Enthusiasm vs. Statistics

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

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

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

Well, here comes the detective part in particle physics.

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

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

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

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

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

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

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

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

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

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

A Higgs and a Higgs make what?

Recently, I have mostly written about increasingly technical details of my work. Though these are absolutely necessary foundations for what I do, they are of limited use when taken out of context. I will try to be a bit more up-to-date and less technical, and will try to write more about what motivates me at a current time. What am I really working on?

So let me start with what I am doing right now, just before I started writing this entry. You will probably all have heard about the Higgs discovery. Or, more appropriately, of a particle of which we strongly suspect, but do not yet know, that it is the Higgs. But let me assume for now that it is. As exciting and important as this discovery is in itself, there is much more to this. One of the fascinating things about modern theories is that they do not only describe one or two phenomena, but have an enormous richness.

Concerning the standard model, and in particular the Higgs sector, there are quite some subtle phenomena going on. Why subtle? Well, the Higgs is actually quite a seclusive type. It does not play very much with the rest of the standard model, perhaps except for the top quark. In our language, we say that it is weakly coupled. The Higgs is not the only such particle in the standard model. Everything which has to do with electromagnetism is also not very strongly coupled.

Nonetheless, electrically charged particles play along very well. They like to group together in what we call atoms. These are so-called bound states of electrically charged particles, like the proton and the electron.

Now, for the Higgs actually something similar applies. It has been already suspected in the early 1980ies that Higgs particles could form bound states. In fact, there are very strong theoretical arguments for it, as soon as you include enough of the standard model. The crucial question was (and still is), how long do such Higgs atoms live? Of course, normal atoms live essentially forever, if no physicist comes by and smashes them or some chemist tries to let them react with each other. This is, because the things making up a normal atom are stable themselves. Electrons and protons are, to the best of our knowledge, very, very stable. Even the neutrons, once packed into a nucleus, remain stable. Well, at least if do not select too exotic a nucleus.

Anyway, this is different in the Higgs case. Here the constituents of these 'atoms', just two Higgses, really, are unstable themselves. Thus, it is at all not clear whether you can ever observe such a thing. But since rather deep theoretical arguments say that this could be, I want to know what the answer is. Even more, I am not satisfied with whether they could exist in principle, but if we can see them in an experiment, say the LHC.

To get an answer to this question, I have to invest everything I know. I first have to gather the basic foundation of the theory describing the Higgs. Then, I use simulations to determine the properties of such Higgs atoms. To be able to do this, I have to simplify quite a lot, because otherwise the simulations would be unbearable slow. Once I have these properties, I put them into a model. This step is necessary, because the simulations are not very efficient to give experimental predictions. Thus, I have to take a detour to get an answer. Such a model can be obtained using the appropriate equations to link both worlds.

Then, finally, I have a description of these atoms, and how they interact. With this, I have finally reached the point to use different types of simulations to make an experimental prediction.

That may sound like an afternoons work. But, unfortunately, it is not. Determining the properties of the atoms, even very roughly, has already required something like eighteen months. Constructing the model took another month in its simplest version. And right now, I just get acquainted with the basic simulations for an experiment. I just finished 'rediscovering' the well-known Z, as a first exercise. I hope that I will be able to present a first result at a small workshop in January, almost two years after I started thinking about this question. This result will be extremely simplified, and will be at best a motivation to go on. I have estimated that to get a real quantitative result, which is correct within about 20-30 percent, will require probably another ten-twenty man-years, and likely a couple of thousand core-years of computing time. But well, if we can find them, that would be really something. But even if not, then we have learned a lot about the theory we are working with. And that would be something in itself. So stay tuned, what will happen next.

Hiding our ignorance

The radiative corrections discussed last time have another important aspect. For this, it is useful to recall the entry on Einstein's famous relation E=m*c*c. This relation told us that you can convert energy to mass, and thus to particles.

Now, quantum physics is a cheater. Always was, always will be. One of the most basic things it cheats about is knowledge. It tells you that certain pairs exist of which you cannot know both at the same time with certainty. If you know one very precisely, you can have only little knowledge about the other. The most important and fundamental such pair is position and speed. If you know the position of a particle well, you cannot know its speed very well. And the other way around. This is an observation of nature, which has been confirmed in numerous experiments. We cannot yet really explain why this is so, and have to accept it for the time being as an experimental fact. What we can do is derive an enormous amount of knowledge from this fact.

Among this is that a very similar relation holds for energy and time. If we know time very precisely, we do not know the energy very precisely. If you combine this with Einstein's formula, you get a very interesting consequence: For very short periods of time, energy is not very well defined, and may be much larger than assumed. Since this energy is equivalent to mass, this means that for very short periods of time you can have particles pop out of nowhere and vanish again. To be precise, you can have a pair of a particle and an anti-particle for very brief moments in time.

This seem to be almost unbelievable: Something hops into and out of existence, just like this. However, you can measure actually this effect, and it has been experimental confirmed very well. Also, it should not be taken too literally. What really happens is that quantum physics does something, and in our mathematical description it appears like you would have these pairs.

So what does this have to do with the radiative corrections? Radiative corrections are quantum corrections. As such they involve precisely this type of process: Something hoping out of the vacuum. It then briefly interacts with whatever you are actually looking at. Then it vanishes again. Therefore, radiative corrections include all the possible interactions of some particle with all other possible particles. Now comes the real boon of this: In reality this happens with all particles, not only those we know of. This has been used in the past to predict new particles, like the top quark, some of the neutrinos, and, yes, also the Higgs.

Great, so I can get everything from it! you may say. Unfortunately, it is not that simple. The heavier the particles, the less their contributions to radiative corrections, and thus the more precise an experiment has to be to detect their influence. As a consequence, the Higgs was the last particle for which we had strong such indirect evidence. And this was already experimentally challenging.

But it is much more troublesome for theory. Since we do not actually know what is there, our calculations have a problem. We create at very short times a lot of energy, but we do not know where to put it, since we do not know all the particles. Our theories thus lack something. And this something haunts us as failures of our theories, when we try to calculate radiative corrections. This was a very big problem for theories for a while, but we finally managed it. The key concept was named 'renormalization', which is again somewhat of a misnomer. Anyway, it gives a name to the process of hiding our ignorance. In fact, what we do is that we introduce in our theories placeholders for all these unknown particles. These placeholders are designed on purpose to remove all the problems we have. The way we designed them they can never described something of nature, but they absorb all the problems we encounter with our ignorance.

Since we know that we have these problems, it also tells us that the standard model cannot be the end - or for that matter any theory having such problems. They only describe our world at (relatively) low energies: The standard model is a low-energy effective theory, as was briefly indicated before. Here, you now have a better view of what the reason for the infinities encountered back then is: That we do not know what particles may appear in our radiative corrections, and thus that we do not know where to direct our energy to. And that the parameters used back then just mock up the unknown particles.

