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1FK7003
Lecture 8
● CP-violation● T-violation ● CPT invariance
2FK7003
Recap
0 10 81 2
0 01 2
10 5 10
ˆ ˆ | ( 1) ; | (
(1) The weak force appears to respect symmetry in many processes.
(2) Kaons studied: comprises two states decaying weakly: ,
(3) Formed eigenstates
CP
K s s
CP K CP K
0 0 0 0 0 01 2
0 0 0 0 0 01 2 1 2
0 0 01 2
1).
1 1| | | | | |
2 21 1
| (| | ) | (| | )2 2
,
; , (7.37)
(7.39)
(4) Hypothesised: eigenstates are the "mass" states observed in the decay
strange
CP
K K K K K K
K K K K K K
CP K K K
0 0
0 01 2( 1) ( -1)
ness oscillation , experimentally proven - we're on the right! track!
(5) conservation ;
The 2 decay will happen faster because of greater phase space
-Hypothes
K K
CP K CP K CP
0 01 1 2 2, 1 , : 1ised: : and (7.40) K CP K CP
3FK7003
Looking for CP violation via kaons decays
Incoming K2 beam
Decay of K2 into 3 pions
0 0
0
0 0 01 2
01 1
1| | |
2
( )
Consider eg a beam of produced, eg, via:
At production, the is a superposition of two eigenstates.
After a period of time the
component should have
K p n K K p p
K CP
K K K
t K
02
02
vanished.
Expect .
Christenson, Conin, Fitch and Turlay (1964).
Use above principle to form beam of -mesons.
Detector > 15m away from production.
Sensitivity to decays.
Principle:
(1) Measu
K
K
re two of the pions.
(2) Sum the momenta - it won't
"point along the beam".
4FK7003
Neutral Kaon system
2
0 0
2 1
0 0 02 12
,|
| ,| .
1| (| |
1 | |
Observed:
45 decays out of 23000 decays.
violation (1980 Nobel prize).
Long and short-lived states physical states:
| are not the -eigenstates:L s
L
K
CP
K K CP
K K
K K K
0 0
0 0 01 22
3
-6
1| (| |
1 | |
2.3 10 " - "
3.5 10
(8.01)
(8.02)
From experiment:
(8.03) ( )
eV (from strangeness oscillations 7.44 ).L S
S
K K
K K K
CP violating effect
Δm m m
Incoming K2 beam
Decay into two pions
5FK7003
Explaining the Cronin/Fitch Experiment
0 0 02 12
01
02
1| (| | )
1 | |
( ) |
( ) |
Two possible contributions to -violatio
LK K K
a K
b K
CP
01
02
( ) |
( ) |
n.
The component decays via a -allowed process to .
indirect -violation - this is dominant.
" violation via mixing"
The component decays via a -forbidden process to
D
a K CP
CP
CP
b K CP
.irect -violation
A tiny effect and discovered around 1996.
CP
6FK7003
CP-violation
0 0 0 0 0 0 02 12 2
0 0
2
0 0 0 0 01 22 2
0 0
1 1| (| | ) | | | |
1 | | 2 1 | |
11 | 1 |
2 1 | |
1 1| (| | ) 1 | 1 |
1 | | 2 1 | |
| ,|
= (8.03)
(8.04)
Proportion of no l
L
S
K K K K K K K
K K
K K K K K
K K
0 0 0 0
0.
| | | |
onger equal in the states when
violation arises from asymmetric mixing.
and occur at different rates.
CP
K K K K
CP
7FK7003
0 0
0
,When dealing with strong interactions: can be thought of as the "particles" with
the definite strangeness (always conserved in strong interaction, eg ).
When dealing with decays, the
K K
p n K K p p
0 0 0 01 2, ,
weak force is responsible. To understand decays
consider (physical states with the definite masses and lifetimes) and their
components!
There is no "right" decision about which "pa
S LK K K K
0 0 0 01 2
0 0 0 01 2
, ; ,
, ,
rticle" should represent a neutral kaon. It depends
on the information available whether you think of it as (a) or with components
or (b) or with ; components. Bo
s L
S L
K K K K K K
K K K K K K th approaches are valid.
Which one is the ”particle” ?
0 0 02 12
0 0 01 22
6
1| (| |
1 | |
1| (| |
1 | |
3.5 10
Physical mass states:
eVL S
L
S
K K
K K K
K K K
m m m
0 0,
Strangeness eigenstates.
The strong force "sees"
these particles. The two
neutral kaons are mass
degenerate.
K su K su
0 0
0 0
,
Strangeness
oscillations:
K K
K K
Produce in strong interaction
Weak interactions break the degeneracy.
