1. QFD, Weak Interactions Some Weak Interaction basics
Weak force is responsible for b decay e.g. n → pev (1930’s)
interaction involves both quarks and leptons
not all quantum numbers are conserved in weak interaction:
parity, charge conjugation, CP
isospin
flavor (strangeness, bottomness, charm)
Weak (+EM) are “completely” described by the Standard Model
 Quarks in strong interaction are not the same as the ones in the weak interaction:
weak interaction basis different than strong interaction basis

2. Weak interaction: Terminology
Leptonic processes
Between leptons
Semi-leptonic processes
Between leptons and quarks
Non-leptonic (hadronic) processes
Between quarks
Experimentally:
weak interaction is universal,
I.e. all processes described by a unique coupling constant: GF

3. QED, QCD and QFD QED: QCD: QFD: m=electron mass y=electron spinor
electron-g
interaction
Au=photon field (1)
Fuv=¶uAv-¶vAu
QCD:
m=quark mass
j=color (1,2,3)
k=quark type (1-6)
q=quark spinor
quark-gluon
interaction
gluon-gluon
interaction
(3g and 4g)
QFD:
Fermions interaction
Gauge particles
Higgs field

4. Quantum-Flavor-Dynamics (QFD) The weak interaction theory
based on a local SU(2) gauge symmetry
field quanta: W+, W and Z0 bosons
Quark sector: W cause: ud, cs and tb transitions
ee,  and  transitions
Z0 causes: uu, dd, cc, etc. transitions
ee, ee, , etc. transitions
W: charged current (qelectric=1) Z0: neutral current (qelectric=0) u d W e e Z0 W- e-

5. Cabibbo Mixing angle d s u How to account e.g. for the p++;
once you accept that the quark structure of the  is (uds)? s u d
Time
Clearly for the p++ decay to take place, the weak interaction must be allowed to destroy s-quarks!
Conventionally the W-transitions are changed to become:
u  d cosC + s sinC and c  d sinC + s cosC
This mixing is expressed in terms an angle:
the Cabibbo mixing angle C13o
Cabibbo favored
Cabibbo suppressed

6. The GIM Mechanism K0 K+ There are no flavor changing neutral currents
In Glashow, Iliopoulos, and Maiani (GIM) proposed a solution to the
to the K0 ®m+ m- rate puzzle. m+ u W+ s nm d
??0 m- K+
allowed K0
forbidden
There are no
flavor changing
neutral currents
The 2nd order diagram (“box”) was calculated & was found
to give a rate higher than the experimental measurement!
amplitude µ sinqccosqc
GIM proposed that a 4th quark existed and its coupling to the s and d quark was:
s’ = scosq - dsinq
The new quark would produce a second “box” diagram with
amplitude µ -sinqccosqc
These two diagrams almost cancel each other out.
The amount of cancellation depends on the mass of the new quark
First “evidence” for Charm quark!

7. CKM Matrix The CKM matrix can be written in many forms:
1) In terms of three angles and phase:
The four real parameters are d, q12, q23, and q13.
Here s=sin, c=cos, and the numbers refer to the quark generations, e.g. s12=sinq12.
2) In terms of coupling to charge 2/3 quarks (best for illustrating physics!)
3) In terms of the sine of the Cabibbo angle (q12).
This representation uses the fact that s12>>s23>>s13.
“Wolfenstein” representaton
Here l=sinq12, and A, r, h are all real and approximately one.
This representation is very good for relating CP violation to specific decay rates.

8. Weak Interaction, SM picture
The W and Z boson do not couple to the same quark states as the strong and Electromagnetic Interaction
We call the the quark states that couple to the strong and EM interactions the Mass Eigenstates
The Weak Interaction couples with the weak Eigenstates:
Note: u=u c=c t=t
d’, s’ and b’ are not d, s and b

9. CKM Matrix
The magnitudes of the CKM elements, from experiment are (PDG2000):
There are several interesting patterns here:
The CKM matrix is almost diagonal (off diagonal elements are small).
The further away from a family, the smaller the matrix element (e.g. Vub<<Vud).
Using 1) and 2), we see that certain decay chains are preferred:
c  s over c  d D0 K-p+ over D0 p-p+ (exp. find 3.8% vs 0.15%)
b  c over b  u B0 D-p+ over B0 p-p+ (exp. find 3x10-3 vs 1x10-5)
Since the matrix is supposed to be unitary there are lots of constraints among
the matrix elements:

10. The Unitarity Triangles
Unitarity of
CKM matrix implies :

11. bd Triangle

12. Measuring the CKM Matrix
Experimentally, the cleanest way to measure the CKM elements is by using
interactions or decays involving leptons.
Þ CKM factors are only present at one vertex in decays with leptons.
Vud: neutron decay: np l  du l 
Vus: kaon decay: K0 p l  su l 
Vbu: B-meson decay: B p l  bu l 
Vbc: B-meson decay: B D0 l  bc l 
Vcs: charm decay: D0 K- l  cs l 
Vcd: neutrino interactions: l d l c dc
“Spectator” Model decay of D0 K-e+ve c u s
e,m
ne,nm W K- D0
Vcs
Amplitude µVcs
Decay rate µ|Vcs|2

13. Three Type of CP Violation in Weak interaction
CP Violation in Decay
CP Violation in Mixing
CP Violation in the Interference Between Decay With and Without Mixing

14. Three Type of CP Violation in Weak interactionIf
CP Violation in decay If
CP Violation in mixing If
CP Violation in interference

15. Good consistency between measurements
Map
Good consistency between measurements
and
Standard Model

16. summary
Weak interaction in SM is based on the similar mathematical structure as QCD and QED.
Weak interaction in the frame work of the SM includes the CP violation.
Experimental results are confirming the level of the CP violation predicted with in the SM so far.

17. Source of the pages and more!
www-pnp.physics.ox.ac.uk/~weber/teaching/Weak%20Interaction.pp
universe-review.ca/R02-14-CPviolation.htm
twist.triumf.ca/~e614/slides/tau2000/Tau2000.pdf