Neutrino Mass andNew Physics Roadmap Beyond MSSM

R. N. MohapatraUniversity of

Maryland

Beijing Flavor workshop, September, 2008.

Plan of the talk:Lecture 1. Neutrino mass from TeV scale Physics: -SM and MSSM: Hopes and problems -SUSY Left-right model: Resolving of problems

- SUSYLR: An LHC friendly incarnation -TeV scale baryogenesis: In SUSYLR extension

Lecture 2. Neutrino Mass and Grand Unification -SU(5): An illustrative model -SO(10) GUT: fermion masses and mixings; proton

decay and strong CP -Beyond SO(10):

Recap. of SM: Fermions: ; ; Higgs boson: ; ;

17 parameter theory; Higgs mass arbitrary. Successful but naturalness issues !!

0H

HH

20 wkvH GeVvwk 246

Why to go beyond SM ? Major puzzles of SM: (i) Origin of Mass: origin and value of <H>: LHC to throw light on it:

(ii) Origin of Flavor: Generations; Fermion masses, mixings, CP and P-

violation in SM; CP violation in strong interaction; Neutrino mass physics, LFV searches and B-physics will

elucidate their origin !

(iii) Cosmological Issues: Dark matter, Origin of matter (also related to flavor

puzzle), inflation etc.

Origin of Mass Higgs boson elementary or

composite ? Elementary:: Supersymmetry Rules are usual QFT; calculable quantum

corrections and precision test possible!! Cosmology easier to visualize in model.

Composite:: Technicolor or warped extra dimensions .

Conceptually beautiful, analogy to QCD attractive but hard to do precise calculations. Hard to do cosmology !!

Supersymmetric Route

Use supersymmetry to solve the mass problem;

Extend it to solve flavor problem e.g. neutrino mass, Dark matter, CP, Strong CP problem etc.

Immediately beyond MSSM: SUSYLR motivated by nu-mass; solves all these problems-

Gauge Hierarchy and Supersymmetry

To every SM particle - a superpartner: Minimal Model -MSSM

Cancels selfmass divergence of Higgs and solves the gauge hierarchy problem:

Bonus 1: Lightest sparticle stable if R-parity exact and becomes dark matter.

QQ~

cc uu ~cc dd~

ll~

cc ee ~

WW~ZZ~ ~

HH~

Bonus 2: Coupling Unification and GUTs

MSSM does not predict coupling unification; Need to assume no new physics till high scale:

Proton decay key test !

For colliders, gaugino unif. important test:

7:2:1:: 321 MMM

Bonus 3: Electroweak symmetry breaking

MSSM provides a simple way to understand the origin of EWSB and hence the origin of mass !

Light Higgs mass bound: Key test of MSSM is upper bound on

light neutral Higgs mass:

Implementing EW baryogenesis puts stronger limits < 120 GeV and light stop

< 200 GeV.

Testable soon at LHC.

GeVmH 135

Problems: MSSM needs fixing-I SM has stable proton- but MSSM

takes a step backward !! protons decay in an instant in MSSM.

Culprit: R-parity breaking terms

Also no stable dark matter-one of the much touted virtues of susy !!

ccccc dduQLdLLeW ' ' ''

How to naturally get an R-P conserving MSSM ?

Recall

A natural way to have automatic RP conservaing MSSM is to have a higher scale theory with built in local B-L symmetry and break B-L by 2 units.

(RNM,86; Font,Ibanez,Quevedo,89; Martin,92)

( R-parity is often assumed as an adhoc symmetry just to guarantee dark matter and stop proton decay- but we may be missing some important clues to new physics that way !!)

SLBR 2)(3)1(

MSSM needs fixing-Part II MSSM has other problems too ! Too many parameters (~105 or so); Large flavor changing neutral

current effects- Too large edm problem (SUSY CP

problem), no solution to strong CP problem:

Mu-problem

Flavor Problems of MSSM

In general, 5 3x3 hermitean sparticle mass

matrices; 15 phases 3 3x3 arbitrary A matrices; 27

phases 3 gaugino mass phases; mu-

phase,B-mu phase; 5 phases; 32 phases for squarks in addition to

CKM phase; SM only one phase.

SUSY breaking- hope for some type II problems:

SUSY breaking mechanism may cure the FCNC and too many parameter problem:

Gravity mediated (MSUGRA) : -FCNC problem ! Gauge Mediated SUSY Breaking: many fewer

parameters: - Mu-Bmu problem; gravitino LSP KeV dark matter only for low

reheating temp !

(ii) Anomaly Med. SUSY Breaking: many fewer parameters -However without new physics beyond MSSM breaks electric charge !

Going beyond MSSM clearly indicated for

various reasons !

A New beyond MSSM roadmap inspired by nu- mass

MSSM SUSY LEFT RIGHT Gauge group:

Solves many problems of SM and MSSM in addition to explaining small neutrinos masses:

(i) Proposed to explain origin of parity violation:

(ii) No SUSY CP and strong CP problems; (iii) Automatic R-parity- stable DM; (iv) Predicts new kinds of light Higgs bosons.

YL USU )1()2( LBRL USUSU )1()2()2(

Why nonzero -mass suggests LR sym.

Starting point for simple understanding of neutrino mass: add

RH neutrino to MSSM :

Seesaw: type I and RH neutrinos:

Large Majorana mass for the RH neutrinos:

Note just like R-parity, Seesaw also

requires B-L=2; Could there be a common theory for both ?

Minkowski’77; Gell-Mann, Ramond, Slansky; Yanagida; Glashow R. N. M.; Senjanovic 79

An important property of -MSSM

A new cubic triangle anomaly free quantum number is B-L unlike MSSM i.e.

MSSM: Whereas with nu^c

added

B-L is gaugeable sym. And minimal such theory is LR model.

0)( 3 LBTr

0)( 3 LBTr

LR Model-A natural framework for seesaw and gauged B-L

Gauge group:

Fermion assignment

Higgs fields Nu-R and new scale automatic !