8FK7003
CP Lear Experiment• Compare rates for the two processes• CP transformations of each other.• CPLEAR Experiment at CERN (pp interactions)• Consider two strong reactions
0000 KKKK and
)1()1()1()1( 00 SKSKppSKSKpp ,
decays. following the of one in or an for lookingby
or a as life ended it if see and particle that ofdecay the Observe
reactions. the of one in
or of presence the for lookingby produced was or a ifIdentify
ee
KK
KKKK
00
00
e+e-
e
K0K0
W-W+
d u
d s
d u
d s
e
9FK7003
CP-Lear Experiment• Measurement made of an asymmetry AT
• K0 K0 and K0 K0 do not occur at the same rate• This ”drives” the CP violation observed in kaon
decays (we believe).• Result and experiment to be discussed further in
the context of time reversal.
0 0 0 0
0 0 0 0
-3
) )
) )
(6.6 1.6) 10 20
(Probability of (Probability of
(Probability of (Probability of
(integrated over time )
T
s
K K K KA
K K K K
(8.05)
10FK7003
Question• The CP-Lear experiment measures events in which a K0 or
a K0 is produced. After a certain time it is checked if the kaon has decayed to two pions. They measure a difference in the amount of . Is this observation consistent with CP-violation ?
0 02 , 2K K
11FK7003
Another CP-violating process
If no CP-violation then CP transforms (a) to (b)
CP non-violation would imply equal rates.
But, positron decay more likely by a fractional
amount 3.3x10-3
Unequal production of matter-antimatter!! Could CP violation in the early universe be responsible for today’s asymmetry ?
( )
( )
e
e
e a
e b
0LK
12FK7003
C,P and CP in the weak force● C and P are maximally violated
● CP violation is rarely seen in weak processes. It is small effect which dominantly arises from neutral meson states which can convert into each other: K0K0 , B0B0
● CP-violation with B-mesons not covered – similar mathematics as for the kaons presented here.
ˆ | ( ) | ( )
ˆ | ( ) | ( )
C lh lh
P lh rh
Not seen!!
0 0
0.1%
Rate difference L e L eK e K e
13FK7003
Implications beyond particle physicsCommunicating with aliens.
Originally from Feynman Imagine communicating with aliens. You want to describe
humans and human behaviour. You describe human height with wavelengths of light. You describe human age by ticks of an atomic clock How do you communicate the custom of shaking right hands
? What is right and left ?
Need to use P and CP violation.
14FK7003
Parity violation● Try to use parity violation to provide a fundamental definition
of left and right.
● Could be useful if we need to send a message to an alien with no knowledge of human convention!
Message to alien:
Study decays (charge of pion the same as the atomic electron). (1) Look at decays in which the charged particle goes up (against gravity - he/she is standing on a planet in a lab.)(2) Consider the situation when you are looking at a plane consisting of the pion, muon and neutrino.(3) The muon is ”rotating” from left to right ( – we choose a ”vertical” z-axis.)
decays
z
15FK7003
Be careful!● The alien extends his/her left
hand for a shake and annihilates your right hand.
● His/her galaxy is made of antimatter and in his/her world the muon is spinning in the opposite direction to ours.
● Why ?● How do we let the alien know
in advance if he/she is living in an antimatter world ?
16FK7003
What we can tell the alien.● With CP violation we can define:
Matter and anti-matter● Antielectrons are favoured in KL decays● The alien goes away and checks if the most favoured lepton in a KL
decay is the same particle found in an atom on his/her world.
Positive and negative charge● positive leptons are favoured in KL decays.
● Now the alien knows our charge definition we use parity violation to define: Left and right
● The muon from the negative pion decay ”spins” from left to right.
17FK7003
Conserved quantities/symmetries
Quantity Strong Weak Electromagnetic
Energy
Linear momentum
Angular momentum
Baryon number
Lepton number
Isospin - -
Flavour (S,C,B) -
Charges (em, strong and weak forces)
Parity (P) -
C-parity (C) -
G-parity (G) - -
CP -
T -
CPT Coming up
18FK7003
T symmetry Do the laws of physics work exactly the same way in
reverse if the time direction is changed t -t ?
If we consider a + b c + d could we tell by looking at the reaction rate if the process was going forward or backward in time ?
( ) ( )
ˆ ˆ: ( , ) ( , )
ˆ
ˆ
Define operator (8.06)
No eigenstate possible for operator
(8.07)
Does not imply that cannot a good symmetry of the Hamiltonian
Expectation values/pr
i px Et i px Et
T T x t x t
T
Te e
T
* *ˆ( )
obabilities unchanged
Eg. free particle (8.08)T
19FK7003
Checking T symmetry
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
( ) ( )
Reaction between particles and
produce and . All particles are spinless.
