Chapter9
¡  ¡
Selectede+e-processes
§  e+,e-fundamentalparticles
§  Finalstatesmucheasierto
analysethanhadronhadroncolliders
⎧e+e− → l +l − ; l = e, µ, τ
⎪ + −
⎪e e → ν lν l
+ −
e e → f f ⎨ + −
⎪e e → q q → 2 − jets
⎪ + −
⎩e e → q qg → 3 − jets
§  Studythevariousprocesses
▪  Feynmandiagram
▪  Interactionresponsible
▪  Relativecrosssection
⎧e+e− → γγ
⎪ + −
⎪e e → γ Z
+ −
e e → G G ' ⎨ + −
⎪e e → ZZ
⎪ + −
+
−
⎩e e → W W
¡
EM(γ)process
§  2vertices,1/q2à
¡
pureweak(Z0)process
§  Relevantathighenergies(Z-peak)
q 2 = p 2 = s = (2Ee )2
2
dσ + −
α EM
+ −
e e →γ → µ µ ) =
1+ cos2 θ )
(
(
dΩ
4s
2
4πα EM
(!c)2
86.8
+ −
+ −
σ (e e → γ → µ µ ) =
=
nb
3s
s[GeV 2 ]
2
4πα EM
(!c)2 2
σ ( e e → γ → qq ) =
⋅ Qq
3s
+ −
¡
PureEM(γ)process
§  2vertices,1/q2à
2
2πα em
(!c)2 ! s $
σT =
ln # 2 &
s
" me %
¡
Varioushadronresonances
§  ρ,ω (u-ubar,d-dbar), φ (s-sbar), J/ψ
(c-cbar), Υ (b-bbar), …, Ζ
σ ( e+e− → hadrons)
§  Continuum
R = R0 ≡
σ ( e+e− → hadrons)
σ ( e+ e− → µ +µ − )
∑σ (e e
+ −
=
n
→ qn qn )
σ ( e+ e− → µ +µ − )
Nf
= N C ∑Qn2
n=1
σ (e e
+ −
R = R0 ≡
σ ee
→ hadrons ) ∑ (
=
σ ( e+ e− → µ +µ − )
+ −
n
→ qn qn )
σ ( e+ e− → µ +µ − )
Nf
= N c ∑Qn2
n=1
)" 2 %2 " 1 %2 " 1 %2 ,
u, d, s
⇒ R = N c +$ + ' + $ − ' + $ − ' . = 2
+*# 3 & # 3 & # 3 & .)" 2 %2 " 1 %2 " 1 %2 " 2 %2 , 10
u, d, s, c ⇒ R = N c +$ + ' + $ − ' + $ − ' + $ + ' . =
+*# 3 & # 3 & # 3 & # 3 & .- 3
)" 2 %2 " 1 %2 " 1 %2 " 2 %2 " 1 %2 , 11
u, d, s, c, b
⇒ R = N c +$ + ' + $ − ' + $ − ' + $ + ' + $ − ' . =
+*# 3 & # 3 & # 3 & # 3 & # 3 & .- 3
& αs )
2 + 3 − jets ⇒ R = R0 (1+ +
'
π*
σ (e e
R=
σ (e e
+ −
σ (e e
∑
)
→ hadrons
=
+ −
+ −
f
→ µ +µ − )
→ qf qf )
σ (e+ e− → µ + µ − )
Nq
= N c ∑ e2f
f =1
)" 2 %2 " 1 %2 " 1 %2 ,
⇒ R = 3+$ + ' + $ − ' + $ − ' . = 2
+*# 3 & # 3 & # 3 & .)" 2 %2 " 1 %2 " 1 %2 " 2 %2 , 10
u, d, s, c ⇒ R = 3+$ + ' + $ − ' + $ − ' + $ + ' . =
+*# 3 & # 3 & # 3 & # 3 & .- 3
u, d, s
u, d, s, c, b
)" 2 %2 " 1 %2 " 1 %2 " 2 %2 " 1 %2 , 11
⇒ R = 3+$ + ' + $ − ' + $ − ' + $ + ' + $ − ' . =
+*# 3 & # 3 & # 3 & # 3 & # 3 & .- 3
14/04/16
Question: Evaluate αs at 40 GeV (from figure)
8
¡
Let’sillustratesomeQCDdiscussions
e+e− → J / ψ + X → e+e− / µ +µ − / hadrons + X
§  StaticpotentialbetweenHeavyquarkandantiquark
§  Boundstates:CharmoniumandBottomonium
(analogywithpositronium)
¡
CharmoniumJ/ψdiscoveryatBNLandSLAC
p + N → J/ψ + X → e + e − + X
14/04/16
F.Ould-Saada
9
J PC (J / ψ ) = J PC (γ ) = 1−−
¡
J/ψ decays
§
§
¡
Mainlytohadrons88%
Alsotoleptons12%
Hadronicdecayà
CrosssectionBW
formula(0.07mb)
§  TobeaddedtotheEM
contributionat3GeV
(20nb)
§  Resonance~4ordersof
magnitude*
continuum!
