Kaons and CP violation
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Transcript Kaons and CP violation
Particle-antiparticle mixing and CP
violation
• There is another type of “mixing” which is
related to quark mixing. This can lead to
observation and studies of CP violation
• consider the mesons which are neutral and
composed of different types of quarks
0
0
0
d
0
s
0
0
0
d
0
s
K (ds ) D (uc ) B (db ) B ( sb )
K (d s) D (u c) B (d b) B ( s b)
• Weak interactions can change particle into
antiparticle as charge and other quantum
numbers are the same. The “strangeness”
etc are changing through CKM mixing
d
K
0
u,c,t
s
W
K0
d
s
u, c,t
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• Depends onVij at each W vertex
• as V and V* are different due to phase,
gives particle-antiparticle difference and CP
violation (any term with t-quark especially)
• the states which decay are admixtures of the
“strong” state(a rotation). They can have
different masses and different lifetimes
K1 K 0 K 0
K2 K 0 K 0
• #particle vs #antiparticle will have a time
dependence. Eg. If all particle at t=0, will be
a mixture at a later time
• the phenomenology of K’s is slightly
different than B/D’s and we’ll just do K’s in
detail. Kaons rotate and give long-lived and
short-lived decays. B/D also rotate but
lifetimes are ~same.
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Neutral Kaon Semi-leptonicDecay
• Properties for “long” and “short” lived
K 0 : m ass 498MeV , mK L mK S 3 1012 MeV
K 1010 sec K 5 108 sec
S
L
• Semi-leptonic (Beta) decays. Positive or
negative lepton tells if K or anti-K decayed
K 0 (ds ) (du ) e or
K 0 (d s) (d u ) e or
• partial width is exactly the same as charged
K decay (though smaller BF for Short and
larger for Long).
4
BF 7 10 K S
BF 0.3K L
BF
BF
0.7 107 sec1
0.6 107 sec1
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Neutral Kaon Hadronic Decays
• Also decay hadronically
K 0 (ds ) or 0 0
K 0 (ds ) or 0 0
K 0 (ds ) 0 or 0 0 0
K 0 (ds ) 0 or 0 0 0
• Both decay to same final states which
means the mixed states K1 and K2 also
decay to these 2pi and 3pi modes. Means
initial states can mix and have interference
K K
0
d
u
d
0
d
u
s
u d
d
d
s
u
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Sidenote C+P for Pions
• Parity operator Pf(x,y,z)=f(-x,-y,-z).
Intrinsic parity for psuedoscaler mesons
(like K,pi) is -1
• Charge conjugation operator C. Changes
particle to antiparticle.
C
C K K
C0 0
C K0 K 0
C (C 0 ) C ( 0 ) 2 0 1
• Can work out eigenvalue. As C changes
charge, C=-1 for photon
C
e-
e+
=
• given its decay, pion has C= +1
0
BF
(
)
0
7
4
10
BF( 0 )
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Neutral Kaon Hadronic Decays
• 2 pion and 3 pion are CP eigenstates with
eigenvalue +1 for 2pi and -1 for 3pi
CP
CP 0 0 0 0
CP 0 0
CP 3 0 3 0
• K1 and K2 also CP eigenstates
1
( K 0 K 0 ) K S CP 1
2
1
( K 0 K 0 ) K L CP 1
2
K1
K2
( K S ) 0.9 1010 s
( K ) 1.2 108 s
( K L ) 5.2 108 s
• different values of matrix element if initial
and final states are the same CP eigenstate
or if they are not CP eigenstates (like K+ or
beta decays)
• if CP is conserved, K1/Ks decays to 2 pions
and K2/KL decays to 3 pions. More phase
space for 2 pions and so faster decay,
shorter lifetime.
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Decay and Interference
• From Schrodinger eq. plane wave solutions
( K S ) AS (t 0)e
( K L ) AL (0)e
(
(
S
2
ims )
L
imL )
2
eiEt / , E m
e t / 1
2
assume: K s K1; K L K2
• the two amplitudes have to be added and
then squared. Gives interference. Example:
start with pure K0
K0
1
1
( K L K S ) AS (0) AL (0)
2
2
• Intensity is this amplitude squared
I ( K 0 ) ( K S ) ( K L ) * ( K S ) * ( K L )
1 S t
e e Lt 2e ( S L )t / 2 cos m t
4
m mL mS 105 eV
• small mass difference between the two
weak decay eigenstates
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Decay and Interference
• Do the same for anti-K
I ( K 0 ) ( K S ) ( K L ) * ( K S ) * ( K L )
1 S t
e e Lt 2e ( S L )t / 2 cos m t
4
• get mixing. Particle<->antiparticle varying
with time.
• At large time get equal mixture = 100% KL
• the rate at which K->anti-K depends on
1/deltam. You need to mix K<->antiK
before they decay to have KS and KL
m S 0.47 " K S " , " K L " decays
But
If
(m) 1 K 0 just " K 0 " decays
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KS Regeneration
KL
1
(K 0 K 0 )
2
• Assume pure KL beam
• strikes a target made up of particles (p,n)
• different strong interaction cross section for
K and anti-K 0
K ( d s ) n (uds ) 0
K 0 n (uds ) 0
• mix of K-antiK no longer 1:1. Example,
assume “lose” 0.5 antiK, 0.0 K. gives
(ignoring phases and so not quite right)
0
K
0
K
aKL bKS
2
a( K 0 K 0 ) b( K 0 K 0 ) a 34 , b
1
4
• First observed by Lederman et al. measures
particle/antiparticle differences. Useful
experimental technique
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CP Violation
•
•
•
•
•
1
2
3
C changes particle to antiparticle
P operator flips space (mirror image)
T time reversal t --> -t
fundamental axiom (theory?) of quantum
mechanics CPT is conserved
Weak interaction violate all 3. CP violation
is the same as T violation. Three
observations (so far) of this
Universe is mostly matter (Sakharov
1960s)
KL decay to 2 pions (Christianson, Cronin,
Fitch and Turlay, 1964)
neutral B decays
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CP Violation in K decays
• Ks and KL (the particles which have
different lifetimes) are NOT eigenstates of
CP. Instead K1 and K2 are
1
(K 0 K 0 )
2
1
KL
( K 2 K1 ) | | 2.2 103
1 | |2
K1, 2
KS
1
1 | |
2
( K1 K 2 )
K0
K
0
KS
K1
KL
K2
• When KL decays, mostly it is decaying to a
CP=-1 state(3 pions) but sometimes to a
CP=+1 state (2 pions)
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CP violation in K decays
• CP is then explained by having a phase in
the mixing between K and anti-K
• other sources of CP violation (“fifth force”)
are ruled out as inconsistent with the
various ways of observing CP violation
K L
BF 2.1103
K L 0 0
BF 9 10 4
K S 0
BF (3) 107
ch arg e asym m etry L 0.3 102
( K L ) ( K L )
(or e)
( K L ) ( K L )
am p( K L 0 0 )
.9950 .0008
am p( K L )
d
K
0
u,c,t
s
W
K0
d
s
u, c,t
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