Abstract
Abstract
The most precise measurement of the the slope of the time-dependent asymmetry defined by the parameter
Δ
Y
f
(
f
=
K
+
K
−
,
π
+
π
−
), of the decay rates of
D
0
and
D
¯
0
mesons into the final states in the decays
D
0
→
K
+
K
−
and
D
0
→
π
+
π
−
were recently reported by LHCb collaboration with the values of
Δ
Y
K
+
K
−
=
(
−
2.3
±
1.5
±
0.3
)
×
1
0
−
4
and
Δ
Y
π
+
π
−
=
(
−
4.0
±
2.8
±
0.4
)
×
1
0
−
4
.
In this study, we have obtained
Δ
Y
K
+
K
−
=
(
−
2.27
±
1.12
)
×
1
0
−
4
and
Δ
Y
π
+
π
−
=
(
−
3.15
±
1.72
)
×
1
0
−
4
where
Δ
Y
constrains possible
CP
violation. The
CP
violation in the decays
D
0
→
K
+
K
−
and
D
0
→
π
+
π
−
have been calculated under the factorization approach. These decay modes include a current-current tree and penguin diagrams that their amplitudes are considered separately, by introducing strong and weak phases with the
δ
and
ϕ
parameters, respectively. We have obtained for both of decays
δ
1
=
0
∘
,
δ
2
=
(
90.04
±
0.01
)
∘
,
ϕ
1
=
0
∘
and
ϕ
2
=
(
68.48
±
1.55
)
∘
.
The
CP
asymmetries are calculated to be
A
CP
(
K
+
K
−
)
=
(
+
0.03
±
0.02
)
%
and
A
CP
(
π
+
π
−
)
=
(
+
0.03
±
0.01
)
%
at
μ
=
1
GeV
.
Finally, from the sum of the amplitudes, we have calculated the total amplitude and obtained comparable results with experimental values for the branching ratios of decays.
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics