–1–
CP
VIOLATION IN
K
L
DECAYS
Updated May 2010 by L. Wolfenstein (CarnegieMellon Univer
sity), T.G. Trippe (LBNL), and C.J. Lin (LBNL).
The symmetries
C
(particleantiparticle interchange) and
P
(space inversion) hold for strong and electromagnetic inter
actions. After the discovery of large
C
and
P
violation in the
weak interactions, it appeared that the product
was a good
symmetry. In 1964
violation was observed in
K
0
decays at
a level given by the parameter
±
≈
2
.
3
×
10
−
3
.
A uniFed treatment of
violation in
K
,
D
,
B
,a
n
d
B
s
mesons is given in “
Violation in Meson Decays” by
D. Kirkby and Y. Nir in this
Review
. A more detailed review
including a thorough discussion of the experimental techniques
used to determine
violation parameters is given in a book
by K. Kleinknecht [1].
Here we give a concise summary of the
formalism needed to deFne the parameters of
violation in
K
L
decays, and a description of our Fts for the best values of
these parameters.
1. Formalism for
violation in Kaon decay:
violation has been observed in the semileptonic decays
K
0
L
→
π
∓
²
±
ν
, and in the nonleptonic decay
K
0
L
→
2
π
.The
experimental numbers that have been measured are
A
L
=
Γ(
K
0
L
→
π
−
²
+
ν
)
−
Γ(
K
0
L
→
π
+
²
−
ν
)
Γ(
K
0
L
→
π
−
²
+
ν
)+Γ(
K
0
L
→
π
+
²
−
ν
)
(1
a
)
η
+
−
=
A
(
K
0
L
→
π
+
π
−
)
/A
(
K
0
S
→
π
+
π
−
)
=

η
+
−

e
iφ
+
−
(1
b
)
η
00
=
A
(
K
0
L
→
π
0
π
0
)
(
K
0
S
→
π
0
π
0
)
=

η
00

e
iφ
00
.
(1
c
)
violation can occur either in the
K
0
–
K
0
mixing or
in the decay amplitudes. Assuming
CPT
invariance, the mass
eigenstates of the
K
0
–
K
0
system can be written

K
S
±
=
p

K
0
±
+
q

K
0
±
,

K
L
±
=
p

K
0
±−
q

K
0
±
.
(2)
If
invariance held, we would have
q
=
p
so that
K
S
would
be
even and
K
L
odd. (We deFne

K
0
±
as

K
0
±
).
CITATION: K. Nakamura
et al.
(Particle Data Group), JPG
37
, 075021 (2010) (URL: http://pdg.lbl.gov)
July 30, 2010
14:34
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CP
violation in
K
0
–
K
0
mixing is then given by the parameter
e
±
where
p
q
=
(1 +
e
±
)
(1
−
e
±
)
.
(3)
violation can also occur in the decay amplitudes
A
(
K
0
→
ππ
(
I
)) =
A
I
e
iδ
I
,A
(
K
0
→
(
I
)) =
A
∗
I
e
iδ
I
,
(4)
where
I
is the isospin of
,
δ
I
is the Fnalstate phase shift,
and
A
I
would be real if
invariance held. The
violating
observables are usually expressed in terms of
±
and
±
±
deFned
by
η
+
−
=
±
+
±
±
,η
00
=
±
−
2
±
±
.
(5
a
)
One can then show [2]
±
=
e
±
+
i
(Im
A
0
/
Re
A
0
)
,
(5
b
)
√
2
±
±
=
ie
i
(
δ
2
−
δ
0
)
(Re
A
2
/
Re
A
0
)(
Im
A
2
/
Re
A
2
−
Im
A
0
/
Re
A
0
)
,
(5
c
)
A
L
=2Re
±/
(1 +

±

2
)
≈
2Re
±.
(5
d
)
In Eqs. (5a), small corrections [3] of order
±
±
×
Re (
A
2
/A
0
)are
neglected, and Eq. (5
d
) assumes the Δ
S
=Δ
Q
rule.
The quantities Im
A
0
,Im
A
2
,andIm
e
±
depend on the choice
of phase convention, since one can change the phases of
K
0
and
K
0
by a transformation of the strange quark state

s
±→
s
±
e
iα
;
of course, observables are unchanged. It is possible by a choice
of phase convention to set Im
A
0
or Im
A
2
or Im
e
±
to zero,
but none of these is zero with the usual phase conventions
in the Standard Model. The choice Im
A
0
= 0 is called the
WuYang phase convention [4], in which case
±
=
e
±
.Theva
lue
of
±
±
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 Spring '11
 Kutter
 Particle Physics, Weak interaction, Ks, CP violation, Kaon

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