(RNM,Senjanovic,79)

LBRL USUSU )1()2()2(

L

L

d

u

R

R

d

u

L

L

e

R

R

e

P P

)0,2,2( )2,1,3()2,3,1(; LR

Parity Violation out of Spontaneous Breaking The weak Lagrangian of model:

Weak Lagrangian Parity Inv. Low energy parity violation due to

][2 RRLL WJWJg

L

ZWZW LRMM

,',

A Much more physical formula for electric charge SM: What is Y ?- a free parameter. LR model:

Implies that: ;

Parity violation implies that neutrino is a Majorana fermion-

23

YIQ L

233

LBIIQ RL

2

)(3

LBI R

Detailed Higgs content and Sym Breaking

021

201

2

12

1

0

'0

0

0

00

Rv

Break symmetry- and in particular B-L by 2 units as required to guarantee

R-parity and seesaw

Quark and lepton masses:

SM:

13 parameters;

LR:

For u,d,e sector same 13 parameters except now Yukawa coupling matrices are hermitean due to LR symmetry.

ReRdRuY eHLhdHQhHuQhL~~

RLfLLRLhQQhL LudeRduLduY ,,,,

Symmetry breaking and seesaw for neutrinos

LBRL USUSU )1()2()2(

YL USU )1()2(

0 R

'0

0

emU )1(

0;0, , lqZW mMML

Rfv0

00

R

L

fvh

hfv

DRDT

L MMMfvm 1 I+II seesaw :

Or as weak int becomes V-A0m as RW

M

Origin of type II term

L

Formula important for determining the scale of B-L;

RMM

Lazaridis, Shafi, Wetterich; R.N.M.,Senjanovic

Summary of bounds on LR Scale: Non-SUSY case Collider limits on WR and Z’:

around 780 GeV- 800 GeV. Low energy limits: K-K-bar, CPV,

edm etc: WR mass > 2.5 TeV. (Zhang,An,Ji,RNM,2008)

Limits from Neutrinoless double beta decay+ vacuum stability:

WR mass > 1.5 TeV. Limits are lower for SUSYLR due

to sparticle FCNC effects. (Zhang,An,Ji 2008)

What is the Seesaw (LR) scale ? GUT vs sub-GUT

Type I term ; so can allow WR anywhere from TeVs up. To right nu masses.

Type II term ; sub-eV neutrino mass would then imply suggest standard standard GUT scenario e.g. SO(10)

with 126 Higgs . Has issues- (see Part 2 of talk) Two questions arise: (i) Why contemplate lower scale LR sym ? -unlike GUT seesaw, TeV and other sub-GUT scale

seesaw testable in colliders; (ii) Doesn’t the type II term need extreme fine

tuning ? -SUSYLR solves this problem.

R

wkL v

vv

2

GeVvR1410

2~ Y eYY ~

SUSY ESSENTIAL FOR LOW SCALE LR SEESAW In Non-susy left-right models, the relation

arises from the term

SUSY LR does not allow such terms and hence implies and thus no restriction on the seesaw scale from type II seesaw.

We will contemplate seesaw (left-right) scales anywhere from TeV up.

R

wkL v

vv

2

)( RLTr

0Lv

Type II seesaw magnitude from SUSY breaking: Susy breaking does induce from diagrams:

Magnitude:

Can be small making type II contribution of right order.

)( RLTr

c

92

22

10)ln(16

~ M

vfh R

Defining Left-Right symmetry Non-SUSY:

SUSYLR: New coordinate

Under parity: But since ;

This implies under parity etc.

RLRL ;;

00; xxxx

*

2

i

* *cQQ

0

0

00

I

I

SUSYLR and Strong CP: Parity definition ( both susy, nonsusy)

; etc; Implies that the Yukawa coupling matrices

defined by:

h are hermitean to be parity invariant. This implies that the quark mass matrices are

hermitean provided the vacuum expectation values are real.

This has several consequences:

..chQQhL bRaLabY ii

*cQQ

Consequences of Hermitean M

Left and Right CKM angles are equal. (less parameters in weak currents)

Solves Strong CP problem – no axion

by parity symmetry

by hermiticity RNM, Senjanovic,78; RNM, Rasin; 95; Kuchimanchi,95; Babu, Dutta, RNM, 2000.

Qg 0g

0.. duMMDetArgQ

Again SUSY essential for strong CP

Mass matrices: h hermitean even for SUSY with given

definition of parity; so M is hermitean if <phi> is real.

In non-susy <phi> is not real due to the presence of arbitrary phases in pot.

Again SUSY does not allow such terms- parity makes all couplings in super-pot real and all vevs real real.

Radiative corrections small; Higher Dim operators must be small.

hM

),()(' RLTreV LLi

~

Phase counting in SUSYLR Mass matrices, A-terms hermitean. Gluino mass real; Left and right wino has only one phase; 2 squark mass matrices related: 3 phases One A matrix diagonal and another with 1

phases. Total of Only 5 phases in addition to the

CKM phase: down from 32 in MSSM No large edm contribution naturally !!

Model Details and Phenomenology:

(i) Minimal Model: Matter:

Higgs: Superpotential:

)1,1,2,1();1,1,1,2();3,3

1,2,1(),3,

3

1,1,2( * cc LLQQ

)1,2,3,1( c

,..),()( cY WWWW

)()( 2,1 baabTrW )()( ccMW

Implications of Minimal SUSYLR: A TeV Scale Theory

(i) In the minimal model, all symmetry breakings related to soft SUSY breakings:

(ii) Ground state breaks parity only if it breaks R-parity :

(iii) There is an upper limit on the WR scale in the TeV

range- so predicts the seesaw scale. (kuchimanchi, RNM, 93,95)

With , neutrino masses OK. Induced CP phase is small and maintains the strong

CP solution.

eYY ~

Two ways to restore R-parity:

(ii) Add non-renormalizable terms: (SUSYLRN)

Requires (Aulakh,Melfo,Senjanovic)

(iii) Model with a singlet S: (SUSYLR+) and include one loop corrections: Also requires

(Babu,RNM,08)

),,,()( 2,1ccWWW ),,( 2

cc

X

cc

M

GeVsMRW

1010

TeVMRW100

Yet they have visible signatures at LHC.

