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:
U (3) Q  U (3) u  U (3) d  U (3)   U (3) e  U (3) N


Hope is that observed flavor structure is a
consequence of breaking this symmetryQuestions: a) Gauge or global symmetry ?
b) Scale of the symmetry breaking?
c) New dynamics of the symmetry ?
Global Flavor symmetry






Continuous:Breaking leads to massless familons (Wilczek)
Must decouple before BBNNot seen in experiments so farLimits on the scale (PDG):
10
M H  10 GeV from   e   and K    
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)
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: Yu ~(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 fermionsAnomaly constraints restrict
gaugeable symmetries to vector subgroups
;
global anomaly freedom)

(needs RH neutrino for
Scale of symmetry breaking set by FCNC :
2
H F  2 

gH
M
2
H
q i  q j q i  q j  h .c .
imply  (for gH~1)
(UTFIT coll. Bona et al)
 1000 TeV
K L  K S , D  D , BS  BS
M
H
Typical structure of these
theories:





Gauge group: G SM  SU ( 3 ) H ,V
Sym Br. Higgs: SM H + Yu , ij (Y-flavon fields)
< Yu , ij> breaks flavor sym;
 H breaks SM; Y
u ij, ij
Fermion
masses
arise
from
(typically)
Q i Hu j


Implies e.g. that: Y u , 33  Y u , 22  Y u ,11
H F  2 ~

.M
H
g
M
2
H
2
H
 Y u , ij 

q i , L  q j , L q i , L   q j , L  L  R  ..
New approach:


Use Quark seesaw:
Add vector like quarks to SM ( 
seesaw like mass matrices:
M
q
 0

m
 q R
m q L 

M  
u ,d
) and use
m
m q R
mM
q L
m
~
u
,
d

M MQQ
1


In Left-Right models  M u , ij  v wk v R  u , i M  , ij  u , j
# of parameters: for quarks only 24 in LR; 48 in SM
(Davidson, Wali’87;… Babu and RNM’89,…..)
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:
1
M q ,ij   v wk M  q M  ,ij
2
q
Note inverted hierarchy for
masses !!
 Flavor scale is same as vector like quark mass
One flavor scale comes down to TeV range;
New vector like quarks in the LHC range;

Basic reason for lower scale

Inverse relation between quark and vector like masses
 for Horizontal scale:
Y u , 33  Y u , 22  Y u ,11
m
2
H F  2 
gH
M
2
H
1
t
:m
1
c
:m
1
u
m u gH
q i  q j q i  q j  h .c .H

F  2
2
22
q  q j qi q j
2 2 i
2
M
 h .c .
M  V Hv wk
Huge suppression Lower flavor gauge scale for
higher flavors.
A Conceptual problem



Gauge protection of fermion masses : “all fermion
masses must arise from a gauge symmetry breakingotherwise 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, ( d R , ), ( u R , ) pairs have
same gauge quantum numbers and get arbitrary
gauge unprotected mass.
No neutrino mass
d
L
u
L
Flavor gauging with LeftRight Symmetry


Guadagnoli, Mohapatra , Sung, arXiv: 1103.4170 JHEP 04, 093 (2011)
LR allows more economical flavor gauging:
U (3)  U (3)  U (3)  U (3)  U (3)  U (3)
From
(SM)
U (3) Q , L  U (3) Q , R  U (3)  , L  U (3)  , R
to
(LR)
Q
u
d

e
N
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
Details of Model

Anomaly free Fermion and Higgs assignment:
Some details: TeV parity

Quark sector: Fermions: Q L , R   V , L , R ;
Vectorlike quarks
Higgs fields: LR doublets:  L , R
Flavon fields: Y u , d ( 3 , 3 ) (EW singlets)
Yukawa couplings and fermion mass protection:
LY=

Flavor from sym br.




