Melbourne Neutrino Theory Workshop

June 2-4 2008

Ferruccio FeruglioUniversita’ di Padova

Lepton flavor violation and

based on work with Claudia Hagedorn, Yin Lin and Luca Merlo, in preparation

from A4 flavor symmetry

lepton dipole moments

!

sin2"

12= 0.326#0.04

+0.05

!

sin2"

23= 0.45 #0.09

+0.16

!

sin2"

13< 3.2 #10

$2

C.L.)] (95% errors 2[ !

!

"12

= 34.8#2.5+3.0( )

0

!

"23

= 42.1#5.3+9.2( )

0

!

"13

<10.30

!

sin2"

13

TB= 0

!

sin2"

23

TB=1

2

!

sin2"

12

TB=1

3

!

UTB

=

2

6

1

30

"1

6

1

3"1

2

"1

6

1

3

1

2

#

$

% % % % % %

&

'

( ( ( ( ( (

Lepton mixing angles

Tri-Bimaximal mixing

[Fogli, talk at Neutrinos in Venice 2008]

[Harrison, Perkins and Scott]

Gf=A4xZ3xU(1)FN

GSGT

UTBT mν UTB= (mν)diag

A4 is the subgroup of SO(3) leaving a regular tetrahedron invariant it is generated by

!

S2

= T3

= (ST)3

=1S generates a subgroup Z2 of A4T generates a subgroup Z3 of A4

a minimal model for TB mixing: A4

mechanism to generate TB mixing from A4

!

me

<< mµ << m"

explains why

!

"T,...

!

"S,...

keeps separate φT and φS at the LO

[Ma, Rajasekaran 2001; Ma 0409075; Altarelli & F. 0504165 & 0512103Altarelli, F, Lin 0610165]

[He, Keum, Volkas 0601001Lam 0708.3665 + 0804.2622]

Gf=A4xZ3xU(1)FN

!

l = (3,",0)

!

ec = (1," 2

,+2)

µc = (1''," 2,+1)

# c = (1'," 2,0)

!

" #

"T/$ = (3,1,0)

"S/$ = (3,%,0)

& /$ = (1,%,0)

' /$ = (1,1,(1)

)

*

+ +

,

+ +

vacuum alignment

!

"T/# = (u,0,0) +O(u

2)

"S/#$ (u,u,u) +O(u

2)

% /#$ u +O(u2)

& /# ' t

!

0.001< u < "2

t # "2

tau Yukawa coupling < 4π

!

ye ( " ) =

ce t2u 0 0

0 cµ t u 0

0 0 c# u

$

%

& & &

'

(

) ) )

+O(u2)

corrections toTB mixing

can also be extended to the quark sector[F, Hagedorn, Lin, Merlo 0702194, Altarelli,F, Hagedorn 08020090]

symmetry breaking sector

!

" = 0.22 Cabibbo angle

!

"13

=O(u)from subleadingcorrections

Energye.w. scale

0

ν massesν oscillations0νββ decay ?

M≈(1÷10) TeV

- (g-2) discrepancy- dark matter- gauge coupling unification- hierarchy problem

the energy region close to M will be explored by LHC soon

additional assumption: there is new physics at a scale M≈(1÷10) TeV << <φ> <<Λ

extended gauge symmetry?additional d.o.f.like νc, superheavy gauge bosons,MGUT …

!

"

!

"

additional tests of A4 are possible here

at energies E<M, after integrating out the d.o.f. associated to the scale M

Leff local operator, still invariant under Gf [by treating <φ> as spurions][neglecting RGE effects, still controlled by <φ>, but not local in <φ>]

!

Leff = LSM + L(m" ) + ie

M2ecH

+ # µ"Fµ"( )M ( $ )l + h.c.+ ...

[4-fermion operators]

low-energy effective Lagrangian

- effects with 1/M2 suppression can be observable

- flavor pattern in Leff controlled (up to RGE effects) by the same SB parameters <φ> that control me and mν

- in the basis where charged leptons are diagonal

!

Im M ( " )[ ]ii

!

Re M ( " )[ ]ii

!

M ( " )[ ]ij

2

(i # j)!

di

!

ai =(g " 2)i

2

!

Rij =BR(li " l j#)

BR(li " l j$ i$ j )

electric dipolemoments

anomalous magneticmoments

LFV transitions

!

µ " e#

$ " µ#

$ " e#

!

µ " eee

# " µµµ

# " eee

...

- correlations among di, ai, Rij and ϑ13 from the pattern <φ>- bounds on the scale M, from the present limits on di, ai, Rij

!

M ( " )[ ]ii

=# i (ye )ii + ...

O(1) (complex) coefficients

!

de

<1.6 "10#27 e cm M > 80 TeV

dµ < 2.8 "10#19 e cm M > 80GeV

$ae

< 3.8 "10#12 M > 350GeV

$aµ % 30 "10#10

M % 2.7 TeV

α approximately real?