Why is R-parity breaking mandatory ?

Treat Delta part separately since phi and Delta parts are decoupled (No singlet)

Similar to MSSM, but different in the sense that D-term has a peculiar property:

For the ground state , ,

For ground state, , for arbitrary v and v-bar. Different from MSSM.

SDF VVVV cccc

SF MMMVV 1222

222

1 ||||2

2

][4

caccacD Tr

gV

0

00;

00

0

v

v cc 0DV

0DV201

10 vc

201

10 v

c

2

More D-flat Directions compared to MSSM

MSSM, only D-flat direction is: For SUSYLR many: E.g. (i) with

(ii) ;

(iii) ;

etc. ->more constraints on parameters

du HH

0

00;

00

0

v

v cc vv

201

10 vc

01

10

2

vc cc ,

;0'' ss c

01

10

No Parity Violation without R-parity Violation

Potential for the system with V + Compare with MSSM Potential: very similar:

Difference: MSSM positivity constraint : :sym br. Cond: For SUSYLR: as in MSSM; but

for QED breaking direction another constraint:

implying i.e. NO PARITY VIOLATION !!

cc , 0~ cx

2222

1222

222

1 )(4

~2 duuduMSSM vv

gvvmvmvmV

02 212

22

21 mmm

2

2

0212

22

21 MMM

02 21221 MMM 0 cc

02 21221 mmm

Situation is more interesting: No EWSB either

The most general potential for bidoublets:

Unlike MSSM, there are more D-flat directions in SUSYLR bidoublets thereby giving new positivity constraints which imply that the global minimum is

No EWSB without R-P breaking at the tree

level !!

)]()([)( 2, baabbaabbaa TrBTrmV 2

2

][8 aiaaTrg

0 a

Why not add a singlet ? Consider the Higgs sector to have:

The superpotential: This theory breaks parity and SU(2)_R but has a

problem: Since charge breaking ground state has D-term

zero, it is the global minimum at tree level.

V > V

HOW TO CURE THESE PROBLEMS ?

Scca ,,,,

...)( 2 Rcc vSW

0

00;

00

0

v

v cc

201

10 vc

With R-parity breaking parity and EWS break !

If , there are new contributions to potential in the VS and VD terms and

both parity breaking and EWSB occur in QED vacuum.

Second: Parity breaking scale has an upper limit:

About 3-4 TeV for f=0.1. Testable at LHC. Low energy bound on WR mass for susyLR: > 2 TeV. (Zhang, Ji, An, 07)

Several Implications of this R-P breaking Th.

0~ c

f

MgM susy

WR 4

)(

Numerical Search for minimum

Global minimum with spontaneous R-parity breaking:

One Loop Effects: One loop effects: (Babu,RNM’08)

+ If loop contribution is asymptotically

smaller, then No parity violation without R-P violation; same result persists.

If not in a narrow range of parameters R-parity can be conserved:

)1( loopVV 2 221 ||)( cM

(i) Unstable gravitino dark matter and SUSY LR

Getting neutrino masses from TeV scale seesaw implies that R-P breaking couplings are of the form:

If gravitino is the LSP with m <10 GeV, its lifetime is > sec. naturally and hence it can be a dark matter.

Decay mode: (Ji,RNM, Nussinov, Zhang:

arXiv:0808.1904 ) Idea of unstable gravitino dark matter: Ibarra et al;

Takayama, Yamaguchi;…)

0'';10', 6

2710

G~

Cures problems with stable Gravitinos in Cosmology

Gravitino density of universe with inflation

DM gravitino mass around 100 GeV. If not LSP and DM, decay ruins BBN; If LSP, NLSP decays ruin BBN’s successes. Longlives Unstable gravitino better for

dark matter cosmology ! Possibility that it can explain some cosmic ray

anomalies e.g. EGRET gamma ray excess, HEAT positron excess etc.

)

(ii) New upper bound on light Higgs mass: MSSM:

SUSYLR with TeV scale WR

(Zhang, An,Ji and RNM, 2008, PRD)

GeVM h 135

TeVvR 5.1

2

2

~Rv

m2

2

hm

m

LHC signals of low mass WR Looking for TeV scale at

LHC : Signal: Very little background; already used in

D0, CDF ; Present limits: 780 GeV (Does not depend on )

(Keung, Senjanovic, 83; del Aguila and Augilar-Savedra)

',ZWR

Xjjpp

RWl

l

ud

N

u

d

N

Displaced vertices at LHC from NLSP decays:

NLSP decay times are around 10^-11 sec. and can give mm size displaced vertices in LHC detectors from their production.

New Higgs fields with sub-TeV mass In these theories, there are new type of

lepton number carrying Higgs fields: They modify the low energy theory to

MSSM+left triplets+right doubly charged Higgs field coupled to leptons.

Different from MSSM, NMSSM etc: which only have neutral and singly charged Higgs

cccMSSM

RPnew efefllWW

),,,( 00 HAHh

Phenomenology of New Higgses: (i) Doubly charged Higgs:

Very different from known Higgs in that it couples only to leptons and not to quarks: Coupling not small.

One coupling to left and another to the right sector:

Both decay to lepton pairs (from coupling)

For left Delta,

,,ee LL

R

LR

L

R

L

LL W lL lW

0 MMM

,, ee

Present lower bounds on doubly charged Higgs mass:

Drell-Yan pair production main mechanism at hadron colliders: Signal: pp --> or all muon

Collider: CDF, D0: GeV HERA > 141 GeV Low energy: Muonium-anti-muonium osc. (PSI)

For , M++ >250 GeV. g-2 of muon: 100 GeV order.

