ELECTR OMA GNETIC (QED) Muon Decayvjm/Lectures/ParticlePhysics... · 2012-09-14 · Vud =0.974...

Beta DecayWeak Nuclear Decay

!+ decay (A,Z) ! (A,Z"1) + e+ + !e.

!" decay (A,Z) ! (A,Z+1) + e" + !"e.

Nuclear Interpretation

n!p e" !"e

Modern quark level picture

Weak charged current mediated by exchange of virtual W± boson

d!u W

# e" !"e

Continuous energy spectrum of e± ⇒

at least two decay products.

This led Pauli to postulate the neutrino.

9

Experimental measurements

• "µ = 2.19703 # 10"6 s

• mµ = 105.658369#105 MeV/c2

used to extract GF (and gW)

⇒ GF =1.16637(1) ! 10"5 GeV"2

Muon DecayHow does a muon µ! decay?

• Must decay into lighter particles: e±, $, !. In particular, all hadrons are heavier than mµ.

Le, Lµ, L" conservation ⇒ only decay is µ"!e" ""e "µ

Maximum momentum transferred by the W boson is

! ! |M|2 ! g4W

(q2 "m2W )2

M ! g2W

q2 "m2W

! g4W

m4W

" G2F

q = (mµ !m!µ)c

6

Summary of Standard Model Vertices

! At this point have discussed all fundamental fermions

and their interactions with the force carrying bosons.

! Interactions characterized by SM vertices

ELECTROMAGNETIC (QED)

!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR

WEAK Charged Current

W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR

For QUARKS: coupling

BETWEEN generations

WEAK Neutral Current

Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR

Dr M.A. Thomson Lent 2004

µ!

e!

!µ

!"e

W

4th year project: measure "µ and mµ

Width (or decay rate) %µ = ℏ/"µ ∝ # measures how quickly the decay happens:

• % has dimensions of energy, [E];

• GF2 has dimensions [E]"4

To balance dimensions, use mµ (only other scale in the problem)

full calculation gives:

!µ ! G2F

!µ = G2F m5

µ/(192 !3)

!µ = K G2F m5

µ (K: dimensionless constant)

gW

gW

10

Lepton Universality

Tau Lepton Decay

• m" = 1.777 GeV/c2 > mµ, m%, m&, ...

• Several weak decay modes possible

Decays #"!e" ""e "# and #"!µ"

""µ "# have same matrix element as µ"!e"

""e"#

Compare to measured "" = (2.906 ± 0.011) # 10"13 s

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


"!

e!

!"

!"e

W

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


"$

d

!"

u "W %

"}

M ! g2W

q2 "m2W

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


"!

µ!

!"

!"µ

W

!(!! ! e! "̄e "! ) = 0.178 !! " G2F m5

!

!(!! ! e!"̄e "! )!(µ! ! e!"̄e "! )

=0.178 !!

!µ=

0.178 !µ

!!=

m5!

m5µ

! !! = BF(! " e!"e"! ) !µm5

µ

m5!

= 2.91# 10!13 s

Decay ModeBranching Fraction

&"!e" !"e !& BF=17.8%

&"!µ" !"µ !& BF=17.4%

&"!hadrons+!& BF=64.7%

BF =!(!! ! X)

!!

Coupling of to W-boson to all leptons is equal = gW

LEPTON UNIVERSALITY

gW

gW

gW

gW

11

How do quarks interact with the W boson?

• Quarks decays are enhanced by number of quark colours, NC=3.

• Tau decay: W! boson in can decay into u "+d or u "+s

• All other quarks (and hadrons) are too heavy

Coupling at Wud We! Wus vertices not equal

Quark coupling suppressed by a flavour-dependent factor V:

Vud=0.974 Vus=0.227 Vub=0.004

Vcd=0.230 Vcs=0.972 Vcb=0.042

Vtd=0.008 Vts=0.041 Vtb=0.999

Vud=0.974 Vus=0.227 Vub=0.004

Vcd=0.230 Vcs=0.972 Vcb=0.042

Vtd=0.008 Vts=0.041 Vtb=0.999

Weak Interactions of Quarks

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


"$

d

!"

u "W

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


"$

s

!"

u "W

gWVusgWVud gW

(values from experimental

measurements)

Couplings within a generations are the largest.

