–1–
CPT
INVARIANCE TESTS IN NEUTRAL KAON
DECAY
Updated October 2009 by M. Antonelli (LNFINFN, Frascati)
and G. D’Ambrosio (INFN Sezione di Napoli).
theorem is based on three assumptions: quantum
feld theory, locality, and Lorentz invariance, and thus it is
a ±undamental probe o± our basic understanding o± particle
physics. Strangeness oscillation in
K
0
−
K
0
system, described
by the equation
i
d
dt
·
K
0
K
0
¸
=[
M
−
i
Γ
/
2]
·
K
0
K
0
¸
,
where
M
and Γ are hermitian matrices (see PDG review [1],
re±erences [2,3], and KLOE paper [4] ±or notations and previous
literature), allows a very accurate test o±
symmetry;
indeed since
requires
M
11
=
M
22
and Γ
11
=Γ
22
,themass
and width eigenstates,
K
S,L
,havea
violating piece,
δ
,in
addition to the usual
conserving parameter
±
:
K
S,L
=
1
q
2
(
1+

±
S,L

2
)
h
(
±
S,L
)
K
0
+
(
1
−
±
S,L
)
K
0
i
±
S,L
=
−
i
±
(
M
12
)
−
1
2
±
(Γ
12
)
∓
1
2
·
M
11
−
M
22
−
i
2
(Γ
11
−
Γ
22
)
¸
m
L
−
m
S
+
i
(Γ
S
−
Γ
L
)
/
2
≡
±
²
δ.
(1)
Using the phase convention
±
(Γ
12
) = 0, we determine the phase
o±
±
to be
ϕ
SW
≡
arctan
2(
m
L
−
m
S
)
Γ
S
−
Γ
L
. Imposing unitarity to
an arbitrary combination o±
K
0
and
K
0
wave ±unctions, we
obtain the BellSteinberger relation [5] connecting
CP
and
violation in the mass matrix to
and
violation in
the decay; in ±act, neglecting
O
(
±
) corrections to the coeﬃcient
o± the
violating parameter,
δ
, we can write [4]
[
Γ
S
+Γ
L
Γ
S
−
Γ
L
+
i
tan
φ
SW
][
³
(
±
)

±

2
−
i
±
(
δ
)] =
1
Γ
S
−
Γ
L
X
f
A
L
(
f
)
A
∗
S
(
f
)
,
(2)
CITATION: K. Nakamura
et al.
(Particle Data Group), JPG
37
, 075021 (2010) (URL: http://pdg.lbl.gov)
July 30, 2010
14:34