The standard model of particle physics describes all the interactions (neglecting gravity) between elementary particles. Those interactions or forces are called strong, weak and electromagnetic force. All these forces or sectors of the standard model describe different kinds of physics. But at very high energies it could be that these three forces are just different parts of one unified force. Of course a theory of a unified force should also be consistent with what has already been measured. What usually comes along in such unified scenarios is that next to the known particles of the standard model, additional particles are predicted. These new particles are typically very heavy and thus makes them very hard to detect in experiments in the near future (if one of those unified theories really describes nature).

What physicists often use to make predictions in an unified theory is perturbation theory. But here comes the hook: what one does in this framework is to do something really arbitrarily, namely to fix a so-called “gauge”. This rather technical term just means that we have to use a mathematical trick to make calculations easier. Or to be more precise, we have to use that trick to even perform a calculation in perturbation theory in those kinds of theories which would be impossible otherwise.

Since nature does not care about this man-made choice, every quantity which could be measured in experiments must be independent of the gauge. But this is exactly how the elementary particles are treated in conventional perturbation theory, they depend on the gauge. An even more peculiar thing is that also the particle spectrum (or the number of particles) predicted by these kinds of theories depends on the gauge.
This problem appears already in the standard model: what we call the Higgs, W, Z, electron, etc. depends on the gauge. This is pretty confusing because those particles have been measured experimentally but should not have been observed like that if you take the theory serious. 

This contradiction in the standard model is resolved by a certain mechanism (the so-called “FMS mechanism”) which maps quantities which are independent of the gauge to the gauge-dependent objects. Those gauge-independent quantities are so called bound states. What you essentially do is to “glue” the gauge-dependent objects together in such a way that the result does not depended on the gauge. This exactly the miracle I wrote about in the beginning: one interprets something (gauge-dependent objects as e.g. the Higgs) as if it will be observable and you indeed find this something in experiments. The correct theoretical description is then in terms of bound states and there exists a one-to-one mapping to the gauge-dependent objects. This is the case in the standard model and it seems like a miracle that everything fits so perfectly such that everything works out in the end. The claim is that you see those bound states in experiments and not the gauge-dependent objects.

However, it was not clear if the FMS mechanism works also in a grand unified theory (“Does the miracle repeat itself?”). This is exactly what my research is about. Instead of taking a realistic grand unified theory we decided to take a so called “toy theory”. What is meant by that is that this theory is not a theory which can describe nature but rather covers the most important features of such kind of theory. The reason is simply that I use simulations for answering the question raised above and due to time constraints and the restricted resources a toy model is more feasible than a realistic model. By applying the FMS mechanism to the toy model I found that there is a discrepancy to perturbation theory, which was not the case in the standard model. In principle there were three possible outcomes: the mechanism works in this model and perturbation theory is wrong, the mechanism fails and perturbation theory gives the correct result or both are wrong. So I performed simulations to see which statement is correct and what I found is that only the FMS mechanism predicts the correct result and perturbation theory fails. As a theoretician this result is very pleasing since we like to have nature independent of a arbitrarily chosen gauge.

The question you might ask is: “What is it good for?” Since we know that the standard model is not the theory which can describe everything, we look for theories beyond the standard model as for instance grand unified theories. There are many of these kinds of theories on the market and there is yet no way to check each of them experimentally. What one can do now is to use the FMS mechanism to rule some of them out. This is done by, roughly speaking, applying the mechanism to the theory you want to look at, count the number of particles predicted by the mechanism, compare it to the number particles of the standard model. If there are more the theory is probably a good candidate to study and if not you can throw it away.

Right now Axel, a colleague from Jena University, and myself look at more realistic grand unified theories and try to find general features concerning the FMS mechanism. I am sure Axel or maybe myself keep you updated on this topic.

Writing a review

As I have mentioned recently on Twitter, I have been given the opportunity, and the mandate, to write a review on Higgs physics. Especially, I should describe how the connection is established from the formal basics to what we see in experiment. While I will be writing in the next time a lot about the insights I gain and the connection I make during writing, this time I want to talk about something different. About what this means, and what the purpose of reviews is.

