Gauged Flavor

R. N. Mohapatra

GUT 2012, Kyoto, 2012

Two Fundamental puzzles of SM

(i) Origin of Mass: two problems:

(a) quark masses : SM Higgs (b) neutrino masses; New Higgs, New symmetries

(ii)Origin of Flavor: Fermion masses, mixings, CP and P, strong CP

Understanding Flavor Zero fermion masses SM + RH nu

flavor symmetry group:

Hope is that observed flavor structure is a consequence of breaking this symmetry-

Questions: a) Gauge or global symmetry ?

b) Scale of the symmetry breaking? c) New dynamics of the symmetry ?

NeduQ UUUUUU )3()3()3()3()3()3(

Global Flavor symmetry Continuous:Breaking leads to massless familons

(Wilczek)

Must decouple before BBN- Not seen in experiments so far- Limits on the scale (PDG): from and decays: (Jodidio et al. ; Atiya et al )

Discrete :Domain wall problem; not favored by string theories unless gauged

(an argument in favor of gauged flavor)

GeVM H1010 e K

Gauged Flavor Symmetry

SM provides an excellent description of flavor violation. Accident or something fundamental ?

Minimal Flavor violation hypothesis: (Chivukula, Georgi; Buras et al; D’Ambrosio et al)

-Any Flavor [U(3)]6 breaking effect is proportional to

SM Yukawa type spurions: Y u ~(3, 3* , 1), etc.

Example of a theory where this happens: SUSY with universal scalar masses or GMSB etc.

Universal scalar masses

Need for Flavor gauging

A natural speculation: the spurions are vevs of actual scalar fields:

If flavor symmetry is not gauge symmetry, there will be massless Goldstone bosons and

are troublesome for cosmology.

How to implement this in a proper way and does it have any observable effect ?

Naïve Gauged Flavor and gauged flavor scale

No extra fermionsAnomaly constraints restrict gaugeable symmetries to vector subgroups

; (needs RH neutrino for global anomaly freedom)

Scale of symmetry breaking set by FCNC :

imply (for gH~1) (UTFIT coll. Bona et al)SSSL BBDDKK ,,

TeVM H 1000

..2

2

2 chqqqqM

gH jiji

H

HF

Typical structure of these theories:

Gauge group: Sym Br. Higgs: SM H + (Y-flavon fields)

< > breaks flavor sym; H breaks SM; Fermion masses arise from (typically) Implies e.g. that:

.

VHSM SUG ,)3(

ijuY ,

11,22,33, uuu YYY

..~ ,,,,2

2

2 RLqqqqM

gH LjLiLjLi

H

HF

ijuH YM ,

New approach: Use Quark seesaw: Add vector like quarks to SM ( ) and use seesaw like mass matrices:

In Left-Right models # of parameters: for quarks only 24 in LR; 48 in SM (Davidson, Wali’87;… Babu and RNM’89,…..)

du ,

Mm

mM

R

L

q

q

q

0

M

mmRL qq

juijiuRwkiju MvvM ,1,,,

Full Flavor Gauging Advantage of seesaw approach in SM: Full chiral flavor group can be anomaly

free and can be gauged (Grinstein, Redi and Villadoro’09)

Quark masses:

Note inverted hierarchy for masses !! Flavor scale is same as vector like quark massOne flavor scale comes down to TeV range;New vector like quarks in the LHC range;

1,

2,

ijwkqijq MMvMq

Basic reason for lower scale

Inverse relation between quark and vector like masses for Horizontal scale:

Huge suppression Lower flavor gauge scale for higher flavors.

11,22,33, uuu YYY

..2

2

2 chqqqqM

gH jiji

H

HF

2

22

VM

mu

2wkv

111 :: uct mmm

A Conceptual problem Gauge protection of fermion masses : “all fermion

masses must arise from a gauge symmetry breaking- otherwise it could be of the order of Planck mass !!”

e.g. in QED, electron mass is not gauge protected but

in SM, it is.

In GRV model, pairs have same gauge quantum numbers and get arbitrary gauge unprotected mass.

