QFD, Weak Interactions

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QFD, Weak Interactions

• Some Weak Interaction basics
• Weak force is responsible for b decay e.g. n ?
  pev (1930s)
• 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

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Weak interaction Terminology
Experimentally weak interaction is universal,
I.e. all processes described by a unique
coupling constant GF
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QED, QCD and QFD
QED
Auphoton field (1) FuvuAv-vAu
melectron mass yelectron spinor
electron-g interaction
QCD
gluon-gluon interaction (3g and 4g)
mquark mass jcolor (1,2,3) kquark type
(1-6) qquark spinor
quark-gluon interaction
QFD
Fermions interaction
Gauge particles
Higgs field
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Quantum-Flavor-Dynamics (QFD)The weak
interaction theory
based on a local SU(2) gauge symmetry field
quanta W, W? and Z0 bosons
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Cabibbo Mixing angle
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The GIM Mechanism
In 1969-70 Glashow, Iliopoulos, and Maiani (GIM)
proposed a solution to the to the K0 m m- rate
puzzle.
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!
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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 ssin, ccos, and the numbers refer to
the quark generations, e.g. s12sinq12.
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
s12gtgts23gtgts13.
Wolfenstein representaton
Here lsinq12, and A, r, h are all real and
approximately one. This representation is very
good for relating CP violation to specific decay
rates.
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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 uu cc tt
• d, s and b are not d, s and b

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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. VubltltVud).
• 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

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The Unitarity Triangles
Unitarity of CKM matrix implies
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bd Triangle
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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-eve
Amplitude µVcs Decay rate µVcs2
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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

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Three Type of CP Violation in Weak interaction
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Map
Good consistency between measurements and
Standard Model
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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.

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Source of the pages and more!

• www.physics.ohio-state.edu/kass/P780_L10_sp03.ppt
  
• www.nikhef.nl/pub/linde/LECTURES/ParticlePhysics
• www-pnp.physics.ox.ac.uk/weber/teaching/Weak20In
  teraction.pp
• universe-review.ca/R02-14-CPviolation.htm
• www.bnl.gov/NPSS/files/ppt/SnowNPSS2.pps
• twist.triumf.ca/e614/slides/tau2000/Tau2000.pdf
• www.slac.stanford.edu/BFROOT/www/doc/PhysBook/phys
  Book.html
• http//www.lancs.ac.uk/users/spc/teaching/py302/PH
  YS302-part3.ppt
• http//www.kvi.nl/sohani/sohani-cpv-talk.ppt