What happens if gluons meet?

We have published a new paper on how gluons interact, which is described by the strong force. In fact, how exactly one gluon interacts by being absorbed or emitted by another one. There can be interactions with more of them. These are much more complicated to determine, and so we concentrate on this simplest one.

You may ask yourself, how we cannot yet know this, and still do stuff like calculate the mass of a hadron? And not even bother to do more than this simplest process? Because for the proton we need to now what gluons do, right? Well, not exactly. When we want to calculate the properties of a proton we need to know only how they do so in a particular way of averaging. We do not need to resolve the full details. But if we really want to understand how they interact in detail, this is not enough. And this is crucial, if we want to be able to build up not only the proton, but any particle or thing we want to measure. Being able to do a particular averaging good enough is not sufficient to do all of them as well.

In fact, this way of gluons interacting is the simplest way they can interact. Because of this, we know already quite a bit of it, if the gluons are very energetic. But we know less about how they interact, if they have little energy or travel over very long distances. And there a surprise arose some years back. It was raised in a much older work by myself and other people. It indicated that the gluons undergo a drastic change when they start to traverse distances of the order of the size of a proton or even further (inside bigger hadrons, because of confinement). It appears that at distances of the order of a proton diameter they stop interacting. But they become much stronger interacting again at even longer distances. This is, of course, a very interesting insight what happens, in a sense, at the boundary of a proton.

We used simulations for this back then. But we very limited at this time, because of the available computing power. This was aggravated, because at this time, I was working as a postdoc in Brazil. Which, as a disadvantaged country, does have bright minds, but much less resources than I have nowadays in Austria. At any rate, the result nonetheless got people excited, and there were a lot of follow-up works since then. Still, while most results supported the indications, it is not yet possible to give a fully satisfactory answer.

In our latest work, we picked up the idea of looking at the behavior in a world with one direction less. This saves a lot of computing time. And we did not yet had a final answer there either. This we provided now. There is a clear answer, confirming the behavior described above: First getting weaker, until the interaction vanishes at roughly a (flat) proton across, and then becoming quickly much stronger.

Still, doing the same in our world was too expensive. But we did a trick. Having the results from the fewer dimensions, we knew what to anticipate. So we used this information to test our world for consistency. And this checked out surprisingly well. In fact, we could even predict how much more computing time would be needed for a final confirmation also for our world. Could be done in the next few years. So hang around just a little longer for the final answer.

And, perhaps, we can then also do more complicated interactions. But this is a really tedious business. So you need patience and a long-term perspective.

Tackling ambiguities

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Building a dead star

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

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

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

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

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

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

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

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

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

Redundant ghosts

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

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

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

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

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

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

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

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

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

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

Searching for structure

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

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

Unfortunately, theories are more complicated than wall climbing.

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

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

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

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

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

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

Digging into a particle

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

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

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

Why did I do this? There are two reasons.

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

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

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

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

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

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

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

Playing indirectly

One of my research areas are neutron stars. To understand them requires to understand how the strong interactions behave when the matter is enormously densely packed. A new PhD student of mine has now started to work on this topic, and I would like to describe a little bit what we will be looking at.

I have already written in the past that this type of situation is very hard to deal with, because we cannot just do simulations. This is unfortunate, since simulations have been very successful in uncovering what happened in the early universe. In that case, the system is hot rather than dense. Though the reason for the problem is 'just' technical, chances are not too bright to resolve it in the near future.

Hence, I had already quite some time ago decided that a possibility is to play indirectly. The basic idea is that there are other methods, which would work. The price we have to pay is that we need to make approximations in these methods. But we would like to check these approximations, ideally against simulations. But we cannot, because there are no. So how to break the circle?

To escape this problem, we can again use a detour. We did this once, because we hoped that we will learn more about the qualitative features. That we can get some insight into this type of physics. Now, we have a much more quantitative approach. We use theories, which are very similar to the strong interactions (also called QCD), but are not QCD, but which can be simulated. And these we will use to break the circle.

