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.