136M

23

8103

M

ffGA eeFee

2

1.0 ffee

LHC prospects: Gunion, Loomis and Petit; Akyroid, Aoki; Azuelos et al.,

Mukhopadhyaya,Han,Wang,Si; Huitu,Malaampi,Raidal; Chou, Xing,Si,Zhou;

Main Bg ZZ production: LHC Mass Reach ~TeV with 300 fb^-1.

Singly charged signal Properties of singly charged

different from MSSM singly charged couples only to leptons- has L=2

Present bound on mass comes from wrong kind of muon decay:

and nuTeV expt looking for

L

L HL

,, ee

L

ee ee

Bounds on NuTeV bound (Formaggio et al, 2001)

Mass bound in 100 GeV range for reasonable values of f-couplings.

New proposal NUSONG expt (Conrad et al. 2007) will improve this limit by a factor of 4 .

L

FG13.0

Origin of Matter: History

Baryon number violation;

CP violation Out of Thermal Equilibrium (Sakharov) Raised the possibility that protons must

be unstable or some other form of .

Mid- 70’s- GUT theories had proton decay and scenarios for baryogenesis

Started intense search for proton decay.

0B

Things changed in 80’s

Rise of Sphalerons in SM; Inflationary Universe: Seesaw proposed 1979: Leptogenesis proposed 1986

(Fukugita,Yanagida): No need for proton decay; Seesaw enough.

Produces lepton asymmetry and sphalerons convert it to baryons.

Problem with Leptogenesis

Problem: Gravitino constraint limits reheat after inflation to be less than 10^7 GeV (Kohri et

al), whereas adequate leptogenesis requires T>10^9 GeV (Davidson,Ibarra):

Post-sphaleron baryogenesis:

Basic Idea: (Babu,Nasri,RNM’06)

Baryogenesis occurs after Sphalerons decouple: GeV;

Need new particle S with mass ~100 GeV to TeV; decaying violating B;

S must couple to B-violating current. B-violating processes must go out of

Eq. at low temperature. Fits very well into TeV scale left-right

extended to SU(4)_color.

200T

Basic ingredients Requires extending SUSYLR Delta’s to

include diquarks: with a new coupling of the form: = S Y X^2

Key feature is that if decay of S goes out of equilibriunm below

T=100 GeV and produces baryons directly using CKM phase.

Actual decay takes place at few tens of MeV temp

cccccc dudduu ,,

cccccccc dddduu

ZYXS MM ,,

Embedding into PS Model

G = Fermions:

Higgs:

of our model.

cRL SUSUSU )4()2()2(

)10,3,1()15,2,2();1,2,2( R

RLF ,

..chLRFfFL RRRY

ZYXR ,, S

Observable N-N-bar oscillation

Delta^4 contains SXXY, SXZZ int. NN-bar diagram (RNM,Marshak,80)

Present limits on NN-bar -> 1 -100 TeV or less depending on f-couplings.

Out of Eq. condition for baryogenesis

S Decays go out of Eq. around 2 TeV ;

The S-particle does not decay until -> T= few tens of MeV After which it decays and

produces baryon-anti-baryon asymmetry:

The S-decay reheats the Universe to TR giving a dilution of .

S

R

M

T

H 1

B violating decay of S

22

13 )()/100( hgMGeV S

CP Asymmetry:Two classes of one loop diagrams

)(i

)(ii

Model Predictions for B:Class (ii) diagrams

)(

][Im

4 42

ggTrm

MVMgVMMgTr

W

duduT

B

Diquark Higgs at colliders through cc or anti-c anti-c annihilations

We concentrate on the final states which include

at least one (anti-) top quark

Top quark with mass around 175 GeV electroweakly decays

before hadronizing, so can be an ideal tool to prove new physics!

(Okada, Yu, RNM’07)

c

c

c

c

So, our target is

These processes have no Standard Model counterpart!

As a conservative studies, we consider pair production

in the Standard Model as backgrounds

top quark identification

To measure diquark mass (final state invariant mass)

difficult to tell top or anti-top?

Cross section for tt production: tt and t+jet from sea quarks:

Case (ii): Nonrenormalizable version:

Key operators: allow non-ren terms with coeff ~1:

= ;

New terms overwhelm the vanishing D-term in the QED breaking vacuum provided

Ground state preserves R-parity and electric charge.

Requires parity scale to be very high !! (Aulakh, Melfo, Senjanovic,98)

),,( 2

cc

X

cc

MnrW

GeVM

v

X

R 1002

wkRX vvM

Light Higgs despite High seesaw scale-Role of SUSY

Naïve logic: Higgs mass is of the order of symmetry breaking scale; Not always true !

Most general SUSYLR superpotential:

Has U(6,c) global symmetry which breaks down to U(5,c) (in the absence of higher dim term.)

eleven massless complex Higgs bosons: 3 absorbed in gauge sym. breaking from SU(2)RxU(1)B-L to U(1)Y.

Remaining Eight are two doubly charged Higgs bosons and two SU(2) left triplets;

(Aulakh,Melfo,Senjanovic; Chacko, RNM)

,

,...)( ccW

How do they get masses ?

Since SUSYLR is an effective theory, there can be higher dim. nonrenormalizable term

, is the new physics scale

It breaks the accidental global symmetry

and give mass to fields. Mass is of order:

and can be in the TeV range. Simple expectation is

MX=MPl ; so There are also for light B-L=2 SM triplets.

X

cc

M

Tr 2)(

XM

X

R

M

vM

2

~

GeVvR1110

Pros and cons of Non-ren. version

(i) WR scale can be higher but must satisfy the condition:

Otherwise light doubly charged particles < 100 GeV.

(ii) Low energy th. conserves R-parity Conventional Neutralino DM

(iii) Strong CP constraint . GeV

(iv) Type II seesaw constraint: OK

GeVM

v

X

R 1002

72

10X

R

M

v

GeVM

v

X

wk 92

10

Singlet SUSYLR model with R-P and Strong CP soln. (iii)

In singlet model with one loop effects taken into account, things change drastically for a parameter range: (Babu, RNM, 2008)

One new contribution to potential:

With B>0; So for , positivity constraints do not restrict the parameters as before so that global minimum is now P-breaking with good R-P.

