qfd, weak interactions some weak interaction basics weak force is responsible for b decay e.g. n →...
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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
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
QED, QCD and QFD
uvuv
uu
uu FFAemiL
4
1)(
uva
auv
aujka
ujkjku
ujk GGGqqgqmiqL
4
1)()(
QED:
m=electron mass=electron spinor
electron- interaction
Au=photon field (1)Fuv=uAv-vAu
m=quark massj=color (1,2,3)k=quark type (1-6)q=quark spinor
quark-gluoninteraction
QCD:
gluon-gluoninteraction(3g and 4g)
)())((4
1
4
1
VDDGGFFDi ii LQFD:
Fermions interaction Gauge particles Higgs field
Quantum-Flavor-Dynamics (QFD)The weak interaction theory
based on a local SU(2) gauge symmetryfield quanta: W+, W and Z0 bosons
Quark sector: W cause: ud, cs and tb transitions ee, and transitions
Z0 causes: uu, dd, cc, etc. transitions ee, ee, , etc. transitions
W: charged current (qelectric=1) Z0: neutral current (qelectric=0)
u
d W
e
e W
Z0
WW-
e-
e
WZ0
e
e
u
d
c
s
t
b
Q2 / 3|e|
Q 1/ 3|e|
e
e
Q |e|
Q 0
Cabibbo Mixing angleTim
e
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 cosC + s sinC and c d sinC + s cosC
How to account e.g. for the p++; once you accept that the quark structure of the is (uds)?
s
u
du
u
du d
This mixing is expressed in terms an angle:the Cabibbo mixing angle C13o
u c
d s
Cabibbo favoredCabibbo suppressed
The GIM MechanismIn 1969-70 Glashow, Iliopoulos, and Maiani (GIM) proposed a solution to theto the K0 + - rate puzzle.
890
1064.0
107
)(
)(
KBR
KBR
+
u
W+
s
+
d
??0
s
-
K+
allowed
K0
forbidden
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 - dsinqThe 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!
There are noflavor changing
neutral currents
CKM Matrix
d'
s'
b'
=
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
d
s
b
The CKM matrix can be written in many forms:1) In terms of three angles and phase:
b
s
d
ccescsscesccss
csesssccessccs
escscc
b
s
d
ii
ii
i
132313231223121323122312
132313231223121323122312
1313121312
1313
1313
13
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.
b
s
d
AiA
A
iA
b
s
d
1)1(
2/1
)(2/1
23
22
32
“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.
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=uc=ct=td’, s’ and b’are notd, s and b
b
t
s
c
d
u
e
e
:
:
Quarks
Leptons
CKM Matrix
9993.09990.010)3.45.3(10)4.14.0(
10)3.47.3(9749.09734.0225.0219.0
10)52(226.0219.09757.09742.0
22
2
3
tbtstd
cbcscd
ubusud
VVV
VVV
VVV
The magnitudes of the CKM elements, from experiment are (PDG2000):
There are several interesting patterns here:1) The CKM matrix is almost diagonal (off diagonal elements are small).2) The further away from a family, the smaller the matrix element (e.g.
Vub<<Vud).3) 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)4) Since the matrix is supposed to be unitary there are lots of constraints
among the matrix elements:
0
1***
***
tdtbcdcbudub
tdtdcdcdudud
VVVVVV
VVVVVV
The Unitarity Triangles
Unitarity of CKM matrix implies :
tbtstd
cbcscd
ubusud
VVV
VVV
VVV
11
21
21
23
22
32
AiA
A
iA
bd Triangle
Measuring the CKM MatrixExperimentally, the cleanest way to measure the CKM elements is by usinginteractions or decays involving leptons.
Þ CKM factors are only present at one vertex in decays with leptons.
Vud: neutron decay: np l du l Vus: kaon decay: K0 p l su l Vbu: B-meson decay: B p l bu l Vbc: B-meson decay: B D0 l bc l Vcs: charm decay: D0 K- l cs l Vcd: neutrino interactions: l d l c dc
“Spectator” Model decay of D0 K-e+ve
c
u
s
u
e,
e,W
K-D0 Vcs
Amplitude µVcs
Decay rate µ|Vcs|2
• CP Violation in Decay
• CP Violation in Mixing
• CP Violation in the Interference Between Decay With and Without Mixing
Three Type of CP Violation in Weak interaction
fcp
fcp
fcpfcp A
A
p
q
Three Type of CP Violation in Weak interaction
1fcp
fcp
fcp
fcp
fcp
fcp
AA
AA
fcpPfcpP
fcpPfcpPa
1
1
00
00
BqBpB
BqBpB
L
H
1fcp
fcp
A
AIf CP Violation in
decay1
p
qIf CP Violation in mixing
00 KK
0Im&1 fcpfcp If CP Violation in
interference
00 BB
Map ,
Good consistency between
measurements
and
Standard Model
21
;2
1
2
2
)(05.0)(14.059.02sinIm syststatfcp
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.
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/Weak
%20Interaction.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/
physBook.html • http://www.lancs.ac.uk/users/spc/teaching/py302/PHYS302-part
3.ppt• http://www.kvi.nl/~sohani/sohani-cpv-talk.ppt