 Yd

 Y d  


Ys



Y b 
;

 Y u  V CKM
 Yu




Yc


V CKM
Y t 
Consequences:








Seesaw matrix:
 0

 u v R
 u v L  similarly for d

 Yu  
All flavor consequence of symmetry breaking;
Two new scales beyond SM
Right hand weak scale: vR , Flavor scales <Y>;
Quark seesaw  Y  Y  Y
u
c
t
 Ymixings.
 Yt
Flavor gauge boson masses determined
by Yu quark
c
2
æ mu g 2ö
FCNC interactions given by~ ç
H  F  2  H2÷ q i  q j q i  q j  h .c .
vR Hø
è lu vwkM
KL –KS imply Yu > 2000 TeV;  top partner ψ ~200 GeV for
v ~ TeV.
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  ~ 10 fb

CMS: pp->QQ-bart+Z+t-bar+Z
MQ > 475 GeV
Other consequences


Reduction of top width
t  cg
probe
Parameterize: L eff   t R 
SM prediction  ~ 10
5

c L G 
(TeV )
1
5
D0:
 ~<.018
10 (TeV )
Our model: intermediate top partner mediated graph
3



1
 3 TeV  5


  10  ~ 10 (TeV )
Y

 u , 33 
1
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)
V CKM  (1 
1
 )U
T
L 
2
vL
M  ui
Effects small; < 1-2 %
 Collider constraints and prospects:
LHC pp     X ,

t
t
t  H  bWb b

Striking LHC signal 6b+2W
Origin of flavor hierarchies


 :<YU,D> encode the flavor pattern. How to
understand this ?
Step I: Higgs potential V  VU  V D  VUD

U

U

U

U
VU   M TrY YU  1 (TrY YU )   2 Tr (Y YU Y YU )
2
U




2
For  2  0 , 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 :
More flavor structure




Add new term to V:

Generates hierarchical masses:
Add Det Yu  induces <Yu1 1 > ≠ 0;
induces <Yd >
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 I   u u 
L+R


L
 RY '
[Y’=
]
<Y’>≠ 0
Generates hierarchical fermion masses and mixings
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:
M




q
 0

 v I
 q R
qvL I 

 Y q  
 Arg Det M = 0 at tree level.   tree  0
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)
Estimating θ

2-loop

(Babu, RNM’89)
e.g.
Lepton sector

Lepton sector similar

Neutrinos Dirac in the minimal model:

For    eSM , 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


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 pdecay problem

If model supersymmetrized, allows only R-P breaking
terms of type: ψuc ψdcψdc

After sym breaking uR dRdR

Leads to neutron-anti-neutron oscillation:


Very similar to MFV models (Smith’09; Grossman et al’11)
Usual SUSY GUTs: Planck induced QQQL/MPl needs 107 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
  dc 1 


c2
 d 
 c3 

 d 
  


 e L
0







 u ,3
  u ,2
u1
0
 u ,1
c
u2
0
u3
c
c
0
d1 

d2 

d3

c
e 

0 
+ L R
L
anomaly free G H  U ( 3)  U ( 3)10  U ( 3) 5  U ( 3) N ; non-chiral
Examples: SU(3)H , SO(3)H
Some Implications of
unifying seesaw

Seesaw matrix from Lagrangian: SU(3) case
L  ( h d T F H Y d , 6  hu TTHY
) / M P   d F L  5 , 5 F R   u T L  10 ,1 0 T R
u ,6
u

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 !!
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 vectorlike fermionsrealization of MFV
LR version “protects all fermion masses”, solves
strong CP problem and gives neutrino masses.
Flavor mixings and hierarchies out of flavor breakingCan 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:(  L   R ) minimal model:
M WR 

(An,Ji,Zhang,RNM ’07)
4 TeV
Parity as C (as in SUSY i.e.   
c
) (Maezza, Nemesvek,Nemevsek,Senjanovic’10)
M W R  2 . 5TeV





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: g L  g R weaker bounds on MWR
No large tree level Higgs effect unlike canonical LR models.
Bounds on New Physics from
FCNC


Bounds on scale:
Is the dynamics of flavor then experimentally
inaccessible ?