You may wonder whether this is a generic sickness of quantum theories. This is very hard to tell for a realistic theory. Of course, we assume that if we would know the theory of everything, it should not have these problems. We can indeed construct toy theories of toy worlds, which do not have these problems, so we think it is possible. Whether this is true in the end or not, we cannot say yet - perhaps we will need in the end a whole new theoretical concept to deal with the real world. For now, renormalization prevents us from the need to know everything already. This permits us to discover nature step by step.

What means 'radiative correction'?

A term, which comes up very often when one reads about the Higgs, are radiative corrections. The thing hiding behind this name is also very essential in both my own work, and in particle physics in general. So what is it?

Again, the name is historic. There are two parts in it, referring to radiation and to correction. It describes something one comes across when one wants to calculate very precisely something in quantum physics.

When we sit down to calculate something in theoretical quantum physics, we have many methods available. A prominent one is perturbation theory. The basic idea of perturbation theory is to first solve a simpler problem, and then add the real problem in small pieces, until one has the full answer.

Usually, when you starts to calculate something with perturbation theory in quantum physics, you assume that the quantum effects are, in a certain sense, small. A nice starting point is then to neglect quantum physics completely, and do just the ordinary non-quantum, often called classical, part. To represent such a calculation, we have developed a very nice way using pictures. I will talk about this soon. Here, it is only necessary to say that the picture of this level of calculation looks like a (very, very symbolic) tree. Therefore, this simplest approximation is also known as tree-level.

Of course, neglecting quantum effects is not a very good description of nature. Indeed, we would not be able to build the computer on which I write this blog entry, if we would not take quantum effects into account. Or have the Internet, which transports it to you. In perturbation theory we add these quantum contributions now piece by piece, in order of increasing 'quantumness'. This can be mathematically very well formulated what this means, but this is not so important here.

If the quantum contributions are small, these pieces are just small corrections to the tree-level result. So, here comes the first part of the topic, the correction.

When people did this in the early days of quantum mechanics, in the 1920ies, the major challenge was to describe atoms. In atoms, most quantum corrections involve that the electron of an atom radiates a photon or captures a photon radiated from somewhere else. Thus, the quantum corrections where due to radiation, and hence the name radiative corrections, even if quantum corrections would be more precise. But, as always, not the best name sticks, and hence we are stuck with radiative corrections for quantum corrections.

Today, our problems have become quite different from atoms. But still, if we calculate a quantum correction in perturbation theory, we call it a radiative correction. In fact, by now we have adapted the term even when what we calculate is no small correction at all, but may be the most important part. Even if we use other methods than perturbation theory. Then, the name radiative correction is just the difference between the classical result and the quantum result. You see, there is no limit to the abuse of notation by physicists.

Indeed, calculating radiative corrections for different particles is a central part of my research. More or less every day, I either compute such radiative corrections, or develop new techniques to do so. When I finally arrive at an expression for the radiative correction, I can do two things with them. Either I can try to understand from the mathematical structure of the radiative corrections what are the properties of the particles. For example, what is its mass. Or how strongly does it interact with other particles. Or I can combine the radiative corrections for several particles or interactions to determine a new quantity. These can be quite complicated. Recently, one of the things I have done was to use the radiative corrections of gluons to calculate the temperature of the phase transition of QCD. There, I have seen that at a certain temperature the radiative correction to the behavior of gluons change drastically. From this, I could infer that a phase transition happened.

So you see, this term, being used so imprecisely, is actually an everyday thing in my life as a theoretician.

Using E=m*c*c

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

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

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

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

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

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

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

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

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

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

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

The speed of light - and its consquences

So far, I did not say anything about gravity. This will remain so. However, I will have to say something about special relativity. Somehow, special relativity is often associated with gravity. This is actual not the case. Einstein's theory of special relativity does not make any reference to gravity. Only the theory of general relativity, of which special relativity is just a small subset, does so.

If special relativity is not about gravity, what is it about? Well, it is about the fact that our universe is a bit more weird than one expects.

What do you expect of a law of nature? One property is likely that it is always valid. This simple requirement has quite profound consequences. Assume for a second that you and your experiment are alone in the universe. This means ta you have no point of reference. If now the experiment moves, you could not say whether it is moving, or you. Still, you would expect that it gives the same results, irrespective of whether it or you are moving. We made experiments to test this idea, and it was confirmed beautifully. This fact that experiments are independent of relative motion, is one of the basic observations leading to special relativity.

The next ingredient is much more harder to believe. Take a light beam. What speed does it have? Well, the speed of light, of course. Now, if you move the thing creating the light at a fixed speed, how fast should the light move? Naively, one would expect that the light would now move faster. Unfortunately, our universe does not tick that way: The light still moves with the same speed. Actually, the light is actually made up out of massless photons, which travel at the speed of light. And this observation is the same for anything which is massless: All massless particles move at the speed of light. And the speed of light is always the same, no matter how fast the light source moves.

This is nothing we can really explain. It is an experimental fact. Our universe is like this. But this observation is the second basic fact underlying special relativity.

If we cannot explain why this second fact comes about, can we at least describe it? We can, and that is what leads to special relativity.

Now, how do we describe this? Well, this is a bit more involved. Take the universe. Then at each instance you have three directions in space. Distances you measure do not depend on the direction in space. You can also measure time elapsing. Works out also nicely. But now, try to measure a space-time distance. You do this by measuring a distance in the space direction. Then you take the elapsed time, and calculate what distance a light ray would have moved during this time. By this, you can talk about a distance in time direction.

The speed of an object is given (if the speed does not change) by the ratio of distance over time required to move over this distance. If you now want that the speed of light is independent of whether the light source moves or not, something peculiar is found: To get this, a distance in space-time direction is obtained by subtracting the distance in the time direction and in the space direction, when you do your Phytagorean geometry. That is completely different than what you have in the three time directions, but the only way to get the light speed to agree with experiment. The geometry of space-time is hence quite different from the one we know just from space.

As a theoretician, I say that the way we measure the distances is not like the ordinary one in three space directions (a so-called Euclidean measure), but we have rather a Lorentz measure. This is in honor to the first one who has described it. Again, we cannot yet explain why this is the case, it just is an experimental fact.

You may wonder why you never noticed this in real lifer. The answer is that when the light source moves very slowly compared to the light ray, the effect is negligible. This becomes only relevant, if you move at a considerable fraction of the speed of light. But then all the nice effects result of which you may have heard in Science Fiction movies or novels: Things like the twin paradox, time dilatation, length contraction, and so on. All of these result from these two basic observations. And are described by the theory of special relativity.

