In collaboration withJ.-M. Frere (ULB), F.-S. Ling (ULB),E. Nugaev (INR), S. Troitsky (INR)
Flavour puzzle orWhy Neutrinos Are Different?
Maxim LibanovINR RAS, Moscow
Dual year Russia-Spain,11--11--11
Flavour Puzzle Maxim Libanov
The Flavour Puzzle In A Nutshell
XWhy three families in the SM?
Hierarchical masses + small mixing angles
XWhy massive neutrinos?
Tiny masses + two large mixing angles
XWhy very suppressed FCNC?
Strong limits on a TeV scale extension of the SM
Proposed solution:A model of family replication in 6D
1
3 Families from 1 Maxim Libanov
3 Families In 4D From 1 Family In 6D
Core of the vortex --
Our 3D World
ϕ
r
Our 3D World is a core of Abrikosov-Nielsen-Olesen vortex:
scalarΦ(r,ϕ) = F(r)eiϕ
Ug(1)gaugefieldAr = A(r)
2
3 Families from 1 Maxim Libanov
We do not consider gravity. Extra dimensions can be flat (and infinitelylarge?) or compact, e.g., spherical.
◦ A vortex on a sphere is in fact like a magnetic monopole configurationin 3D
3
3 Families from 1 Maxim Libanov
6D FermionIn general, 6D spinor contains 4 Weyl spinors
Ψ =
ψ+R
ψ+L
ψ−L
ψ−R
where
± ⇔1±Γ7
2
L, R⇔ Left, Right 4D chirality
4
3 Families from 1 Maxim Libanov
Fermion zero modes.Chiral fermionic zero modes are trapped in the core due to specificinteraction with the A and Φ. Specific choise of Ug(1) fermionic gaugecharges ⇒
axial(3,0) ⇒ Φ3Ψ1−Γ7
2Ψ ⇒ 3 L zero modes
0ψ+L
ψ−L
0
axial(0,3) ⇒ Φ3Ψ1+Γ7
2Ψ ⇒ 3 R zero modes
ψ+R
00ψ−R
Zero modes⇔ three 4D fermionic families
5
3 Families from 1 Maxim Libanov
Field Content
Fields Profiles Charges RepresentationsUg(1) UY(1) SUW(2) SUC(3)
scalar Φ F(r)eiϕ +1 0 1 1F(0) = 0, F(∞) = v
vector Aϕ A(r)/e 0 0 0 0A(0) = 0, A(∞) = 1
scalar X X(r) +1 0 1 1X(0) = vX, X(∞) = 0
scalar H H(r) --1 +1/2 2 1Hi(0) = δ2ivH, Hi(∞) = 0
fermion Q 3 L zero modes axial (3, 0) +1/6 2 3fermion U 3 R zero modes axial (0, 3) +2/3 1 3fermion D 3 R zero modes axial (0, 3) −1/3 1 3fermion L 3 L zero modes axial (3, 0) −1/2 2 1fermion E 3 R zero modes axial (0, 3) −1 1 1fermion N Kaluza-Klein 0 0 1 1
spectrum
r
6
3 Families from 1. Hierarchy. Maxim Libanov
4D Fermion masses. Hierarchy.