§
σ e+e− →J /ψ →hadrons = π ! 2
2J +1
Γ ee Γ h
(2s1 +1) (2s2 +1) ( E − Mc 2 )2 +Γ 2 / 4
$ Γ ee Γ h &
=
≅ 1.197) 2 * = 0.07mb
2
2
$
&
% Γ '
4 %( E − M ) +Γ / 4'
3π ! 2 Γ ee Γ h
M = 3097MeV, J = 1 ; ! = "c / pc ≅ 197MeV fm / 2 × 3097MeV ≅ 0.127 fm
¡
WhyisJ/ψresonancesomuchnarrowerthanotherhadronicresonances(~10’s
MeV)?
J / ψ (3097) ≡ cc QNs : n = 1, 2S+1LJ = 3S1
J / ψ → hadrons (88%) but ΓJ /ψ ~ 90keV !!
/ DD : M J /ψ < 2M D
J /ψ →
¡
¡
Lowestorder
decaytohadrons
diagramisnot
allowed
14/04/16
F.Ould-Saada
Higher
orders
allowedbut
contribute
muchless!
11
J PC ( J /ψ ) = 1− −
C − parity = −
3
⇒ ggg ⇒ (α s )
§  g-exchangeànosuppression
butm<2mDànotpossible
§  3-gluonexchangeàsuppression
ànarrowwidth
J / ψ (3097) → ηc (2980) + γ
Charmoniumspectroscopy
14/04/16
F.Ould-Saada
ψ (3686) → ηc (2980) + γ
ψ (3686) → χ ci + γ
i = 1, 3
m > 2mD ⇒ decay to open charm
⇒ decay width ~MeV
12
¡
Upsilon(9880)discovery
§  FermilabE288experiment
§  Ledermanetal.1977
p + Be → ϒ + X → µ +µ − + X
ϒ ≡ bb ; mb ≈ 4.3GeV
¡
Energylevelsfor(a)positroniumand(b)charmonium.
§  Scaleonordinateis[eV]in(a)and[MeV]in(b)
¡
Atomicphysics–Coulombpotential §  Vem=-αEM/r
§  En=-α2EMmec2/4n2
4 αs
+ Kr
3 r
cc ⇒ α s ≈ 0.3
VQCD (r) = −
n 2S+1LS
11 S0 → orthopositronium - C=+1 → 2γ
K ≈ 1GeV / fm
13 S1 → parapositronium - C=-1 → 3γ
⎧ α
⎪ − s ;r ≤ 0.1 fm ⇒ Asymptotic Freedom
V (r) = ⎨
r
⎪ +K ⋅ r ;r ≥ 1 fm ⇒ Confinement
⎩
& a(!c)
( −
(
r
V (r) = '
( + b⋅r
() !c
•  Similaritiesàflavorindependence!
