Sit down and relaxion

New ideas are rare in particle physics these days. Solutions to the naturalness problem of the Higgs mass are true collector's items. For these reasons, the new mechanism addressing the naturalness problem via cosmological relaxation have stirred a lot of interest in the community. There's already an article explaining the idea in popular terms. Below, I will give you a more technical introduction.

In the Standard Model, the W and Z bosons and fermions get their masses via the Brout-Englert-Higgs mechanism. To this end, the Lagrangian contains  a scalar field H with a negative mass squared  V = - m^2 |H|^2. We know that the value of the parameter m is around 90 GeV - the Higgs boson mass divided by the square root of 2. In quantum field theory,  the mass of a scalar particle is expected to be near the cut-off scale M of the theory, unless there's a symmetry protecting it from quantum corrections.  On the other hand, m much smaller than M, without any reason or symmetry principle, constitutes the naturalness problem. Therefore, the dominant paradigm has been that, around the energy scale of 100 GeV, the Standard Model must be replaced by a new theory in which the parameter m is protected from quantum corrections.  We know several mechanisms that could potentially protect the Higgs mass: supersymmetry, Higgs compositeness, the Goldstone mechanism, extra-dimensional gauge symmetry, and conformal symmetry. However, according to experimentalists, none seems to be realized at the weak scale; therefore, we need to accept that nature is fine-tuned (e.g. susy is just behind the corner), or to seek solace in religion (e.g. anthropics).  Or to find a new solution to the naturalness problem: one that is not fine-tuned and is consistent with experimental data.

Relaxation is a genuinely new solution, even if somewhat contrived. It is based on the following ingredients:

1.  The Higgs mass term in the potential is V = M^2 |H|^2. That is to say,  the magnitude of the mass term is close to the cut-off of the theory, as suggested by the naturalness arguments. 
2. The Higgs field is coupled to a new scalar field - the relaxion - whose vacuum expectation value is time-dependent in the early universe, effectively changing the Higgs mass squared during its evolution.
3. When the mass squared turns negative and electroweak symmetry is broken, a back-reaction mechanism should prevent further time evolution of the relaxion, so that the Higgs mass terms is frozen at a seemingly unnatural value.       

These 3 ingredients can be realized in a toy model where the Standard Model is coupled to the QCD axion. The crucial interactions are  

Then the story goes as follows. The axion Φ starts at a large value such that the Higgs mass term is positive and there's no electroweak symmetry breaking. During inflation its value slowly decreases. Once gΦ < M^2, electroweak symmetry breaking is triggered and the Higgs field acquires a vacuum expectation value.  The crucial point is that the height of the axion potential Λ depends on the light quark masses which in turn depend on the Higgs expectation value v. As the relaxion evolves, v increases, and Λ also increases proportionally, which provides the desired back-reaction. At some point, the slope of the axion potential is neutralized by the rising Λ, and the Higgs expectation value freezes in. The question is now quantitative: is it possible to arrange the freeze-in to happen at the value v well below the cut-off scale M? It turns out the answer is yes, at the cost of choosing strange (though not technically unnatural) theory parameters.  In particular, the dimensionful coupling g between the relaxion and the Higgs has to be less than 10^-20 GeV (for a cut-off scale larger than 10 TeV), the inflation has to last for at least 10^40 e-folds, and the Hubble scale during inflation has to be smaller than the QCD scale.   

The toy-model above ultimately fails. Normally, the QCD axion is introduced so that its expectation value cancels the CP violating θ-term in the Standard Model Lagrangian. But here it is stabilized at a value determined by its coupling to the Higgs field. Therefore, in the toy-model, the axion effectively generates an order one θ-term, in conflict with the experimental bound  θ < 10^-10. Nevertheless, the same  mechanism can be implemented in a realistic model. One possibility is to add new QCD-like interactions with its own axion playing the relaxion role. In addition, one needs new "quarks" charged under the new strong interactions. These masses have to be sensitive to the electroweak scale v, thus providing a back-reaction on the axion potential that terminates its evolution. In such a model, the quantitative details would be a bit different than in the QCD axion toy-model. However, the "strangeness" of the parameters persists in any model constructed so far. Especially, the very low scale of inflation required by the relaxation mechanism is worrisome. Could it be that the naturalness problem is just swept into the realm of poorly understood physics of inflation? The ultimate verdict thus depends on whether a complete and  healthy model incorporating both relaxation and inflation can be constructed.

Certainly TBC.