This all sound pretty weird, and it is. It is nothing we have a real handle on with our everyday experience. Just like the quantum effects. The universe is just this way.

As you see, gravity enters here nowhere. And also no quantum stuff. If you add gravity, you get to the theory of general relativity. If you add quantum stuff, you end up with quantum field theory. The standard model is of the latter kind. And this combination leads to very interesting effects, which I will discuss in more detail next time.

Two worlds: Theory and experiment

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

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

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

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

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

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

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

In most cases, things roughly proceed as follows:

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

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

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

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

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

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

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

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

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

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

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

Where physicists go to

You may wonder, why it is so quite here. The reason is that I do what all physicists do from time to time: We go to conferences, present and discuss our ideas and listen to other people's ideas. This exchange is incredible important to make progress, because only in discussions we can remove the flaws we do not see ourselves, and get the inspiration to find new ideas.

I am right now at two such conferences in Australia - since the people are spread all over the world, it does not really matter where we meet. Someone has always to travel far. Thus, the next entry on topic will take some time, likely until August, but that is just how it is. But until then, I will post everything interesting I hear directly on Twitter, so stay tuned.

Technicolor

Last time, I described our reasons and attempts to go beyond the standard model. Among the myriads of possibilities of extensions of the standard model there is one, on which I work. Let me describe it first. Then, I will tell you, why I find especially this one interesting.

This extension of the standard model is called technicolor. It is one of the bottom-up approaches. It was mainly conceived to cure problems we have with the Higgs particle. One particular annoying problem with the Higgs is that its mass is not constrained in the standard model. Well, this is not yet really a problem, since neither are the masses of any of the other particles. But the Higgs mass is in so far different as it is very sensitive to the rest of the standard model. If we change the properties of the standard model by a factor of, say, a hundred, the electron mass will only change by a factor of two, or so. But the Higgs mass will change by a factor ten thousand. Both statements are, of course, very rough, but you should get the idea: To get the Higgs mass to the value we will, hopefully soon, measure, we have to be very careful with the standard model. We have to tune it very finely. This is called the fine-tuning problem, or also the hierarchy problem. It is actually a perceived problem only. Nature may be "just so". But so far, whenever nature seemed to be "just so", there was actually a deeper reason behind it.

Thus, people have set out to find an explanation for this extreme sensitivity of the Higgs mass. Well, actually, people rather have searched for an alternative to the standard model, where this is not the case.

One of the possibilities, which has been conceived, was technicolor. The rather poetic name comes from the historical fact that QCD with its colors has been a role model for technicolor. However, in the decades after its original inception in the 1970ies, technicolor has changed a lot. Today, this theory has only remote similarities to QCD, but, of course, the name stuck once more.

So how does technicolor works? Actually, technicolor is not really a single theory. Since we do not yet have any experimental information about the Higgs, we are not yet able to restrict such extensions of the standard model very well. Thus, there are many theories, which could be called technicolor. It is more an idea than a strict mathematical concept, and it can come in many disguises. The basic idea is that the Higgs is not an elementary particle. Rather, it is made out of other particles, which are called techniquarks. These are held together by exchanging technigluons - once more you see how QCD has been inspirational to the naming.

You may ask what one wins by making the Higgs a more complicated object. The answer is that the Higgs mass, once made out of other (fermionic) particles, is no longer so sensitive, but behaves like the other masses in the standard model. Thus, this solves the problem one has set out to solve.

Of course, as long as we do not yet have found the Higgs, we cannot yet tell whether it is really made up out of other particles. And even when we find it, it will be very complicated to determine whether it is, and it will take a lot of time and a lot of experiments.

But it turns out that things do not come so freely. As you may remember, we needed the Higgs also to provide mass to the other particles in the standard model. And this becomes much more complicated once the Higgs is made out of techniquarks. The reason is that the standard model Higgs is rather flexible, and we can adjust its interactions with the other particles so that the right mass of, say, the electron comes out. This is no longer easily possible once the Higgs has a substructure. This has led in the 1980ies to the believe that technicolor cannot work.

In 1990ies, and now after 2000, however, clever people found a way to make it work. The original problem came about because in the beginning technicolor was made too much alike to QCD. Once one is satisfied with a theory being more different from QCD, and being willing to add a few more particles, the situation improves. Unfortunately, without guidance by experimental results it becomes somewhat ambiguous how to solve the problem, but it seems feasible after all.

So far, this is the status of technicolor. Why am I interested in it?

If you want to make the Higgs from two techniquarks and at the same time simulate the Higgs effect, it is necessary to introduce a new mechanism to the theory. When you look at QCD, its strength depends on the energy. Actually, it does so in a very violent way, and QCD changes from strongly interacting to weakly interacting very quickly. To make the technicolor idea work, this had to change. Technicolor needs to change from strongly interacting to weakly interacting very slowly. To make this distinction more vivid, QCD is called a running theory while technicolor is called a walking theory. This means that technicolor is strongly interacting for a large range of energies. As with any strongly interacting theory, its description is very complicated. Since we know such theories only since a couple of years, we are really at the beginning of understanding them, even the very basic mechanisms of them. But this is what we need to do, if we ever want to make a real quantitative comparison to experiment. And that interests me. I want to understand how such theories work at a very fundamental level. They are so strange compared to the rest of the standard model, and to many other proposal beyond the standard model, that they are a very fascinating topic. And that is, why I am studying them.

Above and beyond

Before I can introduce my last research topic, I have first to go above and beyond the standard model. Given that I am calling this blog a tourist guide to the standard model, this is a bit like trespassing. But that is how my research went over the last years. So let me keep the name, but nonetheless venture beyond.

With keeping the name, I am using a very important concept in scientific naming: For historic reasons. For historic reasons, this blog was named, but then reality overtook it. This is something very often happening in physics. In the beginning, we encounter a phenomena. To not always have to describe it, we give it a name, based on what we have encountered so far. Very often, when we really understand what is going on, this name would no longer be appropriate. But at this time, the name stuck, and thus we stick with it. You should keep this in mind, when you think that the name of something seems to have nothing to do with the thing. Then the name is just there for historic reasons. And that is something one will also encounter beyond the standard model.

So let us go beyond the standard model. As I told you, the standard model is just that: A model. It has its limits. We know today, mostly for reasons of mathematical consistency and for astronomical observations that the standard model cannot be the end. We know that with what we have we cannot explain what happens at very high energies. We also cannot explain with the standard model why the outer rims of the galaxies rotate faster than they should. We do not know why the universe is expanding faster and faster. We do not know why the particles have precisely the masses they have. We cannot tell, why nature is such that the sun can shine: Given the standard model, we can explain how the sun shines. But we cannot explain why the standard model is such that this is possible. And there are many other things.

