Yesterday, the ATLAS and CMS experiments at CERN announced the discovery of a Higgs boson at 125 GeV. Surely, this will become one of the most important discoveries of the century. It also caused quite a few interesting 4th of July parties (for once, with a good justification for the fireworks).

For theoretical physicists, this is as much a good reason of excitement as for the experimentalists. Although a measurement of the Higgs self interaction will only come after the upgrade at 14 TeV of the LHC, the current measurement already suggests interesting questions (for example, there appears to be a deficit in the WW channel of decay, which may be an accident, or an indication of something more interesting).

As it is well known, the noncommutative geometry models of particle physics generally give rise to a heavier Higgs (originally estimated at around 170 GeV, then lowered in more recent versions of the model, but still well above 125 GeV). The usual method, in these models, to obtain estimates on the Higgs, is to impose some boundary conditions at unification energy, dictated by the geometry of the model, and running down the renormalization group equations (RGE). The geometric constraints impose some exclusion curves on the manifold of possible boundary conditions, but do not fix the boundary conditions entirely: in fact, recent work on the NCG models observed a sensitive dependence on the choice of boundary conditions (within the constraints imposed by the geometry). Moreover, the renormalization group flow typically used in these estimates is the one provided by the one-loop beta function of the minimal Standard Model (or in more recent versions, of effective field theories obtained from extensions of the MSM by right handed neutrinos with Majorana mass terms, that is, the RGEs considered in hep-ph/0501272v3), rather than a renormalization group flow directly derived from a quantum field theoretic treatment of the action functional of the NCG model, the spectral action.

Perhaps more interestingly (as what one is after, after all, are extensions of the MSM by new physics), while the original NCG models of particle physics focussed on the MSM, there are now variants that include new particle: a first addition beyond the MSM was a model with right handed neutrinos with Majorana mass terms, which accounts for neutrino mixing and a see-saw mechanism.

More recently, a very promising program for extending the NCG model was developed by Thijs van den Broek and Walter van Suijlekom (arXiv:1003.3788), for versions with supersymmetry. While their first paper on the subject deals only with the QCD sector of the model, they are now well on their way towards including the electroweak sector.

I apologize for the plot spoiler, but given the occasion I think it is worth mentioning: the model that van den Broek and van Suijlekom are currently developing appears to be fairly close to the MSSM, although it is

Falsifiability is the most important quality of any scientific theory. Indeed, having explicit experimental data that point out the shortcomings of a theoretical model is the best condition for a serious re-examination of assumptions and techniques used in model building.

Cheers to the LHC, the ATLAS and CMS collaborations, for a great job!

For theoretical physicists, this is as much a good reason of excitement as for the experimentalists. Although a measurement of the Higgs self interaction will only come after the upgrade at 14 TeV of the LHC, the current measurement already suggests interesting questions (for example, there appears to be a deficit in the WW channel of decay, which may be an accident, or an indication of something more interesting).

As it is well known, the noncommutative geometry models of particle physics generally give rise to a heavier Higgs (originally estimated at around 170 GeV, then lowered in more recent versions of the model, but still well above 125 GeV). The usual method, in these models, to obtain estimates on the Higgs, is to impose some boundary conditions at unification energy, dictated by the geometry of the model, and running down the renormalization group equations (RGE). The geometric constraints impose some exclusion curves on the manifold of possible boundary conditions, but do not fix the boundary conditions entirely: in fact, recent work on the NCG models observed a sensitive dependence on the choice of boundary conditions (within the constraints imposed by the geometry). Moreover, the renormalization group flow typically used in these estimates is the one provided by the one-loop beta function of the minimal Standard Model (or in more recent versions, of effective field theories obtained from extensions of the MSM by right handed neutrinos with Majorana mass terms, that is, the RGEs considered in hep-ph/0501272v3), rather than a renormalization group flow directly derived from a quantum field theoretic treatment of the action functional of the NCG model, the spectral action.

Perhaps more interestingly (as what one is after, after all, are extensions of the MSM by new physics), while the original NCG models of particle physics focussed on the MSM, there are now variants that include new particle: a first addition beyond the MSM was a model with right handed neutrinos with Majorana mass terms, which accounts for neutrino mixing and a see-saw mechanism.

More recently, a very promising program for extending the NCG model was developed by Thijs van den Broek and Walter van Suijlekom (arXiv:1003.3788), for versions with supersymmetry. While their first paper on the subject deals only with the QCD sector of the model, they are now well on their way towards including the electroweak sector.

I apologize for the plot spoiler, but given the occasion I think it is worth mentioning: the model that van den Broek and van Suijlekom are currently developing appears to be fairly close to the MSSM, although it is

*not*the MSSM. In particular, the renormalization group equations in their model are going to be different than the equations of MSSM. In particular this means that the "cheap trick" used so far in the NCG models, of importing RGE equations of known particle physics models and running them with boundary conditions imposed by NCG, will not apply to the supersymmetric version and Higgs estimates within this model will involve a genuinely different RGE analysis. It will be interesting to see how the Higgs sector changes in their version of the NCG model, and whether it gives a more realistic picture close to the observed results.Falsifiability is the most important quality of any scientific theory. Indeed, having explicit experimental data that point out the shortcomings of a theoretical model is the best condition for a serious re-examination of assumptions and techniques used in model building.

Cheers to the LHC, the ATLAS and CMS collaborations, for a great job!

## 5 comments:

It seems fairly urgent to understand what was going on in Shaposhnikov and Wetterich's paper, that managed to predict the mass based on some sort of RG argument.

There is also this interesting extension to Connes' model : arxiv.org/abs/0901.4676

It predicts a light higgs ~ 120GeV and a heavier > 170GeV

No second higgs so far but we'll see...

Any feedback about this extension?

I ponder if the NCG SM can also be seen as a composite Higgs. For instance, in 15.2 of the second book, the Higgs field is build from a sort of composition of two elements a_i(x) and a'_i(x). This is a pattern already visible in the first models with bialgebras, and reminders me of the typical composite Higgs of Contino et al. And in fact now I believe to remember that during my first involvement in the theory, in 1995-96, I was interested on using this separation to understand an antiferromagnetic Higgs field, but that is very ancient history.

There are some arguments around telling that composite higgses could be better candidates for the excess of gamma gamma events in experiment. But to me, the interesting point is that it allows to think on symmetries in each of the composite pieces separately; some people in the net has been worried in the last years for very surprising symmetries that appear not in the yukawa coefficient but in its square root.

@ Mitchell: an answer to your question is available in arXiv:1208.5023

That was quick. Well, if you want a real challenge, try combining the work that Alejandro was talking about (arXiv:1101.5525, arXiv:1111.7232, some earlier RG analysis in arXiv:hep-ph/0601031) with the methods of Sumino (arXiv:0812.2103).

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