[warning: relation between the scale M and new particlemasses M’ can be not trivial. In a weakly interacting theoryg M/4π≈M’]

[from recent reviewby Raidal et al 08011826]

charged lepton Yukawa couplings

!

M ( " )[ ]ij in A4 # ...

!

M ( " ) =

O(t2u) O(t

2u2) O(t

2u2)

O(tu2) O(tu) O(t u

2)

O(u2) O(u

2) O(u)

#

$

% % %

&

'

( ( (

in the basiswhere chargedleptons arediagonal;operatorscontribute to bothMii and Mij (i≠j)

!

Rµe " R#µ " R#eup to O(1) coefficients independently from ϑ13

!

" # µ$ " # e$ below expected future sensitivity

!

Rµe <1.2 "10#11(10#13)$u

M2

<1.2 "10#11(1.1"10#12) GeV #2

!

u > 0.001" M >10(30) TeV

u # 0.05 " M > 70(200) TeV

probably above the region of interest for the (g-2)µ and for LHCis this inescapable?

Mij (i≠j) from two sources

!

"T/# = (u,0,0) +O(u

2)- NLO corrections to φT

- double flavon insertions of the type

!

" +#S, "#

S

+ [other combinationsvanish]

in a SUSY version of the model, with SUSY softly broken, a chirality flip requires an insertion of φT , at the LO in the SUSY breaking parameters. Example:

!

d2"

SUSY# echd

$T

%l

&

' (

)

* + "SUSY

2m

SUSY

!

d2"

SUSY# echd

$T

%l

&

' (

)

* +

other insertions can give rise to a chirality flip, but are suppressedby powers of (mSUSY/Λ)

!

1

"d2#

SUSYd2#

SUSY$ echd

% +&S

"2l

'

( )

*

+ , #SUSY

2 # SUSY

2m

SUSY

2

if the only sources of chirality flip are fermion and sfermion (LR) masses, then there is no contribution to Mij (i≠j) from [at LO in mSUSY] and the main effect comes from φT alone[we take this as a definition of SUSY case in the present context]

!

" +#S, "#

S

+

!

M ( " )[ ]ij in A4 # ...

!

M ( " ) =

O(t2u) O(t

2u2) O(t

2u2)

O(tu3) O(tu) O(t u

2)

O(u3) O(u

3) O(u)

#

$

% % %

&

'

( ( (

in the basiswhere chargedleptons arediagonal

!

M ( " )[ ]ij

i > j( )off-diagonal elements below the diagonal are down by a factor of O(u) compared to generic non-SUSY case

!

Rµe " R#µ " R#eup to O(1) coefficients independently from ϑ13

!

Rµe <1.2 "10#11(10#13)$u2

M2

<1.2 "10#11(1.1"10#12) GeV #2

!

u > 0.001" M > 0.3(1) TeV

u # 0.05 " M > 2(7) TeV

SUSY case

!

BR µ " e#( ) =12$ 3%

em

GF

2mµ4

&aµ( )2

0.0014'&aµ

30'10(10

)

* +

,

- .

2

1 2 4 4 3 4 4

#/13[ ]

4

O(1) coefficient

Minimal Flavor Violation [MFV]

!

Gf = SU(3)l " SU(3)e c " ...

!

l = (3 ,1) ec

= (1,3)

the largest Gf

!

" #ye = (3, 3 )

Y = (6,1)

$ % &

Gf broken only by the Yukawa coupling of LSM and L5

ye and Y can be expressed in terms of lepton masses andmixing angles

!

ye = 2me

diag

vY =

"L

v2U*mv

diagU

+

[D’Ambrosio, Giudice, Isidori, Strumia 2002Cirigliano, Grinstein, Isidori, Wise 2005]

!

M ( " )[ ]ii

diagonal elements are of the same size as in A4x…similar lower bounds on the scale M

!

L5

"L

=( ˜ H

+l)Y ( ˜ H

+l)

"L

!

M ( " )[ ]ij

= # (yeY+Y )ij + ...

= 2#(ml )ii

v

$L

2

v4%msol

2Ui2U j 2

* ± %matm

2Ui3U j 3

*[ ] + ...

+ for normal hierarchy- for inverted hierarchy

a positive signal at MEG 10-11 <Rμe< 10-13÷10-14 always be accommodated[but for a small interval around ϑ13≈0.02 where Rμe=0]

non-observation of Rij can be accommodated by lowering ΛL

!

Rµe

R"µ

#

$ % %

&

' ( ( )

2

3r ± 2 sin*

13ei+

2

<1 r ,-m

sol

2

-matm

2

0 0.1 0.2

!

Rµe <1.2 "10#11

implies

R$µ <10#90.02

could be above futuresensitivity

!

µ " e# and $ " µ#

!

here µ " e# vanishes

ϑ13

both

[Cirigliano, Grinstein, Isidori, Wise 2005]

0 0.1 0.2

!

