High P T Hadron Collider Physics

FNAL Academic Lectures - May, 2006 1

High PHigh PTT Hadron Collider Physics Hadron Collider PhysicsHigh PHigh PTT Hadron Collider Physics Hadron Collider Physics

Outline

• 1 - The Standard Model and EWSB

• 2 - Collider Physics

• 3 - Tevatron Physics• QCD• b and t Production• EW Production and D-Y


Backup TextBackup TextBackup TextBackup Text


UnitsUnitsUnitsUnits

Recall that coupling constants indicate the strength of the interaction and characterize a

particular force. For example, electromagnetism has a coupling constant which is the electron

charge, e and a “fine structure” constant

ce _πα 4/2=

that is dimensionless. The electromagnetic potential energy is

rereVrU /)()( 2==

and V(r) is the electromagnetic potential. The dimensions of e 2 are then energy times length,

2[ ] [ ( ) ]e U r r=

, the same as those of

c_

. Thus, in the units we adopt,

1c= =_

, e is also dimensionless. With α ~ 1/137, we find e ~ 0.303. Coupling constants for the two other forces, the strong and the weak, will be indicated by

gi, and the corresponding fine structure consta nts by αi with i = s, W.

The units for cross section, σ, which we will use are barns (1 barn = 10 -24 cm2). Note that

2 2( ) 0.4c GeV mb=_

where

27 21 10mb cm−=

. The units used in COMPHEP are pb = 10 -12 b for

cross section and Ge V for energy units. As an example, at a center of mass, C.M., energy,

s

, of 1 TeV = 1000 GeV, in the absence of dynamics and coupling constants, a cross section scale

of

s/1~σ

~ 400 pb is e xpected simply by dimensional arguments.


Tools NeededTools NeededTools NeededTools NeededWe will extensively use a single computational tool, COMPHEP . The aim was to ex pand a

slightly formal academic presentation to a more interactive mode for the student, giving “hands

on” experience. The plan was that the stud ent would work the examples and then be fully

enabled to do problems on her own. COMPHEP runs on the Windows platform, which was why

it was chosen since the aim was to provide maximum applicability of the tool. A LINUX version

is also available for students usi ng that operating system

The COMPHEP program is freeware. We have taken the approach of first working through the

algebra. That way, the reader can make a “back of the envelope” calculation of the desired quantity.

Then she can use COMPHEP for a more detailed examination of the qu estion. The use and description

of COMPHEP is e xplained in detail . A web address where the executable code (zipped) and a users

manual are avail able. The autho r has also posted these it ems: http://uscms.fnal.gov/uscms/dgreen .

Freeware to unzip files can be found at http://www.winzip.com/ and http://www.pkware.com/ .

(will use both during lecture demonstrations)

( Google them all – also Ghostview and Acrobat reader )


COMPHEP – Models and ParticlesCOMPHEP – Models and ParticlesCOMPHEP – Models and ParticlesCOMPHEP – Models and Particles

Can edit the couplings – e.g. ggH

Use SM Feynman gauge

Watch for LOCK


COMPHEP - ProcessCOMPHEP - ProcessCOMPHEP - ProcessCOMPHEP - Process

1-> 2,3

1-> 2,3,4

1,2 ->3,4

1,2 ->3,4,5

1,2-> 3,4,5,6 (slow)

*x options

No 2 -> 1


COMPHEP –Simpson, BRCOMPHEP –Simpson, BRCOMPHEP –Simpson, BRCOMPHEP –Simpson, BR

Find simple 2->2. Graphs (with menu)

Results can be written in .txt files

Several PDF, p and pbar,

Check stability of results


COMPHEP - CutsCOMPHEP - CutsCOMPHEP - CutsCOMPHEP - Cuts

May be needed to avoid poles or to simulate experimental cuts, e.g. rapidtiy or mass or Pt.


COMPHEP - CutsCOMPHEP - CutsCOMPHEP - CutsCOMPHEP - Cuts


COMPHEP - VegasCOMPHEP - VegasCOMPHEP - VegasCOMPHEP - Vegas

Full matrix element calculation – interference. Watch chisq approach 1. Setup plots, draw them and write them.


COMPHEP - DecaysCOMPHEP - DecaysCOMPHEP - DecaysCOMPHEP - Decays

Strictly tree level. Does not do “loops” or “box” diagrams.

Explore this very useful tool. If there are problems bring them to the class and we’ll try to fix them.


1 - The SM and EWSB1 - The SM and EWSB1 - The SM and EWSB1 - The SM and EWSB

• 1.1 The Energy Frontier

• 1.2 The Particles of the SM

• 1.3 Gauge Boson Masses and Couplings

• 1.4 Electroweak Unification

• 1.5 The Higgs Mechanism for Bosons and Fermions

• 1.6 Higgs Interactions and Decays


Higgs boson

t quark

b quark

s quark

ISR

Tevatron

SPEAR

SppS

TRISTAN

LEPII

CESR

Prin-Stan

Accelerators

electron

hadron

W, Z bosons

c quark

LHC

PEP

SLC

1960 1970 1980 1990 2000

Starting Year2010

10-1

100

101

102

103

104

Constituent CM Energy (GeV)

Historically HEP has advanced with machines that increase the available C.M. energy. The LHC is designed to cover the allowed Higgs mass range. Colliders give maximum C.M. energy.

The Energy The Energy FrontierFrontier


The Standard Model of Elementary The Standard Model of Elementary Particle PhysicsParticle Physics

The Standard Model of Elementary The Standard Model of Elementary Particle PhysicsParticle Physics

• Matter consists of half integral spin fermions. The strongly interacting fermions are called quarks. The fermions with electroweak interactions are called leptons. The uncharged leptons are called neutrinos.

• The forces are carried by integral spin bosons. The strong force is carried by 8 gluons (g), the electromagnetic force by the photon (), and the weak interaction by the W+ Zo and W-. The g and are massless, while the W and Z have ~ 80 and 91 GeV mass respectively.

J = 1 g,, W+,Zo,W- Force Carriers

J = 1/2

u

d

c

s

t

b

e

e

Q/e=

2/3

-1/3

1

0

Quarks

Leptons

J = 0 H


Gravity – Hail and FarewellGravity – Hail and FarewellGravity – Hail and FarewellGravity – Hail and Farewell

UG(r) = G NM2/r, depends on mass in comparison to the electrical energy U EM(r) = e 2/r. The

quantity G N is Newton’s gravitational constant. The fine structure constants of the forces

appearing in the SM, such as electromagnetism, where

137/1~4/2 ce _πα =

, are dimensionless and mass independent. The gravitational analogue,

2 / 4Gr NG M cα π= _

, is not.

