Transcript Recent Progress in 4 Dimensional GUT - kyoto

𝐸6 Grand Unified Theory
and Family Symmetry
with Spontaneous CP Violation
Nobuhiro Maekawa (Nagoya Univ. KMI)
with M. Ishiduki, S.-G. Kim, K. Sakurai, A. Matsuzaki, T. Yoshikawa,
H. Kawase, T. Takayama, Y. Muramatsu, Y. Shigekami
1.
2.
3.
4.
5.
6.
7.
Introduction
𝑬𝟔 Grand Unified Theory
Family Symmetry
Spontaneous CP Violation
Predictions (FCNC and Nucleon decay)
Impact of LHC
Summary
Overview of this talk

𝐸6 grand unified theory (GUT)
Various hierarchies of quark and lepton masses and
mixings can be explained. (𝑈𝑒3 ~𝜆)

𝐸6 GUT+non-Abelian family symmetry
The explanation is so natural that realistic Yukawa
couplings can be realized after breaking the symmetries.
Modified universal sfermion masses are predicted.
1 𝑚3 ≪ 𝑚 is interesting.
a. light stop… weak scale stablity
b. heavy sfermion…suppress FCNC, CP
2. All FCNC are sufficiently suppressed.
3. Several are within reach of future exp.
4. New type of SUSY CP problem looks serious.
𝑚2
.
.
2
2
𝑚10 =
.
𝑚
. ,
.
.
𝑚3 2
𝑚2
.
.
2
2
𝑚5 = .
𝑚
.
.
.
𝑚2
Overview of this talk

𝐸6 GUT+family sym. with sp. CP violation
(Discrete sym. is introduced.)
Not only old type but also new type of SUSY CP problems
can be solved.
Several bonus (light up quark, 𝑉𝑢𝑏 ~𝜆 4 , predictive power)
Examining the neutrino sector
Same predictions as the usual 𝐸6 GUT but non-trivial.
Introduction
Grand Unified Theories
２ Ｕｎｉｆｉｃａｔｉｏｎｓ

Gauge Interactions

Matter
Experimental supports for both unifications
GUT is promising
Grand Unified Theories

Unification of gauge interactions
quantitative evidence:
Non SUSY

SUSY GUT
Unification of matters
qualitative evidence:
have stronger hierarchy than
hierarchies of masses and mixings
lepton >>quark (in hierarchies for mixings)
ups >> downs, electrons >> neutrinos (in mass hierarchies)
Masses & Mixings and GUT
4
Log[Mf/GeV]
2
0
-2
-4
-6
-8
-10
-12
180
160
140
120
100
80
60
40
20
0
up
do wn
1st c h arg e d l e pto n
2nd n e u tri n o
3rd
up
down
u, c, t
Strongest
Neutrinos Weakest
e, μ，τ Middle
d, s, b
Middle
charged neutrino
lepton
CKM
small mixings
MNS
large mixings
These can be naturally realized in SU(5) GUT!!
SU(5) SUSY GUT
Albright-Barr
Sato-Yanagida…
have stronger hierarchy than
Stronger hierarchy leads to smaller mixings
Quark mixings(CKM)
Lepton mixing(MNS)
Mass hierarchy and mixings

Stronger hierarchy leads to smaller mixings
Stronger hierarchy
Smaller mixings
SU(5) SUSY GUT
have stronger hierarchy than
Stronger hierarchy leads to smaller mixings
Quark mixings(CKM)
Lepton mixing(MNS)
Good agreement with masses & mixings
𝐸6 Grand Unified Theory
The assumption in SU(5) GUT
10𝑖 have stronger hierarchy than 5𝑖
can be derived.
Various Yukawa hierarchies can be induced from one
Yukawa hierarchy in 𝐸6 GUT.
Ｕｎｉｆｉｃａｔｉｏｎ
Three of six
Guisey-Ramond-Sikivie,
Aichiman-Stech, Shafi,
Barbieri-Nanopoulos,
Bando-Kugo,…
become superheavy after the breaking
Once we fix
three light modes of six
,
are determined.
We assume all Yukawa matrices
Milder hierarchy for
Bando-N.M. 01
N.M, T. Yamashita 02

fields from
become superheavy.
Superheavy
unless

Light modes
have smaller Yukawa
couplings and milder hierarchy than
•Larger mixings in lepton sector than in quark sector.
•Small
•Small neutrino Dirac masses Suppressed radiative LFV
How to obtain various Yukawas?
SO(10) GUT relations
Large 𝑈𝑒3 ∼ 𝜆
Right-handed neutrinos
• The same hierarchy
LMA for solar neutrino problem
1st Ｓｕｍｍａｒｙ
unification explains why the lepton sector has
larger mixings than the quark sector.(Large 𝑈𝑒3 ∼ 𝜆)
 Suppressed radiative LFV