Main quark flavour changes are:

d ↔ u s ↔ c b ↔ t

Any change (Q=+2/3 e quark) ↔ (Q="1/3 e quark) is allowed

gW

gW

gWVud

gWVus

12

Weak Hadron DecaysAs the strong and electromagnetic forces conserve S, C, B

Lightest hadrons with non-zero S, C, B quantum numbers must decay by weak force!

Consider the interactions of the constituent quarks.

6

SummaryofStandardModelVertices

!At thispoint havediscussedall fundamental fermions

andtheir interactionswiththeforcecarryingbosons.

!InteractionscharacterizedbySMvertices

ELECTROMAGNETIC(QED)

!

e-

e-

e

" =

e2

4#

!

q

q

Q e

Cou

ples to

CH

AR

GE

Doe

s N

OT chan

ge

FLA

VO

UR

STRONG(QCD)

" s =g s

2

4#

g

q

q

g s

Cou

ples to

CO

LO

UR

Doe

s N

OT chan

ge

FLA

VO

UR

WEAKChargedCurrent

W-

e-

$ e

g w

" w =g w

2

4#

W+

u

d’

g wV ck

m

Chan

ges FL

AV

OU

R

For Q

UA

RK

S: cou

pling

BETW

EEN

gen

erat

ions

WEAKNeutralCurrent

Z0

e- , $ e

e- , $ e

Z0

q

q Doe

s N

OT chan

ge

FLA

VO

UR

DrM.A.Thomson

Lent2004µ+

!µW+

u

d "{%+

6

SummaryofStandardModelVertices

!At thispoint havediscussedall fundamental fermions

andtheir interactionswiththeforcecarryingbosons.

!InteractionscharacterizedbySMvertices

ELECTROMAGNETIC(QED)

!

e-

e-

e

" =

e2

4#

!

q

q

Q e

Cou

ples to

CH

AR

GE

Doe

s N

OT chan

ge

FLA

VO

UR

STRONG(QCD)

" s =g s

2

4#

g

q

q

g s

Cou

ples to

CO

LO

UR

Doe

s N

OT chan

ge

FLA

VO

UR

WEAKChargedCurrent

W-

e-

$ e

g w

" w =g w

2

4#

W+

u

d’

g wV ck

m

Chan

ges FL

AV

OU

R

For Q

UA

RK

S: cou

pling

BETW

EEN

gen

erat

ions

WEAKNeutralCurrent

Z0

e- , $ e

e- , $ e

Z0

q

q Doe

s N

OT chan

ge

FLA

VO

UR

DrM.A.Thomson

Lent2004µ+

!µW+

u

s"{K+

M(K+ ! µ+!µ) =g2

W Vus

q2 "m2W

M(!+ ! µ+"µ) =g2

W Vud

q2 "m2W

• e.g. %+!µ+!µ K+!µ+!µ

Confirmed experimentally!

• e.g. B"!D0µ+!µ

u "b!u "c µ+!µ

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


b

c

Wµ+

!µ

u "

u "

!(K+ ! µ+!µ)!("+ ! µ+!µ)

=V 2

sd

V 2ud

= 0.055

gWVud

gWVus

13

Electroweak Theory

The weak and electromagnetic interactions are manifestations of a underlying force: the electroweak force.

• Couplings of the $, W, Z boson are related:

• Mass of the W and Z bosons are related:

Just three fundamental parameters e.g. $EM, GF, sin 'W required to describe:

• couplings of W, Z and $ to quarks and leptons

• boson masses

• self-interactions of the {W,Z,$}

Glashow, Weinberg & Salam: Noble Prize in Physics 1979

"for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, inter alia, the prediction of the weak neutral current"

e = gW sin !W = g!W cos !W

m2Z = m2

W /cos2 !W

14

W and Z bosonsVirtual W± and Z0 bosons responsible for weak decays and scattering of neutrinos

e.g. µ"!e" ""e "µ "e

e"!"e e"

q2 =E2

W

c2! !pW · !pW "= m2

W

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


µ!

e!