So what is a review good for? Physics is not static. Physics is about our understanding of the world around us. It is about making things we experience calculable. This is done by phrasing so-called laws of nature as mathematical statements. Then making predictions (or explaining something what happens) is, essentially, just evaluating equations. At least in principle, because this may be technically extremely complicated and involved. There are cases in which our current abilities are not even yet able to do so. But this is technology and, often, resources in form of computing time. Not some conceptual problem.

But there is also a conceptual problem. Our mathematical statements encode what we know. One of their most powerful feature is that they tell us themselves that they are incomplete. That our mathematical formulation of nature only reaches this far. That are things, we do not even yet know what they are, which we cannot describe. Physics is at the edge of knowledge. But we are not lazy. Every day, thousands of physicists all around the world work together to push this edge daily a little bit farther out. Thus, day by day, we know more. And, in a global world, this knowledge is shared almost instantaneously.

A consequence of this progress is that the textbooks at the edge become outdated. Because we get a better understanding. Or we figure out that something is different than we thought. Or because we find a way to solve a problem which withstood solution for decades. However, what we find today or tomorrow is not yet confirmed. Every insight we gain needs to be checked. Has to be investigated from all sides. And has to be fitted into our existing knowledge. More often that not some of these insights turn out to be false hopes. That we thought we understood something. But there is still that one little hook, this one tiny loop, which in the end lets our insight crumble. This can take a day or a month or a year, or even decades. Thus, insights should not directly become part of textbooks, which we use to teach the next generation of students.

To deal with this, a hierarchy of establishing knowledge has formed.

In the beginning, there are ideas and first results. These we tell our colleagues at conferences. We document the ideas and first results in write-ups of our talks. We visit other scientists, and discuss our ideas. By this we find many loopholes and inadequacies already, and can drop things, which do not work.

Results which survive this stage then become research papers. If we write such a paper, it is usually about something, which we personally believe to be well funded. Which we have analyzed from various angles, and bounced off the wisdom and experience of our colleagues. We are pretty sure that it is solid. By making these papers accessible to the rest of the world, we put this conviction to the test of a whole community, rather than some scientists who see our talks or which we talk to in person.

Not all such results remain. In fact, many of these are later to be found to be only partly right, or still have overlooked a loophole, or are invalidated by other results. But this stage already a considerable amount of insights survive.

Over years, and sometimes decades, insights in papers on a topic accumulate. With every paper, which survives the scrutiny of the world, another piece in the puzzle fits. Thus, slowly a knowledge base emerges on a topic, carried by many papers. And then, at some point, the amount of knowledge has provided a reasonable good understanding of the topic. This understanding is still frayed at the edges towards the unknown. There is still here and there some holes to be filled. But overall, the topic is in fairly good condition. That is the point where a review is written on the topic. Which summarizes the finding of the various papers, often hundreds of them. And which draws the big picture, and fits all the pieces into it. Its duty is also to point out all remaining problems, and where the ends are still frayed. But at this point usually the things are well established. They often will not change substantially in the future. Of course, no rule without exception.

Over time, multiple reviews will evolve the big picture, close all holes, and connect the frayed edges to neighboring topics. By this, another patch in the tapestry of a field is formed. It becomes a stable part of the fabric of our understanding of physics. When this process is finished, it is time to write textbooks. To make even non-specialist students of physics aware of the topic, its big picture, and how it fits into our view of the world.

Those things, which are of particular relevance, since they form the fabric of our most basic understanding of the world, will eventually filter further down. At some point, the may become part of the textbooks at school, rather then university. And ultimately, they will become part of common knowledge.

This has happened many times in physics. Mechanics, classical electrodynamics, thermodynamics, quantum and nuclear physics, solid state physics, particle physics, and many other fields have undergone these level of hierarchies. Of course, often only with hindsight the transitions can be seen, which lead from the first inspiration to the final revelation of our understanding. But in this way our physics view of the world evolves.

Structuring internationality

I wrote some time ago about the immense importance of diversity and multiculturality for research. How important exchange is by going abroad and to have people from many different places around oneself. Also, and probably even more important so, at home. How this is indispensable to make research possible, especially at the utmost frontiers of human knowledge.

