In the standard model a relatively baroque structure of many wheels interacts in a quite intricate pattern...

 Towards a refined beyond standard model building technology ?

... we used the Fröhlich-Morchio-Strocchi mechanism to investigate the differences of the physical spectrum and the spectrum of the elementary fields for a number of prototype theories, but also for the bosonic sector of a more realistic GUT. In this course, we derived predictions for the physical spectra, which in almost all cases differed from the expectation from the elementary fields. These differences are almost always qualitative, and can therefore not be expected to be removed by radiative corrections. In particular, based on these arguments the usual construction of SU(5) as an extension of the standard model would be ruled out already on structural grounds as a possible candidate for a grand-unified theory, even if it would not be ruled out for quantitative reasons [... 35]. Besides the actual particle spectrum, our investigations demonstrate that, for instance, the computation of a possible proton decay has to indispensably be rethought. In addition a variety of other aspects with cosmological implications might change. The predictions for the gauge-invariant physical states can be checked using non-perturbative methods. Of course, once the mechanism has been established, analytic predictions for other theories can be made with similar ease, and confidence, as in ordinary perturbation theory. In those cases where such checks have been made, they support the results here [9, 10, 15]. This gives confidence in the methods and predictions. A next logical step, besides continuing checks on the lattice, would be to investigate current candidates for beyond Standard Model physics, including also the fermionic sector along the lines of [6, 7, 12], to see whether conflicts arise for some of them as well. This does not need to be the case, as the explicit example of two-Higgs-doublet model shows [14], but may happen as have been seen here. It would also be good to further develop the tools designed here to allow a quicker assessment of which theories may harbor conflicts, and which not. 

On the observable spectrum of theories with a Brout-Englert-Higgs effect

Axel Maas, René Sondenheimer, Pascal Törek

(Submitted on 21 Sep 2017)

Not loosing sight of the fundamental theory for its effective one

Appreciating fully the fact that the weak interactions are a non-Abelian gauge theory leads to a very intricate structure of the standard model as a whole. In particular, it requires to reevaluate our view of what is the structure of the observed particles on a very fundamental level, with the possible exception of right-handed neutrinos. The standard-model then tells a story of intricate cancellations, leading on an effective level to a much simpler theory. In particular, it leads to the usual phenomenology established using perturbation theory, and is thus in beautiful agreement with existing experimental results. However, this is only possible due to the particular structure of the standard model. 

While the agreement with current experiments is reassuring, it can only be the first step. Such an intricate interplay on a fundamental level needs to be established in detail theoretically, and eventually experimentally. Lattice calculations and simulations of restricted sectors of the standard model provided so far good confirmation. But as any non-perturbative methods they are yet far from exact. Also, they are limited until now to bosonic sectors. A full non-perturbative analysis of the full standard model, or at least including part of the Yukawa sector, at the level of gauge-invariant and observable quantities remains desirable. But given the inherent technical challenges this will remain a future perspective for some time to come. 

A quite different challenge is the fact that such an intricate structure needs to induce eventually deviations from a phenomenology based entirely on perturbation theory. The parameters of the standard model, and the very good agreement to experiment so far, strongly suggest that these will be small, or even tiny, deviations. Thus, true precision measurements will be needed to uncover them. For theoretical calculations it remains a challenge to quantify them, and make a prediction what kind of experimental effort would be needed to detect them. Provided that fermionic corrections are not on a very large quantitative, or even qualitative, level this appears easier and more within reach than a full inclusion of fermions. Methods to calculate the size of bound-states [356, 357] or (quasi) distribution functions [318–320] are available or are being developed, and could be applied in a straight-forward way to the observable scalars and vectors. This should provide a first estimate of the size of the effects. 

In total, while quantitatively (yet) a tiny effect, gauge invariance invites us to reevaluate the qualitative way of how we think about the elementary particles we know and we hunt for. 

For the standard model, these insights only change the way how we perceive particles. It does not necessarily change how we treat them. And the identification of the elementary particles with the observed particles, while not literally correct, will remain certainly a valid, and pretty good, approximation. But this is not the case for beyond-the-standard model scenarios. 

As has been seen in section 4.7, and has also been supported by first lattice simulations [176, 179], there could be distinct, qualitative differences between the observable and elementary spectrum of such theories. This problem still needs full classification [148]. But it seems likely that a correct prediction of the physical spectra should be rather based on the gauge-invariant perturbation theory of section 4.4 using the FMS mechanism than conventional perturbation theory. The implications moreover also pertain to theories without elementary Higgs, as discussed in section 6.5. Model building needs to take this into account. Fortunately, the technical changes appear to be comparatively small [148], and much what has been done can be reused. 

In the end, what remains is that particle physics is on a fundamental level more complex than expected. Recognizing the observed particles for what they are - relatively involved composite objects - may actually be an inspiring principle. Especially, as sections 4.6.1- 4.6.3 showed, in the standard model a relatively baroque structure of many wheels interact[s] in a quite intricate pattern. But then, whenever it was understood in particle physics that something has a composite, intricate structure, this gave us a new handle to understand the systematics of what lies below.

Brout-Englert-Higgs physics: From foundations to phenomenology

Axel Maas

(Submitted on 13 Dec 2017)