!µ

!"e

W

16

QCDin

Annihilation

Directevidencefortheexistenceofcolourcomes

from

Annihilation.

!Compare

,:

e-e+

µ-µ+

! 1 q2

"#"#

e-e+

qq

! 1 q2

"#Qq"#

Qq

Ifweneglectthemassesofthefinalstate

quarks/muonsthentheONLYdifferenceisthe

chargeofthefinalstateparticles(

,

=or

)

Startbycalculatingthecrosssectionforthe

process

.(

representa

fermion-antifermionpair

e.g

.or

).

seeHandoutIIforthecasewhere

DrM.A.Thomson

Lent2004

e! e!

!e !e

q2 =E2

Z

c2! !pZ · !pZ "= m2

ZZ

Discovery of W and Z bosons at CERN in 1983 at the Spp "S collider.

Ep = Ep " = 270 GeV

pp "!W"!e" !"e event at UA1 experiment

Real W± and Z0 bosons can be produced in high energy collisions: e+e" or pp"

Detect clean signature of leptons decays: W!e!, W!µ!, Z!ee, Z!µµ

e+e"! Z0

e+e"! W+W!

u u" ! Z0 , d d " ! Z0 u" d ! W" , d " u ! W+

q2 = m2Z

15

Nobel Prize for Physics 1984

To Carlo Rubbia and Simon van der Meer, from CERN

“For their decisive contributions to large projects, which led to the discovery of the field particles W and Z, communicators of the weak

interaction.”

31

Nobel Prize for Physics 1984

• Given to Carlo Rubbia and

Simon van der Meer

• “For their decisive

contributions to large

projects, which led to the

discovery of the field

particles W and Z,

communicators of the

weak interaction.”

16

W and Z boson tests at LEP

The world’s highest energy e+e" collider:

• 27 km circumference.

• Ran from 1989 to 2000

• Energy of mass energy,

• Four experiments: Aleph, Delphi, L3, Opal

Z-boson production

• Resonant production at (s=mZ

• ~4 million e+e"!Z0 events

W-boson production

• Resonant production at (s ) 2mW

• ~8000 e+e"!Z!W+W! events

LEP Measurements

• Properties of the W and Z bosons: mass, width, couplings

• QCD measurements, weak decays

• Precision tests of the Standard ModelNuclear and Particle Physics Franz Muheim 5

Experimental Tests Experimental Tests -- LEPLEP

!"#$% !&'()$"*)+,'-.$#-/0,'-.$1-**02)'!"#$%&'(%)%* +,--./%#0( 12(34 +.#+546%#%7+%

8%7'#%*,6*4"&&(%7%#$9((!&(:(;<(= 1<<(>%?

@A%#"'.,7"-(6#,4(B;C; ',(1<<<

D,5#(%EA%#.4%7'&F(G-%AH0(I%-AH.0(!J0(@KG!

34$$5-/-./$&,$!"#L%&,7"7+%(A#,/5+'.,7("'(!&(:(MN

OP(4.--.,7(%)(%*" N< %Q%7'&R%EA'

6! 5-/-./$&,$!"#K#,/5+'.,7 "'(!&(# 1(MS(

OC<<<(%)(%*" S)(S* %Q%7'&R%EA'

!"#$7)&/8')9).,/M"&& "7/(T./'H ,6(N< "7/(S! U,&,7&

N< "7/(S! U,&,7(+,5A-.7$& ',(V5"#3&("7/(-%A',7&((

S%"3(/%+"9& ,6(H%"Q9(4%&,7&

W8I(4%"&5#%4%7'&

K#%+.&.,7 '%&'&(,6(:,&.2&'2$7-2)*$-;$#&',0+*)$#<=/0+/

hadrons0

!!!"#

qqZee

Nuclear and Particle Physics Franz Muheim 5

Experimental Tests Experimental Tests -- LEPLEP

!"#$% !&'()$"*)+,'-.$#-/0,'-.$1-**02)'!"#$%&'(%)%* +,--./%#0( 12(34 +.#+546%#%7+%

8%7'#%*,6*4"&&(%7%#$9((!&(:(;<(= 1<<(>%?