However, irritatingly, all our experiments here on earth have been in accordance with the standard model.

This is very unsatisfactory, to say the least. As a consequence, almost since the birth of the standard model in its present form people have started to consider extensions of it. This is commonly known as beyond-the-standard-model models, or BSM for short. Unfortunately, the observations listed above are not pointing all in the same direction. Actually, most just point somewhere, for the amount of knowledge we have of them. Thus, we are, right now, very much in the dark when it comes to figure out how we should extend the standard model.

This lead to very many proposals. Even listing all conceptual proposals would easily fill a couple of months worth of blog entries. But they can be broadly distinguished by their approach. Some have a top-down approach. They try to envisage the underlying theory, which will solve all (or many) of the known problems in one strike. You may have heard of (super)string theory. This is one example of this approach. The other is bottom-up. Here, one just tries to resolve a single problem. The ones I am working on belong to the latter category.

Now, what is the state of affairs? Top-down approaches are often rather complicated theories, and it is often very complicated to calculate anything at all. Thus, progress on this side is naturally slow. The bottom-up approaches are often more tractable. It is often not too complicate to design a theory, which solves the problem one was setting out to solve. However, in doing so one usually gets for a completely different thing a result which disagrees with the known experiments. Thus, one is forced to modify the model to sate this problem. But then the next springs up, and one finds oneself adding bits and pieces to the model, until it becomes rather baroque.

You may say now: Well, if things are either too complicated or too much mingling, maybe you are on the wrong track. And I would not really disagree with you. Of course, nothing prevents nature from being really complicated or baroque. Just because both versions do not look aesthetically pleasing to us does not mean it cannot be. But this way of thinking has never been right in the history of physics. When something got complicated, and any amendment made it worse, then we were on the wrong track.

So, why do we not abandon everything we did, take the standard model as the basis, and start over from scratch? This has actually been done many times, and so far was not successful. On the other hand, going back to the complicated theories, one hope is that by making the theory more complex by making more and more things agree with experiment, we can hope that at some point a pattern emerges. This has occurred in the past, and is thus a real possibility.

Thus, today, all of these possibilities are followed. We try to imagine solution to the problems, test them against experiments, both old and new, and reiterate. A spectacular new observation at any experiment would greatly help. That is why any ever so slight deviation from the standard model expectation is greeted with great enthusiasm by the theorist. Even if we know that in most cases this will be a coincidental fluke, which will go away when we keep looking more carefully.

Where will this lead us to? We do not know yet. That is the really exciting part of particle physics: We try to push the boundaries of knowledge, and we can only speculate what we will find there.

The Higgs beyond the obvious

It is very likely that you have heard in the media of my next research topic: It is the Higgs particle. Well, actually it is not just the Higgs particle alone. In isolation, without its connection to the weak interactions and all the rest of the standard model, the Higgs is actually a very boring particle. In fact, the Higgs particle in isolation is almost every particle theorists first encounter with particle physics. Because it is so boring and simple. Just that it is then not called the Higgs particle, but usually phi, and the theory is called the phi-to-the-fourth theory. Much less fancy.

I guess from all the attention the Higgs has received you may be assuming that many people are working on it. That is true. So, what is particular about my research? What is the specific twist of this thing that I am interested in?

Most people nowadays are interested in either of two aspects of the Higgs: What are its properties? More precisely, what is its mass? And how does it play along with the rest of the bunch? Or: Where does it come from? Is there some theory where the standard model is just a special case of? And if yes, what role does the Higgs plays there?

Me, I am more interested in some more subtle questions. Actually, in three.

The first question concerns the validity of our theoretical description of Higgs physics. As you may remember, the standard model is only valid up to a certain amount of energy. We assume that there will be another theory including it and resolving all (or at least a fair amount of) our questions. Until we figure out this theory, we try to hide our ignorance. For a theory like QCD, this works very well. There we can hide our ignorance just in a few numbers, which we can determine unambiguously in an experiment. After that, we are fine, and we can make predictions. With the Higgs, this is different. And the difference is here in the word 'unambiguous'.

The theory with only Higgs particles I mentioned before is actually a sad story. It turns out that it has the same problems as the standard model, but we cannot hide them unambiguously. And thus our predictions for it are flawed. We can only prevent this by switching off all the interactions. But then the theory is boring, because nothing happens. That is what we call a trivial theory.

The question I am interested in is, what happens when we put the Higgs in the standard model. Does it remain ambiguous? Or do the interaction with the other particles cure this problem in some fancy way? Right now, the judge is still out. If it cannot be cured, the search for the new theory becomes even more important. Because then the standard model would be much more flawed. Deciding what is the case is one of the questions I am looking into.

To even ponder the other two questions, I assume that the combination of the Higgs and the weak interactions do not have such a problem. Or that the resolution of the problem is not altering the answer to the two questions substantially. This may seem a bit like cheating or evading the problem. But we quite often come across problems not immediately solvable. These maybe so hard that we will take a long time to solve them. To get not totally stuck, we do often assume such solutions do exist, and carry on. Of course, we do not forget these questions, but work on them further, to have eventually an answer. This has the risk that some of what we may do then becomes invalid once we solved the problem. In fact, this has happened often. But as often it has also resolved the original problem, or gave us fundamental new insights. That is one thing we have to do in science: Always explore all the possibilities. Since we do not know what lies ahead, this is the only way to eventually find the right answer.

But after this detour, back to the two questions.

One is again rather fundamental. The theory with the Higgs is very peculiar. If you would switch off the Higgs effect, you would end up with a theory like QCD. Especially, the weak interactions would confine the Higgs particles, just like the strong interaction confines quarks. In fact, both phenomena could even be linked in a very abstract fashion. Merely two sides of the same coin. This is something which has been noticed already back in the 1970s. We do not yet understand what this is really about. One of the reasons was that back then confinement was not well understood. We understood much more about confinement since then, especially in the last ten years. Armed with this knowledge, I reinvestigate this connection. And try to clarify what is going on.

The last question concerns bound states. That is right! We have not yet discovered the Higgs alone, but I am already try to understand how two Higgs particles could come together and form something like a Higgs meson. That is a rather new problem I came across recently. There are some fascinating consequences of it. Some people speculate that we can observe such objects at the LHC. I am currently trying to understand, whether we have a realistic chance of seeing them. And if yes, how they are build up.

What the strong interactions, temperature, and density have to do with each other

After the preparation with the last entry, I can now move forward to my next research topic.

Let me just collect what we had so far about the strong interactions, QCD. QCD is the theory that describes the interaction between quarks and gluons. It tells you how these make up the hadrons, like the proton and the neutron. It also describes how these combine to the atomic nuclei. The quarks and gluons cannot be seen alone: The strong force confines them. At the same time, the strong force makes the quarks condense, and thereby creates the illusion of mass. Well, this is what one can call a complicated theory.

