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Flavour puzzle or Why Neutrinos Are Different?
Maxim Libanov
INR RAS, Moscow

In collaboration with J.-M. Frere (ULB), F.-S. Ling (ULB), E. Nugaev (INR), S. Troitsky (INR)

QFTHEP, September 30, 2011


The Flavour Puzzle In A Nutshell
Why three families in the SM? Hierarchical masses + small mixing angles Why massive neutrinos? Tiny masses + two large mixing angles Why very suppressed FCNC? Strong limits on a TeV scale extension of the SM

1

Proposed solution: A model of family replication in 6D

Why Neutrinos Are Different?

Maxim Libanov


3 Families In 4D From 1 Family In 6D
Nielsen-Olesen vortex: Ug(1) gauge eld A+scalar

2

Our 3D World is a core of AbrikosovCore of the vortex -Our 3D World

There is only single vector-like fermionic r generation in 6D Chiral fermionic zero modes are trapped in the core due to speci c interaction with the A and . Speci c choise of Ug(1) fermionic gauge charges Number of zero modes = 3 Zero modes 4D fermionic families

Why Neutrinos Are Different?

Maxim Libanov


Field Content
Fields scalar Pro les v 1 0 =0

3

F(r)ei F(0) = 0, F(1) = vector A A(r)=e A(0) = 0, A(1) = scalar X X ( r) X(0) = vX, X(1) = scalar H H(r) Hi(0) = 2ivH, Hi(1) fermion Q 3 L zero modes fermion U 3 R zero modes fermion D 3 R zero modes fermion L 3 L zero modes fermion E 3 R zero modes fermion N Kaluza-Klein spectrum

Charges Representations Ug(1) UY(1) SUW(2) SUC(3) +1 0 1 1 0 +1 --1 axial (3 axial (0 axial (0 axial (3 axial (0 0 ; ; ; ; ; 0 0 +1/2 0) +1=6 3) +2=3 3) 1=3 0) 1=2 3) 1 0 0 1 2 2 1 1 2 1 1 0 1 1 3 3 3 1 1 1

r
Maxim Libanov

Why Neutrinos Are Different?


Hierarchical Dirac Masses
ei 0 H(r) ei
1

4

3 zero modes have different shapes, and different angular momenta n = 0; 1; 2 ^ J
n

(r) e
i2



i@ + 3
n

1+ 2

7 n

n

=n

n

(r 0) r
n m

2

R

r 0 0 depends on the parameters of the model. Hierarchy arises at 0:1 4 1 4 2 4 2 CKM m2 : m1 : m0 : : 1 10 : 10 : 1 U 1 2 1

mnm d dr ¯

HX(or )

2n( 1)

nm(±1)

Generation number Angular momentum
The scheme is very constrained, as the pro les are dictated by the equations

Why Neutrinos Are Different?

Maxim Libanov


Neutrinos masses. Why is it different?
N -- additional neutral spinor Free propagating in the extra dim (up to dist. R (10 100TeV) 1). Majorano-like 6D mass term M 2 ¯ NcN + h:c:

5

Kaluza-Klein tower in 4D (no zero mode) Effective 6D couplings with leptons allowed by symmetries ¯L HS+¯
S+

1+ 2

7

N+
S

HS ¯ L

1 2

7

N + h:c:

S+ = X ;
2



;X

2 2

;:::

Non-zero windings more composite structure of the mass matrix

S = X ;X ;

;:::

4D Majorano neutrinos masses are generated by See-saw mechanism
Why Neutrinos Are Different? Maxim Libanov


Neutrinos:
2 R

Charged fermions: d drF(r; ) ¯cL LL L
0 2 R

6

mmn
0 2

mmn

charged


0 2

d
0

drF(r; ) ¯






0

dei

(4 n m+:::)



4+:::;m+n


0

de
4

i(n m+:::)



n;m :::

1
2




2



1


diag

1


4

Uym U diag( m; m; m 2) U 1= 2 1= 2 1= 2 1= 2 1

mcharged diag( U
CKM

;
4

2

;)

1 1
2





1

Why Neutrinos Are Different?

