Chapter5
¡
Anyinteractionbetweentwofermionsisseenastheprocess
ofemission/absorptionofavirtualboson–carrierofthefield
responsiblefortheinteractionatwork
§  Virtualparticles“hidden”byuncertaintyprinciple
¡
Fourfundamentalinteractions
§  gravitational,
§  weak,
§  electromagnetic
§  strong
¡
Gravitynegligibleatsubatomiclevel
§  OnlyrelevantatveryearlyUniverse–Planckscale
¡
Gravityunifies
!
mm !
F = −GN 1 2 2 r̂
r
GN = 6.672 ⋅10 −8 cm 3g−1s −2
§  Forceresponsibleforfallofbodies
§  Forceactingoncelestialbodies
¡
Gravitationalforcealwaysattractive
= 6.672 ⋅10 −11 Nm 2 kg−2
§  Principleofgeneralrelativity
§  Inertialmass/gravitationalmass:mi/mg=constantforallbodies
¡
Couplingconstant,dimensionlessparameter
§  àinteractionstrength
§  Intermsofuniversalconstants
§  Planckscale–whengravityisimportant
¡
Nosatisfactoryquantumtheoryof
gravitationyet
Graviton,spin-2
§  Ifextraspacedimensions,gravitycould
becomeimportantatnottoofarscales
§
m 2p
α G = GN
= 5.90 ⋅10 −39
!c
M pl =
!c
= 1.221⋅1019 GeV = 2.18⋅10 −8 kg
GN
l pl =
!c
!GN
=
= 1.616 ⋅10 −35 m
2
3
M pl c
c
t pl =
l pl
!GN
=
= 5.4 ⋅10 −44 s
5
c
c
¡
WI
§  radioactivedecaysofatomicnuclei
A(Z, N ) → A(Z +1, N −1)e−ν e
§  Nucleusbetadecayàneutrondecayàd-quarkdecay
¡
Allprocessesinvolvingneutrinosareweak
§  Chargedcurrents(W±exchange,mW=80.3GeV)(a,b)
§  Neutralcurrents(Z0exchange,mZ=91.2GeV)(c)
¡
Lepton&baryonnumbersconserved
e− ↔ ν e ; µ − ↔ ν µ ; τ − ↔ ν τ
n → p e− ν e
B
Le
1 1 0 0
0 0 1 −1 µ − → e− ν e ν µ
Lµ
1 0 0 1
Le
0 1 −1 0 n → pe−ν e
d → ue−ν e
(a) ν µ p → µ + n
(b) ν e p → e+ n
(c) ν µ e− → ν µ e−
¡
¡
¡
(a)NeutralCurrents(NC)
(b-e)Chargedcurrents(CC)
Quarkinteractionsanddecay
processesinvolvingflavour
quantumnumbervariation
(strangenessSorcharmC,
bottomnessB,…)
§  Flavourchangingforbiddenin
strongandEMinteractions
§  AllowedinWis
§  (e)Σ-ànπ-
Σ− → n π −
S
−1 0 0
⎧⎪
s → uW − → u(du) → uπ −
Σ ⎨
⎩⎪ dd → dd → dd → dd
−
⎫⎪
⎬
⎭⎪
¡
(f)Weakgaugebosonself-coupling
¡
¡
IntensityofWI
π − → νµµ −
τ W = 2.6 ⋅10 −8 s
§  Comparepiondecays(WIvsEM)à
π 0 → γγ
τ EM = 8.4 ⋅10 −17 s
2
τ W WEM α EM
∝
∝ 2
τ EM WW α W
Bosonicpropagator
§  Couplingconstantgincreaseswithenergy
§  Transitionprobability
g2
αW
WWI ∝ f (q ) = 2
=
q + mW2 ,Z q 2 + mW2 ,Z
1/2
1/2
⎛ 10 −16 ⎞
αW ⎛ τ EM ⎞
−4
∝⎜
⎟ ≅ ⎜ −8 ⎟ ≅ 10
α EM ⎝ τ W ⎠
⎝ 10 ⎠
2
§  Atlowenergies
▪  Fermicontactinteraction–Fourier
transformofaconstantinmomentum
spaceisaδ-functionincoordinatespace
▪  Couplingandamplitudeconstant
§  Dimensionlesscouplingatprotonmass:
2
q << m
2
W ,Z
GF
g2
=
2 8mW2
g2
→ f (q ) ≅ 2 = const
mW ,Z
2
GF = 1.1664 ⋅10 −5 GeV −2
αW = (m p c 2 )2 GF = 1.027 ⋅10 −5
¡
WIviolatesanumberofconservationlaws/symmetries ν ≡ ν P →
L
§  Parity,Chargeconjugation,Timereversal,flavourQNs,…
§  Wcouplesonlytoleft-handed(LH)objects
§  Formν=0,onlyLHneutrinosandRHantineutrinosexist
¡
Highenergies
§  e+e-àZ0àW+W-possible
▪  (writedowntheFeynmandiagramandcomment)
§  Collisionenergyatleast2mW=161GeV
¡
Introductionofsuchdiagrams(involvingZ)importantto
compensateforthedivergenceofthetransition
probabilitiesinvolvingonlyWathighenergies
S⇐
ν ≡ ν R P → S⇒
¡
Atfundamentallevel,SI