A basic Yukawa hierarchy
The other Yukawa hierarchies
Hierarchy of
Three
is stronger than that of
come from the first 2 generation of
Family symmetry
All three generation quark and leptons can be unified into a single (or two)
field(s)
By breaking the horizontal symmetry, realistic quark and lepton masses
and mixings can be obtained.
Peculiar sfermion mass spectrum is predicted.
𝑚10
2
𝑚2
=
.
.
.
𝑚2
.
.
𝑚2
. , 𝑚5 2 = .
𝑚3 2
.
.
𝑚2
.
.
.
𝑚2
Family Ｓｙｍｍｅｔｒｙ
Dine-Kagan-Leigh
Pomarol-Tommasini
Barbieri-Hall…
•Origin of Yukawa hierarchy
•Semi-universal sfermion masses to suppress FCNC
• The 1st 2 generation have universal sfermion masses.
• Large top Yukawa coupling
Not sufficient to suppress FCNC
Large neutrino mixings and FCNC
• The universal sfermion masses only for the 1st 2
generation do not suppress FCNC sufficiently
if
．
Universality for all three generations is required!
unification solves these problems
N.M.02,04
• Various Yukawa hierarchies can be obtained
from one basic hierarchy.
Breaking
gives the basic hierarchical structure.
• All the three light
fields come from
and therefore have universal sfermion masses.
Important for suppressing FCNC sufficiently,
because the mixings of
are large.
Ｄｉｓｃｕｓｓｉｏｎ
• Extension to
is straightforward.
All three generation quarks and leptons
are unified into a single multiplet
• If it is local, D term must be cared.
• Peculiar sfermion spectrum
Universal
Different
Experimentｓ
• Any mechanisms for the basic hierarchy.
Extra dimension
Stringy calculation
Froggatt-Nielsen mechanism
(Anomalous U(1))
•
Higgs sector (Doublet-triplet splitting)
Anomalous U(1)
N.M.-Yamashita 02,03
Generic interactions with O(1) coefficients.
Orbifold breaking
2nd Ｓｕｍｍａｒｙ
• In
GUT, one basic hierarchy for Yukawa
couplings results in various hierarchical structures
for quarks and leptons including larger neutrino
mixings.
• Family symmetry can easily reproduce the basic
hierarchy, and suppress FCNC naturally.
• The simpler unification of quarks and leptons
explains the more questions.
larger neutrino mixings
SUSY flavor problem
Spontaneous CP violation
Old and new type SUSY CP problems
can be solved and several bonuses
SUSY CP Problem
Old type

EDM constraints => Real SUSY parameters.
problem is
must
be by
solved
solved
anomalous U(1)
 Complex Yukawa couplings => CEDM
New type
Hisano-Shimizu04
Griffith et.al.09
in E6 GUT with SU(2)
Complex Yukawa =>
is complex generically
Additional (discrete) symmetry solves both problems
Decoupling features of
SUSY CP problem

EDM constraints from 1 loop

CEDM from Hg(neutron) even if
Hisano-Shimizu ‘04
Contributions through stop loop are
not decoupled. Complex Yukawa
couplings induce them generically.
Spontaneous CP violatoin in SU(2) model

Doublets under SU(2) family symmetry
Real
and
and
require non-trivial discrete charge for
.
A solution for
problem
Negative Higgs charges=> massless Higgs
SUSY(holomorphic) zero mechanism
 SUSY breaking induces the non-vanishing
VEV of superheavy positive charged singlet

2
𝑊 = 𝑆𝐻𝑢 𝐻𝑑 + Λ 𝑆 + Λ𝑆𝑍
Additional discrete symmetry
𝑊 = 𝑆𝐻𝑢 𝐻𝑑 + Λ2 1 + 𝐹𝐹 𝑆 + Λ𝑆𝑍
Complex
Non trivial discrete charge for
to forbid
What happens by the discrete symmetry?
real
complex
SUSY zero mechanism
is real ,
is complex
A model with a discrete symmetry
Ishiduki-Kim-N.M.-Sakurai09
Bonus 1
 Real up-type Yukawa couplings
real
CEDM constraints can be satisfied.
 Complex down-type Yukawa couplings
KM phase can be induced.
 The point
: real,
: complex
A model with a discrete symmetry

Bonus 2: small up quark mass is realized.
Usually, to obtain the CKM matrix
Too large 
good value!
A model with a discrete symmetry

Bonus 3?: # of O(1) parameters =9-12
13 physical parameters

One of the relations
Interesting result(perturbation in

)
is obtained
Kawase, N.M 10
This cancellation depends on the adjoint VEV.
(B factory measured the direction of GUT breaking?)

