sin2β
The mixing induced CP asymmetry, aJ/Ψ K0,
in the Bd → J/Ψ K0 decays allows to determine the
sine of the angle 2β almost without any hadronic uncertainties.
In this case the CP asymmetry appears in the interference between amplitudes describing
decays with and without mixing. The simples case is when the final state is a specific
CP state. The following time dependent asymmetry is studied :
The decay is dominated by a single (tree level) amplitude ( the same process can be described
by a Penguin diagram which brings corrections at order ~ λ4 ). It implies
that Cf ~ 0 and the expression simplify to :
The constraint on sin2β is obtained combining the experimental
measurement on B0 → J/Ψ K0 decays to
the data-driven determination of the theoretical error, obtained
from the time-dependent asymmetry of B0 → J/Ψ
π0 and the determination of decay rate and the C
parameter of the time-dependent asymmetry in B0 →
J/Ψ K0, following the prescription of hep-ph/0507290. The constraint on sin2β from
B0 decays to K0 and higher charmonium states
is not included, since the experimental information to determine the
theoretical error on that is missing.
The world averages for the experimental observables (taken from HFAG when not specified)
are summarized in the table below
Observable
|
B0 → J/Ψ π0
|
B± → J/Ψ π±
|
B0 → J/Ψ K0
|
Branching Ratio [10-5]
|
2.02 ± 0.25
|
4.8 ± 0.4
|
86.3 ± 3.5
|
C / -ACP
|
-0.11 ± 0.20
|
-0.09 ± 0.08
|
0.002 ± 0.021
|
S
|
-0.68 ± 0.25
|
-
|
0.668 ± 0.026
|
Using these values, we obtain the following shapes for the theoretical error (top-left) and the
value (top-right) of sin2β, shown also on the
(EPS)
[JPG]
|
theoretical error on sin2β
ΔS = 0.000 ± 0.012
|
|
(EPS)
[JPG]
|
Distribution of sin2β from B0 → J/Ψ K0
sin2β = 0.668 ± 0.028
|
|
(EPS)
[JPG]
|
sin2β bound from B0 → J/Ψ K0
shown on the (ρ,
η) plane
|
|