1. Symmetry and Symmetry Violation in Particle Physics对称 违反
Lecture 3 March 21, 2008

2. Summary Lecture 2
Antimatter predicted by Dirac & discovered by Chao & Anderson
1933 Nobel prize  Dirac
1936 Nobel prize  Anderson (but not Chao)
Electron & positron have opposite parity
Charge “reversal”  Charge “conjugation”
Particle Antiparticle (not just charge)
C=+1  even # of g’s; C=-1 odd # of g’s
p and K mesons = qq with L=0, S=0 & P=-1

3. Summary Lecture 2 (pg 2)
t+ = p+p+p- & q+p+p0 puzzle led Lee & Yang to question L-R symmetry of nature
C.S. Wu discovered P viol. in Co60Ni60 e-n
1957 Nobel Prize to Lee & Yang (but not Wu)
t+ and q+ are the same particle, the K+ meson
C & P violation differences seen in m-/m+ decay
But CP seems okay
Large matter vs antimatter asymmetry in the present-day Universe implies CP is violated.
K0K0 transitions 2nd-order W.I.

4. Reminder P C, P & CP for p and K mesons C CP Particle |p+ -1 +|p-

5. My tentative plan for this class is as follows:
Lecture 1. Definition of symmetry, why they are important in
physics. Symmetries of the laws of nature. Relation
of symmetry and conservation laws. Discrete symmetries
C, P & T. Violation of parity (P) in beta-decay
Lecture 2. Antimatter, and matter-antimatter symmetry. Quark content
of hadrons & discrete symmetries of hadrons. Violation of parity
(P) and charge conjugation (C ) symmetry in beta-decay Particle-
antiparticle mixing.
Lecture 3. K0K0 mixing. CP violation in K decay. Difficulties with
incorporating CP violation into a physics theory. KM 6-quark model for
CP violation. Role of B mesons in the theory
Lecture 4. Studying CP violation in the B meson system. Experimental
techniques and results. What is left for the future.
Lecture 5. Exam

6. Discovery of CP violation in the neutral K meson system
outline
Neutral K meson decay mechanisms
K0 – K0 mixing  KS and KL mesons
Discovery of KLp+p-
CP violation in KLp+e-n/p-e+n decays
“Direct” CP violation in KLpp decays

7. K0  p+p- decays via weak interactionu K0 d
DS=-1 s
W.I. d W+ p+ u

8. K0 also decays to p+p- p+ d u K0 d
DS=1 S
W.I. W- u p- d

9. K0 K0 possible as a 2nd order weak interaction process
|DS|=2 p+ d W+ K0 d u
W.I. S
W.I. s u K0 W- d p- d
This is a so-called “long-range” process. It occurs on
a size scale determined by the p mesons: ~ 10-15m
1 fermi

10. K0 K0 in short-range quark
|DS|=2 u c t
W.I.
W.I. S d W- W+ K0 K0
W.I.
W.I. s d u c t
This is a so-called “short-range” process. It occurs on
a size scale determined by the t-quark: ~ m
10-3 fermi

11. What happens when two identical systems are coupled?
Energy transfers
back-and-forth
between the two
oscillators

12. Steady-state “normal modes”

13. Shrodinger Equation: ..
H Y = EY H Y Y
If CP symmetry holds:

14. Eigenvalues and Eigenstates
特征值
Find the eigenvalues
and eigenvectors for:
Answer
Homework: Please check that these answers are correct

15. In standard (textbook) notation

16. If CP symmetry is good:

17. CP of K1 and K2
Recall:
CP = +1
CP = -1

18. K1 decays K1  p+ p- ? K1  p+ p- p0? CP= (-1)x(-1) = +1OK
CP= (-1)x(-1) = +1
CP +1
K1  p+ p- p0? NG
CP = (-1)x(-1)x(-1) = -1

19. K2 decays K2 p+ p- ? K2  p+ p- p0? CP= (-1)x(-1) = +1NG
CP= (-1)x(-1) = +1
CP -1
K2  p+ p- p0? OK
CP = (-1)x(-1)x(-1) = -1

20. K2  p+ p- p0 has little phase space
K1 & K2 lifetimes
相空间
K2  p+ p- p0 has little phase space
QK2 = MK – 3Mp  80 MeV
K1  p+ p- has more phase space
QK1 = MK – 2Mp  215 MeV
tK1<<tK2
Easier for K1 to decay

21. 1956: Search for long-lived K0
Brookhaven-Columbia Expt

22. Can you see it?

23. KS & KL mesons Two neutral K mesons were discovered:
KS  p+p- tKS  0.1 nanosecs (10-10s)
500x bigger
KL  p+p-p0 tKS  50 nanosecs (5x10-8s)
(Are they the CP eigenstates K1 and K2?)