Numerical calculation
Ishiduki-Kim-N.M.-Sakurai09

O(1) coefficients(10 parameters)
Ref:Ross-Serna07 MSSM 2loop RGE
Heavy fields’ contribution must be taken into account.
E6 Higgs sector

N.M.-Yamashita02
Ishiduki-Kim-N.M.-Sakurai
09
E6 can be broken into the SM gauge group.
1, Natural doublet-triplet splitting
2,
,
is realized
3, consistent with the discrete symmetry
Neutrino sector

5 fields at the low energy are determined as 3 massless modes of this 3 × 6 matrix.
.
51
52
53





N.M.-Takayama 11
′
51
0
𝑄𝐵−𝐿 𝜆5
0
′
′
51
52
53
−𝑄𝐵−𝐿 𝜆5 0 0
𝜆4
𝜆2 𝜆5+𝑟
3+𝑟
𝜆2
1 𝜆
52
53
𝜆5+𝑟
0
0
𝜆3+𝑟
0
0
′
𝜆𝑟 ≡
𝐻
For lepton doublets, 51 of three massless modes,
53 , because 𝑄𝐵−𝐿 = 0 for lepton doublets.
𝐶
𝐻
′
51 , 51 , 52 , has no mixing with
′
Yukawa couplings of charged lepton in 51 can be obtained through 𝑌𝐶 16𝑖 101 16𝐶
′
Dirac neutrino Yukawa couplings of 51 through 𝑌𝐻 1𝑖 101 10𝐻 is vanishing because
𝑄𝐵−𝐿 = 0.
⟶ 𝑚𝜈𝜇 = 0 That’s a problem.
Fortunately, we have higher dimensional interactions
𝜖 𝑎𝑏 27𝐻 27𝑎 27𝑏 27𝐻 27𝐻 ⟶ 12 101 10𝐻
We have many parameters on the right-handed neutrino masses.
Predictions on neutrino masses and mixings are the same as the usual 𝐸6 GUT.
27𝐻 27𝐻 can couple with many interactions, but the effects are only for the neutrino
sector in the model.
3rd Summary

KM theory is naturally realized by spontaneous CP
violation in E6 GUT with family symmetry
1, Real
and
parameters are realized by
introducing a discrete symmetry.
2, The symmetry solves CEDM problem.
:real
:complex
3, Predicted EDM induced by RGE effect is sizable.
4,
5,
6, E6 Higgs sector consistent with the above
scenario with natural realization of D-T splitting
D term problem

Non vanishing D terms spoil the universality
𝑚2 0
0
𝐷𝑆𝑈(2)𝐻
2
2
𝑚10 = 0 𝑚
+
0
2
0
0 𝑚3 2
1
𝑚2 0
0
𝐷
𝑆𝑈(2)
𝐻
𝑚5 2 = 0 𝑚 2 0 +
0
2
0
0
0 𝑚2
1 0 0
0 −1 0 + 𝐷𝑉 ′
0 0 0
0 0
1
1 0 + 𝐷𝑉 ′ 0
0 −1
0
1
0
0
0
−2
0
0
1
0
0
1
0 + 𝐷𝑉 0
1
0
0
−3
0 + 𝐷𝑉 0
1
0
0
1
0
0
2
0
This may induce too large FCNC.
This problem looks to be serious before LHC.
We expected some hints from LHC.
0
0
1
0
0
−3
Predictions of 𝐸6 × 𝑆𝑈(2)𝐹 × 𝑈(1)𝐴
Flavor physics : Kim-N.M.-Matsuzaki-Sakurai-Yoshikawa 06,08
𝑚3 must be around the weak scale,
because of the stability of the weak scale,
while 𝑚 can be taken larger.
10:
5:
Nucleon decay: Y. Muramatsu-N.M. 13,14
Important prediction of Natural (Anomalous U(1)) GUT
N.M. 01
Nucleon decay via dim. 6 operators is enhanced,
while nucleon decay via dim. 5 is suppressed.
Non universal SUSY breaking

Universal sfermion masses for

Non universaltiy for
fields

Weak scale stability requires
but almost no constraint for
fields
Structures suppressing FCNC for
Small Yukawa couplings
 Small
 Universal sfermion masses for

can increase without destabilizing the weak
scale. (Effective SUSY)

How does FCNC processes take place in this model?
flavor violating
10:
No source of flavor violation
5:
For example, for the right-handed charged slepton sector,
Since 10 contains Q, the form of unitary matrix V is CKM-like. We can parametrize it with
Cabibbo angle λ.
Non decoupling feature of this model (in lepton flavor violation)


By picking up the 3-2 element, the size of τ→μ transition rate is order
.
For μ→eγ, there are two passes to change the flavor μ→e. Both they are order
.
If we raise overall SUSY scale m …
Propagator suppression from 1 or 2 generation becomes stronger, but mass difference
increase. As a result, both transition rate remain finite, and don’t decouple!
Can we discover the LFV
at the future experiments?
 1.0 1011
8
 7.0 10
(exclude)
(exclude)
MEG
experiment
(super-)KEKB
 7.0  109
 1.0 1014
τ→μγ
Detectable, when tanβ is large and
μ→eγ
Detectable if
<400GeV
<250GeV
This model says that
final state lepton tends to be right-handed.

