heavy-meson physics and avour violation with a single

Heavy-meson physics and flavour violation with a single

generation1

I. Timiryasov

in collaboration with: M. Libanov N. Nemkov E. Nugaev

June 29, Erice, Sicily

1based on JHEP 1208 (2012) 136Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 1 / 17

Motivation

Problems:

Gauge hierarchy

Family replication

Mass hierarchy

Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 2 / 17

Model with LED and a single generation

Model with large extra dimensions and a single generation [Libanov, Troitsky,

Frere ’00, Libanov, Troitsky, Frere, E. Nugaev ’03]

Extra dimensions are compactified into the two-dimensional sphere

M4 ⊗ S2 (R − radius of the sphere)

Processes with FCNC and flavour violation appear in the model due to KK

modes of gauge bosons

One could bound R via studying rare processes: lepton number violation and

flavour violation


Model with LED and a single generation: vortex

3D World

ϕθ

Observable world is a core of

Abrikosov-Nielsen-Olesen vortex.

LV =√|g |(− 1

4 FABFAB+(DAΦ)†DAΦ−λ2 (|Φ|2−v2)2),

where A is Ug (1) gauge field and Φ is a

scalar

There is only one generation of

six-dimensional fermions


Model with LED and a single generation: fermions

Zero modes of fermions localized in a core of vortex due to interaction with

vortex:

Lint = g Φ Ψ1− Γ7

2Ψ

Generalized momentum

J = −i∂φ − k1 + Γ7

2(1)

is conserved in a vortex background.

6D zero modes ↔ 4D chiral fermionic families

J ↔ generation number in 4D effective theory


Origin of mass hierarchy

θ

e i·0·φ

e i·1·φ

e i·2·φ

H(r) Φ(r)

Zero modes with different

momentum (n = 0, 1, 2)

have different shape in extra

dimensions:

J Ψn ≡ −(

i∂ϕ + 31 + Γ7

2

)Ψn = nΨn

Ψn(θ → 0) ∼ (θ)3−n · e i(3−n)φ

Four dimensional masses

generated by Higgs field H:

mnm ∝2π∫

0

dϕ

π∫0

sin θdθΨnΨmHΦ


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 1

SM gauge Zµ,... Kaluza-Klein 0 SM SM SMfields spectrum

r


Rare processes

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 6= 0 are suppressed by orders of small mixing parameter ε∆G , ε ∼ 0.1.

B0 → τe

∆G = ∆J = 0

∼ #M2

Z′

B0s → µµ

∆G = ∆J = 1

∼ ε #M2

Z′


Calculation of B0s → µe decay width

B0s → µe decay BR(B0

s → µe) < 2.0 · 10−7

[Beringer et al. ’12]

Coupling in the effective four-dimensional Lagrangian:

g

2 cos θW

∞∑l=1

Zµl,1

{E l,1

23 sγµ

(−1

2γ5

)b + E l,1

12 eγµ

(2 sin2 θW −

1

2− 1

2γ5

)µ

}


Calculation of B0s → µe decay width

Decay width:

Γ(B0s → µ+e−) =

G 2Fm4

Z ζ2R4f 2

BsmBs m

2µ(1 + (1− 4 sin2 θW )2)

128π,

where∑∞

l=1E l,1

23 E l,112 R2

l(l+1) = ζR2, ζ ' 0.47

Using

BR(B0s → µe) = Γ(B0

s → µe)τB0s< 2.0 · 10−7

We obtain restriction on R:

1

R> 0.7 TeV.


B0 → K 0µe decay

Three-particle decay B0 → K 0µe

Width:

Γ = m4W

G 2F ζ

2R4F 21 (0)m5

Bd(C 2

V + C 2A)

6π3,

where CV and CA - numerical coefficients.

We get restriction:1

R> 3.3 TeV.


Processes with ∆G 6= 0

Total change of generation number ∆G = 0 due to the conservation of

momentum J.

Processes with ∆G 6= 0 are allowed due to the mixings.

For B0 → µe decay:

g

2 cos θW

∞∑l=2

Zµl,2E l,2

13

{bγµ(−1

2γ5)d + εLαLeγµ(2 sin2 θW −

1

2− 1

2γ5)µ

}

1

R> mZ

(G 2F ξ

2(εLαL)2f 2Bd

mBdm2µτ(Bd)(1 + (1− 4 sin2 θW )2)

64πBB0→µe

) 14

= 0.15 TeV.


Experimental data and results

BR ∆G 1/R >,TeV

B0s → µe < 2.0 · 10−7 0 0.7

B0 → τe < 2.8 · 10−5 0 0.65

B0 → K 0µe < 2.7 · 10−7 0 3.3

D0 → µe < 8.0 · 10−7 0 0.3

K 0L → µe 2 < 2.4 · 10−12 0 60

B0 → µe < 6.4 · 10−8 1 0.15

B0s → µ+µ− 3.2 · 10−9 1 0.46

D0 → µ+µ− < 1, 3 · 10−6 1 0.11

B0s ↔ B

0

s ∆mB0s≈ 1.17 · 10−8 MeV 2 0.09

2The stringent bound from kaon physics, [hep-ph/0309014]Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 13 / 17

Conclusions

We found that the best limit 1/R > 3.3 TeV arises from the three-particle

decay B → Kµe. This bound is much less stringent than the constraint

arising from the two-particle decay K → µe in kaons. The reason is the still

too poor statistics: the experimental bound on the branching ratio of

K → µe is 2.4 · 10−12 while for the B-meson decay is 2.7 · 10−7.

The distinctive feature of the model would be an observation of K → µe and

B → Kµe decays without observations of other flavour-changing processes at

the same precision level.


THANK YOU!


Effective 4-dimensional interaction of the fermionic zero modes with KK

tower of gauge boson is given by (all fields depend on 4-dimensional

coordiantes only)

L4 = e · Tr(Aµj∗µ),

with

Aµ = (Aµ)† =∞∑l=0

E l,011 Aµl,0 E l,1

12 Aµl,1 E l,213 Aµl,2

E l,121 Aµ∗l,1 E l,0

22 Aµl,0 E l,123 Aµl,1

E l,231 Aµ∗l,2 E l,1

32 Aµ∗l,1 E l,033 Aµl,0,

,

and

jµmn = a†mσµan,

where an are two-component Weyl spinors.


To incorporate quark mixings in a model, additional field X is required.

If one rewrites the current jµ in terms of the mass eigenstates, then the

matrix Aµ, should be replaced by

Aµ = S†dAµSd .

Explicit form of Aµ:


heavy-meson physics and avour violation with a single

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