(1)
After time reversal
(2)
Apply parity
a b c d
c d a b
c d
a b
c d
a p b p c p d p
c p d p a p b p
c p d p
( ) ( ) (3)
Can compare rates of reactions 1 and 2
(test invariance) and reactions 1 and 3
(test invariance)
Comparisons known as "detailed balance"
studies.
a ba p b p
T
PT
)( apa )( bpb
)( cpc
)( dpdt
)( apa
)( bpb
)( cpc
)( dpd
t
Apply T transformation
20FK7003
T symmetry
forces strong and em via rates
greater far at interact and
since observe to difficult -
observable -
p
p
p
Take into account initital momenta.
T invariance demonstrated so far for the strong andelectromagnetic forces.Best em limit from neutron’s electric dipole moment
What about the weak force ? Detailed balance experiments difficult since
Study T invariance with reactions such as :pnddpn and
21FK7003
Did this earlier!
T violation in the weak force• Compare rates for the two weak processes• Oscillations easier to study than ”detailed balance” experiments. • CPLEAR Experiment CERN (pp interactions)• Consider two strong reactions
0000 KKKK and
)1()1()1()1( 00 SKSKppSKSKpp ,
e+e-
e
K0K0
W-W+
d u
d s
d u
d s
e
decays. following the of one in or an for lookingby
or a as life ended it if see and particle that ofdecay the Observe
reactions. the of one in
or of presence the for lookingby produced was or a ifIdentify
ee
KK
KKKK
00
00
22FK7003
Observation of T violation• Measurement made of an asymmetry AT
• There is a difference in rates for forward and reversed versions of the same reaction.
• T is violated in the weak force. • K0 K0 and K0 K0 do not have the same rates!• Could be deduced from CP violation. • Necessary that neutral kaons show CP and T
violations.
0 0 0 0
0 0 0 0
) )
) )
20-3
(Probability of (Probability of
(Probability of (Probability of
(6.6 1.6) 10 (integrated over time )
T
s
K K K KA
K K K K
(8.09)
23FK7003
T violation and CPT
● A small amount of T-violation in the weak force is a consequence of CP-violation. T-violation also occurs due to mixing. Many weak processes respect T-symmetry.
● The combined symmetry CPT is always respected in the weak (and em and strong) forces.
● CPT symmetry required for any quantum field theory in which signals do not propagate faster than light! CPT is believed in!
24FK7003
CPT symmetry
ˆ ˆ ˆ
ˆ ˆ ˆ | ( , ) | ( , ) ( )
ˆ ˆˆ ˆ ˆ ˆ,
The operator turns a particle into its antiparticle, inverts space and
reverses time.
(8.10) for particle (antiparticle)
If is a good symmetry
a a
CPT
CPT r t r t a a
CPT CPT
ˆ 0
ˆ ˆˆ ˆ ˆ ˆ ˆ| ( , ) | ( , ) | ( , )
ˆˆ ˆ ˆ ˆ| ( , ) | ( , ) | ( , )
.
Take simple case of a particle at rest.
(8.11)
(8.12)
(8.13)
Proof valid for stable pa
a a a a a
a a a a
a a
H
CPTH r t m CPT r t m r t
HCPT r t H r t m r t
m m
rticles - similar derivation possible for decaying particles
CPT symmetry implies a particle and an antiparticle have the same mass!
25FK7003
Tests and consequences of CPT invariance
Consistent particle and anti-particle masses imply CPT symmetry.
+ CPT invariance implies particles and anti-particles have the same lifetime.
+ CPT invariance also implies that if CP and T are violated then there must be at least 3 quark generations.
0 0
0 0
0 0
0 0 0 0 18| |
| | | | 10, (current experimental limit)K KK K
K K
m mm K H K m K H K
m m
-410 (current experimental limit)
b sd
t cu ( ) ( ) ( )
26FK7003
More CPT tests
M. Sozzi, Discrete Symmetries and CP violation
Finding a violation of CPT would be of greater importance than discovering the Higgs or supersymmetry (IMO).
Pspositronium (covered in next lecture)
Penning trap: Device for storing charged particles with constant B and non-uniform E-field.
27FK7003
Conserved quantities/symmetries
Quantity Strong Weak Electromagnetic
Energy
Linear momentum
Angular momentum
Baryon number
Lepton number
Isospin - -
Flavour (S,C,B) -
Charges (em, strong and weak forces)
Parity (P) -
C-parity (C) -
G-parity (G) - -
CP -
T -
CPT
28FK7003
Lecture summary● C and P are symmetries respected by the strong and
electromagnetic forces but are maximally violated by the weak force.
● CP is violated in the neutral kaon system by a small amount by the weak force. This is dominantly caused by mixing.
● P violation allows a left-right distinction to be made. ● CP violation allows a distinction to be made between
matter and anti-matter.● CPT symmetry is observed by all forces.● We are now able to tell an alien which hand should be
shaken without fear of annihilation.