14/04/16
F.Ould-Saada
r ≤ 0.1 fm ⇒ Asymptotic Freedom
r ≥ 1 fm ⇒ Confinement
αs b ⋅ r
+
r
!c
cc + bb ⇒ a ≈ 0.48 , b ≈ 0.18 GeV 2
V (r) = −
15
9.5Thetau-leptonτ
e+e− → e+e− ; e+e− → µ +µ − (coplanar)
Conservationofleptonflavor
allowsleptonicandotherreactions
¡
e+e− → π + π − (coplanar)
e+e− → π + π − π 0 (acoplanar)
¡
Forbids
¡
Ifheavyleptonexists,itwouldleadtoacoplanare+µ-ore-µ+pairs
e+ e− → e+µ − , µ + e−
e+e− → τ + τ −
τ + → e +υeυτ ; τ − → µ −υµυτ
¡
Apparentviolationofleptonflavors
§  Compensated by the presence of neutrinos
14/04/16
F. Ould-Saada
16
Thetau-leptonτ
¡
Taudiscovery,Perletal.,1975
§  SPEAR (e+ e– collider @ 8 GeV)
Most recently discovered SM fermion
•  First reported by DONUT experiment at Fermilab in 2000
16/04/16
F. Ould-Saada
17
¡
ReadSection9.6inthebook
§  Wesawmostofthestuffintermsofparticleinteractions
inmedia,particleidentificationinvariousdetectors…
§  Therewillbeasession–partofassignmentII–whereyou
wouldbeanalysingATLASmasterclassdata
§  Inthenextslidesweconcentrateonquarksandgluons
andtheirmanifestationasjetsofhadronsindetectors
e +e − →qq → jet − jet
e+ e− →
€qq → hadrons
2m q ≤
¡
¡
s , pq =
s
2
Quarksnotseenasfreeparticles
Quarkandantiquarkhadroniseandappear
asafluxinanarrowsolidanglewiththe
shapeofajet
§  Typicalmomentaofhadrons~0.5-1GeV
§  Openingangleof“jet”ofhadronsà
pT
0.5
1
≈
=
p
s /2
s
s = 30GeV ⇒ φ ~ few °
§ 14/04/16
Atlowenergies,hadronsdistributedoverallsolidangle:nojetstructure
19
JADE detector at PETRA e+e- collider
14/04/16
20
e + e − → qq → jet + jet
dσ z 2α 2
2
=
1+
cos
θ)
(
dΩ
s
! jet !
q = ∑ hi
i
Quarkisspin½
pointlikeparticle
Absolute value because
quark and antiquark jets
cannot be differentiated
14/04/16
21
e+ e − → qq g → 3 − jets
¡
Attypicale+e–energiesof30-100GeV,a
thirdjetappearsinthedetectorin~αs≈
10%ofthetime
¡
“Hard”gluonhadronisestoajetina
similarwayasthequarkandantiquark
Guon and quark jets are in general similar
¡
JADE detector at PETRA e+e- collider
§  Classify jet energies: E1< E2<E3 §  Gluon=jet 3 in ~70% of the cases 14/04/16
22
e+ e − → qq g → 3 − jets
¡
Defineandplotangle φ definedas
§  Transform to jet1-jet2 c.o.m system and
compute angle φ between direction of
pair and jet3
§  distribution depends on spin of gluon
TASSO at PETRA
Gluonisspin1
JP=1–
14/04/16
23
•
Quarksandgluonshavecolor,
whilehadrons(the
asymptoticstates)are
colorless.
•
Theprocessof
“hadronization”occursat
energyscaleswhereQCDis
strong~Λsothat
perturbationtheorycannotbe
used.
•
Thismakesdirect
experimentalQCDpredictions
difficult.
calorimeter jet
CH
§
¡
EventGeneratorsmaybe
§  partonlevel:
▪  PartonDistributionfunctions
▪  Hardinteractionmatrixelement
§  andmayalsohandle:
▪  Initialstateradiation
▪  Finalstateradiation
▪  Underlyingevent
▪  Hadronisationanddecays
SeparateprogramsforDetectorSimulation
§  GEANT–mostcommonlyused
γ
EM
π
K
q
g
Time
¡
expecttoreproduceboththeaveragebehaviorand
fluctuationsofrealdata
FH
hadrons
particle jet
¡
A“MonteCarlo”isaFortranorC++programthat
generatesevents
Eventsvaryfromonetothenext(random
numbers)
parton jet
¡
•
p
•
q
p
Hard Perturbative scattering:
Modelling of the
soft underlying
event
Multiple perturbative
scattering.
