Natural SUSY's last stand". That title is a bit misleading as it makes you think of General Custer at the eve of Battle of the Little Bighorn, whereas natural supersymmetry has long been dead bodies torn by vultures. Nevertheless, it is interesting to ask a more general question: are there any natural theories that survived? And if yes, what can we learn about them from the LHC run-2?
For over 30 years naturalness has been the guiding principle in theoretical particle physics. The standard model by itself has no naturalness problem: it contains 19 free parameters that are simply not calculable and have to be taken from experiment. The problem arises because we believe the standard model is eventually embedded in a more fundamental theory where all these parameters, including the Higgs boson mass, are calculable. Once that is done, the calculated Higgs mass will typically be proportional to the heaviest state in that theory as a result of quantum corrections. The exception to this rule is when the fundamental theory possesses a symmetry forbidding the Higgs mass, in which case the mass will be proportional to the scale where the symmetry becomes manifest. Given the Higgs mass is 125 GeV, the concept of naturalness leads to the following prediction: 1) new particles beyond the standard model should appear around the mass scale of 100-300 GeV, and 2) the new theory with the new particles should have a protection mechanism for the Higgs mass built in.
There are two main realizations of this idea. In supersymmetry, the protection is provided by opposite-spin partners of the known particles. In particular, the top quark is accompanied by stop quarks who are spin-0 scalars but otherwise they have the same color and electric charge as the top quark. Another protection mechanism can be provided by a spontaneously broken global symmetry, usually realized in the context of new strong interactions from which the Higgs arises as a composite particle. In that case, the protection is provided by the same spin partners, for example the top quark has a fermionic partner with the same quantum numbers but a different mass.
Both of these ideas are theoretically very attractive but are difficult to realize in practice. First of all, it is hard to understand how these 100 new partner particles could be hiding around the corner without leaving any trace in numerous precision experiments. But even if we were willing to believe in the Universal conspiracy, the LHC run-1 was the final nail in the coffin. The point is that both of these scenarios make a very specific prediction: the existence of new particles with color charges around the weak scale. As the LHC is basically a quark and gluon collider, it can produce colored particles in large quantities. For example, for a 1 TeV gluino (supersymmetric partner of the gluon) some 1000 pairs would have been already produced at the LHC. Thanks to the large production rate, the limits on colored partners are already quite stringent. For example, the LHC limits on masses of gluinos and massive spin-1 gluon resonances extend well above 1 TeV, while for scalar and fermionic top partners the limits are not far below 1 TeV. This means that a conspiracy theory is not enough: in supersymmetry and composite Higgs one also has to accept a certain degree of fine-tuning, which means we don't even solve the problem that is the very motivation for these theories.
The reasoning above suggests a possible way out. What if naturalness could be realized without colored partners: without gluinos, stops, or heavy tops. The conspiracy problem would not go away, but at least we could avoid stringent limits from the LHC. It turns out that theories with such a property do exist. They linger away from the mainstream, but recently they have been gaining popularity under the name of the neutral naturalness. The reason for that is obvious: such theories may offer a nuclear bunker that will allow naturalness to survive beyond the LHC run-2.
The best known realization of neutral naturalness is the twin Higgs model. It assumes the existence of a mirror world, with mirror gluons, mirror top quarks, a mirror Higgs boson, etc., which is related to the standard model by an approximate parity symmetry. The parity gives rise to an accidental global symmetry that could protect the Higgs boson mass. At the technical level, the protection mechanism is similar as in composite Higgs models where standard model particles have partners with the same spins. The crucial difference, however, is that the mirror top quarks and mirror gluons are charged under the mirror color group, not the standard model color. As we don't have a mirror proton collider yet, the mirror partners are not produced in large quantities at the LHC. Therefore, they could well be as light as our top quark without violating any experimental bounds, and in agreement with the requirements of naturalness.
A robust prediction of twin-Higgs-like models is that the Higgs boson couplings to matter deviate from the standard model predictions, as a consequence of mixing with the mirror Higgs. The size of this deviation is of the same order as the fine-tuning in the theory, for example order 10% deviations are expected when the fine-tuning is 1 in 10. This is perhaps the best motivation for precision Higgs studies: measuring the Higgs couplings with an accuracy better than 10% may invalidate or boost the idea. However, the neutral naturalness points us to experimental signals that are often very different than in the popular models. For example, the mirror color interactions are expected to behave at low energies similarly to our QCD: there should be mirror mesons, baryons, glueballs. By construction, the Higgs boson must couple to the mirror world, and therefore it offers a portal via which the mirror hadronic junk can be produced and decay, which may lead to truly exotic signatures such as displaced jets. This underlines the importance to search for exotic Higgs boson decays - very few such studies have been carried out by the LHC experiments so far. Finally, as it has been speculated for long time, dark matter may have something to do the with the mirror world. Neutral naturalness provides a reason for the existence of the mirror world and an approximate parity symmetry relating it to the real world. It may be our best shot at understanding why the amounts of ordinary and dark matter in the Universe are equal up to a factor of 5 - something that arises as a complete accident in the usual WIMP dark matter scenario.
There's no doubt that the neutral naturalness is a desperate attempt to save natural electroweak symmetry breaking from the reality check, or at least postpone the inevitable. Nevertheless, the existence of a mirror world is certainly a logical possibility. The recent resurgence of this scenario has led to identifying new interesting models, and new ways to search for them in experiment. The persistence of the naturalness principle may thus be turned into a positive force, as it may motivate better searches for hidden particles. It is possible that the LHC data hold the answer to the naturalness puzzle, but we will have to look deeper to extract it.