Download Naturalness, Hierarchy and Physics Beyond the Standard Model

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 nonperturbative)
• Unification of gravity and quantum mechanics implies
a minimal length in nature (see last year talk).
New picture
of the
Universe
SM
Extended Higgs sector
Minimal length
From astro-ph/0609541
(J. R. Primack)
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 ha  hb
• This implies a Z 2 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!