Final state lepton has different chirality from initial one.
q  p  p
ei

p
p
Opposite from
MSSM+
ej
Intermediate state must be right-handed to pick up
the
.
How can we see this feature experimentally?
spin


Lefthanded
e
e
Righthanded
spin


It is possible to check this feature experimentally by measuring the angular distribution
of final state lepton.
Predictions (Quark sector)
The maginitudes are
the same order as of
the RGE effects in the universal mass case.
 New CP phases!!
The CP violation in B meson system may be
detectable

CP violation in B meson
SM
O(0.04)
E6
O(0.006)
<0.15
0.006
<0.01
very small
very small
For
Bd  φKs,η’Ks
is possible.
Gluino contribution is decoupled.
Chargino contribution is not decoupled.
in the limit
O(0.1) deviation in B factory may be confirmed
in SuperB factory.
Summary table of E6 predictions
SM
O(0.04)
E6
O(0.006)
<0.15
0.006
<0.01
very small
Discussions

Strictly speaking,
when
e.g.
This can be consistent with the experiments,
but the predictions can be changed.
If we take
, this model dependent
parts can be neglected.
No weak scale instability!!
Nucleon decay
N.M.-Y.Muramatsu 13,14
Natural(Anomalous U(1)) GUT
N.M. 01
N.M. T. Yamashita, 02









Natural: All the interactions which are allowed by the
symmetry are introduced with O(1) coefficients. (incl.
higher dimensional int.)
We can define the model only by fixing the symmetry of the
model(except O(1) coefficients) . The parameters for the
definition are mainly about 10 charges for the fields.
The predictions are expected to be stable under the
quantum corrections or gravity effects.
This assumption is quite natural.
Infinite number of interactions can be controlled.
Doublet-triplet splitting problem can be solved.
Realistic quark and lepton masses and mixings.
Non trivial explanation for gauge coupling unification.
Anomalous U(1) gauge symmetry plays an essential role
Natural Gauge Coupling Unification
New Explanation for the success




N.M. 01, N.M-Yamashita 02
Fix a model
with
Calculate
Ｃａｌｃｕｌａｔｅ
ｗｉｔｈ
Ａｌｗａｙｓ ｍｅｅｔ ａｔ
a scale
ＭＳＳＭ
Nucleon decay via dim. 6 is enhanced

Unification scale becomes lower.


Proton decay via dimension 6 op.
𝜏 𝑝 → 𝑒𝜋 ∼ 2 − 8 × 1034 years (Λ 𝑈 ∼ Λ 𝐺 /2)
𝜏𝑒𝑥𝑝 𝑝 → 𝑒𝜋 > 1.4 × 1034 years

Generic interactions
GUT model identification by nucleon decay
two important ratios of partial decay widths to identify GUT
model
to identify grand
unification group
to identify Yukawa
structure at GUT scale
GUT
GUT
GUT
: dimension-6 operators which
have anti electron in final state
: dimension-6 operators which
have anti neutrino in final state
𝟏𝟎3 model
points
𝑹𝟐 =
𝟏𝟎𝟒 model
points
𝑹𝟏 =
4th Summary

Observed (or observing)
𝑉13 ∼ 𝜆, ( 𝛿𝑙𝑒𝑝𝑡𝑜𝑛 ∼ 𝑂 1 )
(𝑉𝑢𝑏 ∼ 𝜆4 )
 Not yet
Nucleon decay
FCNC
large
Unfortunately most of FCNC processes are
decoupled when SUSY breaking scale is large.
Impact of LHC
125 GeV Higgs
Stop mass (𝑚3 ) must be larger than 1 TeV
 No SUSY particle
⇒ SUSY breaking scale may be larger than we
expected.
The little hierarchy problem is more serious.
FCNC problem (D term problem) is milder.