Why is it possible to perform simulations for this type of theories? Well, the main reason is the difference between particles and anti-particles. In QCD, a quark and an anti-quark are fundamentally very different objects. Hence, a large density can mean two things. A large density could be having many more quarks than anti-quarks, but still have plenty of both. Or it could be just to have many of one type. For a neutron-star both situations are relevant. And thus, there may be actually many more particles present then we would think, just many of them anti-particles. This is at the heart of the problem, that there is so much more than just the superficial number of particles.

This problem is evaded by using a theory instead where there are no anti-quarks. To be more precise, a theory in which anti-quarks are the same as quarks. There exists a number of such theories. However, such a change is very drastic. It thus may happen that the so changed theory is so radically different from QCD that any comparison becomes meaningless. Thus, it is necessary to ensure that the theory is close enough to the original.

Two candidates for such theories have been identified so far. One is the so-called G2QCD, of which I talked about previously. Another one is very close to QCD, but instead of three color charges is has just two different ones. Both cases have their own merits. The first is closer to QCD. In this theory there are protons and neutrons. The latter does not have these, but it is very cheap to simulate. Both theories are hence quite different, but actually share both also many other traits with QCD.

It therefore stands to reason that whatever approximation describes both well will also work for QCD. Thus, we will now use the simulations of both theories to test the approximations made in the other methods. Especially, we will look at the properties of the quarks and gluons. We will then use the insights gained to improve the approximations. Until we describe both theories well enough. Then we will translate the approximations back to QCD. And if everything works out, we will have then an acceptable description of a piece of neutron star matter.

The nature of particles

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

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

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

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

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

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

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

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

More on big blobs and little blobs

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

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

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

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

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

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

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

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

Big blobs

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

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

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

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

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

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

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

Precision may matter

The latest paper I have produced is an example of an often overlooked part of scientific research: It is not enough to get a qualitative picture. Sometimes the quantitative details modify or even alter the picture. Or, put more bluntly, sometimes precision matters.

When we encounter a new problem, we usually first try to get a rough idea of what is going on. It starts with a first rough calculation. Such an approach is often not very precise. Still, this creates a first qualitative picture of what is going on. This may be rough around the edges, and often does not perfectly fit the bill. But it usually gets the basic features right. Performing such a first estimate is often not a too serious challenge.

But once this rough picture is there, the real work begins. Almost fitting is not quite the same as fitting. This is the time where we need to get quantitative. This implies that we need to use more precise, probably different, but almost certainly more tedious methods. These calculations are usually not as simple, and a lot of work gets involved. Furthermore, we usually cannot solve the problem perfectly in the first round of improvement. We get things a bit rounder at the edges, and the picture normally starts to fit better. Still not everywhere, but better. Often, a second, and sometimes many more, rounds are necessary.

Fine, you may say. If things are improving, why bother doing even better? Is not almost fitting as good as fitting? But this is not quite the same. The best known examples we find in history. At the beginning of the 20th century, the picture of physics seem to fit the real world almost perfectly. There were just some small corners, where it seems to still require a bit of polishing. These small problems actually led to one of the greatest change in our understanding of the world, giving birth to both quantum physics and the theory of relativity. Actually, today we are again in a similar situation. Most of what we know, especially the standard model, fits the bill very nicely. But we still have some rough patches. This time, we have learned our lesson, and keep digging into these rough patches. Our secret hope is, of course, that a similar disruption will occur, and that our view of the world will be fundamentally changed. Whether this will be the case, or we just have to slightly augment things, we do not yet know. But it will be surely a great experience to figure it out.