Ignore gravity. However, gravity is a precursor gauge theory which is non-Abelian. The gauge quanta are “charged” non-linearity. The gravity field carries energy, or mass. Therefore, “gravity gravitates”. This is also true of the strong force (gluons are colored) and the weak force (W,Z carry weak charge). The photon is the only gauge boson which is uncharged.


How do the Z and W acquire mass and not How do the Z and W acquire mass and not the photon?the photon?

How do the Z and W acquire mass and not How do the Z and W acquire mass and not the photon?the photon?

Gravity - Physics is the same in any local general coordinate system --> metric tensor or spin 2 massless graviton coupled universally to mass = GN.

Electromagnetism - Physics is the same regardless of wave function phase assigned at each local point --> massless, spin = 1, photon field with universal coupling = e

These are “gauge theories” where local invariance implies massless quanta and specifies a universal ( GN, e ) coupling of the field to matter.

Strong interactions are mediated by massless “gluons” universally coupled to the “color charge” of quarks = gs.

Weak interactions are mediated by massive W+,Z,W- universally coupled to quarks and leptons. gWsinW = e. How does this “spontaneous electroweak symmetry breaking” occur? (Higgs mechanism)


Lepton Colliders - LEPLepton Colliders - LEPLepton Colliders - LEPLepton Colliders - LEP

Z peak

L and R leptons have different couplings to the Z. There is Z-photon interference which leads to a F/B asymmetry. A way to measure the Weinberg angle. gW measured from muon decay.


Field TheoryField TheoryField TheoryField Theory

2 2 2,E P M P P M= + ⋅ =

2( ) Mφ φ φφ= ∂ ∂ −l

To describe quantum fields we will use

ψ

for fermion ( J = _ ) fields,

φ

for scalar ( J = 0 ) fields, and

ϕ

for vector (J = 1) gauge fields in this text. For masses, m is used for fermions and

M for bosons.

2

( )( ) ( )( )

~ ( ) ,I

D D

g g

ϕ ϕ ϕ ϕϕ ϕϕ ϕϕϕϕ

∂ ∂ →

∂l

P_

by

AeP__

−

ieAD −∂=→∂

ggggggg, ZWWWW −+−+ , −+−+−−+−+ WWWWZZWWZWWWW ,,,

Classical Special Relativity

Lagrangian density, P is an operator

Classical gauge replacement

Quantum gauge replacement


WW in e+e- CollisionsWW in e+e- CollisionsWW in e+e- CollisionsWW in e+e- Collisions

Test of self-coupling of vector bosons. There are s channel Z and photon diagrams, and t channel neutrino exchange. Test of VVV couplings.

In COMPHEP play with the Breit-Wigner option as s dependence of the cross section depends crucially on the W width – i.e. technique to measure W width..


Simpson –Angular DistSimpson –Angular DistSimpson –Angular DistSimpson –Angular Dist

Cross section without neutrino exchange in the t channel. Note divergent C.M. energy dependence – voilates unitarity.


WW Cross Section at LEPWW Cross Section at LEPWW Cross Section at LEPWW Cross Section at LEP

COMPHEP point shown. Proof that the WWZ triple gauge boson coupling is needed and that there are interfering amplitudes that themselves violate initarity.


WWWW at LEP at LEPWWWW at LEP at LEP

Probe of quartic couplings.

LEP data confirms SM

WWAA, WWZA

Cross section in COMPHEP with all final state bosons having Pt > 5 GeV is 0.36 pb


ZZ at LEPZZ at LEPZZ at LEPZZ at LEP

SM has only the single Feynman diagram. There are no relevant triple or quartic couplings – in the SM. Use the data to set limits on couplings beyond the SM.


e+e- Cross Sectionse+e- Cross Sectionse+e- Cross Sectionse+e- Cross Sections

WW, ZZ, and WW are seen at LEPII. At even higher C.M. energies, WWZ and ZZZ are produced - indicating triple and quartic V couplings. New channels open up at the proposed ILC.

Try a few (red dots) processes yourself…..


ILC Process - ExampleILC Process - ExampleILC Process - ExampleILC Process - Example

Cross section ~ 1 fb at 500 GeV in COMPHEP. Approximate agreement with full calculation.


The Higgs Boson PostulatedThe Higgs Boson PostulatedThe Higgs Boson PostulatedThe Higgs Boson Postulated

422 ||||)( φλφφ +=V

λφ 2/22 −=><

~ ( ) ( )Vφ φ φ∂ ∂ +l

4~)( ><>< φλφV

Potential Lagrangian density

Minimum at a non-zero vev “cosmological term”

This is Landau-Ginzberg superconductivity – much too simple?


How the W and Z get their MassHow the W and Z get their MassHow the W and Z get their MassHow the W and Z get their Mass

Covariant derivative contains gauge fields W,Z. Suppose an additional scaler field ϕ exists and has a vacuum expectation value. Quartic couplings give mass to the W and Z, as required by the data [ V(r) ~e(exp(-r/λ)/r) - weak at large r, strength e at small r].

2 2 2 2 2 22 1 2

( )( ) ( )( )

0~

( )( ) ~ / 2 ( ) / 2 (0)W W Z Z

D D

D D g g g e

φ φ φ φ

φφ

φ φ φ ϕ ϕ φ ϕ ϕ ϕ ϕ

∂ ∂ →

⎡ ⎤⎢ ⎥< >⎣ ⎦

⎡ ⎤ ⎡ ⎤< > + + < > +⎣ ⎦ ⎣ ⎦

WWZ

W

MggM

gM

M

φ

φ

cos/2/

2/

0

22

21

2

=+><=

><=

=


Numerical W, Z Mass PredictionNumerical W, Z Mass PredictionNumerical W, Z Mass PredictionNumerical W, Z Mass Prediction

The masses for the W and Z are specified by the coupling constants. G comes from beta decays or muon decay.

2 2 5 2

2

/ 2 / 8 , 10

/ / 2

2 / 4 , 174

W W

W W

G g M G GeV

M g

G GeV

φ

φ φ

− −= ≈

=< >

< > = < >=

2

2

sin ~ 0.231, ~ 28.7 , sin 0.481

~ 1/137, / sin ~ 1/ 31.6, ~ 0.63

oW W W

W W Wg

α α α

=

=

/ 2 ~ 80

/ cos ~ 91W W

Z W W

M g GeV

M M GeV

φ

= < >=


Higgs Decays to BosonsHiggs Decays to BosonsHiggs Decays to BosonsHiggs Decays to Bosons

Field excitations ==> interactions with gauge bosons VVH, VVHH, VVV, VVVV

2( ) / ~ ( /16)( / )H W H WH WW M M Mα βΓ →

Higgs couples to mass. Photons and gluons are massless to preserve gauge symmetry unbroken. Thus there is no direct gluon or photon coupling.

