It shows the phase diagram for models of natural electroweak symmetry breaking. These models can be characterized by 2 quantum numbers:
- B [Baroqueness], describing how complicated is the model relative to the standard model;
- S [Specialness], describing the fine-tuning needed to achieve electroweak symmetry breaking with the observed Higgs boson mass.
To allow for a fair comparison, in all models the cut-off scale is fixed to Λ=10 TeV. The standard model (SM) has, by definition, B=1, while S≈(Λ/mZ)^2≈10^4. The principle of naturalness postulates that S should be much smaller, S ≲ 10. This requires introducing new hypothetical particles and interactions, therefore inevitably increasing B.
The most popular approach to reducing S is by introducing supersymmetry. The minimal supersymmetric standard model (MSSM) does not make fine-tuning better than 10^3 in the bulk of its parameter space. To improve on that, one needs to introduce large A-terms (aMSSM), or R-parity breaking interactions (RPV), or an additional scalar (NMSSM). Another way to decrease S is achieved in models the Higgs arises as a composite Goldstone boson of new strong interactions. Unfortunately, in all of those models, S cannot be smaller than 10^2 due to phenomenological constraints from colliders. To suppress S even further, one has to resort to the so-called neutral naturalness, where new particles beyond the standard model are not charged under the SU(3) color group. The twin Higgs - the simplest model of neutral naturalness - can achieve S≈10 at the cost of introducing a whole parallel mirror world.
The parametrization proposed here leads to a striking observation. While one can increase B indefinitely (many examples have been proposed the literature), for a given S there seems to be a minimum value of B below which no models exist. In fact, the conjecture is that the product B*S is bounded from below:
BS ≳ 10^4.One robust prediction of the minimum BS conjecture is the existence of a very complicated (B=10^4) yet to be discovered model with no fine-tuning at all. The take-home message is that one should always try to minimize BS, even if for fundamental reasons it cannot be avoided completely ;)