Returning to my own research, it is precisely this situation which I am looking at. However, rather than looking at the whole world, I have been just looking at a very simplified theory. One that involves only the gluons. This is a much simpler theory than the standard model. Still, it is so complicated that we were not (yet) able to solve it completely. We made great progress, though, and it seems that we almost got it right. Still, also here, some rough edges remain. In this paper, I am looking precisely at these edges, and just check how rough they really are. I am not even trying to round them further. I am not the first to do it, and many other people have looked at them in one or the other way. However, doing it more than once, and especially from slightly different angles, is important. It is part of a system of check and balances, to avoid any error. Tt is also in science true: Nobody is perfect. And though there are many calculations, which are correct, even the greatest mind may fail sometime. And therefore it is very important to cross check any result.

In this particular case, everything is correct. But, by looking more precisely, I found some slight deviations. These were previously not found, as precision is almost always also a question of the amount of resources invested. In this case, the resources are mostly computing time, and I have just poured a lot of it into it. These slight deviations do not require a completely new view of the whole theory. But it changes some slight aspects. This may sound like not much. But if they should be confirmed, they provide closure in the following sense: Previously, some conclusions remained dangling, and seemed to be not at ease with each other. There were some ways out, but the previously known results rather suggested a more fundamental problem. My new contribution shifts these old results slightly, and makes them more precise. The new interpretation fits now much better with the suspected ways out rather than with a fundamental problem. Hence, looking closer has in this case improved our understanding.

Hence, theoretical physics has often more in common with a detective's work. We start with a suspicion. But then tedious work on the details is required to uncover more and more of the whole picture, until either the original suspicion is confirmed, or it shifts to a different suspect, which may have even been completely overlooked in the beginning. However, at least normally nobody tries to kill us if we come too close to the truth.

The trouble with new toys

You may remember that one of the projects I am working on is understanding so-called neutron stars. These are the remnants of heavy stars, which die in a gigantic explosion called a supernova. One of the main problems with understanding these neutron stars is that it is far too expensive to simulate them in detail using computers. We try in our research to circumvent this problem by using not the original theory describing neutron stars, but a slightly modified version. For this modified theory, we actually can do simulations. So is now everything shiny? No, unfortunately not. And about these problems we have published a new paper recently. Today, I will outline what we did in this paper.

So what is actually the problem? The problem is that some of our theories are not linear. What does now linear mean? Well, a theory is called linear, if we apply an external input to it, and the effect is has on theory is of (roughly) the same size as whatever we applied. In contrast, for anything which is non-linear, the response can be much larger, or much smaller, than whatever we applied. Unfortunately, the strong interactions, which is responsible for neutron stars, is non-linear. Hence, even though we modified it just a little bit, we can potentially have very strong changes. Therefore, we have to make sure that whatever we did was not having unplanned and strong effects. This task led to the mentioned paper.

The main question we have to answer is: If the theory is so sensitive to modifications, were the effects of our modifications still harmless enough? Can we still learn something?

The answer is, as always, it depends. To judge the similarities, we have looked at the hadrons, the particles build up from quarks and gluons. In the strong force, the masses of these hadrons follow a very special pattern. Especially, there are some unusually light ones, the a few intermediate ones, and then, already quite heavy, the first one which plays an important role in everyday life: The proton, the nucleus of a hydrogen atom. We found that in our modified theory this pattern repeats itself. This is already a good sign. However, we also found some indications that not all is well. Some of the lighter particles have a number of different details than in nature, especially the lightest ones.

Since we are mostly interested in neutron stars, we also did the calculations at large densities. There, we saw that indeed the slightly different properties of the lightest particles play a role. At quite small densities, we observe a behavior, which we are reasonably sure will not occur in nature. So is then all lost? It does not seem so. While at these densities the behavior is different, this will probably not play an important role for the densities we are really interested in. And indeed, at higher densities the theory behaved similar to the expectations: It seems to behave in a way which we would guess based on the observations of real neutron stars, and general arguments. This is quite encouraging. Still, we also encountered two more challenges. One is that to make a definite statement, we will need much more precision: Some of what we see is sensitive to details. We need to understand this better. And this will require much more calculations.