§  Interactionbetweenquarksand
¡
§  InanalogywithQED:electriccharge(±)
gluons
§  Collisionsbetween2quarks
§  Interactionbetween3quarksto
formbaryon
§  Interactionbetweenquarksand
antiquarkstoformmesons
¡
Residualstrongforceresponsible
fornuclearforce
§  similartoEMforcebetweenatoms
toformmolecules
QuantumChromoDynamics(QCD)
§
§
§
§
¡
issourceofEM,whichismediatedby
masslessphoton
ColorchargeissourceofSI
3colors:r,b,gandthreeanti-colors
8masslessgluonsmediateSI,
Gluonscarrycolor-anticolor
SIs
§  conserveflavor(flavor-blind)
§  Changecolor
▪  whereasWIschangeflavor,insensitiveto
color
¡
Color
§  3colors:r,b,gandthreeanti-colors
§  8gluonscarrycolor-anticolorè
§  Illustrationofred-bluequarks
g6 = BG, g7 =
1
RR − GG )
(
2
1
RR + GG − 2BB )
(
6
g8 =
Strongcouplingconstant
N * → Nπ
τ S ≈ 10 −23 s
Σ0 → Λ 0γ
τ EM ≈ 10 −19 s
interaction
§
¡
g1 = RG, g2 = RB, g3 = GR, g4 = GB, g5 = BR
è
Flavour(u,d,s,…)NOTchangedbySI
§  Atlowenergies,αSlarge è
§  Conditionofvalidityof
perturbationtheoryfails
§  Calculationsdifficult
1/2
−19 *1/2
'
*
'
αS
τ EM
10
∝)
, ≅ ) −23 , ≅ 100 → α S ≈ 1
α EM ( τ S +
( 10 +
¡
Highmomentumtransfer
§  Shortdistances,αSdecreasesto0.12at91GeV
§  Perturbationtheoryokand1storderdiagrams~sufficient
¡
Gluoninteractionspossibleasgcarriescolor
§  3-gluonvertex(and4-g)
§  EMhasnovertexwith2ormorephotons!
¡
Quasi-staticpotentialbetween2quarkswithina
hadron
§  Coulomb-typeterm(1/r)dominatesatsmalldistances,
decreaseswithenergyE
▪  notdivergentasαSdecreaseswithE,leadingtoequilibrium
▪  àasymptoticfreedom
§  2ndtermlinearlyincreaseswithdistanceà
confinementofquarkswithinhadrons
▪  Relatedtointeractionsofgluons
VS (r) = −
4 αS
+ K ⋅r
3 r
¡
“Coupling
constants”ofEMI,
WI,SI
§  Slightlyenergy-
dependent
§  Possiblysame
valueat~1016GeV
¡
Grandunification–
GUT?
§  on-setofquark-
leptonsymmetry
§  newgauge
bosons“linking”
thetwofermion
types
¡
Particleinteractions
§  AllfermionsinteractthroughWI
▪  NeutrinosonlyfeelWI
§  electricallychargedparticles“feel”EM
§  particlesmadeofquarks(hadrons)subjecttoSIthroughcolorcharge
¡
Classificationaccordingto
§  Stability(lifetime)
§  Spin
§  BaryonandLeptonnumbers
¡
Quantumnumberconservation
§  Relatedtoconservationprinciples
§  Relatedtosymmetries
§  èChapter6:Invarianceandconservationprinciples
¡
Stability(lifetime)
§
§
§
§
§
Stableparticles(e±,γ), (ν, p,antiproton)
10-6–10-12àWeakdecays
10-16–10-20àEMdecays
10-23–àStronghadrondecays
10-25W,Zweakbosons
▪
¡
(manypossibilitiestodecay…largephasespace!)
Spin–conserved
§  Bosons,integerspin;Bose-Einsteinstatistics;WFofsystemofidenticalbosonsymmetricin
exchangeofany2bosons;lasereffect
▪
Gaugebosons(1),Higgs(0),Mesons(0,1,2…)
§  Fermions,½integerspin,Fermi-Diracstatistics;Pauliexclusionprinciple;WFofsystemof
identicalfermionsantisymmetricinexchangeof2fermions
▪
Leptonsandquarks(1/2),Baryons(1/2,3/2,…)
¡
BaryonandLeptonnumbers–conserved
§
§
§
§
Baryons(B=1),antibaryons(B=-1),bosonsandleptons(B=0)
n → p e− ν e
e-andνe(Le=1),e+andanti-νe(Le=-1);restLe=0 B
1 1 0 0
+
µ-andνµ(Lµ=1),µ andanti-νµ(Lµ=-1);restLµ=0 L
0 0 1 −1 e
τ-andντ(Lτ=1),τ+andanti-ντ(Lτ=-1);restLτ=0
µ − → e− ν e ν µ
Lµ
1 0 0 1
Le
0 1 −1 0