A more complicated photon

The photon - the particle which makes up light - is probably one of the best known elementary particles. Nonetheless, everything can be made more involved. Thus, we studied a more complicated version of it in our most recent paper.

"Why in the world should we do this?" is a valid question at this point. That proceeded in multiple stages. I have written quite some time ago that for a particle physicist it is baffling that chemistry works. Chemistry works, among other things, because the electric charge of nuclei and electrons are perfectly balanced. Well, as perfect as we can measure, anyhow. In the standard model of particle physics there is no reason why this should be the case. However, the standard model is mathematical consistent only if this is the case. In fact, only if the balance is really perfect. Mathematical consistency is not a sufficient argument why a theory needs to be correct. Experiment is. So people have investigated this baffling fact since decades. In this process, the idea came up that there is a reason for this. And that reason would be that the standard model is only a facet of an underlying theory. This underlying theory enforces the equality of the electric charges by combining the weak, strong, and electromagnetic forces into one force. Such theories are called grand-unified theories, or short GUTs.

Such GUTs use a single gauge theory to combine all these forces. This is only possible with a certain kind, which is fundamentally different from the one we use for electromagnetism alone. It is more similar to the ones of the strong and weak force. We have investigated this type of theories for a long time. And one central insight is that in such theories none of the elementary particles can be observed individually. Only so-called bound states, which are made from two or more elementary particles, can be. That is very different from the ordinary photon of electromagnetism, which is, essentially, elementary.

The central question was therefore whether any such bound state could have the properties of the photon which we know from experiment. Otherwise a GUT would (very likely) not be a possible candidate to explain the balance of electric charges in chemistry. The photon has three important features. It does not carry itself electric charge. It is massless. And it has one unit of so-called spin.

Thus we needed to build a bound state in a GUT with these properties. The spin and absence of charge is actually quite simple, and you get this almost for free in any GUT. It is really the fact that it should not have mass which makes it so complicated. It is even more complicated to verify that it has no mass.

We had some ideas from our previous work, using pen-and-paper calculations, how this could work. There had also been some numerical simulations looking into similar questions in the early 1980ies, though they were, given resources back then, very exploratory. So we set up our own, modern-day numerical simulations. However, it is not yet possible to simulate a full, realistic GUT. For this all computing power on earth would not suffice, if we want to be done in a lifetime. So we used the simplest possible theory which had all the correct features relevant to a true GUT. This is an often employed trick in physics. One reduces a problem to the absolutely essential features, throwing away the rest, which has no or little impact on the particular question at hand. And by this getting a manageable problem.

So we did. And due to some ingenious ideas of my collaborators, especially my PhD student Vincenzo Afferrante, we were able to perform the simulations. There was a lot of frustrating work for the first few months, actually. But we persevered. And we were rewarded. In the end, we got our massless photon in exactly the way we hoped! We thus demonstrated that such a mechanism is possible. We got a massless photon made up out of elementary particles! A huge success for the whole setup. In addition, the things which make up the photon are (partly) very massive. That a bound state can be lighter than its constituents is an amazing consequence of special relativity. For us, this is an added bonus. Because you cannot see the fact that a particle is made up of other particles if you have not enough energy available to create the constituents. Again, this comes from the theory of relativity. In this scenario one of the constituents is indeed so heavy that we would not be able to produce it in experiments yet. Hence, with our current experiments, we would not yet detect that the photon is made up from other particles. And this is indeed what we observe. So everything is consistent. Very reassuring. Unfortunately, it is so heavy that also none of the currently planned experiments would be able to do so. Hence, we will not be able to test this idea directly experimentally. This will need to resort to indirect evidence.

Of course, I gloss over a lot of details and technicalities here, which took most of our time. Describing them would fill multiple entries.

Now, the only thing we need to do is to figure out whether anything we neglected could interfere. None of it will at a qualitative level. But, of course, we have very good experiments. And thus to make the whole idea a suitable GUT to describe nature, we also need to get it quantitatively correct. But this will be a huge step. Therefore we broke it down in small steps. We will do them one by one. Our next step is now to get the electron right. Let's see if this also works out.

What is a proton made of?