Now imagine for a while what happens, if you heat up matter. Really make it hot, much hotter than in the interior of stars. Heat is something like energy. You can imagine that the hotter something is, the faster the movement of particles. The faster they go, he hotter they are. But the higher the energy, the smaller the things are which get involved. Hence, if things get very hot, the quarks and gluons are the one to really feel it.

When this happens, two things occur. One is that the condensate of quarks melts. As a consequence, the quarks can move much more freely. The other is that you can convert some of the energy from the heat to particles. I will come back to the mechanism behind this later. For now, it is enough that this is possible. It is nothing special to the heat case. Anyway, you can convert a small fraction of the heat to particles. If things get hot enough, a small fraction is actually quite a large number. And if things are really hot, you have created so many particles that they do not fit anymore in the space you have available. Then they start to overlap. At that point, even if you have confinement, you can no longer tell the hadrons apart. The things just overlap and you can start to swap quarks and gluons from one to another. You see, when you put enough heat into matter, things start to look very different.

Why is this interesting? I said it must be much hotter than in a star, and actually much hotter even than in a supernova. It does not appear that there is anything in nature being so hot. However, we can create tiny amounts of matter in experiments which is so hot. And also, very far in the past, such super-hot matter existed. Right after the big bang, the whole universe was very densely packed, and the temperature was so high. This was only a fraction of a second after the big bang. So, is this relevant? Well, yes. If we want to look back even further, we have to understand what happened in the transition of the strong force at that time. Since we cannot create universes to study it, we need to extrapolate back in time. And for this, we need to understand each step of going back in time. And hence, we need to understand how QCD works at very high temperatures.

This is not the only case where we need to understand QCD in extreme conditions. The other case is the interior of neutron stars. In these stars, matter is packed incredibly densely. It is very cold there, at least when comparing to the early universe. But it is so dense that hadrons again begin to overlap. Thus, you would expect that you can again exchange quarks and gluons freely between hadrons. But because it is cold, you will keep your quark condensate. In fact, there are quite a lot of speculation, whether you can create also condensates of quarks with different properties than the one usually known. To really understand how neutron stars work, and eventually also how black holes form, we have to understand how QCD works when things become dense.

When you take both cases together, and permit for good measure to also include all possible combinations of dense and hot, you end up with the QCD phase diagram. This phase diagram answers the question: When I have this temperature and that density, how does QCD behave? Determining this phase diagram has been a topic of research ever since these questions were first posed in the 1970s. Very important for this task have been numerical simulations of matter at high temperatures. With them, we have become confident that we start to understand what happens at very small densities and rather high temperature. We understood from this that the universe has undergone a non-violent transition when QCD changed. We can therefore now extrapolate further back in the history of the universe. But we are not yet finished for this case. Right now, we leaned what happens when we are at fixed temperature and density. But these two quantities changed, and we have not yet fully understood how this proceeds.

Things are a lot worse when we turn to the neutron stars. We have not been able to develop efficient programs to simulate the interior of a neutron star. We even suspect that it is not possible at all, for rather fundamental reasons concerning conventional computers. Progress has therefore been mainly made in two ways. One was to rely heavily on (very) simplified models, and more recently using functional methods. Another one was to study artificial theories, which are similar to QCD, but for which efficient programs can be written. From the experience with them we try to indirectly infer what happens really in QCD.

I am involved in the determination of this QCD phase diagram with two angles. One is to develop the functional methods further, such that they become a powerful tool to address these questions. Another one is to learn something from the stand-in theories. Especially in the latter case we just made a breakthrough, on which I will comment in a later entry.

Why colors cannot be seen

Before I can continue to my next research topic, I have to introduce yet another fascinating feature of the strong interactions, QCD. As you may remember, QCD had three charges: Red, green, and blue. There was also anti-matter with the anti-charges anti-red, anti-green, and anti-blue. To have total charge zero, one needed either a charge and an anti-charge, or one of each of the charges (or anti-charges). Total charge zero is then often also called white, just to keep with the analogy.

Now comes the fascinating fact: However hard we tried, and we did try very hard, we were never able to find something with either of the charges alone. Whenever we saw something with, say, red charge, we could be certain that enough other charges have been very close by to make the total charge within a very tiny part of space-time again zero. And tiny means here much less than the size of a proton! That is totally different from electromagnetism. There we had the electric charge and the anti-charge. We can separate such electric charges easily. Every time you move with plastic shoes over carpet and then touch something made from metal, you do so, albeit rather. unpleasantly. In fact, the screen where you read this blog entry is based on this: Without being able to separate the electric charges to very large distances (at least from the perspective of an electron), it would not work. Even the fact that you can see at all is based on this separation. In the nerves of your eyes and your brain, electric charges are separated and joined together when you see something

So why is QCD different? That is indeed a very, very good question. In fact, it is not even simple to find a mathematical way to state what is going on. The general phenomena: "We can not pull the charges apart" is commonly referred to as confinement. The charges are what is confined, and somehow the strong force confines it. That is already a bit strange. The force confines the things on which it itself acts. Not necessarily a simple thing to ponder. It seems to be somehow self-related in a bizarre way.

But it is really not that strange. Think of an atom. It is held together by the electromagnetic force between the electron(s) and the atomic nucleus. The total atom is electrically neutral. But because electromagnetism is not so strong, we can pull the components apart from each other, if we just invest enough force. The reason we can do this is that the force pulling electrons and the nucleus together becomes weaker the farther apart we move the electrons and the nucleus.

The strong force is now, precisely, stronger. In fact, the force between things with color charge is not diminishing with distance. It stays constant. Thus, we cannot really tear anything apart. As soon, as we stop forcing it, it gets back together immediately. So no way we get it apart. That seems to be odd. Indeed, when you look at the equations describing QCD, you will see no trace of this behavior. Only when you solve them, this becomes different. The solutions describing the actual dynamics of QCD show this. But solving them is very hard. Thus, back when QCD was developed, people could not solve them. Hence, this behavior in experiments seemed to appear out of the blue, and made it hard for many people to believe in QCD. And actually, even today we can only solve the equations of QCD approximately. But good enough that we can convince ourselves that this type of behavior is indeed an integral part of QCD. Confinement is there.

As so very often, I am right now dropping quite a number of subtleties. One of them is that I did not say anything about gluons. For them, very similar things apply as for quarks. The only thing is that they have different colors than the quarks, and you have to juggle around with now eight different ones rather than three. A bit more messy. But that is essentially all.

