GAMBIT Is Incomplete But Furthers SUSY Falsification

The community of supersymmetry (SUSY) phenomenologists and kindred beyond the Standard Model (BSM) theorists has come up with a software package called GAMBIT that analyzes the available parameter space of particular beyond the standard model theories, such as various versions of SUSY and another grand unified theories (GUTs) on a global basis in light of the available data.

This makes sense because any given fit of data to a BSM theory is an arduous task, but most of the very sophisticated and difficult parts of the analysis can be generalized to any member of a large class of BSM theories. 

For example, every analysis must appropriately reflect the uncertainties in the values of the measured experimental constants used as model inputs and appropriately weigh the impact of those uncertainties on the likelihood that a place of the parameter space of the BSM model is not ruled out by experiment.

The First Three GAMBIT papers

So far, GAMBIT has been fed real data and produced results reported in three inaugural pre-prints.

* One looks at scalar singlet dark matter models. In this paper (emphasis mine):

We include the dark matter relic density measured by Planck, direct searches with LUX, PandaX, SuperCDMS and XENON100, limits on invisible Higgs decays from the Large Hadron Collider, searches for high-energy neutrinos from dark matter annihilation in the Sun with IceCube, and searches for gamma rays from annihilation in dwarf galaxies with the Fermi-LAT. Viable solutions remain at couplings of order unity, for singlet masses between the Higgs mass and about 300 GeV, and at masses above ∼1 TeV. Only in the latter case can the scalar singlet constitute all of dark matter. Frequentist analysis shows that the low-mass resonance region, where the singlet is about half the mass of the Higgs, can also account for all of dark matter, and remains viable. However, Bayesian considerations show this region to be rather fine-tuned.

This result, in fact, is far too optimistic because it doesn't include a complete set of constraints.

There is simulation based data related to dark matter halo shapes that disfavor models with two significant kinds of dark matter like those in the 125 GeV to 300 GeV mass range, and there is experimental data related to dark matter halo shape and galaxy dynamics that strongly disfavors masses above 1 TeV (or for that matter masses in the range of 125 GeV to 300 GeV, or around 62.5 GeV).

As noted in the SUSY GUT paper below at page 8, in an observation that is true for all GAMBIT parameter fits:

The likelihood that we employ penalises only models that predict more than the observed relic density.

So, models that produce insufficient dark matter are still treated as viable, contrary to the data from dark matter research. This would be a serious problem were it not for the fact that the MSSM and most similar models generically produces too much, and not too little dark matter.

Also, the only reason that direct dark matter detection experiments have not more definitively ruled out dark matter particles heavier than 1 TeV is because the experiments were designed to be sensitive to lighter dark matter particles which were considered far more likely to exist. There is no affirmative experimental data favoring very heavy cold dark matter particles like these, just a lack of precision tests that are sensitive to a mass range thoroughly disfavored by astronomy data, which are also not well motivated by the considerations that led scientists in the 1980s to come up with SUSY theories in the first place.

A paper summing up the results of a June 2012 dark matter conference reached conclusions that have still not been credibly rebutted, which SUSY theorists simply choose to ignore rather than address on the merits:

Evidence that Cold Dark Matter (ΛCDM), CDM+ baryons and its proposed tailored cures do not work in galaxies is staggering, and the CDM wimps (DM particles heavier than 1 GeV) are strongly disfavoured combining theory with galaxy astronomical observations. 

One also needs to accept extremely low cross-sections of interaction with ordinary matter for any these models to be viable due to the LUX data, which are not consistent with naive formulations of SUSY theories that should have cross-sections of interaction of a magnitude comparable to at least the cross-sections of interaction associated with the weak force interactions of ordinary neutrinos, without any plausible theoretical motivation for this in a SUSY framework. As Jester explained in his most recent blog post:

If the WIMP were true to its name, that is to say if it was interacting via the weak force (meaning, coupled to Z with order 1 strength), it would have order 10 fb scattering cross section on neutrons. Unfortunately, that natural possibility was excluded in the previous century. Years of experimental progress have shown that the WIMPs, if they exist, must be interacting super-weakly with matter. For example, for a 100 GeV fermionic dark matter with the vector coupling g to the Z boson, the current limits imply g ≲ 10^-4.

In other words, any interaction between a massive WIMP and ordinary matter is 10,000 times weaker than the weak force that applies to all other Standard Model particles.

Cold dark matter that has thermal relic particles of 1 GeV or more that is not "self-interacting" via a dark matter only 5th force, and is not completely inert with respect to ordinary matter, is pretty much completely ruled out by the astronomy data. And honestly, self-interacting dark matter models are also in serious trouble. Yet, all of the theories analyzed by GAMBIT to date includes dark matter particles of this type.

* One looks at a version of the Minimal Supersymmetric Standard Model called MSSM7 (because it has 7 free parameters).

One non-obvious conclusion of this analysis is that the MSSM generically produces far too much thermal relic dark matter unless one of five specific forms of annihilation of dark matter with other dark matter exists to reduce the amount of dark matter in the universe today. These are:

- chargino co-annihilation;

- stop co-annihilation;

- sbottom co-annihilation;

- A/H funnel; and

- h/Z funnel

The best fit results cluster around just a couple of those five specific forms of dark matter annihilation, although the parameter values for the MSSM7 parameters favored aren't heavily dependent upon the dark matter annihilation mechanisms incorporated in the theory. Specifically, the A/H funnel and sbottom co-annihilation scenarios are closer to the best fit values than that h/Z funnel, and chargino co-annihilation and stop co-annihilation diverge the furtherest from best fits that are not limited to these dark matter annihilation models.