This is, and remains, true. There is no progress without diversity. In this entry, I would like to write a bit about what we did recently to foster and structure such exchange.

The insight that diversity is important is something fortunately embraced also by the European Union. As a consequence, they offer various support options to help with this goal. One possibility are so-called COST networks. These actually involve countries, rather than individuals, with the intention to foster exchange across borders.

Since mid of October, Austria is now member of one such network within one of my core research areas, the physics governing quarks and gluons at high temperatures and densities, relevant for how the early universe evolved, and what the properties of supernovas and neutron stars in today's universe are. In this network I am one of the two representatives of Austria, i.e. speaking on behalf of the scientists in Austria being members of this network. Representatives of the (so far) 26 member countries have met in Brussels in the mid of October to discuss how this exchange should be organized in the future. One important part of this agenda, also very much encouraged by the European Union, is the promotion of minorities and gender equality and to support scientists from countries with economically less support for science.

On this first meeting, which was actually only on these and other issues and not on scientific content, we have established an agenda how the funds available to us in this network will be prioritized to achieve this goal. This includes the possibility for members of the aforementioned groups to receive travel support to meetings and collaboration partners and/or preferential participation in events. We want them to be part of this effort as fully as possible. We need them, and their perspectives, to make progress, and also to reevaluate our own views and endeavors.

Of course, there were also many other issues to be discussed, many of them rather administrative in nature. There were also discussions involved, when there were some different opinions on which was the ideal way forward. But, as a democratic process, this was resolved in a way to which everyone could commit.

It was certainly a quite uplifting experience to sit together with scientists from so many different countries, not with the aim to find an answer to a physics problems as at a conference, but rather with the goal to get people together, to connect. In the roughly four years this structure will run we will have several more meetings. The ultimate goal will be a joint series of so-called white papers. White papers are statements describing the most urgent and challenging problems in a given branch of research. Their aim is to structure future research and to make it more efficient by separating the irrelevant from the relevant questions.

These white papers will then be a truly international effort. People from almost thirty countries will provide a mutual view on some of the most challenging problems at the frontier of human knowledge. Questions important for our origin and of the world we live in. Without such a network, this would surely not happen. Rather, the many groups in different countries would be more isolated. And then there would be too many smaller groups trying to achieve the same purpose. But without such a broad and international basis and connection, the outcome would certainly not have such a broad collection of perspectives. And only by enough views coming together, we may eventually identify the point were all eyes look on, giving us the clue, where the key to the next big leap forward could be hidden.

Redundant ghosts

A recurring topic in our research are the joys and sorrows of the redundancies in our description. As I have discussed several times introducing these redundancies makes live much easier. But this can turn against you, if you need to make approximations. Which, unfortunately, is usually the case. Still their benefits outweighs the troubles.

One of the remarkable consequences of these redundancies is that they even affect our description of the most fundamental particles in our theories. Here, I will concentrate on the gluons of the strong interactions (or QCD). On the one hand because they play a very central role in many phenomena. But, more importantly, because they are the simplest particles exhibiting the problem. This follows essentially the old strategy of divide and conquer. Solve it for the simplest problem first, and continue from there.

Still, even the simplest case is not easy. The reason is that the redundancies introduced auxiliary quantities. These act like some imaginary particles. These phantom particles are called also ghosts, because, just like ghosts, they actually do not really exist, they are only there in our imagination. Actually, they are called Faddeev-Popov ghosts, honoring those two people who have introduced them for the very first time.

Thus, whenever we calculate quantities we can actually observe, we do not see any traces of these ghosts. But directly computing an observable quantity is often hard, especially when you want to use eraser-and-pencil-type calculations. So we work stepwise. And in such intermediate steps ghosts do show up. But because they only encode information differently, but not add information, their presence affects also the description of 'real' particles in these intermediate stages. Only at the very end they would drop out. If we could do the calculations exactly.

Understanding how this turns out quantitatively is something I have been working on since almost a decade, with the last previous results available almost a year ago. Now, I made a little bit progress. But making progress is for this problem rather though. Therefore there are usually no big breakthroughs. It is much like grinding in an MMO. You need to accumulate little bits of information, to perhaps, eventually, understand what is going on. And this is once more the case.

