Neutral Kaon system

1

Neutral Kaon system


2
Ko Ko system

• Kaon mesons in two isospin doublets

Part of pseudo-scalar JP0- meson octet with ?,?
K us Ko ds
K- us Ko ds
I31/2 I3-1/2
S1
S-1

• Kaon production

Ko ?- p ??o Ko But from baryon number
conservation Ko ? p ?K Ko p Or Ko ?-
p ??o Ko n n
Requires higher energy
S 0 0 -1 1
S 0 0 1 -1 0
Much higher
S 0 0 1 -1 0 0
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Kaon oscillations
d
s
W-
u, c, t
u, c, t
_
_
W
-
d
s
K0
K0
u, c, t
_
d
s
W-
W
_
_
_
_
u, c, t
d
s

• So say at t0, pure Ko,
• later a superposition of states

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Ko Decay
Assume CP
KS
show
mass eigenstates
CP1 CP-1
KL

• In that case

KS branching fractions pp- ? 69, p0p0 ? 31 KL
branching fractions p0p0p0 ? 21, pp-p0 ? 13,
??p?n ? 66
Ks??o?o Ks???- KL???-?o KL??o?o?o
CP1 CP-1
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Time dependent probabilities for the neutral
kaon case.
t (1/G)
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Ko Regeneration

• Start with Pure Ko beam
• After time all Ks component decayed
• Introduce slab of material in beam
• reactions

1) Elastic scatttering
2) Charge exchange
3) Hyperon production

• Hence Ko absorbed more strongly

i.e. Ks regenerated
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Discovery of CP Violation
K1??o?o K1???- K2???-?o K2??o?o?o
So if KL K1 CP eigenstate, Observe no two pion
component
CP1 CP-1
But if broken get
Where ? quantifies degree of CP violation

• BUT Can one find KL decaying into ??-?

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J.H. Christenson et al., PRL 13,138
(1964) Discovery of CP violation

• Mass and angular spectrum

KL ? pp-X
m (pp-) lt mK
p- pp pp- q angle between pKL and p- If
X 0, p- pKL cos q 1 If X ? 0, p- ? pKL
cos q ? 1
q
m (pp-) mK
KL
m (pp-) gt mK
KL ?
cos q
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So CP symmetry is violated in the neutral kaon
system.
Mass eigenstates (KS and KL) ? CP eigenstates
Both KS and KL could decay into ?-?-.

• Experimentally well known
• The majority of KS decays into p-p- and KL into
  p-p--p0.

In KL
Small but with profound implications
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CPLEAR revisited
Initial state at t 0
S 0

• Tag Ko/Ko from charged pion/kaon

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CPLEAR R-(t) and R-(t)
K0
_
_
K0
CP violation
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CPLEAR CP asymmetry
_
R-(t) - R-(t) R-(t) R-(t)
_
A-(t)
large difference!

• CP violation in mixing
• The two mass eigenstates are not CP eigenstates

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Kaons CP violation in Decay
CP violation first through existence of certain
decay modes
2.3x10-3
If CP violation is only in mixing, i.e.
independent of decay
So, put channel independent term ? and channel
dependent ?
Hence, by measuring only rates
get
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So, two expts in the 80s did it

• NA31 (CERN)
• E731 (Fermilab)
• Ambiguous result!

So, two expts did it again.
15
NA48
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KTeV
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Measure
Normalisation constants
No normalization is required, but efficiencies,
acceptances etc. have to be corrected
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Effort over 30 years!
Not easy to compare with SM theory
0.0050 ? 0.0005 ? 0 ? h- ? h00
Note 3 Re h-/h00 - 1, i.e. Re
? 0
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CKM parameters with CP conserving parameters

• Vud nuclear Beta decay
• 0.9734??0.0008
• Vus semileptonic Kaon and hyperon decay
  (CCFR) 0.2196??0.0026
• Vcd Neutrino and anti-neutrino production of
  charm off valence d quarks
• 0.224 ??0.016
• Vcs W decays (LEP/me!)
• 0.996??0.013
• Vcb semileptonic inclusive and exclusive B
  decays (LEP/CLEO)
• 0.0412??0.0020
• Vub end point spectrum in semileptonic B
  decays(LEP/CLEO)
• 0.0036 ?0.0007
• Bo mixing xd, lattice gauge inputs VtbVtd
  0.0079 ?0.0015
• Can use Unitarity constraints