SUSY Breaking, Composite Higgs
and Hidden Gravity
Ryuichiro Kitano (Tohoku U.)

Talk at ICEPP meeting, April 1-3, 2009, Tokyo, Japan

What's Higgs?

Elementary particle?

1/H
Something else?
Composite, technicolor,unparticle, string, D-brane...

We can use the quantum field theory to describe a particle, but not
something else. The scale H is the cut-off of the theory.

Where is SUSY?

Q

SUSY is symmatry of superspace.
How is it broken? Where are we in this space?

Hints (problems) that we have:naturalness
FCNC

Gravity Mediationcomposite

Gauge or Anomaly Mediation

elementaryat the messenger scale physics.

The composite vs elementary problem....

Supersymmetry is not a solution to the naturalness problem?

Not really. Naturalness and FCNC are problems in different sectors.
It naturally leads us to this picture:composite-problem OKHiggs
SUSY breaking

Gauge mediation

FCNC OK
Quarks Leptons

elementaryThe dynamics to break SUSY contains the Higgs fields.

OK. What's the model?
I think the simplest setup of the framework ofcomposite
-problem OKHiggs
SUSY breaking

Gauge mediation

FCNC OKQuarks Leptons

elementary
is to take the extreme limit of this scenario.
That is SUSY breaking at (a few – 10) TeV and the Higgs boson comesout as a composite particle. Direct gauge mediation provides mass splittings
in the matter sector.
[Dine, Fischler, Srednicki '81, Dimopulos, Raby '81,
Affleck, Dine, Seiberg '85]

Very similar to the QCD.
Higgs
SUSY breaking

Gauge mediation

Quarks Leptons

elementaryQCD(Chiral symmetry breaking)Gauge interaction

Leptons

elementary
We know that there is a powerful tool to describe physics of hadronsat low energy. That is the nonlinear -model.

Nonlinear SUSY

[Volkov and Akulov '73]

Akulov and Volkov found a funny symmetry in the Dirac equation
for a massless fermion  and wrote down an invariant action:

whereThis action is invariant under is a fermionic parameter.
This is supersymmetry. x is the Goldstino field.

What's that?
A simple formulation of nonlinear SUSY.
SUSY is a translational invariance of the superspace.

QIn order to break the symmetry spontaneously, what we need todo is just...

What's that?
A simple formulation of nonlinear SUSY.
SUSY is a translational invariance of the superspace.
Goldstinocoordinate ofSuperPoincare/Poincare

In order to break the symmetry spontaneously, what we need to
do is just putting a brane in the superspace.

Translation of  axis induces a coordinatetransformation on the brane.

That's the nonlinear transformation of Volkov-Akulov.

The matrix
is the induced metric (like?) on the brane.
This transforms as the vielbein under the SUSY transformation.
is invariant.

Now let's go back to the model. We can formulate the setup in this way.

Elementary fields:
Quarks and leptons are superfields (living in the bulk)
Composite fields: nonlinearly transform under SUSY
Brane localized field.
No superpartners!
We can introduce the Higgs boson as a brane localized field.
Higgsinoless Supersymmetry! [Graesser, RK, Kurachi in progress]

SUSY invariant Lagrangian
For elementary fields such as gauge fields and quarks/leptons, theLagrangian is the same as the usual MSSM Lagrangian:Kinetic terms

We can also write down brane localized kinetic terms:

These are nothing but the soft SUSY breaking terms.

SUSY invariant Lagrangian 2
For the Higgs boson, one can write down an invariant action:
Brane location

Kinetic term
Higgs potential
Covariant derivative made of the vielbein Aa. The action needs to beinvariant under general coordinate transformation induced by SUSY.
There is no -problem because there is no Higgsino!
The Higgs boson mass is a free parameter. No relation to the gauge coupling.
No SUSY finetuning problem.
(actually I hide it in the unknown dynamics.)

SUSY invariant Lagrangian 3
Bulk to brane interaction –Yukawa interactions.

We don't need two kinds of Higgs fields to write down theYukawa interactions.

We could write down a SUSY invariant action without Higgsinos
by compensating the SUSY transformation by the Goldstino.
This action serves as the effective theory of the framework:
Higgs
SUSY breaking

Gauge mediation

Quarks Leptons

elementary
But.... SO WHAT?
Isn't there any interesting prediction other than there isn't Higgsino?
The Higgs mass, mass spectrum are all free parameters.....

Hidden Gravity
The most interesting possibility of this scenario is that we may be able
to access the SUSY breaking sector directly at the LHC.
What kind of resonances do we expect to see?

In QCD,

Compositeresonanceelementary

In the nonlinear sigma model of chiral symmetry breaking, there isa formulation for the vector resonance (the  meson), called
Hidden Local Symmetry[Bando, Kugo, Uehara,
Yamawaki, Yanagida '85]

in which the resonance (massive vector boson) is consistently introduced
as a gauge boson of the unbroken global symmetry (SU(2)V).

The SUSY version of that is

Hidden Gravity(massive spin-2 resonance)
because the unbroken global symmetry is the Poincare symmetry.

Production of composite particles in the SUSY breaking sector

Composite

Spin-2 resonance!!!

elementaryWe can follow exactly the same procedure of introducing the  meson inthe chiral Lagrangian.
As we have seen, there is an operator made of Goldstino which transforms
as a metric under the global SUSY transformation.
(don't be confused!)
One can easily introduce a massive graviton field on the brane by using
the “metric.”
mass term“metric”
gravitonThis is invariant under general coordinate transformation even though
there is a mass term.
Global SUSY invariant formulation of the massive graviton.

Is that a good particle?
Well, at least one can consistently introduce it without spoiling thecalculability (perturbative unitarity).
s-wave amplitudes-wave amplitude

detA

sumgraviton contribution(f: decay constant)
The spin-2 particle partially cancel the grow of the scattering
amplitude of  --> That's the same property as the  meson.

Massive Graviton (SUSY version) at the LHC
The resonance couples strongly to hadrons (Goldstino, Higgs boson).

invisible

hh/ZZ/WW modes

Br(Graviton -->hh) ~ 0.1

(pp-->Graviton-->hh)(preliminary)These are typical signatures forThe Large Extra Dimension (invisible mode)
The Randall-Sundrum model (hh/ZZ/WW modes)

Well, it is probably true that the spin-2 resonance is a signature of
the enlarged spacetime. So,

Discovery of graviton (massive spin-2)

It can be SUSY!

Don't be confused that we find both SUSY and extra-dim. Yes, SUSY isan extra-dim!

Summary
I think this is a good framework.
CompositeHiggs
SUSY breaking

Gauge mediation

Quarks Leptons

Elementary
We may see many unconventional SUSY signals at the LHC.