I have presented the results of the latest steps recently at a conference. A summary of this report is freely available in a write-up for the proceedings of this conference.

I found a few new bits of information. One was that we certainly underestimated the seriousness of the problem. That is mainly due to the fact that most such investigations have so far been done using numerical simulations. Even though we want to do in the end rather the eraser-and-pencil type calculations, ensuring that they work is easier done using numerical simulations.

However, the numerical simulations are expensive, and therefore one is limited in them. I have extended the effort, and was able to get a glimpse of the size of the problem. I did this by simulating not only the gluons, but also simulated the extent to which we can probe the problem. By seeing how the problem depends on our perception of the problem, I could estimate, how big it will become at least, eventually.

Actually, the result was somewhat unsettling, even though it is not hopeless. One of the reason, why it is not hopeless is the way how it affects everything. And there it turned out that the aforementioned ghosts actually carry the brunt of the problem. This is good, as they will cancel out in the end. Thus, even if we cannot solve the problem completely, it will not have as horrible an impact as was imaginable. Thus, we can have a little bit more confidence that what we do makes actually sense, especially when we calculate something observable.

You may say that we could use experiments to check our approximations. It appears easier. After all, this is what we want to describe - or is it? Well, this is certainly true, when we are thinking about the standard model. But fundamental physics is more geared towards the unknown nowadays. And as a theoretician, I try to predict also the unknown. But if my predictions are invalidated by my approximations, what good can they be? Knowing therefore that they are not quite as affected as they could be is more than valuable. It is necessary. I can then tell the experimentalists with more confidence the places they should look, with at least some justified hope that I do not lead them on a wild geese chase.

Searching for structure

This time I want to report on a new bachelor thesis, which I supervise. In this project we try to understand a little better the foundations of so-called gauge symmetries. In particular we address some of the ground work we have to lay for understanding our theories.

Let me briefly outline the problem: Most of the theories in particle physics include some kind of redundancy I.e., there are more things in it then we actually see in experiments. The surplus stuff is actually not real. It is just a kind of mathematical device to make calculations simpler. It is like a ladder, which we bring to climb a wall. We come, use the ladder, and are on top. The ladder we take again with us, and the wall remains as it was. The ladder made live simpler. Of course, we could have climbed the wall without it. But it would have been more painful.

Unfortunately, theories are more complicated than wall climbing.

One of the problems is that we usually cannot solve problems exactly. And as noted before, this can mess up the removal of the surplus stuff.

The project the bachelor student and I am working on has the following basic idea: If we can account for all of the surplus stuff, we should be able to know whether our approximations did something wrong. It is like preparing an engine. If something is left afterwards it is usually not a good sign. Unfortunately, things are again more complicated. For the engine, we just have to look through our workspace to see whether anything is left. But how to do so for our theories? And this is precisely the project.

So, the project is essentially about listing stuff. We start out with something we know is real and important. For this, we take the most simplest thing imaginable: Nothing. Nothing means in this case just an empty universe, no particles, no reactions, no nothing. That is certainly a real thing, and one we want to include in our calculations.

Of this nothing, there are also versions where some of the surplus stuff appears. Like some ghost image of particles. We actually know how to add small amounts of ghost stuff. Like a single particle in a whole universe. But these situations are not so very interesting, as we know how to deal with them. No, the really interesting stuff happens if well fill the whole universe with ghost images. With surplus stuff which we add just to make life simpler. At least originally. And the question is now: How can we add this stuff systematically? As the ghost stuff is not real, we know it must fulfill special mathematical equations.

Now we do something, which is very often done in theoretical physics: We use an analogy. The equations in question are not unique to the problem at hand, but appear also in quite different circumstances, although with a completely different meaning. In fact, the same equations describe how in quantum physics one particle is bound to each other. In quantum physics, depending on the system at hand, there may be one or more different ways how this binding occurs. You can count the number, and there is a set which one can label by whole numbers. Incidentally, this feature is where the name quantum originates from.