Using the Higgs potential, V(φ), expanding about the minimum at

φ φ=< >

, and

identif ying the mass term in

_

as

2H H HM φ φ

, we find that the mass is,

.2462 λλφ GeVM H =><=

Since

λ

is an arbitrary dimensionless coupling, there is no

prediction for the Higgs mass in the SM.

,_ ~ gW2 <φ>[

W W Hϕ ϕ φ

] ~ gWMW [

W W Hϕ ϕ φ

].


ZZH Coupling and ILC ProductionZZH Coupling and ILC ProductionZZH Coupling and ILC ProductionZZH Coupling and ILC Production

ILC at 500 GeV C.M. Higgs production by off shell Z production followed by H radiation, Z* ->Z+H.


Higgs Coupling to FermionsHiggs Coupling to FermionsHiggs Coupling to FermionsHiggs Coupling to Fermions

~ [ ]f L Rg ψ φψl

],[][~ ψψψψφ ff mg =><_

2/)/(

]/2[

WfWf

WWfff

Mmgg

gMggm

=

=><= φ

•The fermions are left handed weak doublets and right handed singlets. A mass term in the Lagrangian, is then not a weak singlet as is required.

•A Higgs weak doublet is needed, with Yukawa coupling,

Yukawa

Mass from Dirac Lagrangian density

Fermion weak coupling constant

( )mψ ψ∂−

( )L R R Lm ψ ψ ψ ψ+


Higgs Decay to FermionsHiggs Decay to FermionsHiggs Decay to FermionsHiggs Decay to Fermions

• The threshold factor is for P wave, β2l+1 since scalar decay into fermion pairs occurs in P wave due to the intrinsic parity of fermion pairs.

• The Higgs is poorly coupled to normal (light) matter

• gt ~ gW (mt/ MW)/2 ~ 1.0, so top is strongly coupled to the Higgs.

2 3( ) / ~ (3 /8)( / )H W f WH qq M m Mα βΓ →


The Higgs Decay WidthThe Higgs Decay WidthThe Higgs Decay WidthThe Higgs Decay Width

The Higgs decay width, Γ scales as MH

3. Thus at low mass, the detector defines the effective resonant width and hence the time needed to discover a resonant enhancement. At high masses, the weak interactions become strong and Γ/M ~ 1.


Higgs Width - WW + ZZHiggs Width - WW + ZZHiggs Width - WW + ZZHiggs Width - WW + ZZ

Higgs decays to V V have widths Γ ~ M3

Try this as a

COMPHEP

example


Higgs Width Below ZZ ThresholdHiggs Width Below ZZ ThresholdHiggs Width Below ZZ ThresholdHiggs Width Below ZZ Threshold

Below ZZ threshold, decays can occur in the tails of the Breit Wigner Z resonance, with Γ ~ 2.5 GeV, M ~ 91 GeV. This compares to the width to the heaviest quark, b at a Higgs mass of ~ 150 GeV. Means that W*W is an LHC strategy.


Early LHC Data TakingEarly LHC Data TakingEarly LHC Data TakingEarly LHC Data Taking

• We have seen that the Higgs couples to mass. Thus, the cross section for production from gluons or u, d quarks is expected to be small.

• Therefore, it is a good strategy to prepare for LHC discoveries by establishing credibility. The SM predictions , extrapolated from the Tevatron, should first be validated by the LHC experimenters.


Vector Bosons and Forces Vector Bosons and Forces Vector Bosons and Forces Vector Bosons and Forces

The 4 forces appear to be of much different strength and range. We will see that this view is largely a misperception.


2 - Collider Physics2 - Collider Physics 2 - Collider Physics2 - Collider Physics

• 2.1 Phase space and rapidity - the “plateau”

• 2.2 Source Functions - protons to partons

• 2.3 Pointlike scattering of partons

• 2.4 2-->2 formation kinematics

• 2.5 2--1 Drell-Yan processes

• 2.6 2-->2 decay kinematics - “back to back”

• 2.7 Jet Fragmentation


Kinematics - RapidityKinematics - RapidityKinematics - RapidityKinematics - Rapidity

One Body Phase Space

NR

φddPPdPdPdPPd TT||2 =Ω=

r

( ) EPdmPPd /224r

=−δ

( )2TPdydπ=

EdPdy /||=

Relativistic

6.9,7.7

,14,2@

,0max

cosh

max

222

=

=+=

=

yTeVpp

momentumbeamPatyPmm

ymE

T

TT

T

Rapidity

If transverse momentum is limited by dynamics, expect a uniform distribution in y

Kinematically allowed range in y of a proton with PT=0


Rapidity “Plateau”Rapidity “Plateau”Rapidity “Plateau”Rapidity “Plateau”

Monte Carlo results are homebuilt or COMPHEP - running under Windows or Linux

Region around y=0 (90 degrees) has a “plateau” with width y ~ 6 for LHC

LHC


Rapidity Plateau - JetsRapidity Plateau - JetsRapidity Plateau - JetsRapidity Plateau - Jets

For ET small w.r.t sqrt(s) there is a rapidity plateau at the Tevatron with y ~ 2 at ET < 100 GeV.


Parton and Hadron DynamicsParton and Hadron DynamicsParton and Hadron DynamicsParton and Hadron DynamicsFor large ET, or short distances, the impulse approximation means that quantum effects can be ignored. The proton can be treated as containing partons defined by distribution functions. f(x) is the probability distribution to find a parton with momentum fraction x.

Proceed left to right


The “Underlying Event”The “Underlying Event”The “Underlying Event”The “Underlying Event”

The residual fragments of the pp resolve into soft - PT ~ 0.5 GeV pions with a density ~ 5 per unit of rapidity (Tevatron) and equal numbers of π+πoπ-. At higher PT, “minijets” become a prominent feature

2.8~,3.1~,/450~

)/(~/2

2

nGeVpGeVmbA

ppAdydpd

o

noTT +πσ

s dependence for PT < 5 GeV is small


COMPHEP - Minijets COMPHEP - Minijets COMPHEP - Minijets COMPHEP - Minijets

p-p at 14 TeV, subprocess g+g->g+g, cut on Ptg> 5 GeV. Note scale is mb/GeV


Minijets - Power Law?Minijets - Power Law?Minijets - Power Law?Minijets - Power Law?

