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Lecture 8

● CP-violation● T-violation ● CPT invariance

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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

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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".

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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

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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

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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

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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.

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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

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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)

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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

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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

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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

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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.

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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

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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 ?

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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.

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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

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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

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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

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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

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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

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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)

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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!

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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!

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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 ( ) ( ) ( )

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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.

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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

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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.