1. Phenomenology of Supersymmetric Gauge-Higgs Unification
Sylvain Fichet
LPSC Grenoble
Collaboration : Felix Brümmer (IPPP Durham), Arthur Hebecker (Heidelberg) and Sabine Kraml (LPSC)
Arxiv :

2. Gauge-Higgs Unification
Theory
Gauge-Higgs Unification 2
What is Gauge-Higgs Unification ?
And with supersymmetry ?
4D spin 1 : gauge
4D spin 0 : Higgs
[Review : ]
5D vector superfield D vector superfield & 4D chiral superfield
4D spin 1 : gauge
4D spin 0 : Higgs

3. SUSY GUTs with Gauge-Higgs Unification
Theory
SUSY GUTs with Gauge-Higgs Unification 3
Where SUSY GHU can appear ?
In orbifold SUSY GUTs
SUSY GUTs motivated by couplings unification
Extra dimensions motivated by doublet-triplet problem, GUT group breaking, proton decay
(5D SU(6) GHU [Burdman, Nomura hep-ph/ ] )
A top-down motivation : SUSY GUT with GHU can naturally come from classes of heterotic strings model.

4. SUSY GUTs with Gauge-Higgs Unification
Theory
SUSY GUTs with Gauge-Higgs Unification 4
Natural way to break SUSY ?
With Radion Mediated SUSY breaking (RMSB)
[Chacko, Luty hep-ph/ ]
Radion T = field associated to extra dimension fluctuation
Compactification implies SUSY breaking :
(radion )
(chiral compensator : gravity effect)
with
Anomaly Mediation contributions are generated at one-loop

5. SUSY GUTs with Gauge-Higgs Unification
Theory
SUSY GUTs with Gauge-Higgs Unification 5
SUSY GUTs with Gauge-Higgs Unification and RMSB generically implies :
at the SUSY breaking scale.
Solves the mu-problem
Giudice-Masiero mechanism [Giudice, Masiero ‘88 Phys.Lett.B206: ]
Reminder :

6. 5D complete realization : gauge-Higgs sector
Theory
5D complete realization : gauge-Higgs sector 6
5D SUSY GUT with SU(6) GHU [Burdman, Nomura hep-ph/ ]
Radius T of the 5th dimension stabilized by an unknown mechanism :
and break the SU(6) adjoint :
2 Higgs doublets

7. 5D complete realization : gauge-Higgs sector
Theory
5D complete realization : gauge-Higgs sector 6
5D SUSY GUT with SU(6) GHU [Burdman, Nomura ’03 hep-ph/ ]
Radius T of the 5th dimension stabilized by an unknown mechanism :
and break the SU(6) adjoint :
2 Higgs doublets
It implies the high-scale relations :
Negative conclusions :
no EWSB
[Choi et al. hep-ph/ ]
But one contribution was not taken into account !

8. 5D complete realization : gauge-Higgs sector
Theory
5D complete realization : gauge-Higgs sector 7
In odd number of dimension, a new term in the Lagangian is allowed :
the Chern-Simons term
e.g. in 5D non-susy : [Review : ]
Fixed in a full theory, but here parametrized with free coefficient .
The high-scale relations become :
[Hebecker et al , Brümmer et al ]
For theory consistency : and
Sign ambiguity :

9. 5D complete realization : matter sector
Theory
5D complete realization : matter sector 8
What about matter fields ?
Matter in the bulk, but can be confined if massive
4D yukawas come from the overlap with Higgs field.
can generate mass hierarchy
for matter fermions
Branes (4D)
Gauge-Higgs
3rd gen
1,2nd gen
Bulk

10. 5D complete realization : matter sector
Theory
5D complete realization : matter sector 8
What about matter fields ?
Matter in the bulk, but can be confined if massive
4D yukawas come from the overlap with Higgs field.
can generate mass hierarchy
for matter fermions
What about soft scalar parameters ?
Only bulk matter couples
to SuSy breaking fields.
similar hierarchy for soft scalars :
, large,
others negligible.
Branes (4D)
Gauge-Higgs
3rd gen
1,2nd gen
Bulk

11. Theory Summary To sum up… Orbifold SUSY GUT with GHU + RMSB9
To sum up…
Orbifold SUSY GUT with GHU + RMSB
Model with 5D SU(6) GHU and Chern Simons term :
Confinement of matter fields controls
mass hierarchies (yukawas couplings) and
soft scalar parameters.
Bulk
Gauge-Higgs
3rd gen
1,2nd gen