More severe is that white things actually can break apart. That may seem to look like a contradiction to what I said above. However, it is not. The subtlety with this is that they break into more white things, and not into their colorful constituents. For example, you can try to break a proton apart. A proton consists out of three quarks, one of each color. If you try to break it apart, at some point you will end up with a proton and a meson. A meson is something which consist of one quark with a color and an anti-quark with the corresponding anti-color. You may be irritated where I have the mass from. That is something different, and has nothing to do with confinement, and I will come back to this later. For now, just accept that this can happen. Anyway, you just do not get that proton apart, you just get more particles.

You see that this confinement has quite striking consequences. It is still something we have neither fully understood, nor do we have yet fully appreciated what it means. It is and remains something to understand for us. We have made great progress in this, but we are still lacking some basic notions of what is actually really going on. In fact, sometimes there are heated debates about what is actually a part of confinement, and what is something else, because we do not yet have a full grasp of what it means.

Irrespective of that, we have this phenomenon. We observed it experimentally. And we are able to get from the equations describing QCD its presence, even if we do not yet fully understand what it means and how it works. And it is this confinement what plays an important role in the next research topic of mine.

Groundwork

The first topic of my research is both very fundamental and very abstract. It has something to do with coordinate systems coordinate systems, but not the ones to describe where event takes place in space and time. A while ago, I have discussed local symmetries. Saying something has a local symmetry means that I can change things at different places in different ways. Back then, I used a grid of billiard balls. I could rotate each of the balls differently, but because the balls are perfect spheres (we over-painted the numbers), this did not change the way the grid looked.

Now, lets assume that for some obscure purpose you would like to keep track of what is going on with the balls. That you want to know the position on each ball in some way. You can do this by introducing coordinates on every ball. Think of painting a point on every ball (actually, you will need two, which are not lying on opposite points on the balls). These points destroy the local symmetry. You can now keep track of all rotations by looking at the points. In exchange for loosing the symmetry you now always know when the balls are rotated. Especially, you can now always talk about a ball pointing in some direction, because you can use the points on the ball to identify a direction.

If you now go to a particle physics theory, you also have such local symmetries. A consequence of these local symmetries was that the amount of numbers you needed to describe a photon was very small. But is was very inconvenient to use this minimal amount. At least that was what I said. If you go to something more complicated than the photons, like the gluons, it becomes even more inconvenient to use the smallest possible number.

Ok, wait a minute. What does these two things have to do with coordinate systems, you my say. And the answer is, actually, quite a lot. The procedure of using more numbers than necessary requires that you use a coordinate system to measure these additional numbers. That is something which we call introducing a gauge or fixing a gauge in particle physics. We have to know the size and the direction of the additional elements we bring into the discussion. That sounds awfully technical, and indeed it is. But at the same time it is very often very convenient. I fear, here I have to ask you to take this statement on faith. Even the simplest case where one sees how powerful this is fills a page with formulas. In fact, most of the page would be filled with the calculations which try to not use the additional coordinates. And only a few lines at the bottom would use the additional coordinates. In calculations with the full standard model, the reduction becomes incredibly large. Thus, we do it often. Only for very few calculations, in particular those done by a computer in a simulation, we can afford to do without.

This was so far only the prelude to my actual research topic. As I have warned, it is very abstract. The topic has now to do with how such coordinate systems can be chosen. So far, it seemed to be quite straightforward to do so. For the balls, we just make points on them, one ball at a time. That is, what we call a local coordinate system. This means, the choice of the coordinates can be done independently at every place. In this case, by working on each ball separately.

But the theories used for particle physics are strange. Imagine a hideous, malevolent demon. Whenever you make a point on one ball, he sneaks behind your back and changes the points you have already made, depending on where you make right now a point. How would you fight such a creature? You would take many, many pencils, and then construct a sophisticated device such that you can make the points on every ball at the same time. With this you trick the demon. What you have done was choosing your coordinate systems all at once everywhere. Since you have constructed the machine, you have no longer the possibility to make an individual choice on each ball just when you pick it up. The choice is fixed for all balls by the machine. That is what we call a global choice of coordinate systems.

Though we do not have demons running around the particles, at least, as far as we know, we have a very similar problem in particle physics. The mathematical structure of the theories in the standard model requires us to make global choices when introducing our additional coordinates. Seems to be not so complicated at first sight, but it is. Constructing appropriate machines is very complicated. Especially it turns out to be very complicated to construct a machine which works wells with every method. But when you want to combine methods, you must use the same coordinates. And thus build a machine which works with more than one method. And this is baffling complicated. In fact, so complicated that we have been struggling with it ever since the problems has been recognized. And that was in the late 1970s.

Why does this not stop us completely in our tracks? The reason is that in perturbation theory the global choice becomes again local. That means, whenever you can do perturbation theory, you can make a much simpler local choice. That is something we can do perfectly. And since perturbation theory is so helpful in many cases, this problem is not a show stopper. The reason is that perturbation theory only admits small changes. And small changes means that we never go far away from a single point we made on the ball. Thus, the demon can never sneak up on us.

Furthermore, when we do simulations, we know how to evade the problem. However, the price we pay is that things become obscure. Everything is just a black box, and in the end numbers come out. But for many problems, this is quite satisfactory, so this is also often fine.

But then there remain some problems where we just cannot evade the demon. We have to fight it. and that is where I enter the scene. One of my research topics is to understand how to make the same global choice with different methods. That is something I have been working on since 2008, and it proved and proves to be a formidable challenge. So far, the current state is that I have made some proposals for machines working with more than one method. Now, I have to understand whether these proposals make sense, and if yes, if they are simple enough to be used. It is and remains a persistent question, and one which will accompany me probably for the rest of my scientific life. But sometimes you just have to bite it, and do things like that. Its pure technical, almost mathematical. There is no physics in it - coordinate systems are choices of humans and not of nature. It is the type of ground work you have to do occasionally in science. It is part of building the tools, which you use then later for doing exciting physics, learning how nature works.

What am I doing?

I have swamped you with a lot of methods, being the important tools I use for research. The natural question is: What do I do with them?

Well, this changes over time. This is quite normal. If you do research, you do not know what lies ahead. As you make progress, things you know change. This may be due to you own research, or by results from other people's research. Some topics may become less interesting as they appeared some time ago. Others become more interesting, and more relevant. This is a slow, but continuous evolution. It is the normal way things go: The most important characteristic of research is that you never know in advance where it will take you. Only when you get there, you will finally know.

Thus, what I will describe now and in the next few entries, is not set in stone. It is, what I am currently working on. In fact, when I started this blog, I was only investigating the standard model. And within it, I was mostly concentrating on the strong interactions, QCD. That was some time ago. By now, the topics I am looking at have became somewhat broader. I have also started to look at topics which are more mathematical, and also at some which are beyond the standard model. Anyway, I will not change the title of the blog: What today is beyond the standard model may be the standard model of tomorrow, you never know. I will also, from time to time, give you an update, when a new topic becomes interesting.

