TeV scale mirage mediation for natural little hierarchy

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TeV scale mirage mediation for natural little
hierarchy

• Ken-ichi Okumura
• Kyushu University
• In collaboration with Kiwoon Choi, Kwang-Sik
  Jeong, Tatsuo Kobayashi

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Low energy supersymmetry is the most attractive
extension of the SM

• Solution of gauge hierarchy problem
• Gauge coupling unification is predicted
• EW symmetry is broken radiatively
• Lightest SUSY particle (LSP) is stable with
  R-parity ?Dark Matter
• Light higgs boson (100 GeV) ? EW precision test

Supersymmetry must be broken softly at 100
GeV1TeV ?hierarchy problem
How to communicate SUSY breaking to visible
sector is most relevant to phenomenology.
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Mirage mediation
K.Choi, A.Falkowski, H.P.Nilles, M.Olechowski,
and S.Pokorski
K.Choi, A.Falkowski, H.P.Nilles and M.Olechowski
M.Endo, K.Yoshioka, M.Yamaguchi
K.Choi, K-S.Jeong, KO

• Mirage mediation
• Moduli mediation Anomaly mediation

similar order
Tree level effect in SUGRA
1-loop effect in SUGRA
A class of string inspired models (e.g. KKLT)
realizes such a situation generally.
Modulus mediation
Anomaly
Phenomenological consequence is totally different
from each of mediation schemes.
SUSY breaking
Our world
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Plan of talk

• Mirage mediation
• Mirage unification of soft masses
• Little SUSY hierarchy problem and TeV scale
  mirage mediation
• Conclusion

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Mirage mediation is generic consequence of
modulus stabilization
Mirage mediation is a consequence of two simple
assumptions

• Gauge coupling modulus (or dilation) is
  stabilized by
• non-perturbative effect.
• ii) SUSY is broken by a brane-localized source
  sequestred
• from observable sector.

e.g. KKLT-type modulus stabilization
Bulk CY
SUSY breaking brane
Warped throat
Visible sector of 4D cut-off
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4D effective action
Volume
From sequestered SUSY breaking brane
Gauge modulus
From T-independent flux or T-independent gaugino
condensation
From T-dependent instanton effects or
T-dependent gaugino condensation
Independently of the detail of SUSY breaking, in
low energy limit,
Should be tuned to make final vacuum energy
density to be nearly zero
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Little hierarchies from modulus stabilization
Little hierarchy structure
is a generic consequences of the two assumption
Anomaly mediation
Modulus mediation
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Mirage unification of soft masses
K.Choi, K-S. Jeong, KO (2005)
Just below the unification scale
Anomaly mediated contributions
Modulus mediated contributions
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Modulus mediated contributions
rational numbers of extra dimensions
Discretized in unit of gaugino mass (up to small
corrections).
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Renormalization group running of gaugino mass
Compare formulas at scale µ,
Because quantum correction in modulus
contribution has exactly same form as anomaly
mediation, they cancel at scale,
?This does not depend on the choice of gauge
group
Their sum can be rewritten as,
Anomaly mediation only shifts the mediation scale
of modulus mediation!
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No new fields (other than modulus) below the
unification scale.
Gaugino unification is mirage , not physical
threshold.
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Renormalization group running of A term and soft
mass
For the first and second generations (y 0) and
Yukawa coupling which satisfy the following
relation,
We obtain similar expressions,
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Compared other SUSY breaking scenarios, e.g.
mSUGRA, GMSB, AMSB, Mirage mediation gives more
compressed superparticles spectrum
Dark matter Y.G. Kims talk
Light higgsino and pseudo scalar Higgs
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little SUSY hierarchy problem
Log running of from the cut-off
M_Z scale
is natural
tuning
Tension !
The lightest Higgs boson mass gt 114 GeV
Tree lt M_Z2
Loop
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Radiative EW symmetry breaking
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Example in CMSSM
Fine-tuning parameter
Worse than a few !
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TeV scale mirage mediation for natural little
hierarchy
K.Choi, K-S.Jeong, T.Kobayashi, KO (2005)
R.Kitano, Y.Nomura (2005)
Suppose
and
With , can be naturally
close to
even when
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(No Transcript)
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Argument by A.Pierce and J.Thaler (2006)
For the models described above,
It is likely that a brane-localized source of
SUSY breaking gives , so
T
T
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But this difficulty of obtaining can
be avoided in models with modulus-(heavy)
dilaton mixing
vev of heavy dilaton fixed by flux
are relatively rational number ( Im(S) axionic ).
can be achieved even for a
sequestered SUSY breaking brane stabilized at the
end of throat (n_P 0).
( General aspects of modulus-dilaton mixing
Talk by T.Higaki

H.Abe )
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Natural Bµfrom nonperturbative effects
Forbid by symmetry which is broken by
nonperturbative effects
We naturally have,
and are rational numbers.
Discrete choice realizes
.
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Two possibilities for in the little
hierarchy
In the above model, and pattern
(I) requires fine-tuning beyond the control of
the model.
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SM Higgs mass bound can be evaded with tuning
less tan 10.
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Conclusion

• Mirage mediation is generic in modulus
  stabilization.
• Compressed SUSY spectrum leads to distinctive
  phenomenology.
• -gt Talk by Y.G.Kim for dark matter
• TeV mirage mediation can be realized with
  sequestered SUSY breaking brane by
  modulus-dilaton mixing.
• Better than 10 tuning in EW symmetry breaking is
  compatible with MSSM.
• (and gauge coupling unification)