Usually calculated at leading order
in QCD, electroweak theory or
some BSM model.
Perturbative Decays
calculated
QCD,State
EW or
Initial andinFinal
parton showers resum the
Finally the unstable hadrons are
some
theory.
largeBSM
QCD
logs. of the
Non-perturbative
modelling
decayed.
hadronization process.
¡
3contributions:
§
§
§
¡
PurelyEM
Interferenceγ-Z
Purelyweak–dominantattheZmass
StartfromBreit-Wignerformulagiveninchapter1(resonance)
§  Hadroniccross-section@LEP@mZ
§  WidthΓff
e+ e− → Z → f f
Γ ee Γ ff / 4
Γ ee Γ ff
4π
2 j +1
12π
σ (s) = 2
= 2 s
2
2
qi ( 2s1 +1) ( 2s2 +1) ( E − M Z ) +Γ Z / 4 mZ ( s − M Z2 )2 + s 2 Γ 2Z / mZ2
qi2 = ( s / 2)2 ; s1 = s2 = 1 / 2; j = 1; E = s 12π Γ ee Γ ff
s = m ⇒ σ ≡ σ (s = m ) = 2
mZ Γ 2Z
2
Z
17/04/16
0
2
Z
F.Ould-Saada
27
¡
¡
TotalmaximumcrosssectionrelatedtoZmass
andtotalandpartialZwidths
FiniteZwidthrelatedtothenumberof
accessiblespeciesoffermionsthatcoupletoZ
§  WidthΓffproportionaltoGFandMZ3
§  afandvf:axial-vectorandvectorcouplingsof
fermionstotheZ;NC=1forland3forq
¡
Experimentalmeasurements:
σ 0 ≡ σ (s = mZ2 ) =
12π Γee Γ ff
mZ2 Γ2Z
GF mZ3 2 2 f
Γ ff =
a f + v f ) N C = 330 ( a 2f + v 2f ) N Cf MeV
(
6 2π
Γνν ≈ 0.066 * 3 = 20%; Γ ll ≈ 0.03* 3 = 9%
Γh ≡ Γuu + Γdd + Γss + Γcc + Γbb
Γll ≡ Γee = Γµµ = Γττ (lepton universality)
Γinvis = Nν Γνν = ΓZ − Γh − 3Γll
ΓZ ≡ Γh + 3Γll + Nν Γνν = Γvis + Γinvis
≅ 2.5GeV ⇒ Nν =
18/04/16
F.Ould-Saada
Γinvis
( Γνν )SM
28
¡
Someofthese
measurementslead
tosomevariables
enteringthe
determinationofthe
numberofneutrino
species
¡
è
14/04/16
F.Ould-Saada
29
σ 0had =
12π Γ ee Γ h
12π Γ ee Γ h
=
40.2 nb
⇒
Γ
=
Z
mZ2 Γ 2Z
mZ2 σ 0had
Γ ff σ 0f
=
Γ ee σ e0
¡
R
; R l0 ≡
Γh
; l = e, µ, τ
Γ ll
MeasurepeakcrosssectionsandR0l
0
invis
Γ invis Γ Z − Γ h − 3Γ ll
12π Rl0
≡
=
=
− R l0 − 3
2
0
Γ ll
Γ ll
mZ σ had
0
R l0, σ 0had , mZ ⇒ Rinvis
= 5.943± 0.016
% Γνν (
Γ invis
0
Rinvis ≡
= Nν '
* = (1.99125 ± 0.00083)Nν
Γ ll
Γ
& ll )SM
⇒ Nν = 2.984 ± 0.008
¡
AfittoallLEPdata(16MZ’s)leadsto:
Nν=2.9835±0.0083
F.Ould-Saada
14/04/16
30
Weakgaugebosonself-couplings
e+e− → ZZ
e+e− → W +W −
14/04/16
F.Ould-Saada
31
¡  14/04/16
F.Ould-Saada
32
¡
Wbosonmass
e+e− → W +W − → qq 'q''q '''
e+e− → W +W − → qq 'lν l
§  Checkthatthehadronic
andsemi-leptonic
channelsrepresent46%
and44%respectively
mW = 80.376 ± 0.033 GeV
ΓW = 2.196 ± 0.083 GeV