The other one is that we are still not quite sure if there is not some special kind of different particle playing a too important role. This special kind of particle is similar to the proton, but not present in nature. It is only a feature of the modified theory. This is a so-called hybrid. In contrast to the proton, which consist out of three quarks and no gluons, it is made out of one quark and three gluons. There are certain technical reasons, why this particle could be a problem when trying to understand neutron stars. So far, it escaped detection in our calculations. We have to find it, to make really sure what is going on. This will be a challenge.

Fortunately, still, even in the worst case scenario of both problems, what we did will not be irrelevant. On the one hand, it was a genuinely new theory we looked at, and we learned already very much about how theories in general work. And the second is - what we created will also serve as a benchmark for other methods. If someone creates a new method to get to the neutron star's core, she or he can test it again our simulations, to build confidence in it.

(Un-)Dead stars and particles

I have already written about some aspects of my research on neutron stars. But what is the problem with them? And what do I want to understand?

First: What are they? If you have a sufficiently massive star, it will not die in a fizzle, like our sun, but it will end violently. It will explode in a supernova. In this process, a lot of its mass gets compressed at its core. If this core is not too heavy, a remainder, a corpse of the star, will remain: A neutron star. If it is too heavy, the remainder will, however, collapse further into a black hole. But this is not the interesting case for me.

Such a neutron star is actually far from dead. It continues its life after its death. But it no longer emits light and warmth, but usually x-rays, neutrinos, and occasionally so-called gravitational waves.

Second: What do I want to understand about them? Neutron stars are enigmatic objects. Their size is about ten kilometers, not more than a larger city. At the same time they have about one to two times the mass of our sun. Thus, they are incredible dense. In fact, they are so dense that there is no place for atoms, but they consist out of the atomic nuclei. That is the case in the outer layers of the neutron star, perhaps the first kilometer or so. Going further inward, the density increases. Then everything gets so tight, that it is no longer possible to separate the nuclei, and they start to overlap. In addition, whatever electrons there still were have already after the first few meters been soaked up to change almost all of the protons into neutrons. In a certain sense, it is just one big atomic nucleus.

And even further in? Well, nobody knows. However, there are many speculations. Do we have there a different kind of matter, so-called strange matter? Such matter is obtained when one starts to replace the up and down quarks in the neutrons with strange quarks. Or does also the neutrons dissolve, and we just have a bunch of quarks? And if yes, how would such quark matter behave? Would it be a fluid, a superconducting metal, or possibly even a crystal?

And that is, where my research starts. What I want to understand is, which form this matter takes. And I am not alone with this. I have just organized a workshop, which partly focused on this subject, and we have worked hard on getting a better understanding, of what goes on in there. That becomes even more interesting as more and more results come in from astronomical observations on neutron stars. They provide us with a lot of indirect evidence on how the matter inside the neutron star's core must behave. But if we understand the strong force correctly, we should be able to calculate this.

The central problem involved in these calculations is the density. The standard approach to particle physics (and to physics in general) is to attempt to simplify the problem, and study its parts in isolation. That is quite well working for many cases, like the Higgs. However, the properties of the neutron star is determined not by the individual neutrons, but in how they interact with each other when there are many of them. Thus, by breaking the system apart you destroy what you want to study. Thus, you have to study the neutrons - or more appropriately the quarks - all together. This enlarges the complexity severely, and it is what stops us in our tracks. Particularly, because it is hard to find efficient ways to calculate anything for a real neutron star.

One way around this is to attempt to indirectly understand it, by studying a simpler system. The alternative is to simplify the system itself. This can be done by making things a bit more fuzzy. This fuzziness is achieved by not tracking each and every quark and what it precisely does. Instead, groups of quarks are tracked, and their activities is averaged. This can be a very simple step. For example, one can treat a neutron instead of being made from three quarks as made from one quark and the rest. And then approximate the rest by a single particle with simple properties. Such an approximation already gives a rough estimate of how things work. Of course, if one wants to get the last bit of precision out of the theory, then one has to return to the original three quarks.