The very low PT fragments change to “minijets” - jets at “low” PT which have mb cross sections at ~ 10 GeV. The boundary between “soft, log(s)” physics and “hard scattering” is not very definite. Note log-log, which is not available in COMPHEP – must export the histogram

pp(g+g) -> g + g


The Distribution FunctionsThe Distribution FunctionsThe Distribution FunctionsThe Distribution Functions

•Suppose there was very weak binding of the u+u+d “valence” quarks in the proton.

•But quarks are bound, .

•Since the quark masses are small the system is relativistic - “valence” quarks can radiate gluons ==> xg(x) ~ constant. Gluons can “decay” into pairs ==> xs(x) ~ constant. The distribution is, in principle, calcuable but not perturbatively. In practice measure in lepton-proton scattering.

x ~ 1/3, f(x) is a delta function

~ , ~ 1 , ~ 0.2 ~x x QCDx P x fm P GeV Λh


Radiation - Soft and CollinearRadiation - Soft and CollinearRadiation - Soft and CollinearRadiation - Soft and Collinear

P (1-z)P

z

PzPE

EEE

PmPmPE

if

/1~

)1(~

)/(1/1~

2/222

Α−−

−=Α+≈+=

,k

cosk

kPP

EE

=

−−−−−−−

+′=

+′=rrr

The amplitude for radiation of a gluon of momentum fraction z goes as ~ 1/z. The radiated gluon will be ~ collinear - ~ k ==> ~ 0. Thus, radiated objects are soft and collinear.

Cherenkov relation


COMPHEP, e+t->e+t+ACOMPHEP, e+t->e+t+ACOMPHEP, e+t->e+t+ACOMPHEP, e+t->e+t+A

Use heavy quark as a source of photons – needed to balance E,P. See strong forward (electron-photon) peak.


Parton Distribution FunctionsParton Distribution FunctionsParton Distribution FunctionsParton Distribution Functions

α)1(~)(

2/1)(

)1(2/7)( 6

xxfx

dxxxg

xxxg

−

=

−=

∫“valence” “sea” gluons

In the proton, u and d quarks have largest probability at large x. Gluons and “sea” anti-quarks have large probability at low x. Gluons carry ~ 1/2 the proton momentum. Distributions depend on distance scale (ignore).


Proton – Parton Density Proton – Parton Density FunctionsFunctions

Proton – Parton Density Proton – Parton Density FunctionsFunctions

g dominates for x < 0.2

At large x, x > 0.2, u dominates over d and g.

“sea” dominates for x < 0.03 over valence.

Points are simple xg(x) parametrization.


2-->2 Formation Kinematics2-->2 Formation Kinematics2-->2 Formation Kinematics2-->2 Formation Kinematics

β

tan/1sinh

sin/1cosh

:0

/,/

)/ln(2~,)/(~,sinh

cosh

/0

,/

,/2

222

||

21

212

21

||

=

=

=

==

+=

Δ=

=

===⇒=

=−==

=

y

y

m

EPmE

Pmm

MsyesMxymP

ymE

sMxxx

xxxsMxx

sPx

TT

yT

T

E.g. for top quark pairs at the Tevatron, M ~ 2Mt ~ 350 GeV. <x> ~ ~350/1800 ~ 0.2

Top pairs produced by quarks.

x1 x2

2

2 2 2 21 2 1 2

~ 4

~ [( ) ( ) ]

s P

M P x x x x+ − −


Linux COMPHEPLinux COMPHEPLinux COMPHEPLinux COMPHEP

g + g->g + g with Pt of final state gluons > 50 GeV at 14 TeV p-p

n.b. To delete diagrams use d, o to turn them back on one at a time

Cross section is 0.013 mb (very large)

Write out full events – but no fragmentation. COMPHEP does not know about hadrons.


gg -> gg in Linux COMPHEPgg -> gg in Linux COMPHEPgg -> gg in Linux COMPHEPgg -> gg in Linux COMPHEP

Note the kinematic boundary, where <x> ~ 0.007 is the y=0 value for x1=x2 for M = 100, C.M. = 14000.


CDF Data – DY Electron PairsCDF Data – DY Electron PairsCDF Data – DY Electron PairsCDF Data – DY Electron Pairs

DY Plateau

x1,x2 at Z mass ~ 0.045


The Fundamental Scattering The Fundamental Scattering AmplitudeAmplitude

The Fundamental Scattering The Fundamental Scattering AmplitudeAmplitude

.| | ~ ( )iq rI IA f H i e V r dr=< > ∫

_ _ _

Fourier transform of the inter action potential, VI(r) where

, ~f iq k k q k= −_ __

is the

magnitude of the momentum transfer in the reaction. A familiar example is the 1/r Coulomb

potential, which yields a Born amplitude ~ 1/ q2 describing how the virtual exchanged photon

propagates in momentum space. In turn this leads to a cross section (Rutherford scattering)

which goes as the square of the amplitude ~ 1/ q4~ 1/θ4 , which should be familiar.

1 1 2

2 3 4

2 2

~

~

[ ] [ ] [1/ ] 1/

x x x vertex

xx x vertex

L M s

αα

σ = = =


Pointlike Parton Cross SectionsPointlike Parton Cross SectionsPointlike Parton Cross SectionsPointlike Parton Cross Sections

Point-like cross sections for parton - parton scattering. The entries have th e generic dep endence already factored out. At large transverse momenta, or scattering angles near 90 degrees ( y ~ 0),

the remaining factors are dimensionless numbers of orde r one .

Process

2A

Value at = π∕2

q q q q′ ′+ → +

2 2 24[ ] /

9s u t+

2.22

q q q q+ → +

2 2 2 2 2 2 24 8[( )/ ( )/ ] ( / )

9 27s u t s t u s ut+ + + −

3.26

q q q q′ ′+ → +

2 2 24[ ] /

9t u s+

0.22

q q q q+ → +

2 2 2 2 2 2 24 8[( )/ ( )/ ] ( / )

9 27s u t t u s u st+ + + −

2.59

q q g g+ → +

2 2 2 2 232 8[ ] / [ ] /

27 3t u tu t u s+ − +

1.04

g g q q+ → +

2 2 2 2 21 3[ ] / [ ] /

6 8t u tu t u s+ − +

0.15

g q g q+ → +

2 2 2 2 24[ ] / [ ] /

9s u su u s t− + + +

6.11

g g g g+ → +

2 2 29[3 / / / ]

2tu s su t st u− − −

30.4

q q g+ → +

2 28[ ] /

9t u tu+

g q q+ → +

2 21[ ] /

3s u su− +

Pointlike partons have Rutherford like behavior

σ ~ π(α1α2)|A|2/s

s,t,u are Mandelstam variables. |A|2 ~ 1 at y=0.