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

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

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

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

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

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

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

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

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

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

Making connections

Over time, it has happened that some solution in one area of physics could also be used in a quite different area. Or, at least, inspired the solution. Unfortunately, this does not always work. Even quite often it happened that when reaching the finer points it turns out that something promising did in the end not work. Thus, it pays off to be always careful with such a transfer, and never believe a hype. Still, in some cases it worked, and even lead to brilliant triumphs. And so it is always worthwhile to try.

Such an attempt is precisely the content of my latest paper. In it, I try to transfer ideas from my research on electroweak physics and the Brout-Englert-Higgs effect to quantum gravity. Quantum gravity is first and foremost still an unsolved issue. We know that mathematical consistency demands that there is some unification of quantum physics and gravity. We expect that this will be by having a quantum theory of gravity. Though we are yet lacking any experimental evidence for this assumption. Still, I also make the assumption for now that quantum gravity exists.

Based on this assumption, I take a candidate for such a quantum gravity theory and pose the question what are its observable consequences. This is a question which has driven me since a long time in particle physics. I think that by now I have an understanding of how it works. But last year, I was challenged whether these ideas can still be right if there is gravity in the game. And this new paper is essentially my first step towards an answerhttps://arxiv.org/abs/1908.02140. Much of this answer is still rough, and especially mathematically will require much work. But at least it provides a first consistent picture. And, as advertised above, it draws from a different field.

The starting point is that the simplest version of quantum gravity currently considered is actually not that different from other theories in particle physics. It is a so-called gauge theory. As such, many of its fundamental objects, like the structure of space and time, are not really observable. Just like most of the elementary particles of the standard model, which is also a gauge theory, are not. Thus, we cannot see them directly in an experiment. In the standard model case, it was possible to construct observable particles by combining the elementary ones. In a sense, the particles we observe are bound states of the elementary particles. However, in electroweak physics one of the bound elementary particles totally dominates the rest, and so the whole object looks very similar to the elementary one, but not quite.

This works, because the Brout-Englert-Higgs effect makes it possible. The reason is that there is a dominating kind of not observable structure, the so-called Higgs condensate, which creates this effect. This is something coincidental. If the parameters of the standard model would be different, it would not work. But, luckily, our standard model has just the right parameter values.

Now, when looking at gravity around us, there is a very similar feature. While we have the powerful theory of general relativity, which describes how matter warps space, we rarely see this. Most of our universe behaves much simpler, because there is so little matter in it. And because the parameters of gravity are such that this warping is very, very small. Thus, we have again a dominating structure: A vacuum which is almost not warped.

Using this analogy and the properties of gauge theories, I figured out the following: We can use something like the Brout-Englert-Higgs effect in quantum gravity. And all observable particles must still be some kind of bound states. But they may now also include gravitons, the elementary particles of quantum gravity. But just like in the standard model, these bound states are dominated by just one of its components. And if there is a standard model component it is this one. Hence, the particles we see at LHC will essentially look like there is no gravity. And this is very consistent with experiment. Detecting the deviations will be so hard in comparison to those which come from the standard model, we can pretty much forget about it for earthbound experiments. At least for the next couple of decades.

However, there are now also some combinations of gravitons without standard model particles involved. Such objects have been long speculated about, and are called geons, or gravity balls. But in contrast to the standard model case, they are not stable classically. But they may be stabilized due to quantum effects. The bound state structure strongly suggests that there is at least one stable one. Still, this is pure speculation at the moment. But if they are, these objects could have dramatic consequences. E.g., they could be part of the dark matter we are searching for. Or, they could make up black holes very much like neutrons make a neutron star. I have no idea, whether any of these speculations could be true. But if there is only a tiny amount of truth in it, this could be spectacular.

Thus, some master students and I will set out to have a look at these ideas. To this end, we will need to some hard calculations. And, eventually, the results should be tested against observation. These will be coming form the universe, and from astronomy. Especially from the astronomy of black holes, where recently there have been many interesting and exciting developments, like observing two black holes merge, or the first direct image of a black hole (obviously just black inside a kind of halo). These are exciting times, and I am looking forward to see whether any of these ideas work out. Stay tuned!

The size of the W

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

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

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

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

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

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

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

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

Looking for something when no one knows how much is there

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

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

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

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

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

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

How to test an idea

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

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

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

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

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

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

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

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

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

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