This 54 page review article from a September 2017 conference in Portugal is a good starting point for people wanting an overall summary of the state of BSM physics theories that is reasonably up to date, and may suggest questions about specific theories that deserve more attention in this forum that don't have any regular contributors advocating for them.
The table of contents is as follows:
Dmitry Kazakov "Beyond the Standard Model' 17" (June 30, 2018).We discuss the status of the SM - The principles - The Lagrangian - The problems - Open questions - The ways beyond. Then we consider possible physics beyond the SM - New symmetries (Gauge, SUSY, etc) - New particles (gauge, axion, superpartners) - New dimensions (extra, large, compact, etc) - New Paradigm (strings, branes, gravity). In conclusion, we formulate the first priority tasks for the future HEP program.
The table of contents is as follows:
It discusses this in general in part 2:1 Introduction: The Standard Model
2 Possible Physics Beyond the Standard Model
3 New Symmetries
3.2 Grand Unification
3.3 Extra symmetry factors
4 New Particles
4.1 Extended Higgs sector
4.2 Axions and axion-like particles
4.4 Dark Matter
5 New Dimensions
5.1 Compact Extra Dimensions
5.2 Large Extra Dimensions
6 New Paradigm
6.1 String Theory
6.2 M-theory and the Theory of Everything
7 Conclusion. The priority tasks of high energy physics
The final highlighted phrase should be anathema to any good scientist. It is classic hand waving without adequate justification for doing so.Let us look at the high energy physics panorama from the point of view of the energy scale (see Fig.5).
Besides the electroweak scale ∼ 102 GeV and the Planck scale ∼ 1019 GeV there is a scale of quantum 1019 String scale Planck scale 1018 Majorana scale GUT scale 1016 1012 Vacuum Stab 1011 EW scale 103 QCD 100 10-1 SUSY ? 102
Fig. 5: The high energy physics panorama from the point of view of the energy scale chromodynamics Λ ∼ 200 MeV, the whole spectra of quark, lepton, intermediate vector boson and the Higgs boson masses, all related to the electroweak scale. Presumably, there is also a string scale ∼ 1018 GeV, the Grand unification scale ∼ 1016 GeV, the Majorana mass scale ∼ 1012 GeV, the vacuum stability scale ∼ 1011 GeV and finally somewhere in the interval from 103 to 1019 GeV there is a supersymmetry scale.
So far there are no indications that all these scales and new physics related to them exist and high energy physics today stays in a kind of fog masking the horizon of knowledge. But sooner or later the fog will clear away and we will see the ways of future science. At the moment we live in the era of data when theory suggests various ways of development and only experiment can show the right road.
The way out beyond the Standard Model is performed along the following directions:
1. Extension of the symmetry group of the SM : supersymmetry, Grand Unified Theories, new U(1) factors, etc. This way one may solve the problem of the Landau pole, the problem of stability, the hierarchy problem, and also the Dark Matter problem.
2. Addition of new particles: extra generations of matter, extra gauge bosons, extra Higgs bosons, extra neutrinos, etc. This way one may solve the problem of stability and the Dark Matter problem.
3. Introduction of extra dimensions of space: compact or flat extra dimensions. This opportunity opens a whole new world of possibilities, one may solve the problem of stability and the hierarchy problem, get a new insight into gravity.
4. Transition to a new paradigm beyond the local QFT: string theory, brane world, etc.
The main hope here is the unification of gravity with other interactions and the construction of quantum gravity.
Note the paradox in modern high energy physics. If usually a new theory emerges as a reply to experimental data which are not explained in an old theory, in our case we try to construct a new theory and persistently look for experimental data which go beyond the Standard Model but cannot find them so far.
The existing small deviations from the SM at the level of a few sigma such as in the forward backward asymmetries in electron-positron scattering or in the anomalous magnetic moment of muon are possibly due to uncertainty of the experiment or data processing.
The neutrino oscillations indicating that neutrinos have a mass will probably require a slight modification of the SM: however, there might also be described inside it Dark Matter, almost the only indication of incompleteness of the SM, yet might be related to heavy Majorana neutrinos and require nothing else.
Nevertheless, there is a vast field of theoretical models of physics beyond the Standard Model. The question is which of these models is correct and adequate to Nature.
Note that the prevailing paradigm in most of the attempts to go beyond the SM is the idea of unification. It dates back to the unification of electricity and magnetism in Maxwell theory, unification of electromagnetic and weak forces in electroweak theory, merging of three forces in Grand unified theory, attempts to unify with gravity and creation of the theory of everything on the basis of a string theory. This scenario, though it did not find any experimental verification, still seems possible and has no reasonable alternative.