02~ clm

B

Upper limits on masses of doubly charged Higgs and slepton

Key predictions of the model (iii): Light doubly charged and slepton

fields:

likely much lower1~1 8.1;7.3 MMMM cl

Summary A simple extension of MSSM that explains

neutrino mass and stable dark matter is minimal SUSYLR with B-L=2 triplets:

(i) TeV scale WR with Rp breaking: has gravitino dark matter not conventional neutralino.

(ii) Second has non-ren terms: no strong CP sol. but fixes AMSB.

(iii) One loop breaking withR-P conserved: Solves

strong CP problem; predicts upper limits on new Higgs, sleptons etc. No need for non-ren terms to be dominant.

Impact of Minimal SUSYLR onSupersymmetry breaking:

Summary: a broad general feature of minimal R-P conserving SUSYLR model

is that it leaves to MSSM plus extra Higgs fields that interact with leptons.

This has important impact on the class of models where SUSY is broken by conformal anomalies (AMSB).

What is AMSB and why it is problematic ?

Superconformal anomaly to generate SUSY breaking effects:

Basic idea: One can get Einstein gravity From Weyl Inv. Action as follows: S=

Set leads to Hilbert action.

Rxgxd )(4

0

How to generalize to supergravity ?

Basic idea is to use superconformal symmetry: What is it ?

Conformal group: Poincare+scale + conformal:

Add SUSY to it: becomes superconformal: Technique: Gauge superconformal group

and fix gauge: (Kaku,Townsend,Van Niuenhuizen; Siegel,Gates; Cremmer et al. 78-80)

Follow the same techniques as before.

generatorsKSPM 15,,,

Superconformal Inv. Action:

Technique: Matter fields Weyl weight w=0; Superpotential must have weight w=3 ; D-terms must have w=0;conformal compensator field Φ w=1. conformal inv. Action: 3324 QdQQdS

Anomaly and Soft SUSY breaking terms

SUSY breaking vev for compensator field from hidden sector:

Renormalization introduces mass

Leads to soft susy breaking terms: Only one parameter describes all susy

breaking terms. (Randall,Sundrum; Giudice,Luty,Murayama,Rattazzi,98)

21 F

2/1)(

Z

SUSY Breaking in AMSB

)(2

23

20 gcmm

2/3)( mYYAY

2/3)( mggM

)(122/3 Ycm

)(gdt

dg

),( gYdt

dY

dY

dc

dg

dc

1,

AMSB in MSSM In MSSM, all Yukawas but are negligible;

Thus all squarks have +ve mass square; but all sleptons have –ve mass square.

Also problem :generic prediction:

AMSB NEEDS NEW PHYSICS !! SUSYLR seems

like the better set-up for AMSB than MSSM !!

th;

16

3)(

2

33

33 gg ;

16

3)(

22

22 gg

2

31

11 16

33)(

gg

B 2/3mB

Presence of light Delta fields with lepton couplings in susyLR makes the difference:-

SUSYLR with vR and MX such that the Delta fields are at TeV scale has no type II seesaw issue and has light Delta fields.

This modifies the low energy theory to MSSM+left triplets+right doubly charged Higgs field coupled to leptons.

cccMSSM

RPnew efefllWW

Slepton masses in SUSYLR + AMSB

)])(([16

2342

22/32

~ fgffgm

ml

)(

16

1),( 22

2fggf

)(

16),( 22

2fg

fgf

New contributions from light Delta couplings to leptons affects lepton masses in AMSB.

5.0,.... fSUSYLRWith(N. Setzer, S. Spinner,RNM, Phys. Rev. D77:053013,2008; JHEP 04 (2008) 091)

Upper limit on new Higgs masses from AMSB

Upper limit for AMSB to work:

Lower limit : muonium-anti-muonium oscillation has an expt upper limit:

Model predicts: PRISM reach:

TeVM 10

23

8103

M

ffGA eeFee

TeVM 1 5106

Fee

GA

410FG

Different gaugino mass ratios as another test. Different prediction for gaugino

mass ratios: GUTs: Gluinos as the most massive

spartner ! For our AMSB: ratio is

This is a crucial signal to test between GUT and sub-GUT models.

3.1:1:3.1:: 123 MMM

7:2:1:: 321 MMM

Gaugino mass ratios after mixing: AMSB: AMSB vs

MSUGRA

21 /MM

Predictions for slepton masses

Bunched spectrum

LSP Wino+ Higgsino DM from gravitino decay:

AMSB upper limit on the Seesaw Scale

Seesaw helps solve the problem of AMSB

This requires that Delta mass be less than 10-20 TeV. If more, it will decouple and not help AMSB.

If only new physics is at the Planck scale

~TeV

fixes the value of seesaw scale to be less than 10^11-10^12 GeV.

Pl

R

M

vM

2

Summary: Contd If gaugino masses indicate AMSB, will

suggest minimal LR seesaw with TeV scale Higgs:

Experimental tests: (muonium-anti-muonium oscillation lower bound, Bunched sparticle spectrum, new Higgs etc.)

Baryogenesis: Either EW baryogenesis from wall reflection or post sphaleron baryogenesis with extra particles using the decay of Re Delta^c: needs addition of diquark Higgses present in SU(4)-color generalization.

LR ,

Grand unification Route Beyond MSSM(i) Grand unification hypothesis: all forces

and all matter become one at high energies no matter how different they look at low energies.

(ii) Many examples of theories where simple renormalization group analysis of the low energy couplings lead to unification at high scales e.g. MSSM at TeV, SO(10) without SUSY etc.

---- Explains charge quantization;----High scale goes well with ideas in cosmology ; ----As we will see, fits very well with neutrino mass

ideas too.