The little hierarchy problem
-Very serious problem must be solved!
N.M.-K.Takayama 14
.
Little hierarchy problem

𝑚ℎ ~125 GeV (LHC) → 𝑚𝑡 > 1TeV (𝐴𝑡 ~2𝑚𝑡 )
𝑚𝑡 > 5TeV (𝐴𝑡 ≪ 𝑚𝑡 )
𝑚ℎ 2 ~𝑚𝑍 2 𝑐𝑜𝑠 2 2β

+
3𝐺𝐹 𝑚𝑡 4
2𝜋2
ln
𝑚𝑡 2
𝑚𝑡 2
+
𝐴𝑡 2
𝑚𝑡 2
1−
𝐴𝑡 2
12𝑚𝑡 2
Higgs mass is fixed by 𝐴𝑡 and 𝑚𝑡 at weak energy scale.
Heavy stop leads to parameters tuning
Δ𝑚𝐻𝑢
2~
3𝑦𝑡 2
− 2
8𝜋
2𝑚𝑡 2 + 𝐴𝑡 2 ln
Λ
𝑚𝑡
1
2
≫ 𝑚ℎ 2
𝑚𝑡 = 5TeV, 𝐴𝑡 ≪ 𝑚𝑡 , Λ = Λ𝐺 → O(0.01%) tuning
𝑚𝑡 = 1TeV, 𝐴𝑡 = 2𝑚𝑡 , Λ = Λ 𝐺 → O(0.1%) tuning
𝑚𝑡 = 1TeV, 𝐴𝑡 = 2𝑚𝑡 , Λ~𝑂(Λ 𝑆𝑈𝑆𝑌 ) → O(1%) tuning
Correction depends on 𝐴𝑡 , 𝑚𝑡 at higher scale and Λ.
Low mediation scale and 𝐴𝑡 ~2𝑚𝑡 are preferable.
Low mediation scale scenarios


Gauge mediation
Mass of the messenger particles can be small.
Unfortunately it is difficult to obtain large 𝐴𝑡
Mirage mediation
Choi-Falkowski-Nilles-Olechowski-Pokorski04,
Jeong-Kobayashi-Okumura05, Kitano-Nomura05
Due to the cancellation between anomaly mediation and RG
effects of moduli contribution, the mediation scale can be lower
effectively.
Special boundary conditions are required
𝑀1/2 = 𝐴𝑡 = 2𝑚𝑡
Unfortunately, 𝐴𝑡 is not sufficiently large.
What happens if special boundary conditions are not required?
Cosmological Gravitino Problem
SUSY is still promising
Decay of gravitino produced in early universe spoils
BBN.
Kawasaki-Kohri-Moroi-Yotsuyanagi08
One solution
O(100TeV) gravitino
It decays before BBN!
High scale SUSY
but destabilizes the
weak scale.
Roughly 𝑚3/2 > 50 TeV
What we would like to show

Gravitino mass 𝑚3/2 = O(100) TeV
to solve the cosmological gravitino problem
 The other SUSY breaking parameters = O(1) TeV
for the naturalness
As in mirage mediation
The little hierarchy problem can be less severe.
O(%) tuning is realized.
Point: anomaly mediation cancels the RG contribution.
𝐴𝑡 can be larger without changing ∆𝑚𝐻𝑢 2
Cancellation property of
anomaly mediation

Gaugino mass
RGE
𝑑
𝑀
𝑑𝑡 𝑎
=
1
2
𝑏
𝑔
𝑀𝑎
𝑎
𝑎
8𝜋2
𝑀𝑎 𝜇 |𝑎𝑛𝑜𝑚𝑎𝑙𝑦 =
𝑀𝑎 𝜇 |𝑔𝑟𝑎𝑣𝑖𝑡𝑦 =
𝑏𝑎 𝑔𝑎 2
𝑚3/2
16𝜋2
𝑏𝑎 𝑔𝑎 2
𝑀𝑎 +
𝑀𝑎
8𝜋2
ln
𝜇
Λ
𝑀𝑎 𝜇 = 𝑀𝑎 𝜇 |𝑎𝑛𝑜𝑚𝑎𝑙𝑦 + 𝑀𝑎 𝜇 |𝑔𝑟𝑎𝑣𝑖𝑡𝑦
= 𝑀1/2 +
Λ𝐺
ln
𝑀𝑚𝑖𝑟
=
𝑏𝑎 𝑔𝑎 2
𝜇
𝑀
ln
1/2
8𝜋2
𝑀𝑚𝑖𝑟
𝑚3/2
2𝑀1/2
𝑀1 = 𝑀2 = 𝑀3 = 𝑀1/2
𝑀𝑚𝑖𝑟 ~1 TeV↔
𝑚3/2
𝑀1/2
~60
Cancellation property(no Yukawa)