24. KL & KS mesons in e+e- annihilation
KS = K-short
pS = 110 MeV
<l> = 6mm p+ p- f
510MeV e+ e-
510MeV p+
pL = 110 MeV
<l> = 3.4m
f = ss
M(f) = 1020 MeV p0
KL = K-long p-

25. KLOE Experiment in ItalyKS
In this event the KL
only travels ~1m
before it decays

26. Usually, the KL traverses to entire 2m radius of the drift chamber
KL “crash”
b= 0.22 (TOF)
KS  p-e+n
KL “crash” 2m KS

27. Neutral K mesons “Basis” sets
These have a
well defined
quark structure
K0-K0
Flavor States
These are the
Particles that
exist in Nature
K1-K2
CP eigenstates
KS-KL
Mass eigenstsate
are these the same?

28. Does KS=K1 & KL=K2? (i.e. is CP conserved?)
These are the
particles that
are observed
in nature
express them in terms of K1 and K2:

29. invert

30. e
If CV is conserved: e=0, KS=K1 & KL=K2

31. Does KL p+p- ? |e|2 =0 if CP is conserved Remember, p+p- has CP=+1
Forbidden(?)
Forbidden(?)
|e|2 =0 if CP is conserved

32. Christenson-Cronin-Fitch-Turlay Experiment (1964)KL p-

33. |e|2 = 4x10-6 p+ KL p- p+ q cosq small,but not 0 M(p+p-)<M(KL)
p+p- “invariant mass”
M(p+p-)=M(KL)
|e|2 = 4x10-6
small,but not 0 p+ KL q p- p+
M(p+p-)>M(KL)
cosq

34. CP is violated!! James Cronin Val Fitch 1980 Nobel Prize for Physics
No prizes for Christenson or Turlay

35. Flavor-non specific K0 (K0) decays特定
Decays that are equally likely for K0 and K0
If you see p+p-,
you don’t know
if it was from
a K0 or a K0
K0 p+ p-
K0 p+ p-
K0 p+ p-p0
Same for p+p-p0,
(& p0p0 & p0p0p0)
K0 p+ p-p0

36. Flavor specific K0 (K0) decays特定
Decays that can only come from a K0 or K0, but not both d p- d p+ u d u d K0 K0
W.I. n
W.I. n s s W+ W- e+ e-
DS=-1
DQ=-1
DS=+1
DQ=+1
Rule:
K0 p- e+ n
K0 p+ e- n
only
DS=DQ
If you see p-e+n,
you know it must be
from a K0, not K0
If you see p+e-n,
you know it must be
from a K0, not K0

37. K0 & K0 in terms of KS & KL
invert

38. Start with a K0 at t=0
KS & KL have
different
t-dependence
using
and

39. Similarly:

40. K0K0 Oscillations GS>>GL (GS500xGL)
Expt NA48 (CERN) K0 K0
CP is violated in KLp+e-n/p-e+n decays
t=t/g (“proper time”)

41. Search for direct CPV in KLpp
In 2002,after 20 yr searches, NA48 (CERN) & KTeV (Fermilab) found direct |DS|=1 CPV in K2pp
CP violation from
|DS|=2 transition
Mass Matrix
Forbidden(?)
Is this true?
Can there be a
“direct” CP violation
in |DS|=1 K2pp?
= e’  1.6 x 10-3 x e
Small, but establishes
existence of “direct”
|DS|=1 CP violation.

42. CPV in neutral K meson system summary
Neutral K mesons mix: K0  K0
CP is violated in the K0-K0 mass-mixing matrix
scale  e  2x10-3
CPV is seen in flavor non-specific & flavor specific modes
KL  pp (CPV  e2  4x10-6)
KL  p+e-n / p-e+n (CPV  e = 2x10-3)
Direct CP is seen in KLpp decays
scale = e’ = 1.6 x 10-3 e

43. CP is violated in the Weak Interactions
Observation of both Mass-Matrix CPV (|DS|=2)
& direct CPV (|DS|=1) rule out theories
where CPV comes from a previously unknown
“fifth” force characterized by |DS|=2

44. C P and the forces of Nature
Slide from last weak
Force C P CP
Gravity √
Electro-magnetic
Strong-nuclear
Weak-Interaction ╳
Force C P CP
Gravity √
Electro-magnetic
Strong-nuclear
Weak-Interaction ╳
OK?

