Seesaw for the Higgs boson Xavier Calmet Université Libre de Bruxelles

Outline Review the motivations for physics beyond the standard model. What do we know for sure? Some minimal modifications of the Standard Model can address these issues Modification of short distance physics Modification in the Higgs sector A gateway to new physics Conclusions

Motivations for new physics

Guiding principles for physics beyond the SM Guiding principles for model building have changed. Till ‘ 03 or so hierarchy and naturalness were the main problems to address: why is the weak scale so small compared to the Planck scale and why is the Higgs boson ’ s mass stable under radiative corrections? Indeed if quantum field theories are only an “ effective tool ” (Wilsonian approach) one has to explain small numbers!

Guiding principles for physics beyond the SM after 2003 Post landscape era: fine-tuning is allowed ( or required: anthropic or statistical arguments). More important we have experimental evidence that the hierarchy and naturalness problems are not necessarily valid guidance principles: Hints from the cosmological constant: not zero and small: unnatural (but observed!!). Effective theories argument would imply new physics at eV! No sign of it! Next surprise: light Higgs and no SUSY (or little Higgs)?

Personal point of view: within the framework of a renormalizable quantum field theory, fine-tuning or hierarchy problems make no sense: a parameter is measured at some scale and one can compute its running. So what is the meaning of small or big? It ’ s an experimental question. There may be an esthetic reason against the Higgs: only fundamental scalar? But main issue is the negative squared mass: it ’ s never free to break a symmetry. We can hope that the LHC will reveal the mechanism that triggers the Higgs mechanism.

What do we know for sure? Two experimental facts: There is dark matter.

What do we know for sure? Two experimental facts: There is dark matter. Most probably dark energy exits as well. Mathematical consistency of the standard model implies that effectively there is a scalar degree of freedom in the standard model (or S matrix is non- perturbative) Unification of gravity and quantum mechanics implies a minimal length in nature (see last year talk).

New picture of the Universe From astro-ph/ (J. R. Primack) SM Extended Higgs sector Minimal length

How to implement these facts in the Standard Model? Minimal length: modify spacetime at short distance: one option is a noncommutative spacetime. What are the physical consequences? New insight for the cosmological constant. What about the electroweak symmetry breaking: extend the Higgs sector. Quite natural to expect that dark matter couples to the Higgs boson, if not it will be very difficult to ever produce it in a collider.

Gravity on noncommutative spaces Hypothesis:  is a constant of nature and it has the same value in every coordinate frame. Well if that is the situation, what are the coordinate transformations allowed by the NC algebra: Let us consider the transformations: and study the NC algebra: It is invariant iff The solutions are: They form a subgroup of 4-vol. preserving coord. transf.

If there is an expansion in  the action must take the form: When we vary the action with respect to the metric, we have to impose the unimodular condition. The eqs of motion are: Using the Bianchi Identities and the conservation of the energy-momentum tensor, we find:

This differential equation can be easily integrated: Plugging this back in the equations of motion, one obtains Remarkable: on a canonical NC spacetime: the cosmological constant is an integration constant uncorrelated to parameters of the action!

Get ready for a bit of speculation!

If one quantized unimodular gravity action, one finds an uncertainty relation for the cosmological constant and the volume: Now on a NC spacetime, the volume is “quantized”, the number of fundamental cells is expected to fluctuate The volume of spacetime then fluctuates with the number of cell In other words and one thus finds: Or assuming that the scale for NC is the Planck scale: which is of the right order of magnitude!!! (critical assumption: natural value for  is 0, plausible by Baum and Hawking.)

Back to the SM of particle physics Let me assume that somehow gravity is taken care of at the quantum level by e.g. spacetime noncommutativity or nonperturbative effects: There is a good chance that Nature is indeed described by renormalizable quantum field theories. The remaining issue of the SM is to understand why the Higgs mechanism takes place.

Seesaw Higgs Mechanism

Seesaw for Higgs Let me consider a generic 2 Higgs doublets model Diagonalization of the mass matrix: Is there a negative root?

Decoupling case: Breaks SU(2) x U(1)Decouples Fine-tuning of the Yukawa couplings

Degenerate case: Scalar potential: Yukawa sector:

Let me diagonalize the mass matrix: Let me assume that the action is invariant under This implies a symmetry for h and H.

In a compact notation: Mass spectrum

Phenomenology Higgs production at LHC Dark matter candidate!

A gateway to a hidden sector

Higgs sector is fascinating: Higgs mass term is the only super-renormalizable term in the SM: door to a hidden sector. New option to break the EW: e.g. hidden technicolor sector Connection to extra-dimension (J. van der Bij recent works)

A simple model Couple a new sector in minimal way This operator can impact Veltman’s relation It improves naturalness of the SM Consider e.g. SM replica model

Different options! Implies interesting new phenomenology e.g.: and dark matter candidates

New Guiding principles and Grand Unification SO(10) is viable, again due to fine tuning in Higgs sector

Conclusions There are two missing blocks in High Energy Physics. Dark energy might just be a cosmological constant which is connected to a minimal length. On a noncommutative spacetime its value is arbitrary. Further hand waving arguments could explain its value. Electroweak symmetry sector is the only SM one which has not be tested yet. Possible connection to hidden sectors/dark matter: LHC will produce DM in most of the scenarios. Were the guiding principles right? We will have answers soon!