r
ei·0·ϕei·1·ϕ
ei·2·ϕ
H(r) F(r)(Φ = F(r)eiϕ)
3 zero modes have different shapes, anddifferent angular momenta n = 1, 2, 3
JΨn ≡ −(i∂ϕ + 3
1 + Γ7
2
)Ψn = (n − 1)Ψn
Ψn(r→ 0) ∼ rn−1
Explicitly
Qn ∼
0
e−iϕ(n−3)f2(n, r)qn(xµ)e−iϕ(n−1)f3(n, r)qn(xµ)
0
Dm ∼
e−iϕ(m−1)f3(m, r)dm(xµ)
00
e−iϕ(m−3)f2(m, r)dm(xµ)
←
ψ+R
ψ+L
ψ−L
ψ−R
7
3 Families from 1. Hierarchy. Maxim Libanov
r
ei·0·ϕei·1·ϕ
ei·2·ϕ
H(r) F(r)(Φ = F(r)eiϕ)
Allowed by symmetries couplings
YX · HXQ1 − Γ7
2D + YΦ · HΦQ
1 − Γ7
2D
mnm ∝2π∫0
dϕR∫
0
drQnDmHX(or F(r)eiϕ)
∼ σ2n(−1) · δ(n − m( + 1)) ∼
σ4 σ3
σ2 σ1
1
Q∗n ∼
0
eiϕ(n−3)f2(n, r)qn(xµ)eiϕ(n−1)f3(n, r)qn(xµ)
0
Dm ∼
e−iϕ(m−1)f3(m, r)dm(xµ)
00
e−iϕ(m−3)f2(m, r)dm(xµ)
←
ψ+R
ψ+L
ψ−L
ψ−R
8
3 Families from 1. Hierarchy. Maxim Libanov
r
ei·0·ϕei·1·ϕ
ei·2·ϕ
H(r) F(r)(Φ = F(r)eiϕ)
σ depends on the parameters of themodel. Hierarchy arises at σ ∼ 0.1
m2 : m1 : m0 ∼ σ4 : σ2 : 1 ∼ 10−4 : 10−2 : 1
UCKM∼
1 σ σ4
σ 1 σσ2 σ 1
Generation number⇔ Angular momentum
X The scheme is very constrained, as the profiles are dictated by the equations
9
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
M2NcN + h.c.
⇒ Kaluza-Klein tower in 4D (no zero mode)⇒ Effective 6D couplings with leptons allowed by symmetries∑
S+
HS+L1 + Γ7
2N +
∑S−
HS−L1 − Γ7
2N + h.c.
S+ = X∗, Φ∗, X∗2Φ, . . .S− = X2, XΦ, Φ2, . . .
Non-zero windings ⇒more composite structure ofthe mass matrix
⇒ 4D Majorano neutrinos masses are generated by See-saw mechanism
10
Why Neutrinos Are Different? Maxim Libanov
Neutrinos:
mνmn ∼
2π∫0
dϕR∫
0
drF(r,ϕ) ·[LcL ∝ LL
]
∼2π∫0
dϕei(4−n−m+...)ϕ ∼ δ(4 − m − n + . . .)
∼
· · 1· σ2 ·1 · ·
0eiϕ(3−n)
eiϕ(1−n)
0
0
eiϕ(3−m)
eiϕ(1−m)
0
←ψ+R
ψ+L
ψ−L
ψ−R
→
Charged fermions:
mchargedmn ∼
2π∫0
dϕR∫
0
drF(r,ϕ) ·[ΨΨ ∝ Ψ∗Ψ
]
∼2π∫0
dϕei(n−m+...)ϕ ∼ δ(n − m − . . .)
∼
σ4 · ·· σ2 ·· · 1
0eiϕ(3−n)
eiϕ(1−n)
0
e−iϕ(1−m)
00
e−iϕ(3−m)
11
Why Neutrinos Are Different? Maxim Libanov
Neutrinos:
mνmn ∼
· · 1· σ2 ·1 · ·
U†νmνU
∗ν ∼ diag(−m,m, mσ2)
Uν ∼
1/√2 1/√2 σ
σ σ 1−1/√2 1/√2 σ
Charged fermions:
mchargedmn ∼
σ4 · ·· σ2 ·· · 1
mdiag
charged ∼ diag(µσ4, µσ2, µ)
UCKM∼
1 σ σ4
σ 1 σσ2 σ 1
m�µ due to See-Saw
12
Why Neutrinos Are Different? Maxim Libanov
Consequences of this structure
mν ∼
· · 1· σ2 ·1 · ·
mdiagν ∼
−m 0 00 m 00 0 mσ2
Inverted hierarchy:
∆m2� = ∆m2
12
∆m212
∆m213∼ σ2 ∼ 10−2
Solar angle automaticaly large
Small reactor angle
Ue3 ∼ σ ∼ 0.1
Uν ∼
1/√2 1/√2 σ
σ σ 1−1/√2 1/√2 σ
13
Why Neutrinos Are Different? Maxim Libanov
Consequences of this structure
mν ∼
· · 1· σ2 ·1 · ·
mdiagν ∼
−m 0 00 m 00 0 mσ2
Pseudo-Dirac structure ⇒The − sign may be absorbed inthe mixing matrix, but contributesdestructively to the effective massfor neutrinoless double beta decay(Pseudo-Dirac structure when fullCabibbo-like mixing is introduced)0νββ decay
partial suppression
|〈mββ〉| '13
√∆m2⊕
•
14