Let me now concentrate on the topics of my current research. I will list them in an order which is not indicating importance. It is rather my, somewhat subjective, view from what is well-founded to what is more speculative.

The first topic is the most mathematical one. As you remember, local symmetries are very important in the standard model. As any new standard model will contain the standard model as a special case, so will local symmetries continue to play an important role. These symmetries have been recognized to be important in particle physics already before the 1940s. At first sight, one may expect that everything is known about them, what there is to know. However, the combination of local symmetry and quantization is very complicated. It becomes especially problematic when you look at an interaction like QCD, which is very strong and complex. For many purposes, we have this problems under control. We can calculate what happens in QCD when we can use perturbation theory. We can also deal with the local symmetry when we calculate something like the proton mass. But in both cases, this more operational then a full solution. Beyond this, things become very complicated, as I will discuss in the next entry.

The second topic is QCD. QCD is a very rich topic, and just saying QCD is not very specific. Let me be more specific. One of nowadays great challenges in QCD is to understand what happens if we have many, many quarks and gluons. In this case, they may be a very dense, and possibly hot, soup. Describing this soup is dubbed 'determining the phase diagram of QCD'. This phase diagram is of great importance. Such a soup is expected to have existed in the early universe. It likely exist today within the core of neutron stars. Thus, in this topic elementary particle physics meets with astrophysics. I will discuss this in detail later.

The third topic is about the Higgs. Or rather about the interplay between the weak force and the Higgs. I am not really interested in what they actually precisely measure at the LHC. At least, not yet. Right now, I am trying to understand some rather basic questions about Higgs physics. These are closely related to the fundamental questions I am working on about local symmetries. However, just recently, this may actually lead to some predictions about what the may measure. You will see more about this in an upcoming entry.

The last topic is rather speculative. I try to understand what may be there beyond the standard model. Right now, we have few hints what may be the next big thing after the standard model. Thus, you are rather free in your speculation. Again, I am more interested in how the things, whatever they are, may function. Nonetheless, I have to be somewhat specific at least about the rough shape of the topic I am considering. Right now, I am most interested in what is called technicolor. I will explain this scenario (and other ideas for beyond-the-standard-model physics) in an upcoming entry. For now, it suffices to say that it has both local symmetry and strong interactions. This makes it rather messy, and therefore interesting. Let me give you the details later, in another entry.

As you see, I am interested in a number of rather different questions. But there is a common theme to all of them. What I want to understand is the mix of local symmetry and strong interactions. What does this mix imply for the physics? What is going on with these two concepts in the standard model, and beyond? How can we mathematically deal with these theories? Do we really understand what they mean? And what possibilities does this combination hold, once we get a full and firm grip on it? These are the questions I want to know the answers to. These are the things which may shake up what we know. Or, they may be just fixing some minor detail in the end. What of both will be the case, I cannot say yet. I will only know it, when I understood it. And to follow these questions is very interesting, very fascinating, and, yes, very exciting. I am very curious about where my research leads me. Let me take you along for the ride.

Methods. United, they are strong.

In the last few postings, I have collected a number of methods: perturbation theory, simulations, and the abstract equations of motion. I have furthermore gave you a bit of a taste of one of our most important strategies: divide and conquer. Or, more bluntly, if the original problem is too complicated, first try a simpler one, which resembles it. This lead us to a stack of models, which bit by bit always included more details of the world.

This list is by no means complete. Over the years, decades, and centuries, physicists have developed many methods. I could probably fill a blog all by its own just by giving a brief introduction to each of them. I will not do this here. Since the man purpose of this blog is to write about my own research, I will just contend myself with this list of methods. These are, right now, those which I use myself.

You may now ask, why do I use more than one method? What is the advantage in this? To answer this, lets have a look at my work-flow. Well, actually this is similar to what many people in theoretical particle physics do, but with some variations on the choice of methods and topics.

The ultimate goal of my work is to understand the physics encoded in the standard model of particle physics, and to get a glimpse of what else may be out there. Not an easy task at all. One, which many people work on, many hundreds, probably even thousands nowadays. And not something to be done in an afternoon, not at all. We know the standard model, more or less, since about forty years at the time of this writing. We think essentially as long as it exists about what else there might be in particle physics.

Thus, the first thing I do is to make the things more manageable. I do this, by making a simpler model of particles. I will give some examples of these simpler models in the next few entries. For now, lets say, I just keep a few of the particles, and one or two of their interactions, not more. This looks much more like something I can deal with. Ok, so now I have to treat this chunk of particles happily playing around with each other.

To get a first idea of what I am facing, I usually start off with perturbation theory, if no one else did this before me. This gives me an idea of what is going on, when the interactions are weak. This hides much of the interesting stuff, but it gives me a starting point. Also, very many insights of perturbation theory can be gained with a sheet of paper an a pencil (and many erasers), and probably a good table of mathematical formulas. Thus, I can be reasonably sure that what I do is right. Thus, whatever I will do next, it has to reduce to what I just did now when the interactions become weak.

Now I turn to the things, which really interest me. What happens, when the interactions are not weak? When they are strong? To get an idea of this, the next step is to perform some simulations of the theory. This will give me a rough idea, of what is going on. How the theory behaves. What kind of interesting phenomena will occur. Armed with this knowledge, I have already gained quite a lot of understanding of the model. I usually know then what are the typical way the particles arrange themselves. How their interaction changes, when looking at it from different directions. What the fate of the symmetries is. And lot more of details.

With this, I stand at a crossroad. I can either go on, and deepen my understanding by improving my simulations. Or, I can make use of the equations of motion to understand the internal workings a bit better. What usually decides for the latter is then that many questions about how a theory works can be best answered when going to extremes. Going to very long or very short distances when poking the particles. Looking a very light or very heavy particles. Simulations cannot do this with an affordable amount of computing time. So I formulate my equations. Then I have to make approximations, as they are usually too complicated. For this, I use the knowledge gained from the simulations. And then I solve the equations, thereby learning more about how the model works.

When I am done to my satisfaction, then I can either enlarge the model somewhat, by adding some more particles or interactions, or go a different model. Hopefully, at the end I arrive at the standard model.

What sounds so very nice and straightforward up to here is not. The process I describe is an ideal. Even if it should work out like this, I am talking about the several years of work. But usually it does not. I run across all kind of difficulties. It could turn out that my approximations for the equations of motion have been too bold, and I can get no sensible solution. Then I have to do more simulations, to improve the approximations. Or the calculations with the equations of motion tell me that I was looking at the wrong thing in my simulations. That the thing I was looking at was deceiving me, and gave me a wrong idea about what is going on. Or it can turn out that the model cannot be simulated efficiently enough, and I would have to wait a couple of decades to get a result. Then, I have to learn more about my model. Possibly, I even have to change it, and start from a different model. This often requires quite a detour to get back to the original model. This may even take many years of work. And then, it may happen that the different method give different results, and I have to figure out, what is going on, and what to improve.

