Writing a serious review of research in particle physics is a refreshing job – all the things that you already knew on that specific topic once sat on a fuzzy cloud somewhere in your brain, and now find their place in a tidily organized space, with clear interdependence among them. That’s what I am experiencing as I progress with a 60-pageish thing on hadron collider searches for diboson resonances, which will appear sometime next year in a very high impact factor journal.

One of the things that the review must cover is a theoretical overview of the models that the searches for these physics processes address. So I thought I would say a few words on this topic here – but bear in mind that this will be quite low-level as I don’t think a blog is the right place for anything but the very basic ideas.

The issue is clear: the standard model of particle physics (SM), the marvellous construction put together thanks to the effort of a few great minds from the fifties to the seventies of the past century (three decades, as I include the pioneering work of Feynman and Schwinger here, as well as ‘t Hooft’s contribution), is extremely successful in explaining the dynamics of subnuclear particles, but it fails to qualify as a final theory for a number of reasons. The obvious one is the absence of an explanation of gravity in the model; but there’s others. Below is a first draft of the paragraph I already wrote on the shortcomings of the SM for the review:

“*Despite its huge successes in explaining the phenomenology of subnuclear physics from low-energy interactions all the way to the TeV scale, the SM is today considered at most an effective theory, one which should eventually break down when higher-energy reactions are studied, to become a low-energy approximation of a larger and more comprehensive theory. There are multiple reasons for this belief. First of all, the SM manifestly fails to include a description of gravity. Secondly, it does not yield a description of the properties of non-massless neutrinos. Yet the most compelling argument demanding some more fundamental theory to replace the SM is the fact that the size of quantum corrections to the Higgs boson mass arising from the contribution of virtual loops involving SM particles exceed the observed value by many orders of magnitude: the physical mass of the Higgs boson, which results from the addition and subtraction of those large contributions, appears exceptionally fine-tuned, ending up to be unnaturally light and close to the electroweak scale. To the above list of clear shortcomings one could add the absence in the SM of other desirable features of a final theory — an explanation, e.g., of the hierarchy of fermion masses, of the weakness of gravity with respect to the other forces, of the observed abundance of dark matter, and of the observed matter-antimatter asymmetry in the universe; or the lack of a common unification scale of running couplings at high energy.* “

So what could we summon to repair the SM, or to extend it such that those shortcomings may find an explanation? This is a question that has kept theorists busy for the last 40 years, and has seen a huge number of tentative answers, so far none of which has met with confirming experimental input. Within the jungle of models, one may identify some common features of the phenomenological predictions. One of these is the presence of some high-mass particle X, yet to be discovered, which can produce pairs of bosons in its decay.

By “boson” I mean elementary particles of integer spin. Exactly five SM particles qualify: the W+ and W- bosons, the Z boson, the photon, and the Higgs boson. However, for completeness one should add to the list any as-of-yet unknown boson that a theory might predict: so, e.g., one should consider the possibility of extra Higgs-like bosons, as many theories do. If those existed, then they, too, might be in pairs the decay product of the new resonance X.

All in all, one is looking at the following classes of decays:

- X→ VV (where V is a W or Z boson)
- X→ HY (where H is the Higgs boson of the SM, and Y is any other boson, like a W, a Z, or a new one).
- X→γY (where again, Y is any other boson, such as e.g. a Z boson or another photon).

Models that predict new resonances X decaying to bosons abound. Let me make a short list below:

- Extended Higgs models: these foresee that the Higgs mechanism is not producing only one physical scalar particle, but more. You cannot have two, or three, though: the simplest extension involves 5 different scalar bosons, and is called “2HDM”: two Higgs doublet model. That is because the vanilla Higgs mechanism involves the inclusion in the Lagrangian density of the SM a complex scalar doublet, which has four degrees of freedom, and then three of those degrees of reedom get absorbed by the W+, W-, and Z bosons to acquire a mass (this is what the “symmetry breaking” magic does). If you include instead two scalar doublets in the theory, then you have eight degrees of freedom, and after the WWZ get their longitudinal polarization state you are left with five parameters, which correspond to the five Higgs particles of the 2HDM. There exist a huge variety of 2HDMs, but most of them predict that some particles decay into boson pairs – the simplest case is the A–>Zh decay of one of the extra Higgses, called “A” (a CP-odd neutral pseudoscalar); also, a heavy H state may decay to H→hh in some region of parameter space. Note that among 2DHMs there are the simplest version of Supersymmetric theories.

- Large extra dimension theories: these introduce the possibility that we live in a higher-dimensional world, and only populate a “TeV brane” -a three-dimensional sheet in the larger space. If only gravity can extend into the “bulk” of the other dimensions, that would make it seem weak in our brane. The theory involves the existence of a spin-2 graviton particle, or a spin-0 radion in some variants. Those particles may decay to bosons pairs – for instance, Higgs pairs.

- Extra gauge groups: a number of theories try to extend the standard model by extending its gauge structure. The SM results from the product of three unitary groups: the SU(3)_C that describes the symmetry of Quantum Chromodynamical “colour” charges; the SU(2)_L group that describes electroweak interactions, and the U(1)_Y group associated with electromagnetism (before the symmetry breaking mixes up the group generator with the SU(2) ones). Now, each of the SM groups calls for the existence of force carriers: SU(3) has eight gluons, SU(2) has the WWZ bosons, and U(1) has an extra boson. If we claim that the true theory has an additional U(1)_Z’ symmetry we can justify the existence of a Z’ boson, which in the simplest case has a behaviour close to the Z boson of the SM. But there is a huge variety of models, and this Z’ can decay in a number of possible ways depending on its “couplings” to SM fermions and bosons. So-called “fermiophobic” Z’ bosons, e.g., will decay to WW or ZZ pairs, or to other combinations of SM bosons.

- Composite models and Technicolor theories try to explain the symmetry breaking of the SM by dynamical effects. Technicolor, e.g., predicts the existence of a number of new particles, called technifermions; these may generate mass terms for W and Z bosons (in alternative to the Higgs mechanism) by their binding energy, as well as give rise to techni-hadrons, bound states of a new strong interaction. The new resonances may thus decay to boson pairs and add to the search list of experimentalists at the LHC. Unfortunately these models are a bit out-fashioned now that a Higgs particle has been discovered, explaining electroweak symmetry breaking by itself. But we keep searching.

So, as you see there is a lot to do at the LHC. All the particles predicted by the above classes of models – extra Higgses, gravitons, radions, Z’ and W’ bosons, techni-whatchamacallits, etcetera, all depend on a number of additional unknown parameters, so it’s really a walk in the jungle to try and search for these things. And no less daring is the job of sifting through over 100 papers produced by ATLAS and CMS that describe searches and measurements connected to these new resonances. Wish me good luck – it will be an intense month.

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