Why Neutrinos Are Different? Maxim Libanov
Semi-realistic numerical example
mdiagν =
−50.03 0 0
0 50.79 00 0 0.7089
[meV], UMNS =
0.808 0.559 0.186−0.286 0.660 −0.693−0.514 0.502 0.696
∆m2
12 = 7.63 × 10−5eV2
∆m213 = 2.50 × 10−3eV2 =⇒
∆m212
∆m213
= 3.05%
tan2 θ12 = 0.471(0.47+0.14
−0.10
)tan2 θ23 = 0.997
(0.9+1.0
−0.4
)sin2 θ13 = 3.46 · 10−2 (≤ 0.036)
Consequence for 0νββ decay
|〈mββ〉| =∣∣∣∑
imiU2
ei
∣∣∣ = 17.0 meV
15
FCNC Maxim Libanov
Flavour Violation
Like in the UED, vector bosons can travel in the bulk of space. From the4D point of view:
1 massless vector boson in 6D=
1 massless vector bozon (zero mode)⇔ SM boson
+ KK tower of massive vector bosons Mn ∼nR
⇒ FCNC
+ KK tower of massive scalar bosons in 4D
⇒ KK scalar modes do not interact with fermion zeromodes
16
FCNC Maxim Libanov
KK vector modes carry angular momentum = family number. In the absenceof fermion mixings, family number is an exactly conserved quantity ⇒processes with ∆G = ∆J ≠ 0 are suppressed by mixing.
K0L → µ±e∓
∆G = ∆J = 0
d
s
Jds = 1
Jµe = 1
∼κ2
M2Z′
JZ′ = 1
µ
e
µ→ eee
∆G = ∆J = 1
µ
JZ′ = 0
Jµ = 1
Je = 2
e
e
∼ σκ2
M2Z′
σ
Jee = 0
e
X κ = 1 for the particular model, but may be � 1 for extensions
17
FCNC Maxim Libanov
Rare (forbidden) processes:
∆G = 0: K0L → µe, K+→ π+µ+e− P ∼ σ0κ4/M4
Z′
Bs→ µτ, Bd→ eτ∆G = 1: µ→ eee, µe-conversion, µ→ eγ P ∼ σ2κ4/M4
Z′
∆G = 2: mass difference KL − KS, CP-violation P ∼ σ4κ4/M4Z′
Bound onMZ′ & κ · 100 · TeV
A clear signature of the model would be an observation
K0L → µe
without observation other FCNC-processes at the sameprecision level
18
FCNC Maxim Libanov
1 2 3 4 5M,TeV
0.050.1
0.51
510
Num
berof
even
ts
1
MZ′ = κ · 100TeV
L = 100 fb−1 √s = 14TeV
K0L → µe
forbidden
LHC beats fixed target
Tevatronlimit
Search at LHC
Search for an «ordinary»massive Z′(W′, g′, γ′)
Search for pp→ µ+e− + . . .
Search for pp→ µ−e+ + . . . ---one order below due to quarkcontent of protons
Search for pp→ t + c + . . . orpp→ b + s + . . . --- expect a few1000’s events, but must considerbackground!
LHC thus has the potential (in a specificmodel) to beat even the very sensitivefixed target K→ µe limit!
19
Flavour puzzle or Why Neutrinos Are Different? Maxim LibanovConclusions
Family replication model in 6D: elegant solution to the flavour puzzleHierarchical Dirac masses + small mixing anglesNeutrinos are different: See-saw + Majorano-like mass for the bulkneutral fermion can fit neutrino dataFamily/lepton number violating FCNC suppressed by small fermionmixings
Predictions for neutrinosInverted hierarchyReactor angle ∼ 0.1Partially suppressed neutrinoless ββ decay
Other predictionsK→ µe will show up earlier than other FCNC-processesMassive gauge bosons with mass ∼ TeV or higherSearch for pp→ µ+e− at LHC can beat fixed targetConstraint on B-E-H (Higgs) boson: should be LIGHT
20