Phenomenology of Supersymmetric GaugeHiggs Unification

1
Phenomenology of Supersymmetric Gauge-Higgs
Unification

• Sylvain Fichet
• LPSC Grenoble
• Collaboration Felix Brümmer (IPPP Durham),
  Arthur Hebecker (Heidelberg) and Sabine Kraml
  (LPSC)
• Arxiv 0906.2957

2
Gauge-Higgs Unification
Theory
2

• What is Gauge-Higgs Unification ?
• And with supersymmetry ?

4D spin 1 gauge
4D spin 0 Higgs
Review 0704.0833
5D vector superfield 4D
vector superfield 4D chiral superfield
4D spin 1 gauge
4D spin 0 Higgs
3
SUSY GUTs with Gauge-Higgs Unification
Theory
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/0210257
  )
• A top-down motivation SUSY GUT with GHU can
  naturally come from classes of heterotic strings
  model.

4
Theory
SUSY GUTs with Gauge-Higgs Unification
4

• Natural way to break SUSY ?
• With Radion Mediated SUSY breaking (RMSB)
• Chacko, Luty hep-ph/0008103
• 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
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.B206480-484
• Reminder

6
Theory
5D complete realization gauge-Higgs sector
6

• 5D SUSY GUT with SU(6) GHU Burdman, Nomura
  hep-ph/0210257
• Radius T of the 5th dimension stabilized by an
  unknown mechanism
• and break the SU(6) adjoint
• 2 Higgs doublets

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Theory
5D complete realization gauge-Higgs sector
6

• 5D SUSY GUT with SU(6) GHU Burdman, Nomura 03
  hep-ph/0210257
• 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/0312178
• But one contribution was not taken into account !

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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 0805.1778
• Fixed in a full theory, but here parametrized
  with free coefficient .
• The high-scale relations become
• Hebecker et al. 0801.4101, Brümmer et al.
  0906.2957
• For theory consistency and
• Sign ambiguity

9
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

10
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.

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Theory
Summary
9

• 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.

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Phenomenology
Spectrum calculation
10

• How to calculate the spectrum of such models ?
• Use a spectrum calculator (SuSpect)
  hep-ph/0211331
• 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

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Phenomenology
Spectrum calculation
10

• How to calculate the spectrum of such models ?
• Use a spectrum calculator (SuSpect)
  hep-ph/0211331
• 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 gt dichotomy)
• Second solution Simply impose
  at high energy.
• input parameters
  
• matter sector parameters (in the 5D model 2
  mixing angles and )

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Phenomenology
Scans and constraints
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• Scans over
  
• with 4 sign combination
  and
• Constraints
• Theoretical (verified in Suspect) EWSB, CCB,
  tachyons
• Collider experiments
• Mass bounds from LEP http//lepsusy.web.
  cern.ch/lepsusy/
• B-physics (2s)
• CDF 0712.1708 hep-ex
• HFAG hep-ex/0603003
• Dark matter (3s)
• WMAP 0803.0586 astro-ph

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Scans and constraints
Phenomenology
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

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RGE analysis
Phenomenology
13

• Why such sign combinations ?
• We have
• And dominated by
• The overall sign is fixed by
• For a given ,
  only one is allowed.

GHU
RGE
EWSB
gt 0
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RGE analysis
Phenomenology
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.

GHU
RGE
EWSB
gt 0
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RGE analysis
Phenomenology
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• If large and positive
• If small or negative

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Phenomenology
RMSB parameter space
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• RMSB parameters for the same points
• is , is not too large
  wrt
• No points for !

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Phenomenology
Relic density
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• Dark matter relic density 3s WMAP measurement
• Assuming standard cosmology !

Not enough
Good
Too much
!
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Phenomenology
Mass spectrum and decays
17

• Masses
• 3 possible LSPs
• small

2
1
0
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Phenomenology
Mass spectrum and decays
17

• Masses
• 3 possible LSPs
• small
• SFOS dilepton

2
65
30
1
50
0
23
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

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• Thanks for your attention !

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• EXTRAS

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Constraint with g-2

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Examples of mass spectrum
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Fixed point vs dichotomy

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Algorithm
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A mSUGRA example
Higgs Gauginos Sparticles
Gluino dominated squark running
Radiative EWSB
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Higgs sector

• Higgs potential (after some gauge rotations)
• -potentiel bounded from below
• -non-trivial minimum
• Minimization

with
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Higgs sector

• The bilinear parameter µ
• The bilinear parameter B (susy breaking)
• Higgs masses (susy breaking)

with
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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
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Couplings and sparticles masses

• Yukawas
• Trilinear couplings (susy breaking)
• Sparticle masses (susy breaking)