Rµe <1.2 "10#11

implies

R$µ <10#90.02

could be above futuresensitivity

!

µ " e# and $ " µ#

!

here µ " e# vanishes ϑ13

0.05

!

disfavoured by A4can be aboveexperimental sensitivity

!

µ " e#

MFV

SUSYxA4

[scale M can be of order 1 TeV]

[scale M can be of order 1 TeV]

both

only

conclusion- additional tests of A4 models from LFV generic prediction

!

Rµe " R#µ " R#e independently from ϑ13 (cfr MFV)

!

" # µ$ " # e$ below expected future sensitivity

- in the generic, non-SUSY, case

!

Rij =BR(li " l j#)

BR(li " l j$ i$ j )%

u

M2

&

' (

)

* +

2 0.001 < u < 0.05 requires M above 10 TeV:no match with M fitting (g-2)µ

- in the SUSY, case

!

Rij =BR(li " l j#)

BR(li " l j$ i$ j )%

u2

M2

&

' (

)

* +

2 M can be much smaller, in therange of interest for (g-2)µ

!

BR µ " e#( ) = 0.0014 $%aµ

30 $10&10'

( )

*

+ ,

2

#-13[ ]

4

O(1) coefficient

other slides

without any extra assumptions

Energye.w. scale

0

ν massesν oscillations0νββ decay ?

extended gauge symmetry?additional d.o.f.like νc, superheavy gauge bosons,MGUT …

!

"

!

"

additional tests of A4 are possible here

|Ue3|<0.05 would select a very narrow (not empty) subsetof existing models

3eU2.01.001.0

MINOSOPERA

doubleCHOOZJPARK-SK

NuMI

05.0

ν-factory

4444444444 34444444444 21

10 yr >> 10 yr

Most of plausible range for Ue3 explored in 10 yr from now

Present

bound

anarchy, inverted hierachy

current precision future < 10 yr

few percent [KamLAND]

--- ---

2

12m! ( ) %]4[eV 103.00.8

25!"± #

2

23m! ( ) %]12[eV 103.05.2

23!"± #

23eV1015.0

!"

%]2[eV1005.0 23!"

#

LBL conventional beams

superbeams

12!

09.0

08.012

245.0tan

+!="

00

12233 ±=!

12

2

12

2sin2tan !"!" # νe scattering rate

of pp neutrinos to 1%

13! C.L.%90)13(23.0 0

<LBL, ChoozII

superbeams

23!

07.0

08.023

252.0sin

+!="

0

0

4

50

1246

+

!="

2323

2sin !""! #down by abouta factor 2

superbeams

down by abouta factor 2: challenging

223sign m!

!> 10 yr> 10 yr

rad10.0

rad05.0

From the theory view point the simplest and more appealing (though still unconfirmed) possibility for δL(mν) is the leading non-renormalizableSU(2)xU(1) invariant operator

...62

6

5

5 +!

+!

+= Lc

Lc

LLSM

Weinberg’s list

a unique d=5 operator (up to flavour combinations)

[80 independent d=6 operators]Λ= scale of new physics

!

L5

"L

=( ˜ H

+l)( ˜ H

+l)

"L

=1

2

v2

"L

## + ...

!

m" = yv2

#L

vy

mf

f2

=

smallness ofdue to

!m

!

v

"L

<<1

!

m" # $m32

2# 0.05 eV% &

L#10

15GeV not that far from GUT scale

the effective theory is “nearly” renormalizablethe first effect of New Physics: neutrino masses and mixing angles!

[for a different scenario see Shaposhnikov’s talk]

Flavor symmetries II (the lepton mixing puzzle)

!

UPMNS

"UTB#

2

6

1

30

$1

6

1

3$1

2

$1

6

1

3

1

2

%

&

' ' ' ' ' '

(

)

* * * * * *

why ?

!

UPMNS

=Ue

+U"

Consider a flavor symmetry Gf such that Gf is broken into two differentsubgroups: Ge in the charged lepton sector, and Gν in the neutrino sector.me is invariant under Ge and mν is invariant under Gν. If Ge and Gν areappropriately chosen, the constraints on me and mν can give rise to theobserved UPMNS.

Gf

GνGe

me diagonal

[TB=TriBimaximal]

UTBT mν UTB= (mν)diag

The simplest example is based on a small discrete group, Gf=A4. It is thesubgroup of SO(3) leaving a regular tetrahedron invariant. The elements ofA4 can all be generated starting from two of them: S and T such that

!

S2

= T3

= (ST)3

=1

S generates a subgroup Z2 of A4T generates a subgroup Z3 of A4

simple models have been constructed where Ge=Z3 and Gν=Z2 andwhere the lepton mixing matrix UPMNS is automatically UTB, at the leading orderin the SB parameters. Small corrections are induced by higher order terms.

the generic predictions of this approach is that θ13 and (θ23-π/4) are verysmall quantities, of the order of few percent: testable in a not-so-farfuture.