It also bears noting that there is not a shred of credible positive experimental evidence for any of the particles involved in any of the three annihilation modes or the A/H funnel. All of those theories are purely "god of the gaps" material whose viability hinges on a lack of sufficient experimental evidence to rule them out for all possible parameter values. Experiments have not fully ruled them out at all masses and in all variations, but they have seen no data to support their existence. Only the h/Z funnel primarily involves particles that are known to really exist and it isn't particular favored by the analysis.

Another point to note is that the case for the MSSM7 hinges heavily on three data points, all of which should be viewed with suspicion. One involved the properties of the Higgs boson has measured at the LHC, which do not yet perfectly square with the Standard Model expectation even though they are converging towards that prediction as more data accumulates. The second involves gamma rays observed with the Fermi-LAT satellite which most observers attribute to astronomy sources in a poorly known background rather than BSM physics. The third and most dominant at this point are the anomalous, lepton universality violations observed in certain B meson decays that have been disappearing as Run-2 data becomes available.

In general, the fits of the data to the MSSM7 tend to favor a light neutralino (ca. 200 GeV), and a very heavy CP-Odd Higgs boson (more than 5 TeV).

Like the scalar singlet dark matter model study above, this analysis fails to consider the rather compelling data from dark matter halo shapes and galaxy dynamics that strongly disfavor the heavy dark matter candidates proposed.

* One looks at SUSY GUTs. The abstract of this paper is as follows (emphasis added):

We present the most comprehensive global fits to date of three supersymmetric models motivated by grand unification: the Constrained Minimal Supersymmetric Standard Model (CMSSM), and its Non-Universal Higgs Mass generalisations NUHM1 and NUHM2. We include likelihoods from a number of direct and indirect dark matter searches, a large collection of electroweak precision and flavour observables, direct searches for supersymmetry at LEP and Runs I and II of the LHC, and constraints from Higgs observables. Our analysis improves on existing results not only in terms of the number of included observables, but also in the level of detail with which we treat them, our sampling techniques for scanning the parameter space, and our treatment of nuisance parameters. We show that stau co-annihilation is now ruled out in the CMSSM at more than 95% confidence. Stop co-annihilation turns out to be one of the most promising mechanisms for achieving an appropriate relic density of dark matter in all three models, whilst avoiding all other constraints. We find high-likelihood regions of parameter space featuring light stops and charginos, making them potentially detectable in the near future at the LHC. We also show that tonne-scale direct detection will play a largely complementary role, probing large parts of the remaining viable parameter space, including essentially all models with multi-TeV neutralinos.

As in the MSSM7 paper, the existence of one of a handful of particular dark matter annihilation methods is critical to making these models viable, because otherwise these SUSY GUT models generically predict the existence of too much dark matter.

And, like all of the other papers, the GAMBIT model ignores the fact that heavy cold dark matter is strongly disfavored by the astronomy data. See, for example, page 4 of the SUSY GUT paper which notes in describing GAMIT's dark matter model that:

Because we do not employ any observables in our fits that depend on the Milky Way density profile, the spatial part of this [dark matter] model plays no role.

Conclusion

Despite all sorts of little corners of the SUSY and GUT parameter space that are not ruled out by GAMBIT, all of these fits hinge heavily on some anomalous early results with limited data that are already starting to go away at the LHC, and all of these dark matter models are made possible only by ignoring important data points from astronomy that strongly disfavor heavy, thermal relic, cold dark matter which all of these models assume.

In truth, the kind of simple SUSY formulations proposed in these models have not been ruled out already only because an army of institutionally committed SUSY theorists are performing CPR upon them with all of their might despite the fact that these patients are already dead - a point that is pretty clear to anyone looking at the forest rather than only at the trees.

GAMBIT considers all sorts of constraints and a mutual and interacting basis, but, it ignores key constraints from astronomy that strongly disfavor cold dark matter of 10 GeV or more based upon issues like halo shape, because including this constraint would annihilate all of the models the software is designed to analyze rendering the whole effort futile at the get go. So, this community has chosen to engage the data only selectively in order to preserve its sacred cows.

This doesn't mean that GAMBIT is useless. It still greatly narrows the part of parameter space that has to be considered by someone seeking to rule out SUSY, so that defeat of these models in detail is, at least in principle, theoretically possible by taking its output and then adding additional constraints that GAMBIT ignores.

GAMBIT also does a relatively good job of demonstrating, by example, that a lot of the key problems with the current batch of SUSY theories are generic over a wide range of SUSY theory variations.

The take home message of this latest round of efforts to confront SUSY with the experimental data is that the assumptions that need to be made to keep SUSY alive are now far outside the parameter space ranges that motivated SUSY in the first place, that essentially all simple SUSY theories in existence are ruled out by adding the full set of constraints to those analyzed by GAMBIT, and that seekers of a BSM theory that works (because we still need, at a minimum, a viable quantum gravity theory and a better explanation of the barrage of Standard Model constants) would be well advised to consider SUSY a dead end and look elsewhere.

Moreover, since SUSY is the low energy approximation of most interesting versions of String Theory, String Theory is also on the endangered list as a viable explanation of our real physical universe, even if it produces cool and sometimes even useful mathematical concepts and tools.