Hadronic Cross SectionsHadronic Cross SectionsHadronic Cross SectionsHadronic Cross Sections

( ) )4321(ˆ)()(/

)4321(ˆ)()(

//ˆ

/ˆ

)4321(ˆ)()(ˆ

210

2211

2

21

212211

+→+=

+→+=

==

==

+→+==

= στττσ

στσ

τ

τ

σσσ

dfCfdydd

dyddxfxCfd

sMss

dydsdysddxdx

ddxdxxfxCfdPPd

y

BA

To form the system need x1 from A and x2 from B picked out of probability distributions with the joint probability PAPB to form a system of mass M moving with momentum fraction x. C is a color factor (later). The cross section is σ ~ (dσ/dy)y=0y. The value of y varies only slowly with mass ~ ln(1/M)


2-->2 and 2-->1 Cross Sections2-->2 and 2-->1 Cross Sections2-->2 and 2-->1 Cross Sections2-->2 and 2-->1 Cross Sections

( ) [ ] ( )

( ) [ ]

31 20

1 2

4 20 1 2 1 2

2

2

21 20

2 2 :

ˆ ˆ/ 2 ( ) ( )

ˆ ˆ/

( / ) ~ [ ( ) ( )] ( )

2 1:

ˆ 4 (2 1),

ˆ ˆ (2 1)( / ), int

/ ( ) ( )

y x

y x

y x

M d dydM C xf x xf x d s

d s

M d dydM C xf x xf x

J partial wave unitarity

ds J M egrate over narrow width

M d dy C xf x xf x

τ

τ

σ σ

σ πα α

σ πα α

σ π

σ π

σ

= =

= =

=

→

=

≈

→

< +

= + Γ

=

∫

D

( ) [ ]

2

12

2 21 2 120

(2 1)/

/ ~" "

/ ( ) ( ) (2 1)

ff

y x

J M

M

M d dy C xf x xf x J

τ

τ

π

α

σ π α

=

= =

⎡ ⎤Γ +⎣ ⎦Γ

⎡ ⎤= +⎣ ⎦

“scaling” behavior – depends only on and not M and s separately


DY Formation: 2 --> 1DY Formation: 2 --> 1DY Formation: 2 --> 1DY Formation: 2 --> 1

At a fixed resonant mass, expect rapid rise from “threshold” - σ ~

(1-M/s)2a

- then slow “saturation”. σW ~ 30 nb at the LHC

, eu u Z e e u d W e + − − −+ → → + + → → +


DY Z Production – F/B AsymmetryDY Z Production – F/B AsymmetryDY Z Production – F/B AsymmetryDY Z Production – F/B AsymmetryCDF – Run I

The Z couples to L and R quarks differently -> parity violating asymmetry in the photon-Z interference.


F/B AsymmetryF/B AsymmetryF/B AsymmetryF/B Asymmetry

23/ cos [ sin ]W W Wg I Q −

Coupling of leptons and quarks to Z specified in SM by gauge principle.

Coupling to L and R fermions differs => P violation ~ R-L coupling. Predict asymmetry , A ~ I3/Q. Thus, A for muons = 1, that for u quarks is 3/2, while for d quarks it is 3.


COMPHEPCOMPHEPCOMPHEPCOMPHEP

At 500 GeV the asymmetry is large and positive – here not p-p but u-U


COMPHEP - AssymCOMPHEP - AssymCOMPHEP - AssymCOMPHEP - Assym

Option in “Simpson” to get F/B asymmetry in COMPHEP


DY Formation of CharmoniumDY Formation of CharmoniumDY Formation of CharmoniumDY Formation of Charmonium

Cross section = σ ~ π2Γ(2J+1)/M3 for W, width ~ 2 GeV, σ = 47 nb. For charmonium, width is 0.000087 GeV, and estimate cross section in gg formation as 34 nb. The PT arises from ISR and intrinsic parton transverse momentum and is only a few GeV, on average. Use for lepton momentum scale and resolution.

g

g

ψ


Charmonium CalibrationCharmonium CalibrationCharmonium CalibrationCharmonium Calibration

Cross section in |y|<1.5 is ~ 800 nb at the LHC. Lepton calibration – mass scale, width?


Upsilon CalibrationUpsilon CalibrationUpsilon CalibrationUpsilon Calibration

Cross section * BR about 2 nb at the LHC. Resolve the spectral peaks? Mass scale correct?


ZZ Production vs CM EnergyZZ Production vs CM EnergyZZ Production vs CM EnergyZZ Production vs CM Energy

VV production also has a steep rise near threshold. There is a 20 fold rise from the Tevatron to the LHC. Measure VVV coupling. ZZ has ~ 2 pb cross section at LHC.

Not much gain in using anti-protons once the energy is high enough that the gluons or “sea” quarks dominate.


WWZ – Quartic CouplingWWZ – Quartic CouplingWWZ – Quartic CouplingWWZ – Quartic Coupling

Not accessible at Tevatron. Test quartic couplings at the LHC.


Jet-Jet Mass, 2 --> 2Jet-Jet Mass, 2 --> 2Jet-Jet Mass, 2 --> 2Jet-Jet Mass, 2 --> 2

Expect 1/M3 behavior at low mass. When M/s becomes substantial, the source effects will be large. E.g. for M = 400 GeV, at the Tevatron, M/s=0.2, and

(1-M/s)12 is ~ 0.07. 3 12/ ~ (1 / )

p p g g

M d dM M sσ

+ → +

−


Jets - 2 TeV- |y|<2Jets - 2 TeV- |y|<2Jets - 2 TeV- |y|<2Jets - 2 TeV- |y|<2

ET ~ M/2 for large scattering angles.

1/M3[1-M/s]12

behavior


COMPHEP LinuxCOMPHEP LinuxCOMPHEP LinuxCOMPHEP Linux

/ 2TP M<


Scaling ?Scaling ?Scaling ?Scaling ?

Tevatron runs at 630 and 1800 GeV in Run I. Test of scaling in inclusive jet production. Expect a function of

only in lowest order.

2 /T Tx P s=


Direct Photon ProductionDirect Photon ProductionDirect Photon ProductionDirect Photon Production

Expect a similar spectrum with a rate down by ratio of coupling constants and differences in u and g source functions. α/αs~14

u/g~6 at x~0.


D0 Single PhotonD0 Single PhotonD0 Single PhotonD0 Single Photon

Process dominated by q + g – a la Compton scattering.