@A%#"'.,7"-(6#,4(B;C; ',(1<<<

D,5#(%EA%#.4%7'&F(G-%AH0(I%-AH.0(!J0(@KG!

34$$5-/-./$&,$!"#L%&,7"7+%(A#,/5+'.,7("'(!&(:(MN

OP(4.--.,7(%)(%*" N< %Q%7'&R%EA'

6! 5-/-./$&,$!"#K#,/5+'.,7 "'(!&(# 1(MS(

OC<<<(%)(%*" S)(S* %Q%7'&R%EA'

!"#$7)&/8')9).,/M"&& "7/(T./'H ,6(N< "7/(S! U,&,7&

N< "7/(S! U,&,7(+,5A-.7$& ',(V5"#3&("7/(-%A',7&((

S%"3(/%+"9& ,6(H%"Q9(4%&,7&

W8I(4%"&5#%4%7'&

K#%+.&.,7 '%&'&(,6(:,&.2&'2$7-2)*$-;$#&',0+*)$#<=/0+/

hadrons0

!!!"#

qqZee

!s = 89 to 206 GeV

LEP - the Large Electron Positron Collider at CERN

17

Z0 resonance

• Need to consider both Z-boson and photon diagrams and interference.

• Near (s=mZ, mainly Z-boson exchange:

• Need to take into account width of the boson % = ℏ/&Z &Z ~10"25 s

• Measurements at LEP:

• mZ = 91.1876 ± 0.0021 GeV/c2

• %Z = 2.49529 ± 0.0023 GeV

e+e- Annihilation in Feynman Diagrams

Dr M.A. Thomson Michaelmas 2006 500

In general e+e- annihilationinvolves both photon andZ exchange : + interference

At Z resonance: Zexchange dominant

Well below Z: photonexchange dominant

Cross Section MeasurementsAt Z resonance mainly observe four types of event:

Each has a distinct topology in the detectors, e.g.

To work out cross sections first count events of each typeThen need to know “integrated luminosity” of colliding beams

Dr M.A. Thomson Michaelmas 2006 501

!(E = q2) = !max!2

Z/4(q2 !mZ)2 + !2

Z/4

10

102

103

104

105

0 20 40 60 80 100 120 140 160 180 200 220

Centre-of-mass energy (GeV)

Cro

ss-s

ecti

on

(p

b)

CESRDORIS

PEP

PETRATRISTAN

KEKBPEP-II

SLC

LEP I LEP II

Z

W+W

-

e+e!"hadrons

Ecm

!GeV"

!h

ad !

nb"

! from fit

QED corrected

measurements (error barsincreased by factor 10)

ALEPH

DELPHI

L3

OPAL

!0

"Z

MZ

10

20

30

40

86 88 90 92 94

e+e! ! Z ! qq̄

!(e+e! ! Z ! ff) " g"W4

(q2 #m2Z)2

18

Number of Neutrinos

Total width of the Z-boson (%Z) is sum of all final state widths:

Lepton universality: partial widths to leptons are equal

0

10

20

30

86 88 90 92 94

Ecm

!GeV"

!h

ad !

nb"

3"

2"

4"

average measurements,error bars increased by factor 10

ALEPHDELPHIL3OPAL

!Z = !(Z ! qq̄) + !(Z ! e+e!) + !(Z ! µ+µ!) + !(Z ! !+!!) + N! !(Z ! ""̄)

Z!" " " leave no signal in the detector. However ... measured width depends on the number of neutrinos flavours the Z decays into.

Consistent with just three neutrinos!

⇒ Only three generations of matter ??

!(Z ! e+e!) = !(Z ! µ+µ!) = !(Z ! !+!!) = 83.984± 0.086 MeV

19

W-bosonAt LEP three diagrams contribute to W+W! production:


WW++WW-- Pair ProductionPair Production

!"#$%#&%'()%*+',-#.&#/0

1! 2)0)$',*3#40!!"#$%&'()*+%,- ./("+'0,/$) *$1"2'*3"45*(3"'%6'$),*,')

*5'*6 ! 15'16 #"'78978*90+'":;"'80'(%9'$,

(#00'#$%'1-%":');'1! 2)0)$<= >"?@ABCD"! @A@;?""E'F"=">"CAGCB"!A@A@BG"E'F

<-"G),

=H 0*%(

<&)00'!*3"-)$'=0 8$*&.4I6('') 2%,J"K<"0('1%L,%/$

!/$.%(9)"'8%),'$L'"/.

