T.Hebbeker

p p

physics

Tevatron 2002

CMS 2007

UA1 1983

LHC 2008 ? 1.0

part II

Thomas HebbekerRWTH

WS 2003/2004

T.Hebbeker

p p

physics

Part I Introduction

Part II Standard Model Physics

Part III Higgs

Part IV New PhenomenaReferences

• cross section calculation• QCD and jets• W and Z• charm and bottom• top

T.HebbekerCross Section

Total inelasticcross section

Pointlike cross section

pp

2252 1010 cmfm −≈≈σ

2362

10 cms

−≈≤ασ

BACKGROUND

SIGNAL

strong

electroweak

p

p

Elastic cross section

strong, electromagnetic

Xsection relatively smallscattering angle tinyLUMINOSITY

LHCSignal / Background 1110−<

LUMINOSITY

T.HebbekerStructure FunctionsMeasurements:

F2 , F3 ... in DIS

(n,p,elm.,weak, Q2-depend.)

valence, sea, gluons...

Fits/parametrisations:• CTEQ

• MRST

T.HebbekerCross section calculation in pp

VdQsd F ),( 2σWanted:

Calculable:

Known:

VdQxxd ji

ijF ),,( 2σ

),( 2Qxf ii

kinematicalvariable

final state

sxx 21='s

),(),(),( 22

,

2

QxfQxfdxdxVdQsd

jjji

iijiF ∑∫=

σ

2Q

VdQxxd ji

ijF ),,( 2σ

Spectator jet

Q2 = („momentum transfer“)2

depends on final state

T.HebbekerCross Sections

at Hadron

Colliders

Note:

may trade:

energy luminosity

Example:

In principle top discovery at SPS !

Estimate of Xsection p p → W −X

Ansatz:

d u → W − (valence quarks)

σW (√

s) =∫ ∫

fd(x1) f u(x2) σdu(√

s′) dx1 dx2

s′ = x1 x2 s

Structure Functions:

Rough parametrisation:

fd(x) =0.2

xfu(x) = 2 fd(x)

Cross section (quark level):

σdu(√

s′) = σ0 ·

s Γ2W

(s′ − m2W )2 + m2

WΓ2W

σ0 =12π

m2W

·Γqq

ΓW

≈12π

m2W

·6

9≈

25

m2W

σdu(√

s′) ≈

25

m2W

·{

1 mW − ΓW /2 <√

s′ < mW + ΓW /20 else

Calculate:

σW (√

s) = 25 · 0.2 · 0.4·1

m2W

·∫ 1

xmin2

1

x2

[∫ xmax1

xmin1

1

x1dx1

]dx2

xmin2 ≈

m2W

s

xmin1 =

(mW − ΓW /2)2

x2 sxmax

1 =(mW + ΓW /2)2

x2 s

σW (√

s) ≈ 25 · 0.2 · 0.4 ·1

m2W

·∫ 1

xmin2

1

x2

[2

ΓW

mW

]dx2

σW (√

s) = −4 ·1

m2W

·ΓW

mW

· lnm2

W

s

Results:

1/GeV = 2 · 10−16 mmW = 80 GeVΓW = 2 GeV

σW (√

s) ≈ 4 nb · ln sm2

W

FERMILAB :σp(

√s) ≈ 25 nb

LHC(pp!) :σp(

√s) ≈ 40 nb

T.HebbekerQCD = Quantum Chromodynamics

Gauge theory: • quarks with 3 colors (r,g,b)

• 8 gluons (color + anticolor r,g,b) SU(3)spin 1

spin 1/2

T.Hebbekerself coupling, running, confinementnonabelian:

„Running“:

~ 1/distance

mesons and baryons „white“:

qqqqq

strongcoupling„constant“ Zm

T.HebbekerHadronization = Fragmentation

time

„string“

String model:

QCD:

soft

uud

d

Hadronization: non-perturbative

need models!

jet(to be defined)

hadrons

g q

q

hadrons

T.HebbekerCalculation of QCD processes

T.HebbekerHigher Order Corrections

Often: higher order corrections to differential cross section

modeled by LO prediction and „K factor“ (typ. 1 ... 2)

can be large in particular for QCD processes!

LO = Leading Order

NLO = Next to Leading Order

Difficulties for p p reactions:

• parton densities and fragmentation functions depend on order!

• factorization scale, renormalization scale, fragmentation scale

(Q2 parton density) (Q2 hard process) ....

