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Particle Physics I Introduction, history & overview (2) Concepts (5) : Units (h=c=1) Relativistic kinematics Cross section, lifetime, decay width, … Symmetries (quark model, …) Quantum Electro Dynamics : QED (7) Spin 0 electrodynamics (Klein-Gordon)

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Vi discrete symmetries and cp violation l.jpg

  • Particle Physics I

  • Introduction, history & overview (2)

  • Concepts (5):

    • Units (h=c=1)

    • Relativistic kinematics

    • Cross section, lifetime, decay width, …

    • Symmetries (quark model, …)

  • Quantum Electro Dynamics: QED (7)

    • Spin 0 electrodynamics (Klein-Gordon)

    • Spin ½ electrodynamics (Dirac)

    • Experimental highlights: “g-2”, ee, …

  • Particle Physics II

  • Quantum Chromo Dynamics: QCD (4)

    • Colour concept and partons

    • High q2 strong interaction

    • Structure functions

    • Experimental highlights: s, ep, …

  • Quantum Flavour Dynamics: QFD (6)

    • Low q2 weak interaction

    • High q2 weak interaction

      • Experimental highlights: LEP

  • Origin of matter? (6)

    • Strange particles

    • GIM (why does the charm exist?)

    • K0-K0, oscillations,

    • CP violation

    • B0-B0 oscillations

    • Current CP violation experiment

  • Origin of mass? (2)

    • Symmetry breaking

    • Higgs particle: in ee and in pp

File on “paling”: graven/ED_MASTER/master2003.ppt

VI. Discrete Symmetries and CP violation

Part of the “Particle and Astroparticle Physics” Master’s Curriculum

Strange particles l.jpg
Strange Particles







Ep threshold (GeV)




Note: long lifetime!

In general: more difficult (i.e. higher threshold) to make S=-1 particles then S=+1 when target is either p or n, and beam consists of p+ or p-

because for S=+1, need to get an antiquark from somewhere…

Quite useful: can make ‘pure’ K0 or K+ sample by running below threshold

Slide3 l.jpg

“V particle”: particles that are produced

in pairs and thus leaves a ‘v’ trial in a

bubble chamber picture

Details: create a new quantum number, “strangeness“

which is conserved by the production process

hence pair production by strong force

however, the decay must violate “strangeness”

if only weak force is “strangeness violating” then it

is responsible for the decay process

hence (relatively) long lifetime…

  • Observations:

  • High production cross-section

  • Long lifetime

  • Conclusion:

  • must always be produced in pairs!

Strange particles4 l.jpg
Strange Particles







  • mK ~ 494 MeV/c2

  • No strange particles lighter than Kaons exist

    • Decay must violate “strangeness”

  • Strong force conserves “strangeness”

    • Decay is a pure weak interaction

  • Hadronic and leptonic decays:

  • particle and anti-particle behave the same

  • Semi-leptonic decays:

  • particle and anti-particle are distinct from one another!

  • “DQ=DS rule”

K 0 decays a problem l.jpg
K0 decays: A problem?

the reason there are no FCNC is that VC is unitary:

Z0 boson will now couple

to uu and d’d’ ...

This generates a “FCNC”, (Flavour Changing Neutral Current)… need to do more.

Or, to put it the other way around:

The absence of FCNC requiresV to be unitary

K 0 decays enter the charm l.jpg
K0 decays: enter the charm

To (almost) cancel this diagram, lets introduce

another up-type quark, and have it interact

through a W with the orthogonal combination

of (d,s)

This new ’c’ quark causes an additional diagram

that (almost) cancels the one above…

If mumc, then the cancellation would be complete! This is called “GIM suppression” leads to a prediction of the charm mass of 1.5—2 GeV, prior to the discovery of J/y

Slide9 l.jpg

In general: the weak eigenstates are not the mass eigenstates!

If all quarks were the same mass, this could not happen as we could take any linear combination of quarks as the mass eigenstates…

And as long as V is unitary, there will be no FCNC!

note: can (and will) extend this to 3 families later

Q: what happens if VC=1 (i.e. qC=0)?

A: the s quark (and thus all S0 particles) would be stable!!!

Q: how many independent parameters does V have when there are 2 generations (i.e. is qC all there is?). How about 3 generations?