Maxim Libanov


Consequences of this structure Inverted hierarchy: ·m2 = ·m2 12 ·m2 13 0 decay ·m2 12
2

m
2

1 1

m
diag



m0

0



7

0 m 0 0 0m2

Pseudo-Dirac structure

·

partial suppression jm j 1 3 ·m2

Why Neutrinos Are Different?

Maxim Libanov


8

Semi-realistic numerical example 50:03 0 0 diag m = 0 50:79 0 0 0 0:7089 ·m2 = 7:63 10 5eV2 12 ·m2 13 tan2
12 3 2

[meV];

UMNS ·m2 12 ·m2 13
23

0:808 0:559 0:186 0:286 0:660 0:693 = 0:514 0:502 0:696





= 2:50 10 eV
+0:14 0:10

= tan2
2

= 3:05%

= 0:471 0:47 sin
2 13

= 0:997 0:9+1::0 04

= 3:46 10

( 0:036)

Consequence for 0 jm

decay j=
i

miU

2 ei

= 17:0 meV

Why Neutrinos Are Different?

Maxim Libanov


Flavour Violation
Like in the UED, vector bosons can travel in the bulk of space. From the 4D point of view: 1 massless vector boson in 6D= 1 massless vector bozon (zero mode) + KK tower of massive vector bosons Mn FCNC + KK tower of massive scalar bosons in 4D KK scalar modes do not interact with fermion zero modes n R

9

Why Neutrinos Are Different?

Maxim Libanov


KK vector modes carry angular momentum = family number. In the absence of fermion mixings, family number is an exactly conserved quantity processes with ·G = ·J K0 L d J
d¯ s ±

10

0 are suppressed by mixing. ee¯ e ·G = ·J = 1 e
2

e

·G = ·J = 0 e Je=1 ¯

Je = 2
2

=1

JZ = 1

M2 Z

J =1 J
Z

e =0 J
e¯ e

M2 Z

¯ s

=0

¯ e = 1 for the particular model, but may be 1 for extensions

Why Neutrinos Are Different?

Maxim Libanov


Rare processes: ·G = 0: K0 e, K+ L ·G = 1: Bound on MZ 100 TeV
++

11

e e KS, CP-violation

P P P

0 2 4

4=M4 Z 4=M
4 Z

ee¯, e-conversion, e

·G = 2: mass diference KL

4=M4 Z

N B : A clear signature of the model would be an observation K0 e without L
observation other FCNC-processes at the same precision level

Why Neutrinos Are Different?

Maxim Libanov


Search at LHC Search for an
+

12

¾ordinary¿ e + ::: e+ + : : : ---

Number of events

massive Z (W ; g ; ) Search for pp

10 5 1 0.5 0.1 0.05

s = 14TeV L = 100 fb
1

K0 e L forbidden LHC beats xed target

Search for pp content of protons

one order below due to quark

4 5 2 3 Tevatron1 100TeV MZ = M,TeV limit Search for pp ¯ + c + : : : or t ¯ pp b + s + : : : --- expect a few LHC thus has the potential (in a speci c 1000's events, but must consider model) to beat even the very sensitive background! xed target K e limit!

Why Neutrinos Are Different?

Maxim Libanov


Conclusions
Family replication model in 6D: elegant solution to the avour puzzle Hierarchical Dirac masses + small mixing angles Neutrinos are different: See-saw + Majorano-like mass for the bulk neutral fermion can t neutrino data Family/lepton number violating FCNC suppressed by small fermion mixings Predictions for neutrinos Inverted hierarchy Reactor angle 0:1 Partially suppressed neutrinoless decay Other predictions K e will show up earlier than other FCNC-processes Massive gauge bosons with mass TeV or higher Search for pp
+

13

e at LHC can beat xed target

Constraint on B-E-H boson: should be LIGHT
Why Neutrinos Are Different? Maxim Libanov