Phenomenological aspects of Generation Twisted Supersymmetric Unification

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Phenomenological aspects of Generation Twisted
Supersymmetric Unification
Based on Kenzo Inoue, K.K., Koichi Yoshioka,
JHEP 0607032 and in preparation
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• SUSY is one of the most promising candidates for
  TeV scale new physics
• solves hierarchy problem in the SM Higgs
  potential
• naturally includes DM candidates
• MSSM predicts gauge coupling unification!

Supersymmetric GUT is well motivated

• Neutrino gives important information to the
  SUSY-GUT

very heavy RH neutrinos SU(3)SU(2)U(1) singlets
This seems to prefer SO(10) or higher GUT theories
But GUTs naively have difficulties about flavor
structure
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Several quarks and leptons are unified into a
multiplet
e.g. minimal SU(5) GUT
Minimal SO(10) GUT
Identified to RH ?
Several types of Yukawa coupling unification are
predicted
SU(5) relation
Symmetric Yukawa matrices
Diagonalization matrices
Good for third generation, Completely false for
the others SU(5) relation must be modified
Same contributions to CKM and MNS naively
conflict with experimental results Asymmetric
matrices are useful
GUTs need nontrivial extensions for the flavor
sector
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Contents of the talk

• SO(10) unification with generation twisting
• Third generation fermion masses and sparticle
  spectrum
• Radiative EWSB and bottom mass prediction
• b?s? and t?µ? processes
• LSP nature and cosmological constraint
• Neutralino relic density
• Summary

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SO(10) unification with generation twisting
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MSSMRH? (assuming the seesaw mechanism)
Asymmetric Yukawa matrices seem to be suitable
for CKM and MNS in GUTs
hierarchical
SU(5) relaltion
Highly asymmetric matrices, so-called lopsided
forms,
same order
Babu, Barr 95
But naïve SO(10) GUT cannot accommodate to the
asymmetry
Symmetric contribution to Yukawa matrices
How can we realize the lopsided forms in SO(10)?
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Generation twisting
In generally, there are many candidates for SU(5)
5 in SO(10) (or higher as E6) multiplets
e.g.
16i
10M
1051 55
1051 55
1051 55
. . .
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It is generally difficult to see or test the
flavor structure of the GUT since MG is very
high. But we may probe into the flavor
structure of the GUT through SUSY particle
spectrum.
In the following, we consider the scenario where

• Large top Yukawa coupling mainly comes from

• Difference between CKM and MNS is the result of
  twisted 5

Lopsided Yd and Ye
Twisted 5 structure
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Third generation fermion masses and sparticle
spectrum
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Yukawa structure at the GUT scale
Considered Yukawa matrices (up to relatively
small entries)

• The angle ? parametrizes down-type Higgs mixing

tanß is decreased with Increasing ?

• SU(5) relation is modified by

b-tmass ratio depends on Xd
Includes SU(5) Contributions to Ye and
Yd are different 1-1/3
Georgi-Jarlskog(79)
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Fermion masses in the MSSM
Depend on SUSY spectrum
Threshold corrections
In large tanß, ?b can be very large

Induced by SUSY
ltlt
(cf. non-renorm. theorem)
Hall, Rattazzi, Sarid (94) Blazek, Raby,
Pokorski (95) Tobe, Wells (03)
Sign of µ ? Sign of ?b

(PQ sym. limit)

(R sym. limit)
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Inclusion of radiative EWSB
µ and B are fixed by the following two equations
at MSUSY
GUT scale SUSY breaking parameters
Solving the MSSM (RH?) RGE
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SO(10) motivated boundary conditions for SUSY
breaking parameters
Now, SO(10) representations of the theory are
Independent SUSY breaking parameters at the GUT
scale
Includes SU(5)
mixed Hd
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Bottom quark mass prediction for different Xd
(Xd1)
(Xd-1/3)
green excluded by b?s? decay
blue excluded by t?µ? decay
gray excluded by Higgs mass bound
different sign of µ different sparticle spectrum
different Xd ? different size of ?b?
xd 1 µlt0, hierarchical spectrum (M1/2,
µltltm0) xd-1/3 µgt0, hierarchy must be weakened
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LSP nature and cosmological constraint
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Suppression of the neutralino relic density
In our scenario, LSP is neutralino
Contribution tends to be too large
Xd1 case R? can be small (Suppressed
µ is consistent with mb)
Suppressed Xd case R? should be nearly
1 (only bino-like LSP is allowed) CP-odd Higgs
resonance can suppresses the density
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Xd 1 case