=M"=N O@ &'(,'8

# $ # $ # $ # $# $ # $ # $ # $

# $ # $%%

%%&%'% &'

lWqqW

tbWeWNcsWudW

lWWWeW

ec

e

(")("*

)("(")(")("

(")(")(")("

!!

+++++

!++++++

2'

0'''

3

1

eeqqWWee %++,+, ((

24

at LEP

! collisions Ws produced in pairs.

! In Standard Model 3 possible diagrams for

e+

e-

W-

W+

!e

e-

e+

W-

W+

"

e-

e+

W-

W+

Z0

0

5

10

15

20

25

150 160 170 180 190 200 210

#s [GeV]

$ WW

[pb

]

$(With Z0)

$(Without Z0)

Cross section sensitive to pres-

ence of the Triple Gauge Boson

vertex

1996-2000, LEP operated above

the threshold for pro-

duction

0

5

10

15

20

160 170 180 190 200 210

Ecm [GeV]

$WW

[pb

]

LEP Preliminary

RacoonWW / YFSWW 1.14

0

5

10

15

20

160 170 180 190 200 2100

5

10

15

20

160 170 180 190 200 210

RacoonWW

YFSWW 1.14

16

17

18

Cross section agrees

with Standard Model

prediction. Confirma-

tion of the existence of

the vertex


24

at LEP

! collisions Ws produced in pairs.

! In Standard Model 3 possible diagrams for

e+

e-

W-

W+

!e

e-

e+

W-

W+

"

e-

e+

W-

W+

Z0

0

5

10

15

20

25

150 160 170 180 190 200 210

#s [GeV]

$ WW

[pb

]

$(With Z0)

$(Without Z0)

Cross section sensitive to pres-

ence of the Triple Gauge Boson

vertex

1996-2000, LEP operated above

the threshold for pro-

duction

0

5

10

15

20

160 170 180 190 200 210

Ecm [GeV]

$WW

[pb

]

LEP Preliminary

RacoonWW / YFSWW 1.14

0

5

10

15

20

160 170 180 190 200 2100

5

10

15

20

160 170 180 190 200 210

RacoonWW

YFSWW 1.14

16

17

18

Cross section agrees

with Standard Model

prediction. Confirma-

tion of the existence of

the vertex


predictions of electroweak model Measurements from LEP

confirms existence of

Z0 W+ W" vertex

W Mass Fits

C. Hays, University of Oxford

Mass fit results blinded with [-100,100] MeV offset throughout analysisUpon completion, offset removed to determine final result

Transverse mass fits:

muonchannel

electronchannel

mW = 80417 ± 48 MeV (stat + sys)for e + µ combination (P(!2) = 7%)

42

Today the Tevatron also investigates W-bosons

pp "!W

From measurements at LEP & Tevatron:

• mW = 80.413 ± 0.048 GeV/c2

• %W = 2.141 ± 0.041 GeV

20

The Higgs BosonThe Higgs boson: missing piece of the Standard Model.

• Interactions of the fermions with the Higgs boson explains the mass of fermions.

• Interactions of the W and Z bosons with the Higgs boson explains the mass of the W and Z bosons.

• Coupling at Higgs vertex is proportional to particle mass.

Peter Higgsemeritus professor in the School of Physics

Finding the Higgs would validate the Standard Model: One of the main reasons for building the LHC collider!

4

Higgs in the Lagrangian

Higgs couples to WW and ZZ

2W

gm

Zgm


Higgs and UnificationHiggs and Unification

!"#$%&'(#)*+,-#'&.!"#$%&# '#(&)"#'#*+&,-. !#'/,01/,23/,24 (*5,&%*6"47*89,:,%*5#;#*5#*+ ;("('#+#"&

!-<#".)8,$-*&+"(%*+&/,$-""#$+%-*&=,>%?>#",-"5#",5%(?"('&

/0112+3#$-)40257*89,'%&&%*?,;("+%$8#,%*,@+(*5("5,2-5#8

@$(8("/,%A# @;%*,B/,

C-*DE#"-,F($))',DG,H88,;("+%$8#&,

($I)%"#,'(&& J9,K%??&,%*+#"($+%-*

K%??&,$-);8%*? # '(&& ?K.. L,!M!6,01,N,'.

