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Intriguing spectra of finite unified theories (FUT)

In November, I discussed FUTs (finite unified theories) which are \(\NNN=1\) supersymmetric grand-unification-inspired versions of MSSM with the additional constraint that the divergences already cancel at the level of the effective field theory. This finiteness boils down to the vanishing of the beta-functions, some anomalous dimensions, and some relationships between the gauge and Yukawa couplings.

This condition doesn't seem to be a "must" – the divergences may very well be taken care of by the high-energy phenomena (string theory ultimately takes care of all divergences so its approximations don't have to be finite by themselves) – but it is an aesthetically intriguing condition, anyway. Now, the same authors released a new paper

Finite Theories Before and After the Discovery of a Higgs Boson at the LHC (S. Heinemeyer, M. Mondragon, G. Zoupanos)
where they calculate some new predictions and intriguing details.

They focus on the third-generation fermions and their superpartners, the Higgs sector, and the gauginos. The nicest FUTs they consider boast names such as FUTA and FUTB – the latter seem particularly attractive. They also take some LHCb results into account. In these models, \(\tan\beta\) is typically rather large, \(\mu\) is almost necessarily negative.

The spectra seem very intriguing and consistent with everything we know. Unfortunately, they're inaccessible to the LHC – or marginally accessible – and perhaps even inaccessible to ILC/CLIC. I like the representative table of a FUTB model here:\[

m_b(M_Z) & 2.74 &&
m_t & 174.1 \\ \hline
m_h & 125.0 &&
m_A & 1517 \\ \hline
m_H & 1515&&
m_{H^\pm} & 1518 \\ \hline
m_{\tilde t_1} & 2483 &&
m_{\tilde t_2} & 2808 \\ \hline
m_{\tilde b_1} & 2403 &&
m_{\tilde b_2} & 2786 \\ \hline
m_{\tilde \tau_1} & 892 &&
m_{\tilde \tau_2} & 1089 \\ \hline
m_{\tilde\chi_1^\pm} & 1453 &&
m_{\tilde\chi_2^\pm} & 2127 \\ \hline
m_{\tilde\chi_1^0} & 790 &&
m_{\tilde\chi_2^0} & 1453 \\ \hline
m_{\tilde\chi_3^0} & 2123 &&
m_{\tilde\chi_4^0} & 2127 \\ \hline
m_{\tilde g} & 3632 && {\rm masses}& {\rm in}\,\GeV
\\ \hline

\] You see that the LSP is the lightest neutralino below \(800\GeV\). Staus are just somewhat heavier, \(900\GeV\) and \(1100\GeV\). Both sbottoms and stops fit the pattern that the lightest and heaviest one is at \(2500\GeV\) and \(2800\GeV\), respectively. The second lightest neutralino and the lightest chargino sit at \(1450\GeV\), the remaining four faces of the God particle find themselves above \(1500\GeV\) while the heavier chargino and the heaviest two neutralinos are above \(2100\GeV\). Finally, the gluino is above \(3600\GeV\).

Particularly the last figure is rather high (in a broader ensemble of models they analyze, the masses may go up to \(10\TeV\) or so). We would have trouble to see such a gluino for years. But this model or at least similar models may be right. From a theoretical viewpoint, I see absolutely no preference when I compare models with gluinos at \(1200\GeV\) and \(3600\GeV\). Some people become very emotional and start to say that one of them has to be right or wrong or its rightness or wrongness means something a priori. Well, it just doesn't. Nature doesn't give a damn whether it's easy or hard for us to observe the superpartners. Once we observe them, many new things start to be clear. If we don't observe them, we are still extremely far from ruling out supersymmetry – and nice special supersymmetric models such as FUTB in this paper.

Its not my – or other humans' – job to rate the beauty of the values of particle physics parameters that emerge from Nature's decisions. It's Her job. Nevertheless, I must say that I would find a spectrum like the table above – or many other tables – elegant. It would probably mean that all these obnoxious idiots who like to say bad things about SUSY could remain loud for many more years. That's an annoying vision from a personal viewpoint but it can't change anything about the reality and it is less important than the actual beauty and physical near-inevitability that is carried by supersymmetry at some scale. If the known – mostly theoretical – evidence makes two models equally plausible and elegant, then one is obliged to love both of them equally, regardless of the fact that one of them may be much more accessible to the experiments. I view this commandment as a part of the scientific integrity.

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reader Vladimir Kalitvianski said...

You know, Bohr postulates about stationary orbits had an empirical input. What is an empirical input for the super-symmetry idea?

reader Dilaton said...

Thanks for this nice article Lumo :-)

I like it to read from time to time some details about supersymmetric models that are not ruled out, it cheers me up.

I have somehow learned to ignore the idiots who say bad things about SUSY, if they dont pop up at places where I absolutely dont expect them and they really should not penetrate ...


reader George Christodoulides said...

Lubos if you know the answer could you please explain why most theoretical particle physicists believe that supersymmetry exists or if it doesn't something similar close to it etc. but most experimental particle physicists for some reason are not convinced that supersymmetry exists?

also i don't understand why particle physicists did not disagree with theoretical particle physicists about the higgs boson but they do about supersymmetry.

reader George Christodoulides said...

some experimental particle physicists not only don't believe supersymmetry exists but they laugh at the claim and make fun of the theoretical particle physicists for it.

reader Luboš Motl said...

Well, it's simple, George. Most experimental particle physicists are "just" experimental particle physicists and they just don't understand theoretical physics well.

So as "mere experimenters", they build their opinions only on things they have already directly seen. They haven't seen SUSY so they don't believe it exists. They will only be forced to change their mind when SUSY is directly observed.

This is true much more generally. "Mere experimenters" really don't know how to make predictions - they only know how to experimentally verify them.

Theoretical particle physicists know that SUSY is almost inevitable at *some* scale because it is 1) a necessary part of any consistent string theory vacua, 2) it seems necessary to guarantee stability, e.g. Higgs potential stability, and the smallness of the Higgs mass and is perhaps helpful for reducing the cosmological constant problem, 3) gives the most natural and automatically realistic dark matter candidates, the WIMP in the form of the LSP, 4) seems to automatically predict gauge coupling unification (when combined with grand unification) that agrees with the observed values of the couplings, and so on, and so on.

Each of these reasons has been described on this blog.

reader George Christodoulides said...

thanks a lot.

reader Vladimir Kalitvianski said...

And my similar question was banned by you. What a shame!

reader Vladimir Kalitvianski said...


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