Signatures of () SUSY GUT in the past and future

Nobuhiro Maekawa (Nagoya Univ. KMI)

1. GUT is attractive!2. Grand Unified Theory3. Family Symmetry4. Spontaneous CP Violation5. Predictions (FCNC and Nucleon decay)6. Impact of LHC 7. Summary

What I would like to talk today Observed SM parameters suggest GUT. Gauge couplings, quark and lepton masses and mixings GUT ( is also), effective (natural )SUSY spectrum : observed?

tan at GUT scale

Large EDM of neutron Nucleon decay modes can identify Impact of LHC(125GeV Higgs, no signal of SUSY) 　 Large SUSY breaking scale(most of FCNC are decoupled)

Large SUSY breaking scale destablizes the weak scale

Heavy gravitino (100TeV) improves the issue.

Sfermion spectrum can be a signature of GUT.

Cosmological signature?

Thermal leptogenesis is possible in GUT, but not in GUT.

Our existence may be an indirect signature.

→Ishihara’s talk of his master thesis.

IntroductionGUT is attractive!

Grand Unified Theories 　　

Gauge Interactions

Matter

　　

２　Ｕｎｉｆｉｃａｔｉｏｎｓ

Experimental supports for both unifications

GUT is promising

Grand Unified Theories Unification of gauge interactions

quantitative evidence:

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)

Non SUSY SUSY GUT

 

Masses & Mixings and GUT

020

4060

80100

120140

160180

up down chargedlepton

neutrino

1st2nd3rd

- 12

-10

-8

-6

-4

-2

0

2

4

Log[M

f/G

eV

]

updowncharged leptonneutrino

u, c, t Strongest

Neutrinos Weakest e, μ ， τ 　　 Middled, s, b Middle

CKM small mixings

MNS large mixings

These can be naturally realized in SU(5) GUT!!

SU(5) SUSY GUT

Quark mixings(CKM) Lepton mixing(MNS)

have stronger hierarchy than

Stronger hierarchy leads to smaller mixings

Albright-BarrSato-Yanagida…

Mass hierarchy and mixings

Stronger hierarchy leads to smaller mixings

Stronger hierarchy Smaller mixings

SU(5) SUSY GUT

Quark mixings(CKM) Lepton mixing(MNS)

have stronger hierarchy than

Stronger hierarchy leads to smaller mixings

Good agreement with masses & mixings

Grand Unified Theory

The assumption in SU(5) GUT

have stronger hierarchy than

can be derived.

Various Yukawa hierarchies can be induced from one Yukawa hierarchy in GUT.

Bando-N.M. 01N.M, T. Yamashita 02

Ｕｎｉｆｉｃａｔｉｏｎ

Three of six become superheavy after the breaking

Once we fix , three light modes of six are determined.

Guisey-Ramond-Sikivie,Aichiman-Stech, Shafi,Barbieri-Nanopoulos,Bando-Kugo,…

We assume all Yukawa matrices

Milder hierarchy for

fields from become superheavy.

Light modes have smaller Yukawa

couplings and milder hierarchy than

Superheavy

• Larger mixings in lepton sector than in quark sector.• Small• Small neutrino Dirac masses Suppressed radiative LFV

unless

Bando-N.M. 01N.M, T. Yamashita 02

How to obtain various Yukawas?

SO(10) GUT relations

Large

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 ) Suppressed radiative LFV

A basic Yukawa hierarchy

The other Yukawa hierarchies

Hierarchy of is stronger than that of

Three come from the first 2 generation of

Family symmetry

GUT can obtain realistic Yukawa structures so naturally that we can obtain a GUT in which all three generation quark and leptons can be unified into a single (or two) field(s) by introducing family symmetry.By breaking the family symmetry, realistic quark and lepton massesand mixings can be obtained.Peculiar sfermion mass spectrum is predicted.

Effective (Natural) SUSY type mass spectrum if SUSY flavor problem is solved with stabilization of the EW scale.

,

Can we discover the LFVat the future experiments?