You see, working on a problem means for me to go over the problem many times, comparing the different results. Eventually, it is the fact that the different methods have to agree in the end what guides my progress. Thus, a combination of different methods, each with their specific strengths and weaknesses, is what permits me to make progress. In the end, reliability is what counts. And with this nothing cuts it like a set of methods all pointing to the same answer.

Modelling reality

Ever wondered why it is called the standard model of particle physics? And what a physicist has in mind, when she talks about models?

Models are the basic ingredient of what a theoretical physicist is doing. The problem is that we do not know the answer, we do not know the fundamental theory of everything. Thus, the best we can do is take what we know, and make a guess. The result of such a guess is a model. Such a model should describe what we see. Thus, the standard model of particle physics is the one model what we know about particle physics right now, as incomplete as it may be. It is called the standard one, because it is our best effort to describe nature so far, to model nature in terms of mathematics. There are also other standard models. We have one for how a sun functions, the standard model of the sun, or how the universe evolved, the standard model of cosmology.

Now, when I say, it is our best guess this implies that it is not necessarily right. Well, actually it is, in a sense. It was made the standard model, because it describes (or, if you read this in a couple of years, perhaps has described) our experiments as good as we can wish for. That means, we have found no substantial evidence against this model within the domain accessible in the experiment. This sentence has two important warning signs attached.

The one is about the domain. We do not know what is the final theory. But what we do know is the models. And any decent model will tell us, what it can describe, and what not. This also applies to the standard model. It tells us: 'Sorry guys, I cannot tell what is happening at very large energies, and on the matter of gravitation, well I stay away from this entirely.' This means that this standard model will only remain the standard model until we have figured out what is going on elsewhere. At higher energies, or what is up with gravitation. However, this does not mean that the standard model will be completely useless once we managed that. As with many standard models in the past, it likely will just become part of the large picture, and remain a well-trusted companion, at least in some area of physics. Happened to Newton's law, which was superseded by special relativity, and later by general relativity. Happened to Maxwell's theory of electromagnetism, which was superseded by Quantumelectrodynamics, and later by the standard model. Of course, there is once more no guarantee, and it may happen that we have to replace the standard model entirely, once we see the bigger picture. But this seems right now unlikely.

The other thing was about the experiment. Models are created to describe experiments (or observations, when we think about the universe). Their justification rests on describing experiments. We can have some experimental result, and cook up a model to explain it. Then we do a prediction, and make an experiment to test it. Either it works, and we go on. Or it does not, and then we discard the model. While people developed the standard model, this was a long, painful process during which many models have been developed, proposed, checked, and finally discarded. Only one winner remained, the model which we now call the standard model.

Ok, nice and cozy, and that how science works. But I was talking about methods the last couple of times, so what has this to do with it? Well, this should just prepare you for an entirely different type of models, to avoid confusion. Hopefully. Now the standard model is the model of particle physics. But, honestly, it is a monster. Just writing it down during a lecture requires something like fifteen minutes, two blackboards, and two months of preparation to explain all the symbols, abbreviations and notions involved to write it in such a brief version. I know, I have done it. If you want to solve it, things go often from bad to worse. That is where models come in once more.

Think of the following: You want to describe how electric current flows inside a block of, say, Aluminum. In principle, this is explained by the standard model. The nuclei of Aluminum come from the strong force, and the electrons from the electromagnetic one, and both are decorated with some weak interaction effects. If you really wanted to try describing this phenomena using the standard model, you would be very brave indeed. No physicist has yet tried to undertake such an endeavor. The reason is that the description using the standard model is very, very complicated, and actually most of it turns out to be completely irrelevant for the electric current in Aluminum. To manage complexity, therefore, physicists investigating aluminum do not use the standard model of particle physics in its full glory, but reduce it very, very much, and end up with a much simpler theory. This models Aluminum, but has forgotten essentially everything about particle physics. This is then a model of Aluminum. And it works nice and well for Aluminum. Applying it to, say, copper, will not work, as Aluminum nuclei have been put into it as elementary entities, to avoid the strong interactions. You would need a different model for copper then, or at least different parameters.

So, we threw away almost all of the power of the standard model. For what? Actually, for a price worth the loss: The final model of Aluminum is sufficiently simple to solve it. Most of our understanding of materials, technology, chemistry, biology (all described by the standard model of particle physics, in principle) rests on such simplified models. With only the standard model, we would not be able to accomplish anything useful for these topics, even knowing so much about particles. In fact, historically, the development was even the other way around. We started with simple models, describing few things, and generalized bit by bit.

Ok, you may say. You see the worth of simplified models for practical applications. But, you may ask, you surely do not simplify in particle physics? Well, unfortunately, we have to, yes. Even when only describing particles, the standard model is so complicated that we are not really able to solve it. So we very often make models only describing part of it. Most what we know about the strong interactions has been learned by throwing away most of the weak interactions, to have a simpler model. When talking about nuclear physics, we even reduce further. Also, when we talk about physics beyond the standard model, we often first create very simple-minded models, and in fact neglect the standard model part. Only, if we start to do experiments, we start to incorporate some parts of the standard model.

Again, we do this for the sake of manageability. Only by first solving simpler models, we understand how to deal with the big picture. In particle physics the careful selection of simplified models was what drove our insight since decades. And it will continue to do so. This strategy is called divide and conquer. It is a central concept in physics, but also in many other areas where you have to solve complicated problems.

Of course, there is always a risk. The risk is that we simplify the model too much. That we loose something important on the way. We try to avoid that, but it has happened, and will happen again. Therefore, one has to be careful with such simplifications, and double-check. Often, it turns out that a model makes very reliable predictions for some quantities, but fails utterly for others. Often, our intuition and experience tells us ahead what is a sensible question for a given model. But sometimes, we are wrong. Then experiment is one of the things which puts us back on track. Or that we are actually able to calculate something in the full standard model, and find a discrepancy compared to the simple model.

In the past, such simplified models were created by very general intuition, and including some of the symmetries of the original theory. Over time, we have also learned how to construct, more or less systematically, models. This systematic approach is referred to as effective field theory. This name comes about as it creates a (field) theory which is an effective (thus manageable) version of a more complicated field theory in a certain special case, e.g. low energies.

Thus, you see that models are in fact a versatile part of our tool kit. But they are only to some extent a method - we have still to specify how we perform calculations in them. And that will lead us then to the important concept of combining methods next time.