Some examples: SUSY Non-SUSY SO(10) SM with seesaw

Other advantages of GUTs (i) Higher symmetry could give better

understanding of fermion masses ;

(ii) Explains charge quantization; (iii) High scale explains proton

stability; (iv) High scale goes well with

cosmological issues such as inflation and baryogenesis.

Simplest example: SUSY SU(5)

Also proton decay problem (see later)…

Add higher dim operators For minimal Higgs content, solution of

fermion mass problem in SU(5) requires adding higher dim operators:e.g. ; corrects mu-s mass relation:

% Perils of adding HD operators: add all e.g. Or only ones you want Affects gauge coupling unification: New proton decay operators (see

later). Lose predictivity…

Plhmhm M/241055

Plh MWW /24

Two broad classes of GUTs: One lesson from SU(5)

(i) Theories where HD operators play a crucial role:

(Risky since we really do not know the coefficients- they could be exponentially suppressed.)

(ii)Those based only on renorm. terms: (If they work, they are more riskfree: such a model for SU(5) needs adding

45_H).

Going beyond minimal SU(5): Neutrino mass via seesaw

SEESAW

Type I: three RH nus: Type II: Need a {15}-dim Higgs; Type III: Need {24} –dim fermion

(Foot,Lew,He,Joshi)

Include neutrino mass via seesaw in SU(5)

Type I: three RH neutrinos: No understanding of scale; Type II: Need a {15}-Higgs; scale OK. Lower limit on

seesaw scale from gauge unif.: 10^11 GeV. Need higher Dim operators for fermion masses.

Type III: Need two or three extra {24}: upper and lower limit on scale: (RNM,Okada,Yu’08)

higher Dim operators for fermions. Grand unification puts lower limit of 10^12 GeV on

seesaw scale. For type I however, we need go beyond SM and

SU(5) sym. to understand scale.

GeVMGeV seesaw1312 1010

Type I seesaw and SO(10) Grand unified theory

Minimal GUT group for high scale type I seesaw is SO(10) since its spinor rep contains all 16 needed fermions (including RH neutrino) in a single rep.

Georgi; Fritzsch, Minkowski (74)

Contains the LR sym. Group and B-L needed to understand why MR<< M_Planck .

B-L if properly broken also allows a naturally stable dark matter in MSSM.

From SO(10) down to the Std Model

SO(10) Nu mass

LR Sym.

Standard Model- -> seesaw

M

0

0

0

M

m

m

0

0)( LB

emc USU )1()3(

cLBRL SUUSUSU )3()1()2()2(

cYL SUUSU )3()1()2(

Introductory remarks on SO(10):

{16} spinor for fermions: includes all SM fermions + nu_R.

{16}x{16}=10 + 120+126 Need {10}, {120} and/or {120} for fermion masses. Under SU(5): {16}=10+5*+1

{10}=5+5* {126}=1+5*+10+15*+45+50* {120}=5+5*+10+10*+45+45*

Under SU(2)xSU(2)xSU(4): {16}=(2,1,4)+(1,2,4*)

{10}=(2,2,1)+(1,1,6)

{120}= (2,2,1)+(2,2,15)+(3,1,6)+(1,3,6)+(1,1,10+10*)

{126}=(1,3,10*)+(3,1,10)+(2,2,15)+(1,1,6)

How is B-L Broken ? {16} vs {126}

In SUSY SO(10), B-L can either be broken by {16}- Higgs by its component.

Specific features of this case: (i) Typical minimal Higgs content:

(ii) M_R arises from non-ren. terms; (iii) Relies heavily on higher dim operators for

constructing realistic models: (Albright, Barr; Babu, Pati, Wilczek; Ji, Li, RNM.)

R

PlHmHm M/

]54[:]45[];10[];61[];16[ sAHHH

Pros and Cons of {16} models:

Pros: (i) Smaller representations and hence controlled threshhold effects;

(ii): Simple string models lead to these reps:Cons: (i) Lead to R-parity breaking from

terms: no stable dark matter without extra assumptions;

(ii) Too many parameters: need new sym. for prediction

(iii) HD operator e.g. {16}^4 gives rapid proton decay and has coeff. 10^-7 whereas needed HD operators require coeff ~1. WHY ? Perhaps a new symmetry ?

Hmmm

Break B-L by 126-Higgs

SM singlet in 126 is which has B-L=2; Leaves Gauged R parity unbroken in

MSSM and gives stable dark matter. Also since 16 X 16 = 10 + 126 + 120Minimal model: -one each of 10+126+ 120. -126 gives mass to charged fermions as well as

RH neutrinos relating RH neutrino spectrum to charged fermion spectrum.

- uses only renormalizable couplings. So no new fine tuning problem. Not an effective field theory.

(Babu, Mohapatra, 93; Fukuyama, Okada, 01; Bajc, Senjanovic, Vissani, 2003; Goh, R.N.M., Ng,

2004)

RR

Understanding of neutrino mixings without symmetries:

How large mixings arise dynamically in the {126}-based models:

Illustrating in Model with only one {10} and {126} Higgs: Key feature: use type II seesaw:

where

If the second term in the seesaw formula is small:

DR

DT

L Mfv

MfvM1

)( ld MMcM 910c

R

wk

L v

vv

2

Dynamically induced Large neutrino Mixings

)( ld MMcM

Realistic models: Including CP violation:

In the 10+126 model, CP violation can arise from complex Yukawas- (but works only for a narrow range of parameters)

In the full minimal 10+126+120 model, CP is more natural; Dynamical understanding of large mixings remain

Dutta, Mimura, RNM (04,05) ; Grimus, Kuhbock (06); Aulakh and Garg (07)

Details of 10+126+120 model

A model that solves strong CP and SUSY CP problems as well as neutrinos: (Dutta, Mimura, RNM)

Theory CP conserving prior to symmetry breaking:

Superpotential:

12 parameters in the Yukawa couplings and 6 vevs.

18 parameter model.