A: 2*22-22-(2*2-1)=1; 2*32-32-(2*3-1)=4

Intermezzo discovery of the j y l.jpg
Intermezzo: Discovery of the J/y

Brookhaven: J

SLAC: y(3105)

By studying the decay of strange particles,

the existence of the charm and its properties

(eg. mass, weak couplings) were predicted before its discovery – but nobody believed it!

Sam Ting and Burt Richter got the

1976 Nobel prize for their discovery

Back to k 0 decays l.jpg
Back to K0 decays…

  • Known:

  • K0 can decay to p+p-

  • Hypothesized:

  • K0 has a distinct anti-particle K0

  • Claims:

  • K0 (K0) is a “particle mixture” with two distinct lifetimes

  • Each lifetime has its own set of decay modes

  • No more than 50% of K0 (K0) will decay to p+p-

Phys. Rev. 97, 1387 (1955)

K 0 and cp symmetry l.jpg
K0 and CP symmetry

Known decay:

Assuming CP symmetry, this

should be possible as well:

Assuming the reverse

reaction is allowed, particle

can “mix” into anti-particle,

and vice-versa…

How does this system evolve in time? (ignore decays for the time being)

Mixing causes tiny off-diagonal element:

With completely different eigenstates!

K 0 decay and cp k 1 and k 2 l.jpg
K0 decay and CP: K1 and K2

Phys Rev 103,1901 (1956)

CP: +1 -1

K1 and K2 are their own

antiparticle, but one is CP

even, the other CP odd:

Only the CP even state (K1) can decay into 2 pions

(which are CP even)

The odd K2 state will decay into 3 particles instead (ppp,pmn, pen,…).

There is a huge difference between K0pp and K0 ppp in phasespace (~600x!). So the CP even state will decay much faster

More on time evolution l.jpg
More on time evolution

Tag K0 and K0 decay by semileptonic decay

(remember the DS=DQ rule?)

K1 decays

K2 decays

Testing cp conservation l.jpg
Testing CP conservation



Effect is tiny:

about 2/1000

Easy to create a pure K2 beam:

just “wait” until the K1 component has decayed…

If CP conserved, should not see the decay to 2 pions in this K2 beam

This is exactely what was tested by Cronin & Fitch in 1957…

Main background: p+p- p0

… and for this experiment they got the Nobel price in 1980…

Interference l.jpg

KL and KS are no longer orthogonal:

T violation in mixing l.jpg
T violation in mixing

CPLEAR, Phys.Rep. 374(2003) 165-270




  • Note:

  • This measurement allows one to make an ABSOLUTE distinction between matter and anti-matter

  • Don’t need to know the specific value of

  • decay amplitudes; only need:

2x 2 ways to decay l.jpg
(2x)2 ways to decay…





3 ways to break cp l.jpg
3 ways to break CP

CP violation in decay

CP violation in mixing

CP violation in the interference

between mixing and decay

The final result l.jpg
The Final Result…








  • If CP were conserved, KL wouldn’t decay to p+p-, and there would be no interference…



If h+-=0:

only “KS” like decays

If h+-0:

not only “KL” like decays, down by |h+-|2, but also interference contribution, down

by |h+-|

The interference term has a sign difference for K0 and K0bar!

Cplear detector@cern l.jpg

Use the strangeness conservation of the strong interactions to perform Tagged K0 and K0 production:

  • At t=0, events with a

  • K+ are a pure K0bar sample

  • K- are a pure K0 sample

Results cp in interference l.jpg
Results: CP in Interference



Mainly KSp+p-decays

Mainly KLp+p decays



Approx equal KSp+p-and KLp+p- rate:

Maximal interference!

Interference maximal:

Note: rates are normalized to each other in the range (,)

decaytime / tS

Cp violation when l.jpg
CP violation: when?

  • Introduce A, Abar into the picture

  • CP violation seems to occurs in interference

  • What kinds of interference can we have?