𝐴𝑖𝑗𝑘
𝐴𝑖𝑗𝑘 𝜇 = 𝐴𝑖𝑗𝑘 −
1
8𝜋2
𝑎
𝛾𝑖 + 𝛾𝑗 + 𝛾𝑘 𝑀1/2 ln
𝜇
𝑀𝑚𝑖𝑟
𝛾𝑖 = 2 𝑎 𝐶 𝑖 𝑔𝑎 2
2
 Scalar fermion mass square 𝑚𝑖
1
𝜇
1
𝜇
2
2
2
2
𝑚𝑖 𝜇 = 𝑚𝑖 − 2 𝛾𝑖 𝑀1/2 ln
− 2 𝛾𝑖 𝑀1/2 ln
4𝜋
𝑀𝑚𝑖𝑟 8𝜋
𝑀𝑚𝑖𝑟
+

3
2 𝑆 ln 𝜇
𝑌
𝑔
40𝜋2 𝑖 1
Λ
2
𝑖 ≠ 𝑡𝐿 , 𝑡𝑅 , 𝐻𝑢
𝑆 = 𝑖 𝑌𝑖 𝑚𝑖 2
These parameters at the mirage scale 𝑀𝑚𝑖𝑟 become gravity
contribution at the cutoff Λ if 𝑆 = 0
What happens for sfermions
with large top Yukawa?


𝐴𝑡 𝜇 = 𝐴𝑡 + 6𝜌 𝐴𝑡 − 𝑀1/2 −
2
1
8𝜋2
𝛾𝐻𝑢 + 𝛾𝑡𝐿 + 𝛾𝑡𝑅 𝑀1/2 ln
𝜇
𝑀𝑚𝑖𝑟
2
𝑚𝑖 𝜇 = 𝑚𝑖 − 𝑘𝑖 𝜌 𝐴𝑡 − 𝑀1/2 1 + 6𝜌 + Σ𝑡 − 𝑀1/2 2
1
𝜇
2
2
− 2 𝛾𝑖 𝑀1 + 𝑘𝑖 𝐴𝑡 − 𝑀1/2 1 + 6𝜌 𝑦𝑡 ln
4𝜋
𝑀𝑚𝑖𝑟
2
2
1
𝜇
2
− 2 𝛾𝑖 𝑀1 ln
𝑖 = 𝑡𝐿 , 𝑡𝑅 , 𝐻𝑢
8𝜋
𝑀𝑚𝑖𝑟
2
2
Special boundary conditions
𝑀1/2 = 𝐴𝑡 = Σ𝑡 ≝ 𝑚𝑡𝐿 2 + 𝑚𝑡𝑅 2 + 𝑚𝐻𝑢 2 → 𝐴𝑡 = 2𝑚𝑡 𝑚𝐻𝑢 = 0
are required to obtain 𝑚𝑖 2 𝑀𝑚𝑖𝑟 = 𝑚2 and 𝐴𝑡 𝑀𝑚𝑖𝑟 = 𝐴𝑡
Generalization of mirage mediation




In the usual mirage mediation, universal sfermion masses are
adopted.
If the conditions 𝑀1/2 = 𝐴𝑡 = Σ𝑡 ≝ 𝑚𝑡𝐿 2 + 𝑚𝑡𝑅 2 + 𝑚𝐻𝑢 2 are
satisfied, any values for the other parameters are OK for
mirage phenomena when 𝑆 = 0.
For example, natural(effective) SUSY type sfermion masses
𝑚32 = 𝑚𝑡𝐿 2 = 𝑚𝑡𝑅 2 = 𝑚𝜏2𝑅 ≪ 𝑚02 = 𝑚𝑖2 (𝑖 ≠ 𝑡𝑅 , 𝑡𝐿 , 𝜏𝑅 )
LHC and FCNC constraints become milder than the usual
mirage mediation with fixed 𝑚3
Asano-Higaki12
In this talk, we do not address 𝑚0 so much because the value
is not so important in our arguments
What happens without special
boundary conditions?
𝑀1/2 = 𝐴𝑡 = Σ𝑡
Without these boundary conditions, the situation becomes
just the situation in which the gravity mediation and anomaly
mediation contribute at the same time.
Sizable anomaly mediation
It is known that anomaly mediation leads to negative mass square
of some of the sfermions. → upper bound of 𝑚3/2
𝑚3/2
𝑀1/2
= 60 ↔ 𝑀𝑚𝑖𝑟 = 1TeV
𝑀1/2 = 2𝑚𝑡 at mirage point
Wide region where
𝑚𝑖2 Λ 𝐺 > 0
in general setup.
𝑚𝑡 /𝑀1/2
Mirage point
Little hierarchy problem
2
2
2
∆𝑚𝐻
= 𝑚𝐻
𝑚𝑆𝑈𝑆𝑌 − 𝑚𝐻
𝑢
𝑢
𝑢
from 𝑚3/2 , 𝑀1/2 , 𝑚𝑡 , 𝐴𝑡 .
We fixed
𝑚3/2
= 60
𝑀1/2
𝑚𝑡 = 2 TeV
𝑚ℎ 2
/∆𝑚𝐻𝑢 2
2
1, O(%) tuning is realized! (←Width of 1% band is O(TeV))
2, Mild dependence on 𝐴𝑡 (Important to obtain heavy Higgs.)
2
𝑚ℎ /2∆𝑚𝐻𝑢
2
𝑚3/2
= 50
𝑀1/2
𝑚3/2
= 70
𝑀1/2
for
𝑚3/2
𝑀1/2
= 50, 60, 70, 80
𝑚𝑡 = 2 TeV
𝑚3/2
= 60
𝑀1/2
𝑚3/2
= 80
𝑀1/2
1, O(%) tuning is realized! (←Width of 1% band is O(TeV))
2, Mild dependence on 𝐴𝑡 (Important to obtain heavy Higgs.)
Little hierarchy problem
2
∆𝑚𝐻𝑢 2 1𝑇𝑒𝑉 = 𝑐0 𝑀1/2 2 + 𝑐1 Σ𝑡 + 𝑐2 𝐴𝑡 + 𝑐3 𝐴𝑡 𝑀1/2