But the problem is complicated, and thus one follows this strategy: Creating less and simpler objects first, an then refine them again. This simpler objects are often called 'effective degrees of freedom', because they effectively mimic many complicated objects. And then we solve the simpler theory describing them, the so-called effective theory. Afterwards, we go back. We refine the effective theory and the simple particles again, introducing the problems bit by bit. And solving them on the way. And that is, where we are currently. Still far away from understanding a neutron stars as a set of elementary particles, as quarks and gluons, but closing in, step by step.

Taking a detour helps

Almost all relevant physical systems are pretty complicated. One I am working on is how the interior of so-called neutron stars look like. Neutron stars is what is left of stars somewhat heavier than our sun, but not too heavy, after they became a supernova. In a neutron star the atoms collapse due to the strong gravitation. Only the atomic nuclei remain, and are packed very densely. Neutron stars have roughly one to two times the mass of our sun, but have a radius of only about ten kilometers, barely larger than a small city. These star remnants are very interesting for astronomy and astrophysics. But I am more interested what happens in their most inner core.

Deep inside the neutron star, everything is even more packed. In fact, even the atomic nuclei are no longer separated, but are mashed into a big mess. Because their are so densely packed, even the nucleons are overlapping. Thus, the substructure of them, the quarks may become the most important players.

But this nobody knows yet for sure. It has been a challenge to understand such matter since more than thirty years. It is a joint effort of theoreticians, like me, people smashing atoms on each other in accelerators, so-called heavy-ion experiments, and people observing actual neutron stars with telescopes of many kinds.

In general, if quarks come into play, very often simulations have been very helpful. But it turns out that we are not (yet) clever enough to simulate a neutron star's interior. The algorithms, which we have developed to deal with single nuclei are just too inefficient to deal with so many nuclei. For technical reasons, this is called the sign problem, denoting the particular technical problem involved. This obstruction is also known since decades, without us being able so far to remove it.

An alternative have been other methods and models, but we would like to have a combination, to be more sure of our results.

One possibility has been to circumvent the problem. We have looked at theories which are similar to the strong nuclear force, but slightly modified. The modification were such that numerical simulations were possible. We made this detour for two reasons. We hoped that we could learn something in general. And we wanted to use these results to provide us with tests for our models and other methods. In a way we cheated: We evaded the problem by doing a simpler problem. And hoped that we would learn enough by this to solve the original problem or get a new insight.

However, so far our detours had serious drawbacks. The replacement theories were only able to solve some problems, but never all at the same time. Some had the problem that the mass creation by the strong force did not work in the right way. This would yield wrong answers for size and mass of a neutron stars. Or the nucleons were not repellent enough, so that all neutron stars would collapse further to so-called quark stars, much smaller than neutron stars and made from quarks.

And here comes my own research into play. Just recently we found another theory, which we call G2-QCD for very technical reasons. Irrespective of the name, it has neither of these problems. However, it is still not QCD. E. g., it has besides the nucleons further exotic objects flying around. But it is anyway the theory closest to the original one so far investigated. And we can actually simulate it. That is something we just done very recently. The results are very encouraging, though we are yet far from a final answer for neutron stars. Nonetheless, we have now an even stronger test for all the models and results from other methods available. This should provide even more constraints on our understanding of neutron stars, though still an enormous amount of work has to be done. But this is research: Mostly progress by small steps. And we thus continue on with this theory.

And this is just one example in my research where it is worthwhile to take a detour, and this is true for physics in general: Often the study of a simpler problem helps to reveal the solution of the original one. Even if we did not (again yet) succeeded, we made progress.

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.

Mass from the strong force

Quite some time ago, I have discussed the Higgs effect, and how it gives the matter particles in the standard model their mass. However, if we look around us, it turns out that most mass we see is actually not due to the Higgs effect.