DhfHhW mmmmmmY '

'' hh T duedue YY ,,,,

Type II dominance Neutrino mixing via type II dominance- two

questions: (i) Origin of type II at tree level ? W= 10.10.54+126.126.54+…. F-term for 54 gives terms that give

left triplet vev and hence type II contribution. (ii) Dominance of type II term: -Requires so that type I small; -Requires left triplet mass ~ 10^13 GeV. -Working model: 10+126+210+54 Higgs.

)( RLTr

GeVv LB1610

CP Violation in 120 Model All couplings real: CP broken

spontaneously by {45}-vev (denoted by A) being imaginary- gives fermion mass formulae: Desired Superpotential:

H10D120A45

With >0.

On EWSB, this leads to hermitean quark mass matrices needed for solving strong CP problem.

)(' 22 MASW2M

120 contributions to fermion masess:

{120} = (2,2,1)+(2,2,15) +……. From 120.45.10 and 210.120.10

couplings only (2,2,1) picks up vev and not the (2,2,15) if {45} vev has form:

Diag{45}={0,0,0,b,b} and {210} vev is along (1,1,1) direction.

Fermion mass formulae: Three

contributions:i

Mass matrices hermitean->Solves the strong,susy CP prob.; Theory has 18-1=17 parameters; Reduce after p-decayconstraints.

i

i

i

i

Proton decay Constraints on SO(10)

Proton decay in SUSY GUTs have two generic sources:

(i) Gauge exchange:

(ii) Higgsino exchange:

SUSY GUT problem Babu, Barr, Raby, Lucas,..

What is the problem ? Color triplet Higgs with GUT scale mass lead to

proton decay: QQQL

Dress up the spartners: Estimate of Amplitude for p-decay

Present limits require: Problem is how does such a small number arise ?

AAmM

ASUSYU

nucwkKp

~

100010212

006.10~

4~

16

2

A~

102 25

810~ A

Situation almost critical:

In SU(5):

Barely of the right order for s; In SO(10), it has contributions from {10},

{126} and {120} couplings but there is no obvious suppression

mechanism without further assumption. Then there is the RRRR operator which grows

with tan beta and is problematic for large tan beta.

2,

21,11,

~

wk

Cscudu v

mmYYA

SO(10) with 10+126 and proton decay There are more diagrams and one can

invoke cancellations to satisfy present constraints for small tan beta e.g.

Again troublesome for large tan beta. In the 10+120+126 models, a new

possibility arises: by choice of flavor structure of couplings, one can satisfy all proton decay constraints for all tan beta.

Dutta, Mimura and R. N. M. (2005)

ijklA~

P-decay constraints neutrino oscillation:

18;6 totalvevs

Dutta, Mimura and R. N. M. (2005)

vevs6

Some predictions of the 120 model:

Prediction for U_e3:

Predictions for the MNSP Phase

08.03 eU

MNSPSin= 0.5-0.7

Dirac phase can be predicted

~

Predictions for long baseline experiments:

Predictions for lepton flavor violation

Coupling Unification with type II seesaw

Usual allegation of large threshold effects Usual allegation of large threshold effects FALSE !!FALSE !! Could have higher unif. scale with SO(10)- Could have higher unif. scale with SO(10)-> SU(5) and Triplet, > SU(5) and Triplet, {15 } of SU(5){15 } of SU(5) at 10^13 GeV; at 10^13 GeV; Goh, Goh, RNM, Nasri,04RNM, Nasri,04

New Threshold approach to suppress proton decay:

Perhaps the GUT scale is not 2.10^16 GeV but much higher.

This will happen if there are new thresholds such that all p-decay mediating fields are at this higher GUT scale:

If the thresholds are associated with Flavor violation, perhaps one can see their effects at low energies:

Examples: SO(10) with 10+126+120: (Dutta,

Mimura,RNM,PRL, 2008)

Testable in B-decay CP asym. RGE extrapolation between GUT and

(8,2..) mass scale will induce low energy FCNC phase and asymmetry in decay which is observable:

(Dutta, Mimura’08)

XBs

Unresolved Issues in GUTs:

(i) Doublet-triplet splitting; (ii) No sign of proton decay yet; (iii) vs

(iv) R-P conserving Dim.5 operators for

proton decay:

0020.01176.0)(exp Zt

s M

129.0127.0)( ZGUTs M

More on (iv): For SU(5): O=

Present proton decay expts imply:

Similar operators in SO(10): [16]^4/M_Pl This is a problem: more urgent for those

models that need non-ren operators to solve nu-mass or fermion masses as {16}_H models or fermion masses in minimal SU(5) since their couplings required to be large unlike the p-decay operator---- WHY ?

mmmmPlM

1010105

710

More HD operator woes:

Once you some include HD operators for making theory realistic, one should all unless forbidden sy symmetries e.g.

WW 45 that destrys GCU.

Curing (iv) – SO(10) example.

In SUSY SO(10) models with {16}_H, one expects couplings of type where by proton lifetime limits.

However, these models use other higher dim operators with order one couplings to understand fermion masses.

How can one reconcile this ?One approach is to have discrete gauge

symmetries which prevent [16]^4 operator as well as R-P violating operators but allow necessary others- They will then be immune to nonpert. Gravitation effects (which are the origin of such operators).

mmmmPM

710

Discrete Gauge Symmetries:

Ibanez, Ross; Hinchliffe,Kaeding, Dreiner,Luhn, Murayama,……

Idea: Supplement the gauge group by an anomaly free discrete symmetry and choose the assignment of symmetry to fields such that all good operators arev allowed and p-decay operator QQQL

Forbidden.

Discrete Gauge symmetry in SO(10)

Smallest anomaly free DGS for SO(10) with {16}-H for 3 gen. is Z_6;

forbids both [16]^4+ RP breaking terms and suppresses proton decay. Only gauge boson exchange responsible for p-decay.