No neutrino mass

),(),,( uLR

dLR ud

Flavor gauging with Left-Right Symmetry

Guadagnoli, Mohapatra , Sung, arXiv: 1103.4170 JHEP 04, 093 (2011)

LR allows more economical flavor gauging: From (SM) to (LR)

All Fermion masses gauge protected-connected to weak, LR

and flavor gauging scales !! (i) generates neutrino mass (ii) Solves strong CP problem from parity (iii) # of parameters: 10 for quarks: connected to symmetries Two versions: TeV parity or no parity TeV SU(2)R

NeduQ UUUUUU )3()3()3()3()3()3(

RLRQLQ UUUU ,,,, )3()3()3()3(

Details of Model

Anomaly free Fermion and Higgs assignment:

Some details: TeV parity

Quark sector: Fermions: Higgs fields: LR doublets: Flavon fields: (EW

singlets) Yukawa couplings and fermion mass protection: LY=

Flavor from sym br.

;

;,,, RLVRLQ RL,

)3,3(,duY

b

s

d

d

Y

Y

Y

Y CKM

t

c

u

CKMu V

Y

Y

Y

VY

Vectorlike quarks

Consequences: Seesaw matrix: similarly for d

All flavor consequence of symmetry breaking; Two new scales beyond SM Right hand weak scale: vR , Flavor scales <Y>; Quark seesaw Flavor gauge boson masses determined by quark

mixings. FCNC interactions given by~

KL –KS imply Yu > 2000 TeV; top partner ψ ~200 GeV for vR ~ TeV.

tcu YYY

uRu

Lu

Yv

v

0

FCNC Bounds on new physics:

Flavor gauge boson and vectorlike quark masses

TeV parity(orange): MVH>10 TeV; M > 5 TeV; otherwise (blue) much lower-both near a TeV.

Special top sector Predicts large top mixings with vector like

quarks due lower Yt large FCNC (in progress)

RH top LH top

LHC searches for vectorlike quarks

Production: ATLAS 1.04fb-1 : 3rd gen. partner

MQ > 760 GeV.

For TeV mass

CMS: pp->QQ-bart+Z+t-bar+Z MQ > 475 GeV

fb10~

Other consequences Reduction of top width probe Parameterize:

SM prediction D0: <.018

Our model: intermediate top partner mediated graph

cgt

GctL LReff

15 )(10~ TeV

3

33,

310

uY

TeV

FCNC and other effects of Gauged Flavor

Possible anomaly can be resolved by new contributions; and predictions are SM –

like. (Buras, Carlucci, Merlo, Stamou’2011)

Full anomaly free gauge group can be extended to have chiral color; The model has axigluon, sometimes

invoked to explain the 3-σ tt-bar asymmetry of CDF

and D0 for Maxi ~ 500 GeV or so.

Other Consequences Non-unitarity of CKM matrix (Branco, Lavoura’86; Branco, Morozumi, Parada, Rebelo’94)

Effects small; < 1-2 % Collider constraints and prospects: LHC ,

Striking LHC signal 6b+2W

UV TCKM )

2

11(

Xpp tt bbWbHt

uiM

vLL

Origin of flavor hierarchies

:<YU,D> encode the flavor pattern. How to understand this ?

Step I: Higgs potential

For , minimum of VU is <Yu>= (a1, 0, 0); induces <Yd >=(b1,0,0) with b1 ~ a1

Generates largest flavon vevs; smallest quark masses

Sym breaks :

UDDU VVVV

)()( 22

12

UUUUUUUUUU YYYYTrYTrYYTrYMV

02

More flavor structure

Add new term to V:

Generates hierarchical masses:

Add Det Y u induces <Y u1 1 > ≠ 0; induces

<Y d >

Next order and mixings More terms in the potential:

can generate the full mixing matrix e.g.

(Admittedly there is fine tuning !!)

A Numerical analysis Minimum of the potential:

Loop alternative Add new interaction of vectorlike quarks: sextet

L+R [Y’= ] <Y’>≠ 0

Generates hierarchical fermion masses and mixings

uuIL 'YRL

Similarity to MFV hypothesis

All flavor structure resides in the scalar multiplets of GH :Yu,d .

All higher order flavor stucture therefore necessarily comes from them, as in MFV hypothesis.

Solution to strong CP problem:

Seesaw Quark mass matrix:

Arg Det M = 0 at tree level. One loop also maintain zero theta. New

contribution at 2 loop. No axion needed. Planck scale corrections small for TeV scale

parity unlike the axion solution.