COMPHEP – 2 TeV p-p


2--> 2 Kinematics - “Decays”2--> 2 Kinematics - “Decays”2--> 2 Kinematics - “Decays”2--> 2 Kinematics - “Decays”

y

y

esMx

yyyesMx−=

+==

]/[

2/)(,]/[

2

431

x1 x2 x,y,M y3, y4 y*, *

Formation System Decay CM Decay

The measured values of y3, y4

and ET allow one to solve for the initial state x1 and x2 and the c.m. decay angle.

3 4ˆ ( ) / 2

ˆ ˆcos tanh( )

y y y

y

= −

=


COMPHEP - LinuxCOMPHEP - LinuxCOMPHEP - LinuxCOMPHEP - Linux

g+g-> g+ g, in pp at 14 TeV with cut of Pt of jets of 50 GeV.

See a plateau for jets and the t channel peaking. Want to establish jet cross section, angular distributions and to look at jet “balance” – missing Et distribution in dijet events. MET angle ~ jet azimuthal angle and no non-Gaussian tails.


Parton-->Hadron FragmentationParton-->Hadron FragmentationParton-->Hadron FragmentationParton-->Hadron Fragmentation

)/ln(~~

/~/

)/ln(~/~)(

)1()(

/,1

/

||

1

/

minmin

Msyn

zdzEdPdy

mPazdzadzzDn

zazzD

Pmzzz

Pkz

Pm

><

=

>=<

−=

=<<=

∫ ∫

απFor light hadrons

(pions) as hadronization products, assume kT is limited (scale ~Λ. The fragmentation function, D(z) has a radiative form, leading to a jet multiplicity which is logarithmic in ET

Plateau widens with s, <n>~ln(s)


CDF Analysis – Jet MultiplicityCDF Analysis – Jet MultiplicityCDF Analysis – Jet MultiplicityCDF Analysis – Jet Multiplicity

Different

Cone radii

Jet cluster multiplicity within a cone increases with dijet mass as ~ ln(M).


Jet Transverse ShapeJet Transverse ShapeJet Transverse ShapeJet Transverse Shape

There is a “leading fragment” core localized at small R w.r.t. the jet axis - 40% of the energy for R< 0.1. 80% is contained in R < 0.4 cone 22 φ+= yR


Jet Shape - Monte CarloJet Shape - Monte CarloJet Shape - Monte CarloJet Shape - Monte Carlo

Simple model with zD(z) ~ (1-z)5 and <kt> ~ 0.72 GeV. “Leading fragment” with <zmax> ~ 0.24. On average the leading fragment takes ~ 1/4 of the jet momentum. Fragmentation is soft and non-perturbative.


Low Mass LHC RatesLow Mass LHC RatesLow Mass LHC RatesLow Mass LHC Rates

2 2 27 2

3 2 20

2 2 2 2

2

" " :

( ) 0.4 , 1 10

( / ) 2[ ( )] ( )( )

( ) ~ [ ( )] [ | | / ]

( ) ~ 7 / 2, ~ 10, ~ 0.1, ~ 1

10 , | | 30 ( )

~ 0.4

y

o s o

s

o

Minijet Rate

c mbGeV mb cm

M d dMdy xg x C d s c

M M y xg x A M

xg x y C

for M GeV A gg gg

mb

σ σ

σ παα

σ

−

=

= =

=

>

= = −−>

h) ) h

34 2

9

Re :

~ 100

~ 10 /( sec)

~ 25 sec

~ 10

~ 25 min / sinx

Total actionRate

mb

L cm

t n

L Hz

n bias events cros g

σ

σ

< >

For small x and strong production, the cross section is a large fraction of the inelastic cross section. Therefore, the probability to find a “small Pt “minijet” in an LHC crossing is not small.


V V Production - W + V V Production - W + V V Production - W + V V Production - W +

The angular distribution at the parton level has a zero. The SM prediction could be confirmed with a large enough event sample. – pp at 2 TeV with Pt > 10 GeV, 0.6 pb

Asymmetry somewhat washed out by the contribution of sea anti-quarks in the p and sea quarks in the anti-proton.


3 –Tevatron -> LHC Physics3 –Tevatron -> LHC Physics 3 –Tevatron -> LHC Physics3 –Tevatron -> LHC Physics

• 3.1 QCD - Jets and Di - jets• 3.2 Di - Photons• 3.3 b Pair Production at Fermilab• 3.4 t Pair Production at Fermilab• 3.5 D-Y and Lepton Composites• 3.6 EW Production

W Mass and WidthPt of W and Zbb Decays of Z, Jet Spectroscopy

• 3.7 Higgs Mass from Precision EW Measurements


Kinematics - ReviewKinematics - ReviewKinematics - ReviewKinematics - Review

2 2 2 2 2 21 2 1 2 1 2 1 2 1 2 1 2

|| ||

( ) ( ) ~ ( ) ( ) ~ [( ) ( ) ]

/ ~ 2 /

M p p p p e e p p P x x x x

x p P p s

= + ⋅ + + − + + − −

=

_ _

21 2 1 2/ ,x x M s x x x= = − =

Initial State


Review Kinematics - IIReview Kinematics - IIReview Kinematics - IIReview Kinematics - II

3 4ˆ( / 2)sinT T Tp p E M = = =

2 23 4 3 42 [cosh( ) cos( )]TM E y y φ φ= − − − 2/)(,2/)( 4343 yyyyyy −=+= _

y

y

esMx

esMx−=

=

]/[

]/[

2

1

Final State


Jet Et Distribution and CompositesJet Et Distribution and Composites

Simplest jet measurement - inclusive jet ET . Jet defined as energy in cone, radius R. Classical method to find substructure. Look for wide angle (S wave) scattering. Limits are Λ ~ s.


CDF Run II – Data ReachCDF Run II – Data ReachCDF Run II – Data ReachCDF Run II – Data Reach


Dijet Et Distribution – Run IDijet Et Distribution – Run I

As |3 - 4| increases MJJ increases and the cross section decreases. The plateau width decreases as ET increases (kinematic limit)


Dijet Mass DistributionDijet Mass Distribution

Falls as 1/M3 due to parton scattering and ~ (1- M/s)12

due to structure function source distributions. Look for deviations at large M (composite variations or resonant structure due to excited quarks). Limits at Tevatron and LHC will increase as C.M. energy.


Initial, Final State RadiationInitial, Final State RadiationInitial, Final State RadiationInitial, Final State Radiation

The initial state has ~ no transverse momentum. Thus a 2 body final state is back-to-back in azimuth. Take the 2 highest Et jets in the 2 J or more sample. At the higher Pt scales available at the LHC ISR and FSR will become increasingly important – determined by the strong coupling constant at that Pt scale.