Requires 2 {10}’s for minimal model with Charge assignment as follows (RNM,Ratz,07)

Are these minimal models realistic ? Doublets are in H, H’ and ,

Mass matrix for Doublets

Color Triplets

HH

Mc

Msb

cMsb

2

1

0

002

32

30

Mc

Msa

cMsa

2

1

0

00

0

),',( dHdd HH

dH

u

u

H

H

'

Minimal model does not work

Light doublets do not give mass to down quarks or charged leptons since

And these multiplets do not couple to matter.

{45}’s with only couplings allowed by Z_6.

)'(dHd

mssmd HH

Minimal Realistic model for 16_H

Three 10-Higgs: H(-2); H’(+2); H”(0) Three 45’s: A(0); A’(-2); A”(+2) One 54-Higgs (S): VeV pattern:

Need one fine tuning to keep a linear comb. Of H and H” doublets light. Model works ! (Azatov,RNM, Phys. Rev. D, 2008)

2)0,0,,,( iaaadiagA

2),,0,0,0(' ibbdiagA 0'' A

"'')(' 1 HAHAMHHW ""' HHM

Prediction for Neutrinos:

Yukawa superpotential:

Suppresses proton decay enough so that only tuning at the level of 0.01 needed for the Planck suppression.

22

126,10 '''HA

MMHW mm

P

HHmmP

mmY

HHHH dHu ;

Experimental signal of HD operator in GUTs in gauginos

GUT scenarios can also have NUGM due to HD operators:

(Table from Bhattacharya, Datta, Mukhopadhyaya;)

Plh MWW /24

Leptogenesis in SO(10): Usual leptogenesis scenario: (Fukugita,Yanagida,86)

Lightest NR decays + Sphaleron interactions; Important connection to SO(10) models is the RH

neutrino spectrum and triplet contributions:

Ji,Li,RNM,Nasri,Zhang Phys.Lett.B651:195-207,2007

Gravitino Issue: Most values of M1, are above the allowed

gravitino bound for MG<20 TeV. So the gravitino could be very heavy or

some other mechanism must be invoked- perhaps higher dimensions…

Left-Right seesaw, Duality and SO(10): Akhmedov, Frigerio, 06; Hostiens, Lavignac, Savoy,06 Abada,Hosteins,Lavignac, Micheaux,08 Type I+type II seesaw

Can be written in the form: with

,

1 XXZ TNNY

Duality Corresponding to any solution for f

giving the right neutrino mixings and masses, there is another given by:

Useful for finding new solutions for RH neutrino masses.

XZXX 1

Leptogenesis in LR SEESAW

In typical models, for three generations, there are 8 solutions:

They find light RH neutrino masses in some fits as low as 10^5 GeV; several with 10^9 GeV and good values for lepton asymmetry.

SUMMARY

Neutrino mass introduces B-L as a symmetry of Nature. What is its scale ?

Very interesting possibility is that B-L scale is GUT scale: Minimal SO(10) realizations with 10+120+126 Higgs are realistic and predictive. Can be tested by forthcoming neutrino experiments !

Unresolved issues Generic GUTs: (A): Resolving p-decay problems

needs extra assumptions e.g. (i) Cancellations; (ii) Discrete symmetries (iii) New thresholds and high GUT

scale (B): Doublet triplet splitting (C): Flavor: new family symmetries…

Specific SO(10) neutrino models: Possible conflict between SUSY SO(10)

and standard leptogenesis due to gravitino problem:

Typical RH neutrino masses needed for leptogenesis (Davidson,Ibarra);

Typical SO(10) predictions above this.

BBN constraints on reheat: (Kohri et al.)

Problem not present in sub-GUT seesaw models !!

GeV910

GeVTR610

Few comments on GUT+ Family symmetry

RossGKingFS .,.. Ma

RossKing,

General strategy:

Case (i)

Case (ii)

Non-abelian groups of interest

Look for groups with 3-dim irreps:

So they can unify all generations. Some groups such as Q8, D4,

D5,D6,Q6,D7 all have max dim =2

A4, S4, have d=3 rep

)3( 2n

Requiring Family groups to also help with proton decay:

A4 and S4 allow dim 4 invariants and are not helpful.

Very interesting group is .

Property: 3X3 = (3-bar) and 3X3-bar 1 ; So 16^4

is not invariant. Hence no proton decay operator till 16^6.

)3( 2n

Possible Model building with SO(10)x Irreps of : 9 {1}+3+3-

bar; 16-Higgs models: Need ; for

seesaw; This implies that there is large R-

parity violation from type operator + many others.

)27(

m16 3

)27(

361 H

m16 H61

Model Building contd.

Possible126- models: No such problem: Assign {10} and 126-bar

so that Yukawa couplings are allowed.

No R-parity violating terms.

3

Fermion masses in SO(10)x with 126_H

Construction of invariants: Assign: {16}-m; H(10), {126-bar}:

{120} belong to {3} of ; Generic Yukawa couplings:

Similarly one for 120 (one matrix): 19 parameters for fermions. Can be Realistic !

)27(

)27(

f

e

d

cb

ca

ba

h ,

0

0

010 126~ f

References: Xing Review at ICHEP08. King, Ross; King: Nu-2008 talk. Ma; Altarelli, Ferruglio, Ma; Babu,He; Koide S_3: Mondragon; Morissi..; Nasri,Yu,RNM;

Beyond SO(10):

Intriguing New features:

Basic rep: {27}M,H {16}1+{10}-2+{1}4

Fundamental coupling: {27}x{27}x{27}; but due to extra U(1) does not lead to RP breaking prior to spont breaking.

However has the problems of {16}_H SO(10) models of B-L breaking large RP breaking.

No D=5 proton decay operator since {27}^4 is not E6 Inv.

Extra new fields….

)1()10(6 USOE

Conclusion: Simple quark-lepton symmetry and

seesaw suggest high scale seesaw and SO(10) grand unification:

Simple predictive models can be constructed.

Proton decay true test of GUTs ! Generic prediction: normal hierarchy

and observable LFV processes. Several issues with GUTs must be

addressed- DT splitting, family replication etc.