Returning to our original problem, we do the following analogy: Enumerating the ghost stuff can be cast into the same form as enumerating the possibilities of binding two particles together in quantum mechanics. The actual problem is only to find the correct quantum system which is the precise analogous one to our original problem. Finding this is still a complicated mathematical problem. Finding only one solution for one example is the aim of this bachelor thesis. But already finding one would be a huge step forward, as so far we do not have one at all. Having it will probably be like having a first stepping stone for crossing a river. From understanding it, we should be able to understand how to generate more. Hopefully, we will eventually understand how to create arbitrary such examples. And thus solve our enumeration problem. But this is still in the future. For the moment, we do the first step.

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.

Digging into a particle

This time I would like to write about a new paper which I have just put out. In this paper, I investigate a particular class of particles.

This class of particles is actually quite similar to the Higgs boson. I. e. the particles are bosons and they have the same spin as the Higgs boson. This spin is zero. This class of particles is called scalars. These particular sclars also have the same type of charges, they interact with the weak interaction.

But there are fundamental differences as well. One is that I have switched off the back reaction between these particles and the weak interactions: The scalars are affected by the weak interaction, but they do not influence the W and Z bosons. I have also switched off the interactions between the scalars. Therefore, no Brout-Englert-Higgs effect occurs. On the other hand, I have looked at them for several different masses. This set of conditions is known as quenched, because all the interactions are shut-off (quenched), and the only feature which remains to be manipulated is the mass.

Why did I do this? There are two reasons.

One is a quite technical reason. Even in this quenched situation, the scalars are affected by quantum corrections, the radiative corrections. Due to them, the mass changes, and the way the particles move changes. These effects are quantitative. And this is precisely the reason to study them in this setting. Being quenched it is much easier to actually determine the quantitative behavior of these effects. Much easier than when looking at the full theory with back reactions, which is a quite important part of our research. I have learned a lot about these quantitative effects, and am now much more confident in how they behave. This will be very valuable in studies beyond this quenched case. As was expected, there was not many surprises found. Hence, it was essentially a necessary but unspectacular numerical exercise.

Much more interesting was the second aspect. When quenching, this theory becomes very different from the normal standard model. Without the Brout-Englert-Higgs effect, the theory actually looks very much like the strong interaction. Especially, in this case the scalars would be confined in bound states, just like quarks are in hadrons. How this occurs is not really understood. I wanted to study this using these scalars.

Justifiable, you may ask why I would do this. Why would I not just have a look at the quarks themselves. There is a conceptual and a technical reason. The conceptual reason is that quarks are fermions. Fermions have non-zero spin, in contrast to scalars. This entails that they are mathematically more complicated. These complications mix in with the original question about confinement. This is disentangled for scalars. Hence, by choosing scalars, these complications are avoided. This is also one of the reasons to look at the quenched case. The back-reaction, irrespective of with quarks or scalars, obscures the interesting features. Thus, quenching and scalars isolates the interesting feature.

The other is that the investigations were performed using simulations. Fermions are much, much more expensive than scalars in such simulations in terms of computer time. Hence, with scalars it is possible to do much more at the same expense in computing time. Thus, simplicity and cost made scalars for this purpose attractive.

Did it work? Well, no. At least not in any simple form. The original anticipation was that confinement should be imprinted into how the scalars move. This was not seen. Though the scalars are very peculiar in their properties, they in no obvious way show confinement. It may still be that there is an indirect way. But so far nobody has any idea how. Though disappointing, this is not bad. It only tells us that our simple ideas were wrong. It also requires us to think harder on the problem.

An interesting observation could be made nonetheless. As said above, the scalars were investigated for different masses. These masses are, in a sense, not the observed masses. What they really are is the mass of the particle before quantum effects are taken into account. These quantum effects change the mass. These changes were also measured. Surprisingly, the measured mass was larger than the input mass. The interactions created mass, even if the input mass was zero. The strong interaction is known to do so. However, it was believed that this feature is strongly tied to fermions. For scalars it was not expected to happen, at least not in the observed way. Actually, the mass is even of a similar size as for the quarks. This is surprising. This implies that the kind of interaction is generically introducing a mass scale.

This triggered for me the question whether the mass scale also survives when having the backcoupling in once more. If it remains even when there is a Brout-Englert-Higgs effect then this could have interesting implications for the mass of the Higgs. But this remains to be seen. It may as well be that this will not endure when not being quenched.