CP violation Lecture 6

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CP violationLecture 6

• N. Tuning

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Recap

• Diagonalize Yukawa matrix Yij
• Mass terms
• Quarks rotate
• Off diagonal terms in charged current couplings

Niels Tuning (3)
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CKM-matrix where are the phases?

• Possibility 1 simply 3 rotations, and put
  phase on smallest

• Possibility 2 parameterize according to
  magnitude, in O(?)

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This was theory, now comes experiment

• We already saw how the moduli Vij are
  determined
• Now we will work towards the measurement of the
  imaginary part
• Parameter ?
• Equivalent angles a, ß, ? .
• To measure this, we need the formalism of neutral
  meson oscillations

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Meson Decays

• Formalism of meson oscillations
• Subsequent decay

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Classification of CP Violating effects

1. CP violation in decay
2. CP violation in mixing
3. CP violation in interference

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Classification of CP Violating effects

• CP violation in decay
• Example
• CP violation in mixing
• Example
• CP violation in interference
• Example

B0?J/?Ks
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Hint for new physics? B0?Kp and B??K?p0
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Hint for new physics? B0?Kp and B??K?p0
T (tree)
C (color suppressed)
P (penguin)
B0?Kp-
B?Kp0
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Remember!

• Necessary ingredients for CP violation
• Two (interfering) amplitudes
• Phase difference between amplitudes
• one CP conserving phase (strong phase)
• one CP violating phase (weak phase)

2 amplitudes 2 phases
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Remember!
2 amplitudes 2 phases
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Next

1. CP violation in decay
2. CP violation in mixing
3. CP violation in interference

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Other ways of measuring sin2ß

• Need interference of b?c transition and B0 ?B0
  mixing
• Lets look at other b?c decays to CP eigenstates

All these decay amplitudes have the same
phase (in the Wolfenstein parameterization) so
they (should) measure the same CP violation
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CP in interference with B?fKs

• Same as B0?J/?Ks
• Interference between B0?fCP and B0??B0?fCP
• For example B0?J/?Ks and B0??B0? J/?Ks
• For example B0?fKs and B0??B0? fKs

Amplitude 2
Amplitude 1

e-if
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CP in interference with B?fKs what is
different??

• Same as B0?J/?Ks
• Interference between B0?fCP and B0??B0?fCP
• For example B0?J/?Ks and B0??B0? J/?Ks
• For example B0?fKs and B0??B0? fKs

Amplitude 2
Amplitude 1

e-if
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Penguin diagrams
Nucl. Phys. B131285 1977
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Penguins??
The original penguin
A real penguin
Our penguin
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Funny
Flying Penguin
Dead Penguin
Penguin T-shirt
Super Penguin
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The b-s penguin
Asymmetry in SM
B0?J/?KS
?

• unless there is new physics!
• New particles (also heavy) can show up in loops
• Can affect the branching ratio
• And can introduce additional phase and affect the
  asymmetry

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Hint for new physics??
?

• sin2ßb?ccs 0.68 0.03

• sin2ßpeng 0.52 0.05

sin2ß
sin2ßpeng
S.TJampens, CKM fitter, Beauty2006
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Hint for new physics? ß with b g s Penguins
0.67 0.02
0.64 0.04
deviation between b g sqq and b g ccs disappeared
over time
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Why bother with all this?

• CKM matrix has origin in LYukawa
• Intricately related to quark massed
• Both quark masses and CKM elements show
  intriguing hierarchy
• There is a whole industry of theorist trying to
  postdict the CKM matrix based on arguments on the
  mass matrix in LYukawa

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Remember P eigenvalues for hadrons

• The p meson
• Quark and anti-quark composite intrinsic P
  (1)(-1) -1
• Orbital ground state ? no extra term
• P(p)-1
• The neutron
• Three quark composite intrinsic P (1)(1)(1)
  1
• Orbital ground state ? no extra term
• P(n) 1
• The K1(1270)
• Quark anti-quark composite intrinsic P
  (1)(-1) -1
• Orbital excitation with L1 ? extra term (-1)1
• P(K1) 1

Meaning Ppgt -1pgt
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Intermezzo CP eigenvalue