T.Hebbekerjets

jets reveal hard processs (direction, energy)

experiment and theory must use the same language:

jets need to be defined: „jet algorithm“

parton (quark, gluon)

theory

Typical: 100 particles total

(14 TeV)

2-5 jets per event

hadrons

experiment

T.Hebbeker

Jet ev

ents

eta

3.7

0.0

-3.7

-1.2

1.2

phi

0.0

2PI

ET GeV

55

Max: 52.4

CDF

D0

T.Hebbekercone jets

potential problems: seed dependence, infrared sensitivity ...

several variations exist

Cone defined in projection, radius R = (typ = 0.7)

Isolated low energy particles are ignored

Sum of 4-momenta of objects inside cone = jet 4-momentum

ϕη , 22 )()( ϕη ∆+∆

T.HebbekerkT jets Example:

... several variations exist

b) each cluster:

2,iTi pd =

22,

2, ),min( ijjTiTij Rppd ⋅=

a) list of hadrons = clusters

each pair of clusters:

c) minimum of

combine or remove from list)

d) iterate: goto b)

till list empty

iij dd ,

T.HebbekerInclusive jet production

D0 1.8 TeV cone radius 0.7

)( 3

sO α

Conclusion: agreement with QCD over many orders of magnitude!

=NLO

T.Hebbekermultijet events

Measurealphas fromrelative fraction of events with2,3,... jets

CDF 1.8 TeV

cone radius 0.7

Test QCD

T.HebbekerSoft hadronic processes (LHC)

Elastic

(20 mb)

Inelastic

(80 mb)

(zero quantum numbers!)

diffractive (25 nb)

non-diffractive (55 nb)

T.HebbekerDouble-Diffractive Event

D0„r

apid

ityga

p“

T.HebbekerW and Z

measured at LEPreference for W mass measurement

• production cross section

• decay modes

• W mass

• W width

• (W polarization in top decays)

• ...

WWZ

W

mm

θθ 222

sin1cos −==

T.HebbekerW and Z discoveryDiscovery:

UA1, UA2

(1983)

Precision measurement

Z mass at LEP:

91.1876 +- 0.0021 GeV

νeW →

eeZ →

T.HebbekerW,Z: production and decay

W decay probability:

)(~ 22AVC ggNBr +

20%

70%

3%

3%

3%eeµµττ

bbccssdduu ++++νν

CNBr ~

33%

33%

11%

11%

11%νeνµντudcs

Z decay probability:

Clearsignature

T.HebbekerW,Z: mass

D0

1.8

TeV

Tevatron combined: GeV059.0456.80 ±GeV015.0±LHC:

LEP: GeV042.0±Run I

)cos1(22ν

ν φlTlTT EEM −=

)cos1(2 12212 φ−= ll EEM

T.HebbekerW: width

... difficult...

GeV047.0160.2 ±

D0 1.8 TeV

Monte Carlo

Tevatron combined: (indirect+direct)

T.HebbekerW,Z: production cross section

theory theory

T.Hebbekerpp-physics with charm and bottom

cross section huge !

• cross section

• new mesons/baryons/hybrids/... ?

• hadron masses

• hadron lifetimes

• branching fractions (rare decays ?)

• B0 mixing

• CP violaton

s

T.HebbekerExample: D meson masses

T.HebbekerReconstruction of decay vertices

D0

bbZ →

T.HebbekerExample:

decay length

L

)/(βγL

decay length:

Lab frame:

βγctL =

++ +→ KJB ψ/

T.HebbekerTop Discovery

Fermilab, 1995 CDF, D0

m ~ 175 GeV

GeVpp 1800

CDF

T.Hebbeker

)ln,(1sin1

2

2/1

HtWFW mmrGm

∆−⋅

=

θαπ

Top Physics• cross section

• decay modes

• top mass

• spin correlations

• ...

T.HebbekerTop Identification

cross section small (at 2 TeV)

l

b

b

ν

p p

E T

jet jet

jet

ldecay:

production:

ttpp →

bWt→Signature:

2 b jets+ leptons/jets/missing energy

νlqqW ,→

T.HebbekerTop event in D0

µ -

MTC

Jet 1

IP

SV

Jet 1

IP

SV

Jet 2

Run II(~ 100 events)

T.Hebbeker

Top event in CDFRun II

(~ 100 events)

T.HebbekerTop Pair Production

gg contributes

• 15% at 2 TeV

• 95% at 14 TeV

T.HebbekerTop Mass

CDF

Run I

νbbqqltt→

GeV1.53.174 ±

Tevatron Run I

CDF + D0:

Using massconstraints

...νlW →

LHC: +- 1 GeV

T.HebbekerTop Cross Section and Top Mass

cross section measurement = indirect mass determination!

T.Hebbeker

Spin of top related to lepton direction in

due to parity violation!

Top quark lifetime

much shorter than „hadron formation time“

Spin Correlations - introduction

smG tF

t25

32 10528 −⋅≈≈π

τ

scfmh24103~/1 −⋅>τ

If is produced in a certain spin state, e.g.

spins of the two quarks are correlated!

lbWbt ν→→

01 Stt

T.HebbekerTop Spin Correlations simulation

LHC

direction

lepton 1 direction lepton 2

ttqq →mostly

in

13 S

ttgg →mostly

in

01 S

(Tevatron)

(LHC)

can distinguish!

T.Hebbeker

p p

physics

Part I Introduction

Part II Standard Model Physics

Part III Higgs

Part IV New PhenomenaReferences

• cross section calculation• QCD and jets• W and Z• charm and bottom• top