45. Next: How are CP-violating asymmetries generated in QM?
How does CP violation fit into the Standard Model for particle physics?
Brief review of flavor mixing/GIM-mechanism
Kobayashi 6-quark model

46. Generating CPV asymmetries in QM

47. (charge has to be complex)
CP: matter
antimatter
“charge”
CP operator:
CP(
) = g q q’ g* q W q W†
some basic process
mirror
For CPV: g  g*
(charge has to be complex)

48.  matter- symmetry is ~“automatic”
QM: processes go as |A|2
Phases tend to cancel out in rate calculations
 g*g
 gg* 2 2 g q’ q’ = g* q q J J†
mirror
even for g* = g (i.e with CPV)
 matter symmetry is ~“automatic”
antimatter

49. Phase measurements in QM: need interference干扰
need a process with 2 competing mechanisms:
Amplitudes should have similar magnitudes:
phase
angle
A & Beif:
|A+B|2=|A|2+|B|2+2|A|B|cosf
2|B|
2|A|B|cosf
cosf
if |A|>>|B|
|A|
|A|2+|B|2
Small number
Relative size of the
interference effect

50. Even this doesn’t work for CPV!!B A
A+B f f B
A+B A =
|A+B|
|A+B|
still!
matter
antimatter
symmetric

51. need a “common phase” d between A & B合用
same sign
eg A=real:
B = |B|eid+if
& B = |B|eid-if f f
A+B
A+B B B d d A A =
|A+B|
|A+B|
matter
antimatter
difference

52. CP violating asymmetries in QM
Even if CP is violated, generating matter-antimatter differences is hard
need a CP-violating phase (f)
need 2 (or more) interfering amplitudes
+ a non-zero “common” phase (d)
(often called a “strong” phase)

53. Common and weak phases B = |B|eid-if |B|eid+if f f A+B A+B B B d d A
“Common” (strong) phase (d): same sign for
matter & antimatter  CP conserving
Weak phase (f): opposite sign for matter
& antimatter  CP violating
B = |B|eid-if
|B|eid+if f f
A+B
A+B B B d d A

54. How does CPV fit into the Standard model?
Clue: CPV is seen in strangeness-changing
weak decays.
It must have something to do with
flavor-changing Weak Interactions

55. Flavor mixing & CP Violation

56. s Brief review of weak int’s in the 3-quark era 3 quarks: 4 leptons:
3 quarks:
q=+2/3
|DS|=1 s
q=-1/3
Weak interactions
4 leptons:

57. Problems
Problem 1: Different weak interaction “charges” for leptons & hadrons:
Fermi Constant m- GF
su
Gs 0.21GF
du
Gd 0.98GF nm Gs Gd s d K- n u u p0 p

58. Cabibbo’s sol’n: flavor mixing
Weak Int
flavor state
Flavor mass
eigenstates
d = a d + b s
b=sinqc=0.21
a=cosqc=0.98
bGF
aGF u GF u u = + s d’ d W- W- W-
Unitarity: |a|2 + |b|2 = 1
a=cos qc; b = sin qc
qc=“Cabibbo angle”

59. Missing neutral currents
Problem 2: no flavor-changing
“neutral currents” seen.
Discovered
At CERN s GN K- d
d,u
d,u p-
flavor-changing neutral currents (e.g. Kp l+l-) are strongly supressed
flavor-preserving neutral currents (e.g. nNnX) are allowed

60. GIM sol’n: Introduce 4th quark
2 quark doublets:
charmed quark
Weak eigenstates
Mass eigenstates

61. d’ & s’ are mixed d & s Mass eigenstates Weak eigenstates 4-quark
flavor-mixing
matrix
Mass eigenstates
Weak eigenstates

62. Mixing matrix must be Unitary
UU† = 1
|a|2 + |b|2 = 1 & a*b - ab* =0

63. Charged currents (u-quark)
|DS|=1
aGF
u(c)
u(c)
bGF
d(s)
s(d) W- W-
GF modified by a
GF modified by b

64. Charged currents (c-quark)
|DS|=1
|DC|=1
|DS|=0
-bGF c c
aGF d s W- W-
GF modified by b
GF modified by a

65. Flavor preserving Neutral Current=1
d,(S)
|a|2+|b| 2GN
d,(s) Z0 =1 =0 =0 =1
From Unitarity =1 OK

66. Flavor changing Neutral Current=0
(a*b+ba*)GN
d(s)
s(d) Z0 =0 =1 =0 =1 =0
From Unitarity
GIM-
Mechanism
FCNC forbidden by Unitarity

67. GIM Mechanism FCNC forbidden by Unitarity if quarks come in pairs of 2
GIM: Glashow Iliopoulis Maiani
No prize for
Iliopoulis & Maiani
Glashow won 1979
Physics Nobel prize

68. Next Friday: Incorporating CPV into flavor mixing

69. Summary Lecture 3 CP is violated Weak-Interactions
Mass-matrix induced; scale  e  2x10-3
Direct CPV; scale = e’ = 1.6 x 10-3 e
Observing CPV requires:
Two interfering amplitudes
One with a CP-violating weak phase
Another “common” or “strong” phase
In the W.I., the d and s quark mix  d’ & s’
d’ =cosqcd +sinq s; s’ =-sinqcd +cosqcs
qc  120 is the “Cabibbo angle
If all quarks are in pairs, FCNC = 0 by Unitarity
(GIM Mechanism)