... the scalar proliferation instability problem is perhaps the least controversial, most generic and most important subcategory of the general naturalness problem. It is not unexpected that solutions to the general naturalness problem can solve or help solve the proliferation problem. Discussions of the general naturalness problem, however, have been plagued often with quasi-mystical arguments involving quantum gravity and arguments involving cancellations of bare mass terms with regulator-dependent cutoff scales, which we have no access to and are mere non-physical intermediate book-keeping devices for calculation. Considering the requirements for stability in the presence of a large number of heavy or condensing scalars in nature – a generic and motivated consideration – is a more concrete problem to address ... the requirement of proliferation stability puts signiﬁcant restrictions on theory, and implies that there is more to discover beyond the Standard Model to complete our understanding of the weak scale.
The introduction of higher Higgs multiplets, or of more than one doublet has the obvious disadvantage that in general no zero mass vector boson survives. In other words, the observed zero photon mass is then an ‘accident.’ For this reason alone these schemes are very unattractive.
A propos de la pertinence et du caractère générique d'éventuels bosons scalaires non chargés
... the Higgs boson operator is the only bosonic one with dimension less than four that is both gauge invariant and Lorentz invariant. In my mind, this is one of the most important realizations that one can make about the Standard Model and about the Higgs boson in particular. As a consequence, hidden worlds have a much better chance of communicating with the Higgs boson than any other particle in the Standard Model. This is one reason why I think the Higgs boson is particularly susceptible to deviations from expected phenomenology at the LHC.
It is often the case that more fundamental theories that try to explain dark matter and inﬂation (Baumann , "TASI Lectures on Inflation" 2009), explain ﬂavor (Babu "TASI Lectures on Flavor Physics" 2009), or which strive to be compatible with a theory of quantum gravity, such as string theory, generically predict that there should be many more particles and much more dynamics than just what is described by the Standard Model. Regarding this last category, one should expect dozens, or perhaps even thousands of more Higgs bosons of exotic sectors that condense and break symmetries (Dijkstra et al. "Supersymmetric Standard Model Spectra from RCFT orientifolds 2005).
... there are several solutions to the proliferation instability problem that we have been describing above. Operationally, any solution theory has the burden of enforcing stability in the presence of a large number of massive or condensing scalars. The prospective solutions include banishing fundamental scalars as in technicolor and composite Higgs theories, banishing high-scale hierarchies as in large extra dimensions or warped extra dimensions, or invoking supersymmetry (Pomarol "Beyond the Standard Model" 2012). Not surprisingly, given our discussion above pointing out the important connection between the proliferation instability problem and naturalness, this triumvirate of general approaches also can potentially solve the proliferation instability problem.
The ﬁrst solution, to banish the entire category of scalars from the theory, clearly would take care of any problem systemic to scalars. However, there are well-known challenges to matching data with this approach (Pomarol 2012), not to mention that the recent discovery of a weakly interacting Higgs boson consistent with being elementary puts strain on this idea.
The second solution is banishing the existence of high scales through extra dimensions. The idea is to reinterpret the singlet number of the very large mass Planck scale of gravity as the ratio of two numbers involving the weak scale and a very large extra dimensional volume or warp factor, in the case of warped extra dimensions (Csaki "Extra-dimensions and Branes" 2004). This approach may not work well to solve the proliferation problem. If we indeed have dozens or more condensing scalars in nature – let’s call the number NH – at scales not too far away from the Higgs mass scale, there is still the potential of destabilizing the hierarchy from large NH. For the Higgs mass to be stable the sum of contributions to the Higgs mass-squared operator would have to be of order the Higgs boson mass, m2H ∼ NHξ2, where ξ is the typical vacuum expectation value of the exotic condensing scalar. Thus, lowering the high-scale nearer to the weak scale through large or warped extra dimensions would soften the destabilization problem some, but may not eradicate it.
The third solution, supersymmetry, is next to consider. It is a remarkable feat of supersymmetry that the Higgs sector is generically completely stable to a large number of extra condensing Higgs bosons, in stark contrast to non-supersymmetric ﬁeld theories. The key is a special property of supersymmetry invariance that requires interactions to be analytic in their ﬁelds ... The only requirements are that there are no pure singlet scalar states in nature under all possible symmetries (Bagger & Poppitz "Destabilizing Divergences in Supergravity-Coupled Supersymmetric theories" 1993), and the technically natural µ term that connects µHu·Hd together is near the weak scale. This is a restriction on two narrow and technical criteria compared to the admittance of a very large number of possible exotic Higgs states charged under many diﬀerent exotic symmetries.
Another response to the proliferation problem is to assume that there simply is no proliferation of Higgs bosons in nature, and so no proliferation instability problem arises. The difficulty with this position is that we would be required to believe that the Higgs boson is very special and that unlike any other representations in nature, the spin 1/2 fermions and spin 1 vector bosons, there is just one Higgs boson and not another. This position fails a modern day Copernican test of making sure our theories do not require us to believe we are particularly special.
We think that Hamlet’s words ‘There are more things in Heaven and Earth, Horatio, than are dreamt of in our Philosophy’ (I, v. 167) are closer to the lessons of the past.
Yuri Ne'eman et Yovla Kirsch, The Particles Hunter, 1996
La dernière citation quant-à elle est tirée d'un commentaire à cet autre billet de Woit.