If we knock on a table, or look at us, then most of this is made up out of atoms. As you might remember, atoms are made up out of nuclei and electrons. The electrons actually get their mass from the Higgs, so that is alright. But they make up less than 0.05% of the mass of the atoms. Thus, one can forget about them for this purpose. Then there are the nuclei. They are made up out of protons and neutrons. These in turn consist out of quarks. But the quarks are rather light, and make up not more than one percent of the mass of the protons and neutrons, and thus of the nuclei. So where does all the remaining mass comes from?

Well, this comes this time from the strong nuclear force, QCD, which has been presented here and here. I have already indicated there that it is a pretty strong force. It is this strength which, indirectly, creates all the mass we are yet missing.

How it works is actually quite complicated in detail, but when being a bit fuzzy about the details, it can be illustrated quite nicely. Looking through such fuzzy glasses, it actually looks like a repetition of the Higgs effect. Remember, the Higgs effect worked by letting the Higgs particles condense. The interaction with this condensate slows particle down, and therefore they behave as having a mass.

Now, how does this proceed in the case of the strong force? The first observation is that the strong force is attractive between quarks, i.e. quarks are attracted to each other. As a consequence, the quarks can form all these nice things like protons. However the force is also attractive between the quarks and their so-called anti-particles. What an anti-particle is I will discuss next time. This time, it is just sufficient to say that it behaves like a quark, but has opposite charges and the same mass.

The strong force now pulls also the quarks and the antiquarks together. The combination of two such particles is then neutral, as all the charges are opposite. It behaves therefore very similar to a Higgs particle. In very much the same way, but this time because of gluons rather than due to the Higgs interacting with itself, this creates also a condensate. That is just like for the Higgs particles. Thus, the universe is filled with quarks and anti-quarks, bound together, and condensed by the strong force. The strong interaction of quarks with this condensate, and the corresponding slowing down, is what provides the remainder mass for the protons and neutrons, and thus for the nuclei. Again, because all the charges cancel, we do not see this condensate, as photons due not directly interact with it.

Putting in numbers, the contribution of the strong force to the mass of the nuclei is much larger than the one due to the Higgs effect. However, the calculation of this was rather challenging. Hence, most of the mass stored in the atoms in the universe is due to the strong force.

It is also said that the strong force provides all the luminous mass in the universe. Here, luminous means actually not only all stars which emit light by themselves, but also everything which reflects light, like planets, interstellar gas clouds, and asteroids. Actually, the latter also emit a kind of light by themselves, but our eyes are not sensitive for the wave-lengths they emit, and therefore we do not see it. The distinction is necessary, because we have indirect evidence that there is also more than just this type of mass in the universe. In fact, we expect that there is about five times more non-luminous, or dark, matter in the universe, than luminous matter. What the origin of mass is in this case is not known.

There is another thing you may wonder about. The quarks have all very different masses due to the Higgs effect. Is the contribution due to the strong interaction also very different for the different quarks? The answer to this is actually no, the contribution from the strong force is about the same for all quarks. Thus, it makes up about 99% of the mass of the light quarks, but less than half a percent for the heaviest one. Thus, while the Higgs makes a difference between the different quark (and lepton) species, the strong force does not. Why this is the case is also yet unknown, and one of the bigger mysteries. Since the different quarks and leptons are also called different flavors of quarks and leptons, it is said that the strong force is flavor-blind, it makes no difference between different flavors. On the other hand, the Higgs makes a different between different flavors.

Finally, it should be noted that the generation of mass can be traced back to a symmetry, though I will not detail this now. This is the so-called chiral symmetry. A thing is called chiral, if it makes a difference between left and right. The associated symmetry in the standard model is a local symmetry. The Higgs effect breaks, loosely spoken, this symmetry to a global one. The strong force then breaks this global symmetry. It is possible, but mathematically involved, to show that these breakings correspond to the existence of mass. Hence, both the Higgs effect and the strong force produce mass. But the above explanations are somewhat more illuminating, I think, though mathematically both views are essentially equivalent. Thus, it is said that mass is created by chiral symmetry breaking, a notion I will right now not dwell on anymore.