““Running” of Running” of ααs s - Measure in 3J/2J- Measure in 3J/2J““Running” of Running” of ααs s - Measure in 3J/2J- Measure in 3J/2J

0)(/1 2 =ΛQCDsα

2 2 2( ) [12 /(33 2 )]/ ln( / )]s f QCDQ n Qα π= − Λ

fmGeVQCD 1~2.0~Λ

2

2

2

((1 ) ) 0.55

((10 ) ) 0.23

( ) 0.15

S

S

S Z

GeV

GeV

M

α

α

α

=

=

=

Energy below which strong interaction is strong


Excited Quark CompositesExcited Quark Composites

q

g

q*

Look for resonant J - J structure, with a limit ~ C.M. energy

*q g q q g+ → → +


t Channel Angular Distributiont Channel Angular Distribution

If t channel exchange describes the dynamics, then distribution is flat - as in Rutherford scattering. Deviations at large scattering angles would indicate composite quarks.

tconsdd

ttdd

propagatorttdd

Eandyyfromt T

tan~/

/1~/

,/1~/

,ˆ),cos1(~

)cos1/()cos1(

2

2

43

σ

σ

)

))

)))

))

))

−

−+= 2

1 3 1 3( ) ( ) 2 (1 cos )p p p p p − ⋅ − =− −

__

2 2 2ˆ ˆˆ ˆ4 / , ( ) , (2 ) /t p p t → → →) )


Diphoton, CDF Run IIDiphoton, CDF Run IIDiphoton, CDF Run IIDiphoton, CDF Run II

2--> 2 processes similar to jets. Down by coupling and source factors Also useful in jet balancing for calibration. Important SM background in Higgs searches. Must establish SM photon signals

u+g-->u+ (Lecture 2)

u+u-->+


COMPHEP – Tree OnlyCOMPHEP – Tree OnlyCOMPHEP – Tree OnlyCOMPHEP – Tree Only

Tevatron, 2 TeV

||<1, ET>10 GeV


B Production @ FNALB Production @ FNALB Production @ FNALB Production @ FNAL

dσ/dPT ~ 1/PT3 so

σ(>) ~ 1/PT2

Spectrum is as expected with PT ~ M/2, g+g --> b + b. Adjustment in b -> B fragmentation function resolves the discrepancy. Establish a b jet signal and b tagging efficiency using 1 tag to 2 tag ratio. Many LHC searches and SM backgrounds (e.g. top pairs) require b tagging.

2minmin /1~)( TTT PPP >σ


B Production – Rapidity B Production – Rapidity DistributionDistribution

B Production – Rapidity B Production – Rapidity DistributionDistribution

Note rapidity plateau which extends to y ~ 5 at this low mass, ~ 2mb scale. At the LHC tracking and Si vertexing extends to |y| < 2.5.


B LifetimesB LifetimesB LifetimesB Lifetimes

Use Si tracker to find decay vertices and the production vertex. (B) ~ (b). For Bc both the b and the c quark can decay ==> shorter lifetime. At LHC establish lifetime scale.

~ , 1/b c b Γ Γ +Γ = Γ <cB cb+ =


Weak Decay WidthsWeak Decay WidthsWeak Decay WidthsWeak Decay Widths

t -> W b

3

2

/ 8 2

~ /16( / )

,

t t

W t W t

Gm

m M m

fast decays no toponium

π

α

Γ =

G2

m W

ee − −→ + +

2 2~| | ~A GΓ

2[ ] 1/ , [ ]G M M= Γ =2 5~ G mΓ

( )eW e − − −→ + → + +

5 3 2/ ~ [ / ]Q t W Q t Wm m MαΓ Γ

Fermi theory

Standard Model

2 5 3/192G m πΓ =

2 body weak decay


Top Mass and Jet Spectroscopy- Run ITop Mass and Jet Spectroscopy- Run I Top Mass and Jet Spectroscopy- Run ITop Mass and Jet Spectroscopy- Run I

D0 - lepton + jets

t-->Wb

W-->JJ, l


Jet Spectroscopy - TopJet Spectroscopy - Top

CDF - Lepton + jets (Si or lepton tags)

t-->Wb so 2 b’s in the eventb c −→ + + ll


tt --> Wb+Wb, W--> qq or ltt --> Wb+Wb, W--> qq or ltt --> Wb+Wb, W--> qq or ltt --> Wb+Wb, W--> qq or l

CDF + D0

Top quark mass from data taken in the twentieth century


Top Mass @ FNALTop Mass @ FNALTop Mass @ FNALTop Mass @ FNALRun I Run II


Top Production Cross SectionTop Production Cross SectionTop Production Cross SectionTop Production Cross Section

> 100x gain in going to the LHC. The discovery at the Tevatron becomes a nasty background at the LHC. However, W-> J+J in top pair events sets the calorimeter energy scale at the LHC.

Are the mass and the cross section consistent with a quark with SM couplings?


Run II Top Cross sectionRun II Top Cross sectionRun II Top Cross sectionRun II Top Cross section

No evidence for deviation from SM coupling of a heavy quark. At the LHC top pair events have jets, heavy flavor, missing energy and leptons. They thus serve as a sanity check that the detector is working correctly in many final state SM particles. The LHC experiments must establish a top pair sample before contemplating, for example, SUSY discoveries.


DY and Lepton CompositesDY and Lepton CompositesDY and Lepton CompositesDY and Lepton Composites

Drell-Yan:

Falls with the source function. For ud the W is prominent, while for uu the Z is the main high mass feature. Above that mass there is no SM signal, and searches for composite leptons or sequential W’, Z’ are made.

* */u u Z + −+ → → +l l

Run I


Extract V,A Coupling to FermionsExtract V,A Coupling to FermionsExtract V,A Coupling to FermionsExtract V,A Coupling to Fermions

F/B asymmetry allows an extraction of the A and V couplings, gA, gV of fermions to the Z at high mass – compare to SM. If a Z’ is seen at the LHC, use the F/B distribution to try to extract the A and V couplings.


Run II – DY High MassRun II – DY High MassRun II – DY High MassRun II – DY High Mass


Run II – DY High MassRun II – DY High MassRun II – DY High MassRun II – DY High Mass

Whole “zoo” of new Physics candidates – all still null. At LHC establish muon and electron momentum scale and resolution with Z mass and width. Explore tail when backgrounds are under control.