• Remember
• P2 1 (x ? -x ? x)
• C2 1 (? ??? ? ? )
• ? CP2 1
• CP f gt ? f gt
• Knowing this we can evaluate the effect of CP on
  the K0
• CP?K0gt -1 K0gt
• CP K0gt -1?K0 gt
• CP eigenstates
• KSgt p K0gt q?K0gt
• KLgt p K0gt - q?K0gt
• Ksgt (CP1) ? p p (CP (-1)(-1)(-1)l0
  1)
• KLgt (CP-1) ? p p p (CP (-1)(-1)(-1)(-1)l0
  -1)

( S(K)0 ? L(pp)0 )
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CP eigenvalue of final state J/yK0S

• CP J/ygt 1 J/ygt
• CP K0Sgt 1 K0Sgt
• CP J/yK0Sgt (-1)l J/yK0Sgt

( S(J/y)1 )
( S(B)0 ? L(J/yK0S)1 )
Relative minus-sign between state and
CP-conjugated state
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Kaons

• Different notation confusing!
• K1, K2, KL, KS, K, K-, K0
• Smaller CP violating effects
• But historically important!
• Concepts same as in B-system, so you have a
  chance to understand

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Neutral kaons 60 years of history
1947 First K0 observation in cloud chamber (V
particle) 1955 Introduction of Strangeness
(Gell-Mann Nishijima)
K0,?K0 are two distinct particles (Gell-Mann
Pais) 1956 Parity violation observation
of long lived KL (BNL Cosmotron) 1960 Dm
mL-mS measured from regeneration 1964 Discovery
of CP violation (Cronin Fitch) 1970
Suppression of FCNC, KL?mm - GIM mechanism/charm
hypothesis 1972 6-quark model CP violation
explained in SM (Kobayashi Maskawa) 1992-2000
K0,?K0 time evolution, decays, asymmetries
(CPLear) 1999-2003 Direct CP violation
measured e/e ? 0 (KTeV and NA48)
the ?0 must be considered as a "particle
mixture" exhibiting two distinct lifetimes, that
each lifetime is associated with a different set
of decay modes, and that no more than half of all
?0's undergo the familiar decay into two pions.
From G.Capon
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Intermezzo CP eigenvalue

• Remember
• P2 1 (x ? -x ? x)
• C2 1 (? ??? ? ? )
• ? CP2 1
• CP f gt ? f gt
• Knowing this we can evaluate the effect of CP on
  the K0
• CP?K0gt -1 K0gt
• CP K0gt -1?K0 gt
• CP eigenstates
• KSgt p K0gt q?K0gt
• KLgt p K0gt - q?K0gt
• Ksgt (CP1) ? p p (CP (-1)(-1)(-1)l0
  1)
• KLgt (CP-1) ? p p p (CP (-1)(-1)(-1)(-1)l0
  -1)

( S(K)0 ? L(pp)0 )
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Decays of neutral kaons

• Neutral kaons is the lightest strange particle ?
  it must decay through the weak interaction
• If weak force conserves CP then
• decay products of K1 can only be a CP1 state,
  i.e.K1gt (CP1) ? p p (CP
  (-1)(-1)(-1)l0 1)
• decay products of K2 can only be a CP-1 state,
  i.e.K2gt (CP-1) ? p p p (CP
  (-1)(-1)(-1)(-1)l0 -1)
• You can use neutral kaons to precisely test that
  the weak force preserves CP (or not)
• If you (somehow) have a pure CP-1 K2 state and
  you observe it decaying into 2 pions (with CP1)
  then you know that the weak decay violates CP

( S(K)0 ? L(pp)0 )
Niels Tuning (30)
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Designing a CP violation experiment

• How do you obtain a pure beam of K2 particles?
• It turns out that you can do that through clever
  use of kinematics
• Exploit that decay of K into two pions is much
  faster than decay of K into three pions
• Related to fact that energy of pions are large in
  2-body decay
• t1 0.89 x 10-10 sec
• t2 5.2 x 10-8 sec (600 times larger!)
• Beam of neutral Kaons automatically becomes beam
  of K2gt as all K1gt decay very early on