O%"#$+,2(&&,P%'%+,2K G,QQR,0#S

T#I)%"# 6)&1#+/)7&'4 8'""07#&++96/8:+&+("+&,%*,6BBU

;<=#&2.55#%&. > ;?;@@V@W,!("+*#"&=,1#"'%-* $ X-&-* .#"'%-* $ &.#"'%-*

V*%.%$(+%-* -.,#8#$+"-<#(Y J-&-*,,,,$ Z%*-

(*5,&+"-*?

%*+#"($+%-*

!Q,L,!#'

!6,L,!4

!:,L,!@,

!#+#",K%??&

!"-.,#'#"%+)&,

V*%F -.,[5%*J)"?>

LEP searched for the Higgs e+e"!Z!ZH with no success! mHiggs > 114.4 GeV/c2.

gw mf

2 mW

21

Weak Interaction Summary

Weak force acts on all quarks and leptons.

Two massive bosons propagate the weak

interaction: W and Z.

Lepton Universality:interactions of all leptons are

identical.

W-boson vertex: fermion flavour change

e"↔!e µ$↔!µ "$↔!"

(Q=+2/3 e quark) ↔ (Q="1/3 e quark)

quark coupling: gW Vqq’ lepton coupling: gW

propagator term:1/(q2$mW2)

Z-boson vertex: no flavour change

coupling: g’W

propagator:1/(q2$mZ2)

At low energies (q2<<mW

2) W-bosons interactions

described by Fermi constant:

Electromagnetic & weak

are manifestations of a

single unified

electroweak interaction.

(with just 3 parameters)

Standard Model describes electroweak and QCD. Beautifully verified by

experiment, apart from missing Higgs boson.

Particle widths, % = ℏ/& ∝ * Total width is sum of all final states widths:

e.g. %& = %(&!µ!!)+%(&!e!!)+%(&!hadrons+!)GF !

g2w

m2W

BF = !(!! ! X)/!!

22

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


QED QCD Weak Neutral Current Weak Charged Current

quantum theory of EM interactions

quantum theory of strong interactions

quantum theory of weak interactions

mediated by exchange of virtual

photons

mediated by exchange of gluons

mediated by exchange of Z

bosons

mediated by exchange of W

bosons

acts on all charged particles

acts on quarks only acts on all quarks and leptons

couples to electric charge

couples to colour charge

does not change quark or lepton

flavour

changes quark and leptons flavours

coupling strength ∝ e ∝ (!

coupling strength ∝ gS ∝ (!S

coupling strength ∝ g’W

coupling strength ∝ gW ∝ (!W

propagator: 1/q2

propagator: 1/q2

propagator: 1/(q2"MZ

2)propagator:1/(q2"MW

2)

Standard Model Interactions

6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR


6






!

e-

e-

e

" =e

2

4# !

q

q

Q e

Couples to CHARGE

Does NOT change

FLAVOUR

STRONG (QCD)

"s =

gs2

4# g

q

q

gs

Couples to COLOUR

Does NOT change

FLAVOUR


W-

e-

$e

gw

"w

=g

w2

4# W+

u

d’g

wV

ckm

Changes FLAVOUR


BETWEEN generations


Z0

e-, $

e

e-, $

e

Z0

q

q

Does NOT change

FLAVOUR

Dr M.A. Thomson Lent 2004 23

The massive bosons: W, Z & Higgs

24

ELECTR OMA GNETIC (QED) Muon Decayvjm/Lectures/ParticlePhysics... · 2012-09-14 · Vud =0.974...

Documents

Transcript of ELECTR OMA GNETIC (QED) Muon Decayvjm/Lectures/ParticlePhysics... · 2012-09-14 · Vud =0.974...