In CMSSM, 𝑐0 = −1.6, 𝑐1 = −0.40, 𝑐2 = −0.082, 𝑐3 = −0.26
∆𝑚𝐻𝑢 2 = −2.34𝑀1/2 2 if 𝑀1/2 = 𝐴𝑡 = Σ𝑡 .

In mirage (anomaly mediation with 𝑚3/2 /𝑀1/2 = 60),
𝑐0 = 0.29, 𝑐1 = −0.40, 𝑐2 = −0.082, 𝑐3 = 0.16
∆𝑚𝐻𝑢 2 = −0.031𝑀1/2 2 if 𝑀1/2 = 𝐴𝑡 = Σ𝑡 .
Reasons for this improvement
1, Smaller coefficients 𝑐𝑖
2, Cancellation (Different signature)
(Naturalness arguments strongly depend on high energy physics)
What happens for other values of 𝑚3/2 /𝑀1/2 ?

What happens for other values of 𝑚3/2 /𝑀1/2 ?
𝑐1 = −0.40, 𝑐2 = −0.082
1, Smaller coefficients 𝑐𝑖
2, Different signature
Improvement is generally expected
Mild dependence on 𝐴𝑡
∆𝑚𝐻𝑢 2 1𝑇𝑒𝑉 = 𝑐0 𝑀1/2 2 + 𝑐1 Σ𝑡 + 𝑐2
𝑐3 2
𝑐0 −
4𝑐2
𝑐3
𝐴𝑡 +
𝑀1/2
2𝑐2
< 0, 𝑐1 < 0, 𝑐2 < 0 → ∆𝑚𝐻𝑢 2 ≠ 0

