VI. Discrete Symmetries and CP violation

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• Particle Physics I
• Introduction, history overview (2)
• Concepts (5)
• Units (hc1)
• 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

File on paling graven/ED_MASTER/master2003.ppt

• VI. Discrete Symmetries and CP violation

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Strange Particles
Ep threshold (GeV) 0.91 1.5 6.0
Note long lifetime!
In general more difficult (i.e. higher
threshold) to make S-1 particles then S1 when
target is either p or n, and beam consists of p
or p-
because for S1, need to get an antiquark from
somewhere
Quite useful can make pure K0 or K sample by
running below threshold
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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!

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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!
• DQDS rule

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Weak decays K- vs. p-
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Universality of weak interactions
Weak doublets
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K0 decays A problem?
?Z0 boson will now couple to uu and dd ...
This generates a FCNC, (Flavour Changing
Neutral Current) need to do more.
Or, to put it the other way around The absence
of FCNC requires V to be unitary
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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 1.52 GeV,
prior to the discovery of J/y
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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 VC1 (i.e. qC0)?
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 222-22-(22-1)1 232-32-(23-1)4
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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
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Back to K0 decays

• Known
• K0 can decay to pp-
• 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 pp-

Phys. Rev. 97, 1387 (1955)
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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!
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K0 decay and CP K1 and K2
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
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2 vs. 3 particle phase space
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More on time evolution
K1 decays
K2 decays
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Testing CP conservation
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 pp- p0
and for this experiment they got the Nobel
price in 1980
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Interference
KL and KS are no longer orthogonal
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T violation in mixing
t
t0
CP

• Note
• This measurement allows one to make an ABSOLUTE
  distinction between matter and anti-matter
• Dont need to know the specific value of
• decay amplitudes only need

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(2x)2 ways to decay
Amplitude
t0
t
CP
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3 ways to break CP
CP violation in decay
CP violation in mixing
CP violation in the interference between mixing
and decay
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3 Ways to break CP
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The Final Result
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!
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CPLEAR Detector_at_CERN
Use the strangeness conservation of the strong
interactions to perform Tagged K0 and K0
production

• At t0, events with a
• K are a pure K0bar sample
• K- are a pure K0 sample

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CPLEAR
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Results CP in Interference
CPLEAR, PLB 1999
Mainly KS?pp- decays
Mainly KL?pp decays
K0bar
K0
Approx equal KS?pp- and KL?pp- rate Maximal
interference!
Interference maximal
Note rates are normalized to each other in the
range (,)
decaytime / tS
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Details
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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

Pbar
P
f
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Basic Equations Neutral Meson Mixing
In general, want to know the time evolution of

• If
• At t0, 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

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Basic Equations Neutral Meson Mixing
Virtual Intermediate States
L is not Hermitian otherwise mesons would only
oscillate, and never decay instead
Real Intermediate States
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Basic Equations Neutral Meson Mixing
L is not Hermitian otherwise mesons would only
oscillate, and never decay instead
M describes oscillations, G decays
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Phase conventions
Because of the requirement of phase independence,
R has only 7 (physical) parameters CPT
invariance T invariance CP invariance Requirin
g CPT reduces this to X parameters (SHOW!)
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Solving the master equations
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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
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Solution (CP violating case)
Nobel Lecture Val Fitch
http//www.nobel.se/physics/laureates/1980/
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Intermezzo KS regeneration
i.e. why the helium bag? Or another way to
measure dm
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Enter the B meson
Third generation -gt VCKM
Long lifetime! -gt Vcb must be tiny!
It mixes! -gt top must be VERY heavy
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And then there were 3The CKM matrix
Unexpected long B lifetime! gt Vcb must be small!
Eg. B to mu not observed, only limits
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Mixing of neutral mesons
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D0 mixing vs. Bd mixing
Mixing dominated by Vtd
Must have heavy (gt100 GeV) top! As VtdVtb2
isnt very large (0.26)
Not yet observed! Experimental limit goes here
How do we measure mixing?? Compute Vtd from the
measured dm values
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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 tiny
Lifetime difference dominated by Vcs Expect
10-20
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CP violation in mixing
Why small? Experimental results Kaons, Bd mesons
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Is P a good symmetry?
Parity violation observed in 60Co experiment in
1956.
e-
q
Parity transformation
Magnetic field
?
?
J
J
60Co
60Co
I(q) 1 a (v/c) cos q with a -1
Observed
C. Yang and T. Lee, 1956 C. S. Wu, 1957
Parity violation
2010
1950
60
70
80
90
2000
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Intermezzo CP
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Exercise
Show CP pipi-gt pipi-gt CP
pipi-pi0gt - pipi-pi0gt
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(No Transcript)
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More details about Mixing regeneration
How do we make sure KL -gt pp- is really the same
final state As KS-gtpipi ? maybe were 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. K0 not mix? It has the same
quark content A it decays to Kpi-, a strong
decay it just isnt stable enough! A2 it is a
vector particle
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Trace Theorems