18/04/16
F.Ould-Saada
33
¡
CompareQEDvsQCD
¡
¡
EMInfiniterangeèαEMincreasewithenergy/decreaseswithdistance
Stronginteractionsaremicroscopic
§  AsymptoticfreedomèαSdecreasewithenergy/increaseswith
distance
§  Colourconfinementèshortrange~fm(~GeV)
α s (mZ ) = 0.1199 ± 0.0052
α s (206 GeV ) = 0.1079 ± 0.0014
18/04/16
F.Ould-Saada
34
¡
Singleelectronsemitandreabsorbphotons
continuously(a)–quantumfluctuations–
§  orphotonmaybeabsorbedbyanotherelectronnearby
àscattering(b)
¡
Higherorders
§  Initialelectronemitsphotonsand(indirectly)e+e-pairs
–seaorvirtuale+e-àvacuumpolarisationeffects
§  Productionofvirtuale+e-pairsleadstoashielding
effectsuchthatαQED isaltered
Coulomb potential :φeff =
α eff
α eff (r)!c
r
! %
'
= α ≈ 1 /137 for r >> rC ≡
me c &
'
r ≤ rC ⇒ α decreases
(
14/04/16
F.Ould-Saada
α em (µ ) =
α (µ 0 )
(
" µ %+
2
1−
α
(
µ
)ln
*
$ '0
3
π
# µ 0 &,
)
35
α s (µ ) =
α s (µ 0 )
"µ%
α s (µ 0 )
1+
(33− 2N f ) ln $ µ '
6π
# 0&
µ 2 >> 1GeV 2
N f < 17 ⇒
Asymtotic Freedom
¡  Gluonself-couplingèanti-screening
α em (µ ) =
14/04/16
α (µ 0 )
(
" µ %+
2
*1− α (µ 0 )ln $ '# µ 0 &,
) 3π
F.Ould-Saada
36
¡
αsmeasurements
14/04/16
F.Ould-Saada
α s (M Z ) = 0.118 ± 0.002
37
s ≤ 208GeV
e+e− → H 0 Z 0 H → bb
¡
¡
¡
CandidateHiggseventcollectedbyDELPHIin
2000,compatiblewiththeassociated
productionofaZbosonandHiggsbosonof
mass113GeV.
Adifferentpairingofthejetscouldleadtoan
interpretationcompatiblewiththeproduction
oftwoZbosons
Otherproductionmechanisms
14/04/16
⇒ MF.H Ould-Saada
> 114GeV / c
2
Z,Hà 4 b-jets?
38
¡
Hcoupling
§  Tofermionsf
proportionaltomf
§  TobosonsV
proportionaltomV2
17/04/16
FYS4560 - F. Ould-Saada
39
¡
125GeV…a
rathergood
compromise
§  ≥5decay
channels
accessible
atLHC
17/04/16
Higgs and more - F. Ould-Saada
40
¡
125GeV…arathergoodcompromise
§  4/5productionprocesses
§  ≥5decaychannels
17/04/16
Higgs and more - F. Ould-Saada
41
Hàγγ
42
HàZZ*àl+l-l+l-
§  Understandingof“background”isimportant
ú  Mostofwhichisduetoimportantphysicsatthe
Higgs and more - F. Ould-Saada
heartofthegaugestructure/symmetryof
electroweakinteraction
ú  Higgsshowedupbetween2relativelybusy
regions!
17/04/16
43
HàWW*àlνlν
§  Understandingofbackgroundiscrucial
ú
ú
Higgsandmore-F.Ould-Saada
Mostofwhichisduetoimportantphysics
attheheartofthegaugestructure/
symmetryofelectroweakinteraction
17/04/16
44