In CMSSM, 𝑐0 =

With anomaly mediation, 𝑐0 > 0 when 𝑚3/2 ≥ 47𝑀1
2
→ ∆𝑚𝐻𝑢 2 = 0 is possible

2
∆𝑚𝐻𝑢 = 0 and
𝜕∆𝑚𝐻𝑢 2
𝜕 𝐴𝑡
2
= 0 → 𝐴𝑡 ~2𝑚𝑡
Important observation

Gravitino mass 𝑚3/2 = O(100) TeV

to solve the cosmological gravitino problem
The other SUSY breaking parameters = O(1) TeV
for the naturalness
The little hierarchy problem can be less severe.
O(%) tuning is realized.
Point: anomaly mediation cancels the RG contribution.
𝐴𝑡 can be larger without changing ∆𝑚𝐻𝑢 2
If 𝑀𝑚𝑖𝑟 ~ O(TeV), we may observe directly the GUT signatures
through the mass spectrum of the other sfermions than stops.
(ex. D-term contributions of GUT.)
Sizable D-term contribution as a
signature of 𝑬𝟔 × 𝑺𝑼 𝟐 𝑭 × 𝑼 𝟏 𝑨
N.M.-Y.Muramatsu-Y.Shigekami 14
Natural (Effective) SUSY type sfermion masses
10:
5:
Most of models which predict natural SUSY sferimion masses
are suffering from CEDM constraints.
If natural SUSY sfermion masses are observed,
this scenario is implied.
Small deviation from natural SUSY sfermion masses can be
a signature of 𝐸6 GUT with family symmetry.
A signature from sizable D-term contributions
𝑚2 0
0
𝐷𝑆𝑈(2)𝐹
2
2
𝑚10 = 0 𝑚
+
0
2
0
0 𝑚3 2
𝑚2 0
0
𝐷𝑆𝑈(2)𝐹 1
2
𝑚5 = 0 𝑚 2 0 +
0
2
0
0
0 𝑚2
1 0 0
0 −1 0 + 𝐷𝑉 ′
0 0 0
0 0
1
1 0 + 𝐷𝑉 ′ 0
0 −1
0
1 0 0
1 0
0 1 0 + 𝐷𝑉 0 1
0 0 1
0 0
0 0
−3 0
−2 0 + 𝐷𝑉 0 2
0 1
0 0
2
2
2
Δ𝑚10,2
≡ 𝑚10,2
− 𝑚10,1
= −DSU 2
2
2
2
Δ𝑚5,2
≡ 𝑚5,2
− 𝑚5,1
2
2
2
Δ𝑚5,3
≡ 𝑚5,3
− 𝑚5,1
An important prediction
How large D-term can be allowed?
We consider FCNC constraints
F
= −3D𝑉 ′ + 5𝐷𝑉
= −DSU
2 F
2
2
Δ𝑚10,2
= Δ𝑚5,3
0
0
1
0
0
−3
FCNC constraints for mass insertion parameters
mass insertion parameter
diagonalizing matrices 𝑈
for 10 matters
1
𝐿𝑢 ∼ 𝐿𝑑 ∼ 𝑅𝑢 ∼ 𝑅𝑒 ∼ 𝜆
𝜆3
𝜆
1
𝜆2
𝜆3
𝜆2
1
for 5 matters
1
𝐿𝑒 ∼ 𝐿𝜈 ∼ 𝑅𝑑 ∼ 𝜆0.5
𝜆
Constraints from 𝜖𝐾 is the strongest
because decoupling feature is weak.
𝜆0.5
1
𝜆0.5
𝜆
𝜆0.5
1
0
0
FCNC constraints from 𝐾 − 𝐾 mixing(𝜀𝐾 )
Ciuchini et al.
(1998)
mass insertion parameter in this model
𝜆 ∼ 0.22
average down type squark mass : 𝑚𝑑
:constraint from
𝑦=
:constraint from
𝑥=
Result 1
When 𝑚𝑑 = 10 TeV
𝑥 ∼ 𝑦 ∼ 0.1
= D-term can be 1 TeV!
signature of 𝐸6 × 𝑆𝑈 2 𝐹 ×
𝑈 1 𝐴 SUSY GUT model
in future experiments (100
TeV proton collider or muon
collider)
5th Summary

Gravitino mass 𝑚3/2 = O(100) TeV

to solve the cosmological gravitino problem
The other SUSY breaking parameters = O(1) TeV
for the naturalness
The little hierarchy problem can be less severe.
O(%) tuning is realized.
Point: anomaly mediation cancels the RG contribution.
𝐴𝑡 can be larger without changing ∆𝑚𝐻𝑢 2
If 𝑀𝑚𝑖𝑟 ~ O(TeV), we may observe directly the GUT signatures through the mass
spectrum of the other sfermions than stops.
(ex. D-term contributions of GUT.)
 Natural SUSY type sfermion masses may be directly observed.
2
2
2
2
𝑚10,2
− 𝑚10,1
= 𝑚5,3
− 𝑚5,1

An important prediction

D term can be 1 TeV! (𝜖𝐾 )
Summary

GUT is promising
Experimental supports for two unifications

𝐸6 GUT is interesting
An assumption in 𝑆𝑈(5) GUT can be derived.
Various Yukawa hierarchies in SM can be obtained from one hierarchy.

+Family symmetry
Unification of three generation quark and leptons with realistic Yukawa
SUSY flavor problem is solved (Natural SUSY type sfermion masses)

+Spontaneous CP violation
Origin of KM phase can be understand
SUSY CP problem is solved. (Even CEDM constraints can be satisfied.)

Natural (anomalous U(1)) GUT
The doublet-triplet splitting problem is solved under natural assumption.
Summary

Predictions
Observed
𝑉13 ∼ 𝜆, (𝛿 ∼ 𝑂 1 , 𝑉𝑢𝑏 ∼ 𝜆4 )
Not yet
Nucleon decay
Sfermion mass spectrum (Natural SUSY type)
D-term contribution can be a smoking gun.
2
2
2
2
𝑚10,2
− 𝑚10,1
= 𝑚5,3
− 𝑚5,1
Signatures for future flavor experiments?

Future works
Cosmology (Inflation, DM, Baryogenesis etc)
More predictions
Issues (generic int., gauge coupling unif. etc)