  • Mixing

  • Decay

  • Mixing vs. Decay




Basic equations neutral meson mixing l.jpg
Basic Equations: Neutral Meson Mixing

In general, want to know the time evolution of:

  • If

  • At t=0, only a(t) and b(t) are non-zero

  • We are only interested in a(t) and b(t), and not ci(t)

  • t is large compared to the strong-interaction scale

  • Then one can make an approximation (Wigner-Weisskopf) which considerably simplifies things:

Basic equations neutral meson mixing29 l.jpg
Basic Equations: Neutral Meson Mixing

Virtual Intermediate States

L is not Hermitian: otherwise mesons would only oscillate, and never decay… instead:

Real Intermediate States

Basic equations neutral meson mixing30 l.jpg
Basic Equations: Neutral Meson Mixing

L is not Hermitian: otherwise mesons would only oscillate, and never decay… instead:

M describes oscillations, G decays

Phase conventions l.jpg
Phase conventions

Because of the requirement of phase independence,

R has only 7 (physical) parameters

CPT invariance:

T invariance:

CP invariance:

Requiring CPT reduces this to X parameters (SHOW!)

Computing dm and dg in k0 mixing l.jpg
Computing Dm and DG in K0 mixing

Or: why is kaon mixing so different from B mixing

And why is D mixing different again???

Actually, why is the B lifetime so large?

as expected, the D lifetime is much less than the K0S one

Show that mixing vanishes if all quark masses are equal

Okun p88?

Cahn-Goldhaber, chapter 15

Solution cp violating case l.jpg
Solution (CP violating case)

Nobel Lecture Val Fitch

Intermezzo ks regeneration l.jpg
Intermezzo: KS regeneration

i.e. why the helium bag?

Or: another way to measure dm

Enter the b meson l.jpg
Enter the B meson…

Third generation -> VCKM

Long lifetime! -> Vcb must be tiny!

It mixes! -> top must be VERY heavy

And then there were 3 the ckm matrix l.jpg
And then there were 3…The CKM matrix

Unexpected long B lifetime! => Vcb must be small!

Eg. B+ to mu+ not observed, only limits

D0 mixing vs bd mixing l.jpg
D0 mixing vs. Bd mixing

Mixing dominated by Vtd

Must have heavy (>100 GeV) top!

As VtdVtb**2 isn’t very large (0.2**6)

Not yet observed!

Experimental limit goes here

How do we measure mixing??

Compute Vtd from the measured dm values

Bd mixing vs bs mixing l.jpg
Bd mixing vs. Bs mixing

Mixing Dominated by Vtd

Mixing Dominated by Vts

Some other effects of O(30%)

lead to the SM expectation of ~18

Not yet observed!

Experimental limit goes here

Lifetime difference dominated by Vcd:


Lifetime difference dominated by Vcs:

Expect 10-20%

Cp violation in mixing l.jpg
CP violation in mixing

Why small?

Experimental results

Kaons, Bd mesons

Is p a good symmetry l.jpg
Is P a good symmetry?




More electrons emitted opposite the J direction.

Parity violation!

  • Sketch and photograph of apparatus used to study beta decay in polarized cobalt-60 nuclei. The specimen, a cerium magnesium nitrate crystal containing a thin surface layer of radioactive cobalt-60, was supported in a cerium magnesium nitrate housing within an evacuated glass vessel (lower half of photograph). An anthracene crystal about 2 cm above the cobalt-60 source served as a scintillation counter for beta-ray detection. Lucite rod (upper half of photograph) transmitted flashes from the counter to a photomultiplier (not shown). Magnet on either side of the specimen was used to cool it to approximately 0.003 K by adiabatic demagnetization. Inductance coil is part of a magnetic thermometer for determining specimen temperature.

Parity violation observed in 60Co experiment in 1956.











I(q) = 1 + a (v/c) cos q

with a = -1


C. Yang and T. Lee, 1956

C. S. Wu, 1957










Exercise l.jpg

Show CP |pi+pi-> = + | pi+pi->

CP |pi+pi-pi0> = - |pi+pi-pi0>

More details about mixing regeneration l.jpg
More details about Mixing: regeneration

How do we make sure KL -> p+p- is really the same final state

As KS->pipi ?

maybe we’re missing a particle that takes away very little momentum?

NOTE: beta decay spectrum was ‘solved’ by introducing a new particle

(the neutrino)

Let them interfere!

Q: why does eg. K*0 not mix? It has the same quark content…

A: it decays to K+pi-, a strong decay – it just isn’t stable enough!

A2: it is a vector particle…