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