The forces of nature III - The strong force (Part II)

As has been told, the hadrons are made up out of quarks. But there is something peculiar about this. When one looks at the constituents of, say, an atom - the nuclei and the electrons - then one can observe all of these also as individual particles. However, this is not applying to quarks. It has not been possible to isolate a quark experimentally. The only thing which can be seen are the hadrons.

When analyzing the structure of the hadrons in search for the reason, it turns out that one can assign to a quark a new charge, the so-called color charge. The name is just fancy and the charge has nothing to do with color. This color charge comes in six types. There are three 'positive' charges, called red, green, and blue (some people occasionally exchange one of the names for yellow), thus carrying the metaphor further. They are like the positive electric charge. Then there are three 'negative' charges, anti-red, anti-green, and anti-blue. They are like negative electric charge. As for electric charges, a negative and a positive color (say anti-green and green) neutralize each other. The amazing difference compared to electric charges is that also three different colors of either type neutralize each other. For example, a red, a green, and a blue quark together are neutral with respect to the color charge.

It is then found that all hadrons are always color-neutral. The mesons are made from one quark with color and one with anti-color, and the baryons are made from three quarks, each carrying one of the colors. In fact, the ones we observe around us are all made of three quarks carrying color. Those which carry anti-color are actually anti-matter, which will be discussed later.

Now, this gives an idea why quarks and hadrons are different. But it does not explain why quarks are not observed. This is now du to the force acting between two color charges. In contrast to all other forces, this force is not getting weaker with distance, but stronger instead. And it gets so quickly stronger that it is not possible to tear a hadron apart into quarks. At least that is what it looks like at the surface. The truth is somewhat more subtle, and not fully understood, and part of my research. Therefore, I will come back to this question many times in the future.

Irrespective of this, the force between colored objects is mediated by gluons. In contrast to photons gluons carry themselves color charges, though they are of a different type than those of quarks, and there are eight different ones, not usually given a name. As a consequence, the enormous strength of the force also binds gluons, and they cannot be observed as freely roaming particles either. In fact, at least in principle it is possible that gluons alone form bound states, much like hadrons. These are called glueballs, but are up to now only hypothetical constructs which have not been observed in nature, though some observations may hint at them. It is an ongoing experimental endeavor to find them.

The justified question is, if the force is so strong, why do we know about quarks and gluons? And why can it still bind the nucleons to nuclei if the nucleons are color-neutral?

Well, the force is not strong at all distances. Indeed, it grows quickly with distance, but on the other hand it diminishes as quickly with shorter and shorter distances. To the best of our knowledge it even ceases completely if one would be able to reduce the distance to zero. That is called asymptotic freedom. Therefore, if one can send a probe close to a quark, then one can identify its existence. For this purpose it helps very much that a quark is not only carrying color charge, but also electric charge. Therefore, it can be registered more easily by hitting it with a photon or an electron. That is somewhat indirect, but that is one of the main sources of experimental information on the quarks. The gluons are even more complicated, since they only carry color charge. Therefore, our evidence for them is rather indirect.

This is then also how nucleons feel each other by the strong force. When they come close to each other, they start to see each others quarks, which then can interact by the strong force. This is a comparatively weak effect, since it is, vastly simplifying spoken, just a bit of penetration what makes them feel each other. Nonetheless, this remainder of the force is so much stronger than the electric force that it makes the nuclei about 100000-times smaller than an atom. This should give an idea of how very strong this force must be that even such a small glimpse of it has such far-reaching consequences.

It is this strong force to which I will return repeatedly, as it is and has been for a long time my major focus of research. The one reason is that our understanding of this force is not very good is because many approaches just have to give up when faced with such an enormous strong force. Only at very short distances we have reliable control over it. Hence, the theory of this force, which is called quantum chromo dynamics (for the Greek word chromos for color and short QCD), is very hard to tackle. There is a simpler version of it, which only deals with the gluons and neglects the quarks (and is therefore not a picture of nature). It is called Yang-Mills theory. Because it contains already many essential features of QCD, it often, and also for me, serves as a prototype theory for the strong force.