( Babu, RNM’89)

qRq

Lqq YIv

IvM

0

0tree

Estimating θ

2-loop e.g.

(Babu, RNM’89)

Lepton sector Lepton sector similar

Neutrinos Dirac in the minimal model:

For , correct nu masses emerge- much less tuning than SM. Predicts Dirac nu as it is ! For Dirac nu, WR bound goes up to 3.3 TeV from

BBN. LFV imply <Yν> ~103 TeV Suspected symmetries could be subgroups of GH

SMe

Implications for B-violation

Forbids D=6 proton decay operator; Lowest allowed operator: QQψdRψdRQQ

ΔB=2 N-N-bar oscillation Also allows sphaleron operator: QQQQQQQQQLLL If SU(3)Q =SU(3)l , allowed operator

Observation of p-decay can rule out model.

Gauged Flavor with SUSY

Need for maintaining susy and sym breaking.

First problem D-terms can split squark masses enough to cause FCNC problems i.e.

However in GMSB framework, our Y does not get susy breaking mass till 3 loop;

OK.

Change of Higgs mass bound

D-term causes increase in Mh over MSSM:

+rad. corr.

(An, Ji, RNM,Zhang’08)

R-parity violation and p-decay problem

If model supersymmetrized, allows only R-P breaking terms of type: ψ uc ψ dc ψ dc

After sym breaking u R d Rd R

Leads to neutron-anti-neutron oscillation:

Very similar to MFV models (Smith’09; Grossman et al’11)

Usual SUSY GUTs: Planck induced QQQL/M Pl needs 10-7

suppression: No such problem in gauged F-models

Possible Grand unification:SU(5)xSU(5) model (in progress)

Where do vector-like fermions come from? Grand unification provides a justification:

SU(5)xSU(5)x GH as an example

+ L R

anomaly free ; non-chiralExamples: SU(3)H , SO(3)H

L

cd

cd

cd

e

3

2

1

0

0

0

0

0

33

221,

112,3,

ce

cu

cu

cu

du

du

du

L

NH UUUUG )3()3()3()3( 510

Some Implications of unifying seesaw

Seesaw matrix from Lagrangian: SU(3) case

different from previous case. (Koide’s talk)

Coupling unification possible and chiral color surviving down to TeV, with extra pair of left and right Higgs doublet. MU = 2.3x1013 GeV

Sin2 θW = Need to have different couplings for

the two SU(5)’s at GUT scale !!

Ru

LuRLdPuudd TTFFMTTHYhYHFThL 01,105,56,6, /)(

Proton decay can explore light heavy mixings

No electroweak sym breaking proton is stable !! Operator generated by GUT gauge boson exchange OB = /MU

2 ;

Coupling unification different from usual MU =1013 GeV

EWSB mixes heavy vector like quarks with light quarks p-decay

Operator:

If vR /Mψ =10-3 , proton life time constraint ok. (For an alternative GUT approach: Feldmann (2011))

.

.

Conclusion New approach to gauged flavor: FCNC allows flavor

scale in TeV range (unlike simple gauged case); Key to this: quark seesaw with new TeV mass vector-

like fermionsrealization of MFV LR version “protects all fermion masses”, solves

strong CP problem and gives neutrino masses. Flavor mixings and hierarchies out of flavor breaking- Can be supersymmetrized. Possibly grand unifiable (work in progress)!! Unbroken subgroups can be used to predict mixings !

LR scale INPUT for TeV parity case

Low energy observables: combination of KL-KS, εK, d_n together.(uncertainty long distance effetcs);

Parity defined as usual:( ) minimal model: (An,Ji,Zhang,RNM

’07)

Parity as C (as in SUSY i.e. ) (Maezza, Nemesvek,Nemevsek,Senjanovic’10)

A recent study by ( Buras, Blanke,Gemmler, Heidesiek’11) Collider (CDF,D0) 640-750 GeV; CMS- 1.7 TeV Muon decay (TWIST) 592 GeV Broken TeV parity: weaker bounds on MWR No large tree level Higgs effect unlike canonical LR models.

RWM

RL

c TeV4

TeVMRW 5.2

RL gg

Bounds on New Physics from FCNC

Bounds on scale:

Is the dynamics of flavor then experimentally inaccessible ?