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 0.001 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/0609541(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 Yukawacouplings

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.

ha ↔ hbZ2

• 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!