The forces of nature III - The strong force (Part I)

If one descends to smaller and smaller scales one always finds that larger things are built up from smaller things. When one looks to a human, she is made from cells. Each cell in turn is built from molecules, small and large.

Each of the molecules, in turn, is made from atoms. These atoms are rather small, like 0,0000000001 m each. There is one thing special about atoms which has not been encountered with molecules and cells: There is only a finite number of different ones of them observed in nature, while there appears to be an infinite number of different molecules and cells. In fact, atoms can be organized into a scheme (ok, this also applies to molecules and to some extent to cells also), the so-called periodic system of atoms. There are roughly hundred of them to be found in nature, and we managed to make a number artificially of them more over the years. Each of the atoms differs by its chemical properties.

So, it seems that atoms can be built, much like molecules. However, it is found that there are some atoms which behave in every respect essentially identical when it comes to chemistry, but they have a different mass. Both facts (and a number of others) suggest that atoms themselves are built from other things.

Indeed, it is found that atoms are made from two parts: Electrons and nuclei. The electrons orbit the nuclei, which is about 100000-times smaller than the atom (the electrons are even smaller as discussed previously). The are different electromagnetically charge with respect to each other, and there is always exactly one nuclei, but so many electrons that the total electric charge is zero.

It turns out that the charge is responsible for the chemistry, so the charge of the nuclei characterizes the atom. The mass of the atom is made essentially by the nuclei, which is about 2000 times heavier than the electrons. So different mass nuclei provide the same chemistry. Why?

Well, it turns out that the nuclei are composed from different objects themselves, the nucleons. That is the reason why new ones can be made and there are chemical identical ones with different mass. They nucleons come in two types, the neutrons and the protons. The latter carry the charge, making the atom chemical active, while the neutrons are chemically essentially inactive. On the other hand both have essentially the same mass. So chemically different atoms differ by their number of protons, but chemically identical atoms having different mass differ by the number of neutrons.

It is found that the nucleons have about the same size as the nuclei, so they are fairly densely packed inside the nuclei (in a typical atom there are a few dozen nucleons). What is keeping them together? It cannot be gravity alone, as it is too weak. If gravity alone should provide this, the nuclei would be much, much larger. It cannot be electromagnetism, as the neutron has no charge. So it must be something different. Indeed it is a new force, the so-called strong (or, since it was discovered in the context of the nuclei, nuclear) force. This force is binding the nucleons together to form the nuclei, and thus shapes the very word we live in as much as electromagnetism does.

The force between the nucleons is created by the exchange of mesons. These particles are usually not observable in nature as they decay too fast by the weak interactions to be discussed later. They can be observed in cosmic rays. The most important meson is the pion, having about an eighth of the mass of the nucleon. So, in contrast to the photon, it is massive. It also can carry charge, there is a positive one, a negative one, and a neutral one. There are also other mesons, the kaon, the rho, and the omega, playing a role in the nuclear force. In fact, as it was started to investigate this, more and more of these mesons have been found. Also, it was found that the nucleons are not the only of their kind. There are other, quite similar objects, like the delta or the cascade particles. Those nucleon-like particles have been termed the baryons, in distinction to the mesons. Both together are called hadrons, to distinguish them from the leptons. These mesons and baryons can again be put into a kind of periodic table, and we can produce new ones of them.

As the experience with atoms already told, this indicates that the baryons and mesons are themselves composites from other particles. Indeed, they are built up from quarks. Mesons consists of two, baryons of three quarks. If there are objects which are constructed from four or five or more quarks is not really known. If so, they are rathe short-lived and decay into mesons and baryons. During the recent years, conflicting experimental results made this a hot debate, and the judge is still out. These objects would be called tetraquarks (four quarks) or pentaquarks (five quarks).

In any case, there has to be a force holding the quarks together inside mesons and baryons. It turns out that this is again the strong force, but in another disguise.