K1 decay early (into pp)
Pure K2 beam after a while!(all decaying into
ppp) !
Initial K0 beam
Niels Tuning (31)
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The Cronin Fitch experiment
Essential idea Look for (CP violating) K2 ? pp
decays 20 meters away from K0 production point
Decay of K2 into 3 pions
Incoming K2 beam
If you detect two of the three pionsof a K2 ?
ppp decay they will generallynot point along the
beam line
Niels Tuning (32)
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The Cronin Fitch experiment
Essential idea Look for K2 ? pp decays20 meters
away from K0 production point
Decay pions
Incoming K2 beam
If K2 decays into two pions instead ofthree both
the reconstructed directionshould be exactly
along the beamline(conservation of momentum in
K2 ? pp decay)
Niels Tuning (33)
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The Cronin Fitch experiment
Essential idea Look for K2 ? pp decays20 meters
away from K0 production point
Decay pions
K2 ? pp decays(CP Violation!)
Incoming K2 beam
K2 ? ppp decays
Result an excess of events at Q0 degrees!

• CP violation, because K2 (CP-1) changed into K1
  (CP1)

Note scale 99.99 of K ?ppp decaysare left of
plot boundary
Niels Tuning (34)
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Nobel Prize 1980
"for the discovery of violations of fundamental
symmetry principles in the decay of neutral K
mesons"
The discovery emphasizes, once again, that even
almost self evident principles in science cannot
be regarded fully valid until they have been
critically examined in precise experiments.
Val Logsdon Fitch   1/2 of the prize  
Princeton University Princeton, NJ, USA b.
1923
James Watson Cronin   1/2 of the prize  
University of Chicago Chicago, IL, USA b. 1931
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Cronin Fitch Discovery of CP violation

• Conclusion weak decay violates CP (as well as C
  and P)
• But effect is tiny! (0.05)
• Maximal (100) violation of P symmetry easily
  follows from absence of right-handed neutrino,
  but how would you construct a physics law that
  violates a symmetry just a tiny little bit?
• Results also provides us withconvention-free
  definition ofmatter vs anti-matter.
• If there is no CP violation, the K2 decaysin
  equal amounts to p e- ne (a) p- e ne (b)
• Just like CPV introduces K2 ? pp decays, it also
  introduces a slight asymmetry in the above
  decays (b) happens more often than (a)
• Positive charge is the charged carried by the
  lepton preferentially produced in the decay of
  the long-lived neutral K meson

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Intermezzo Regeneration

• Different cross section for s(p K0) than s(p?K0)
• Elastic scattering same
• Charge exchange same
• Hyperon production more for ?K0 !
• What happens when KL-beam hits a wall ??
• Then admixture changes KLgt p K0gt - q?K0gt
• Regeneration of KS !
• Could fake CP violation due to KS?pp-

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KS and KL
Usual (historical) notation in kaon physics
Modern notation used in B physics
Regardless of notation
KL and KS are not orthogonal
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Three ways to break CP e.g. in K0? pp-
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Classification of CP Violating effects

1. CP violation in decay
2. CP violation in mixing
3. CP violation in interference

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Time evolution
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B-system 2. CP violation in mixing K-system
CPLEAR, Phys.Rep. 374(2003) 165-270
BaBar, (2002)
CPLear (2003)
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B-system 2. CP violation in mixing K-system
BaBar, (2002)
NA48, (2001)
?L(e) (3.317 ? 0.070 ? 0.072) ? 10-3
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B-system 3.Time-dependent CP asymmetry
B0?J/?Ks
BaBar (2002)
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B-system 3.Time-dependent CP asymmetry K-system
K0?p-p
B0?J/?Ks
50/50 decay as Ks and KL interference!
K0
_
K0
pp- rate asymmetry
CPLear (PLB 1999)
BaBar (2002)
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The Quest for Direct CP Violation
Indirect CP violation in the mixing ?
Direct CP violation in the decay ?
A fascinating 30-year long enterprise Is CP
violation a peculiarity of kaons? Is it induced
by a new superweak interaction?
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B system 1. Direct CP violation K
system
K0?p-p
?K0?p-p
B0?Kp-
?B0?K-p
K0?p0p0
?K0?p0p0
Different CP violation for the two decays ? Some
CP violation in the decay!
e? 0
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