11100.1 (exclude)

9100.7

(exclude)

8100.7

14100.1

MEG experiment

τ→μγ

μ→eγ Detectable if <400GeV

(super-)KEKB

Detectable, when tanβ is large and 　　 <250GeV

𝑚3=𝑚𝜏𝑅=𝑚𝑡𝑅

=𝑚𝑞3

Spontaneous CP violation

Old and new type SUSY CP problems can be solved and several bonuses

2nd 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

Sizable EDM RG induces imaginary of sfermion masses GeV TeV (red, orange) TeV (blue, cyan)

Ishiduki-Kim-N.M.-Sakurai09

Nucleon decay

N.M.-Y.Muramatsu 13,14

Natural(Anomalous U(1)) GUT

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

N.M. 01N.M. T. Yamashita, 02

Nucleon decay via dim. 6 is enhanced

Unification scale becomes lower.

　　　 　　　　　 Proton decay via dimension 6 op.

years () years

Generic interactions

GUT model identification by nucleon decaytwo important ratios of partial decay widths to identify GUT model

to identify grand unification group

to identify Yukawa structure at GUT scale

GUT GU

T

GU

T

: dimension-6 operators which have anti electron in final state

: dimension-6 operators which have anti neutrino in final state

𝑹𝟏=¿

𝑹𝟐=

¿

model points

model points

3rd Summary Observed (or observing)

Not yet

Nucleon decay large

FCNC

Unfortunately most of FCNC processes are

decoupled when SUSY breaking scale is large.

(This is implied by observed Higgs mass.)

Impact of LHC

125 GeV Higgs

Stop mass () 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

125GeV Higgs→Heavy stop→Instability of EW scale This step is not automatic! Instability strongly depends on the explicit SUSY breaking scenario

→ 125GeV Higgs must be a hint for finding the true SUSY breaking scenario.

Little hierarchy problem GeV (LHC) TeV ()

TeV ()

Higgs mass is fixed by and at weak energy scale. Heavy stop leads to parameters tuning

TeV, , O(0.01%) tuning

TeV, , O(0.1%) tuning

TeV, , ) O(1%) tuning

Correction depends on at higher scale and .

Low mediation scale and are preferable.

Low mediation scale scenarios Gauge mediation

Mass of the messenger particles can be small.

Unfortunately it is difficult to obtain large 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

Unfortunately, is not sufficiently large.

What happens if special boundary conditions are not required?

Cosmological Gravitino ProblemSUSY 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 TeV

What we would like to show Gravitino mass 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.

can be larger without changing

Little hierarchy problem

𝑚3/2

𝑀1 /2=60 TeV

from .We fixed

𝑚h2

2/∆𝑚𝐻𝑢

2

1, O(%) tuning is realized! (Width of 1% band is O(TeV))2, Mild dependence on (Important to obtain heavy Higgs.)

Important observation Gravitino mass 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.

can be larger without changing

If 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

N.M.-Y.Muramatsu-Y.Shigekami 14

Natural (Effective) SUSY type sfermion masses

Most of models which predict natural SUSY sferimion massesare 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 GUT with family symmetry.

10: 5:

A signature from sizable D-term contributions

An important prediction

How large D-term can be allowed? We consider FCNC constraints

average down type squark mass :

:constraint from

:constraint from

When TeV

𝑥=¿

𝑦=¿

Result 1

𝑥∼𝑦∼ 0.1= D-term can be 1 TeV!

signature of SUSY GUT model in future experiments ( TeV proton collider or muon collider)

4th Summary Gravitino mass 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.

can be larger without changing

If 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. An important prediction D term can be 1 TeV! (

Summary GUT is promising Experimental supports for two unifications

GUT is interesting An assumption in 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 125GeV Higgs must be a hint for SUSY breaking Predictions

Observed

Not yet

Nucleon decay

Sfermion mass spectrum (Natural SUSY type)

D-term contribution can be a smoking gun. Shigekami’s master thesis

Signatures for future flavor experiments?

EDM of neutron now in progress

Future works Cosmology (Inflation, DM, Baryogenesis etc)

Leptogenesis implies GUT Ishihara’s master thesis

More predictions

Issues (generic int., gauge coupling unif. etc)

Higgsino?