12. How to calculate the spectrum of such models ?
Phenomenology
Spectrum calculation 10
How to calculate the spectrum of such models ?
Use a spectrum calculator… (SuSpect) [hep-ph/ ]
…but the pattern of input and constraints is different from other models :
Usually : and calculated from the 2 equations of Higgs potential minization, at each iteration.
But in our model : fixed from high scale relation…

13. How to calculate the spectrum of such models ?
Phenomenology
Spectrum calculation 10
How to calculate the spectrum of such models ?
Use a spectrum calculator… (SuSpect) [hep-ph/ ]
…but the pattern of input and constraints is different from other models :
Usually : and calculated from the 2 equations of Higgs potential minization, at each iteration.
But in our model : fixed from high scale relation…
First solution : compute and at each iteration.
But unstable for ! (Potential fix : fixed point => dichotomy)
Second solution : Simply impose at high energy.
input parameters : …
+ matter sector parameters (in the 5D model : 2 mixing angles and )

14. Phenomenology Scans and constraints Scans over11
Scans over
with 4 sign combination : and
Constraints :
Theoretical (verified in Suspect) : EWSB, CCB, tachyons
Collider experiments :
Mass bounds from LEP [
B-physics (2σ):
[CDF hep-ex]
[HFAG hep-ex/ ]
Dark matter (3σ):
[WMAP astro-ph]

15. Scans and constraints Phenomenology Scan with LSP : red : blue :12
Scan with
LSP :
red :
blue :
green :
Points excluded by B-physics or too light
~ similar result with
No points for the 2 other combinations

16. Why such sign combinations ?
Phenomenology
RGE analysis 13
Why such sign combinations ?
We have :
And dominated by
The overall sign is fixed by
For a given , only one is allowed.
> 0
EWSB
RGE
GHU

17. Why such sign combinations ?
Phenomenology
RGE analysis 13
Why such sign combinations ?
We have :
And dominated by
The overall sign is fixed by
For a given , only one is allowed.
Which sign is selected depends on running.
is dominated by the gluino mass :
Roughly universal running
Only the initial value matters.
> 0
EWSB
RGE
GHU

18. RGE analysis Phenomenology If large and positive :14
If large and positive :
If small or negative :

19. Phenomenology RMSB parameter space15
RMSB parameters for the same points :
is , is not too large wrt
No points for !

20. ! Phenomenology Relic density16
Dark matter relic density : 3σ WMAP measurement
Assuming standard cosmology !
Not enough
Good
Too much !

21. Mass spectrum and decays
Phenomenology
Mass spectrum and decays 17
Masses :
3 possible LSPs
small 2 1

22. Mass spectrum and decays
Phenomenology
Mass spectrum and decays 17
Masses :
3 possible LSPs
small
SFOS dilepton 2 1
65 %
30 %
~50 %

23. CONCLUSION : TO-DO LIST : SUSY GHU works,…18
CONCLUSION :
SUSY GHU works,…
…has a particular mass spectrum,
… and has a good potential of discovery at LHC
TO-DO LIST :
Discrimination among other models
See what happens in warped geometry (holographic models…)
Include a massive right-handed neutrino

24. Thanks for your attention !

25. EXTRAS

26. Constraint with g-2

27. Examples of mass spectrum

28. Fixed point vs dichotomy
f(x) x
f(x) x
f(x)-x x 1 2 3

29. Algorithm GUT scale EWSB scale Mz scale minization, compute or Phys.
masses/couplings
Check : EWSB
Check :
Spectrum
& guess of
Exp. data
Sparticles mass
matrices
diagonalization
Choice of SuSy breaking model :
high-scale boundary conditions
SuSy finite corrections
to τ, b, t &
sparticles masses
Low scale values modified
iteration

30. A mSUGRA example : Higgs Gauginos Sparticles
Gluino dominated squark running
Radiative EWSB

31. Higgs sector Higgs potential (after some gauge rotations) :
-potentiel bounded from below :
-non-trivial minimum :
Minimization :
with

32. Higgs sector The bilinear parameter µ
The bilinear parameter B (susy breaking)
Higgs masses (susy breaking)
with

33. Interesting features of other RGES
Superpotential parameter corrections are proportional to the parameters themselves :
All susy-breaking parameters depend on gaugino masses
Squark masses receive large negative corrections from the gluino mass :
mass receives large positive corrections from the top yukawa :
with

34. Couplings and sparticles masses
Yukawas
Trilinear couplings (susy breaking)
Sparticle masses (susy breaking)