heavy-meson physics and avour violation with a single
TRANSCRIPT
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
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 3 / 17
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
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 4 / 17
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
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 5 / 17
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
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 6 / 17
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
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 7 / 17
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′
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 8 / 17
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
}
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 9 / 17
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.
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 10 / 17
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.
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 11 / 17
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.
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 12 / 17
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.
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 14 / 17
THANK YOU!
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 15 / 17
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.
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 16 / 17
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:
Inar Timiryasov (INR, MSU) Model with LED June 29, Erice, Sicily 17 / 17