• Xd -1/3 case

Calculated by DarkSUSY

• Higgsino-like LSP suppresses

• CP-odd Higgs mass is relatively light and
  insensitive to m0

• CP-odd Higgs resonance also suppresses the
  density, but where correct mb cannot be achieved.

• Suppression of the density is enough supplied by

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Parameter scan for Xd1 case
Constraints for bottom mass, b?s?, superparticle
masses are included

• Relic density has strong correlation with gaugino
  fraction
• Higgsino components effectively suppress the
  density
• LSP should have negligible higgsino components

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Parameter scan for Xd-1/3 case
Constraints for bottom mass, b?s?, sparticle
masses are included

• The relic density has strong correlation with
  CP-odd Higgs mass
• LSP mass should be near the half of the CP-odd
  Higgs mass
• Sizable t?µ? ratio is expected for relatively
  light SUSY spectrum
• It may be observed near future experimental
  searches

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Summary

• We study low energy remnants of the generation
  twisting.
• Typical sparticle mass spectrum is changed
  depending on the breaking degree of SU(5)
  relation,
• Future searches of SUSY particles and flavor
  violations may be the probe into flavor sector of
  the unified theory

heavy scalars, LSP should have higgsino
components
relatively light spectrum is allowed large LFV
ratio masses of LSP and CP-odd Higgs should be
correlated
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Appendix
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Largely broken SU(5) relation

• SU(5) relation must be broken to reproduce
  observed
• mass pattern of 1st and 2nd generation.

• In generally the breaking appears in large
  asymmetrical entries

Georgi, Jarlskog (79) Ellis, Gaillard (79)
due to group-theoretical factor, non-renorm. o.p.

• Even if the 3-3 entries are unified, bottom-tau
  mass ratio has
• a large deviation from 1 e.g.

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Large threshold correction to the bottom massin
large or moderate tanß regime
?b can be easily large as O(0.5) for tanß50
Sign of µ ? Sign of ?b

(PQ sym. limit)

(R sym. limit)
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Bottom mass prediction without the correction
tanß and ? are correlated
Input parameters
Experimental range
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Implications for superparticle spectrum
Bottom mass prediction and allowed range of ?b
strong correlation due to the lopsided Yd
SU(5) breaking factor xd
Various SUSY spectra are expected depends on xd
and ? (tanß)
e.g.
µlt0 and relatively hierarchical spectrum are
expected for a large value of tanß
xd1
µgt0 and scalars cannot be much heavier
than gauginos and higgsisnos
xd-1/3
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Radiative EWSB conditions
at MSUSY
Solving the RGE

• positive D-term reduce the size of µ

• increasing ?, CP-odd Higgs mass tends to be
  large

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b ? s ? rare decay process
When tanß is not small, three diagrams give
important contributions
Consistent with exp.
The both must be suppressed
or Each of them must be canceled out
(allowed only for µgt0 suppresed Xd case)
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Lepton flavor violating process
RGE between induces irreducible 2-3 mixing in
the mass matrix for scalar lepton doublet
Large 2-3 entry of Ye
D-term contributions amplify non-degeneracy of
the scalar leptons
Non-zero D-term contributions enhances B(t?µ?)
For suppressed Xd case, where relatively light
scalars are allowed, sizable B(t?µ?) is expected
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Xd 1 case (preliminary)
Calculated by DarkSUSY

• Higgsino-like LSP suppresses

• The s-channel pole also suppresses the
• density, but where correct mb cannot be
  achieved.

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Xd -1/3 case

• CP-odd Higgs mass is relatively light and
  insensitive to m0

• Suppression of the density is enough supplied