Thanks to Brian for a great tutorial. 

On the LHC diboson excess

The ATLAS diboson resonance search showing a 3.4 sigma excess near 2 TeV has stirred some interest. This is understandable: 3 sigma does not grow on trees, and moreover CMS also reported anomalies in related analyses. Therefore it is worth looking at these searches in a bit more detail in order to gauge how excited we should be.

The ATLAS one is actually a dijet search: it focuses on events with two very energetic jets of hadrons.  More often than not, W and Z boson decay to quarks. When a TeV-scale  resonance decays to electroweak bosons, the latter, by energy conservation,  have to move with large velocities. As a consequence, the 2 quarks from W or Z boson decays will be very collimated and will be seen as a single jet in the detector.  Therefore, ATLAS looks for dijet events where 1) the mass of each jet is close to that of W (80±13 GeV) or Z (91±13 GeV), and  2) the invariant mass of the dijet pair is above 1 TeV.  Furthermore, they look into the substructure of the jets, so as to identify the ones that look consistent with W or Z decays. After all this work, most of the events still originate from ordinary QCD production of quarks and gluons, which gives a smooth background falling with the dijet invariant mass.  If LHC collisions lead to a production of  a new particle that decays to WW, WZ, or ZZ final states, it should show as a bump on top of the QCD background. ATLAS observes is this:

There is a bump near 2 TeV, which  could indicate the existence of a particle decaying to WW and/or WZ and/or ZZ. One important thing to be aware of is that this search cannot distinguish well between the above 3  diboson states. The difference between W and Z masses is only 10 GeV, and the jet mass windows used in the search for W and Z  partly overlap. In fact, 20% of the events fall into all 3 diboson categories.   For all we know, the excess could be in just one final state, say WZ, and simply feed into the other two due to the overlapping selection criteria.

Given the number of searches that ATLAS and CMS have made, 3 sigma fluctuations of the background should happen a few times in the LHC run-1 just by sheer chance.  The interest in the ATLAS  excess is however amplified by the fact that diboson searches in CMS also show anomalies (albeit smaller) just below 2 TeV. This can be clearly seen on this plot with limits on the Randall-Sundrum graviton excitation, which is one  particular model leading to diboson resonances. As W and Z bosons sometimes decay to, respectively, one and two charged leptons, diboson resonances can be searched for not only via dijets but also in final states with one or two leptons.  One can see that, in CMS, the ZZ dilepton search (blue line), the WW/ZZ dijet search (green line), and the WW/WZ one-lepton (red line)  search all report a small (between 1 and 2 sigma) excess around 1.8 TeV.  To make things even more interesting,  the CMS search for WH resonances return 3 events  clustering at 1.8 TeV where the standard model background is very small (see Tommaso's post). Could the ATLAS and CMS events be due to the same exotic physics?

Unfortunately, building a model explaining all the diboson data is not easy. Enough to say that the ATLAS excess has been out for a week and there's isn't yet any serious ambulance chasing paper on arXiv. One challenge is the event rate. To fit the excess, the resonance should be produced with a cross section of order 10 femtobarns. This requires the new particle to couple quite strongly to light quarks (or gluons), at least as strong as the W and Z bosons. At the same time, it should remain a narrow resonance decaying dominantly to dibosons. Furthermore, in concrete models, a sizable coupling to electroweak gauge bosons will get you in trouble with electroweak precision tests.

However, there is yet a bigger problem, which can be also  seen in the plot above. Although the excesses in CMS occur roughly at the same mass, they are not compatible when it comes to the cross section. And so the limits in the single-lepton search are not consistent with the new particle interpretation of the excess in dijet  and  the dilepton searches, at least in the context of the Randall-Sundrum graviton model. Moreover, the limits from the CMS one-lepton search are grossly inconsistent with the diboson interpretation of the ATLAS excess! In order to believe that the ATLAS 3 sigma excess is real one has to move to much more baroque models. One possibility is that  the dijets observed by ATLAS do not originate from  electroweak bosons, but rather from an exotic particle with a similar mass. Another possibility is that the resonance decays only to a pair of Z bosons and not to W bosons, in which case the CMS limits are weaker; but I'm not sure if there exist consistent models with this property.  

My conclusion...  For sure this is something to observe in the early run-2. If this is real, it should clearly show in both experiments already this year.  However, due to the inconsistencies between different search channels and the theoretical challenges, there's little reason to get excited yet.

Thanks to Chris for digging out the CMS plot.