W - High Transverse Mass W - High Transverse Mass W - High Transverse Mass W - High Transverse Mass

Search DY at high mass for sequential W’. Mass calculated in 2 spatial dimensions only using missing transverse energy.2 2 (1 cos )

TT Tl T lEM P E φ /= / −

Run I


W - SM Mass and Width PredictionW - SM Mass and Width PredictionW - SM Mass and Width PredictionW - SM Mass and Width Prediction

cue W

Color factor of 3 for quarks. 9 distinct dilepton or diquark final states.

1/ 2 2 174G GeVφ< >= =

2 2/ 2 /8 , sinW W W WG g M g e= =

2 22 , ~ 80W W WM M GeVπα φ= < >

, ,ee − − −+ + +

,u d c s+ +( ) ( /12) ~ 0.21

~ 9 ( )

e W W

W e

W e M GeV

W e

α

− −

− −

Γ → + =

Γ Γ → +

2( ) [ / 24][ / cos ] ~ 0.16W Z WZ M GeV α Γ → =l l

Mass:

Width;


COMPHEP – W BRCOMPHEP – W BRCOMPHEP – W BRCOMPHEP – W BR

Check that the naïve estimates are confirmed in COMPHEP for W and Z into 2*x.


W,Z Production Cross SectionW,Z Production Cross SectionW,Z Production Cross SectionW,Z Production Cross Section

Cross section x BR for W is ~ 4 pb for Tevatron Run II


Lumi with W, Z ?Lumi with W, Z ?Lumi with W, Z ?Lumi with W, Z ?

At present in Run II, using W,Z is more accurate than Lumi monitor. Use W and Z at LHC as “standard candles”. Test of trigger and reco efficiencies – cross-check minbias trigger normalization.


W and Z - Width and Leptonic W and Z - Width and Leptonic B.R.B.R.

W and Z - Width and Leptonic W and Z - Width and Leptonic B.R.B.R.

Expect 1/9 ~ 0.11 Expect 9 (0.21 GeV) = 1.9 GeV


Direct W Width MeasurementDirect W Width MeasurementDirect W Width MeasurementDirect W Width Measurement

decay widths of 1.5 to 2.5 GeV

2[ /( )]oM MΓ −

Monte Carlo

Far from the pole mass the Breit – Wigner width (power law) dominates over the Gaussian resolution


W Transverse MassW Transverse MassW Transverse MassW Transverse Mass

D0 and CDF:

Transverse plane only. Use Z as a control sample. At large mass dominated by the BW width, since falloff is slow w.r.t the Gaussian resolution.


W Mass – Colliders, Run IW Mass – Colliders, Run IW Mass – Colliders, Run IW Mass – Colliders, Run I

Hadron

WW (LEP II) production near threshold (Lecture 1 )


W Mass - All MethodsW Mass - All MethodsW Mass - All MethodsW Mass - All Methods

Direct

Precision EW measurements


I.S.R. and PI.S.R. and PTWTWI.S.R. and PI.S.R. and PTWTW

2-->1 has no F.S. PT. Recall Lecture 2 - charmonium production. Scale is set by the FS mass in 2 -> 1.

u

d

W+

g

u d W g++ → +


COMPHEP - PCOMPHEP - PTWTWCOMPHEP - PCOMPHEP - PTWTW

Basic 2 --> 2 behavior, 1/PT

3. . Gluon radiation from either initial quark.


Lepton Asymmetry at TevatronLepton Asymmetry at TevatronLepton Asymmetry at TevatronLepton Asymmetry at Tevatron

We must simply assert t hat the V -A, parity violating, nature of the weak interactions makes

light quarks and leptons, (

eedu ,,, −

in the first generation) left handed (negative helicity,

where helicity is the projection of spin on the direction of the momentum) and the corresponding anti-particles,

, , , eu d e +, right handed (positive helicity).


CDF – Lepton AsymmetryCDF – Lepton AsymmetryCDF – Lepton AsymmetryCDF – Lepton Asymmetry

Positron goes in antiproton direction

Electron goes in proton direction

Charge asymmetry, constrains PDF. Recall u > d at large x.


COMPHEP - AsymmetryCOMPHEP - AsymmetryCOMPHEP - AsymmetryCOMPHEP - Asymmetry

COMPHEP generates the asymmetry in pbar-p at 2 TeV. Can use the PDF that COMPHEP has available to check PDF sensitivity. Generate your own asymmetry and look for deviations.


Z --> bb, Run IZ --> bb, Run IZ --> bb, Run IZ --> bb, Run I

Dijets with 2 decay vertices (b tags). Look for calorimetric J-J mass distribution.

Mass resolution, dM ~ 15 GeV. This exercise is practice for searches of J-J spectra such as Z’ decays into di-jets, or H decays into b quark pairs.


Run II Mass ResolutionRun II Mass ResolutionRun II Mass ResolutionRun II Mass Resolution

Using tracker information to replace distinct energy deposit in the calorimetry for charged particles with the tracker momentum – which is more precisely measured. Seems to gain ~ 20%. This is quite hard – at LHC we will use W->J+J in top pair events.


VV at Tevatron - WVV at Tevatron - W from D0 from D0VV at Tevatron - WVV at Tevatron - W from D0 from D0

The WW vertex as vertex as measured at measured at Run II is Run II is consistent consistent with the SM, with the SM, as it is at LEP as it is at LEP II.II.

Transverse Transverse mass in mass in leptonic W leptonic W decays with decays with additional additional photon.photon.


WW at D0 – Run IIWW at D0 – Run IIWW at D0 – Run IIWW at D0 – Run II

Look at dileptons plus missing transverse energy. Tests the WWZ and WW vertex as at vertex as at LEP - IILEP - II


WW Cross Section Measured at WW Cross Section Measured at CDFCDF

WW Cross Section Measured at WW Cross Section Measured at CDFCDF

Extrapolate to LHC energy. COMPHEP gives a D-Y WW cross section at the LHC of 72 pb. At LHC will be able to begin to explore W-W scattering independent of Higgs searches.


W Mass Corrections Due to Top, W Mass Corrections Due to Top, HiggsHiggs

W Mass Corrections Due to Top, W Mass Corrections Due to Top, HiggsHiggs

We must simply assert that the propagators for fermions (Dirac equation) and bosons (Klein -Gordon equation) are different,

21/ , 1/q q

respectivel y, for massless quanta. T he propagator for massless bosons can be thought of as the Fourier transform of the Coulomb interaction potential. The propagator for fermions foll ows from a study of the Dirac equation .

2 4 2 3 2 2

2 4 2 2 3 4

~ /( ) ~ / ~ ~

~ /( ) ~ / ~ / ~ ln( )

m

M

M d q q q dq q qdq m

M d q q q dq q dq q M

δ

δ

∫ ∫ ∫

∫ ∫ ∫

2 2( ) 0

( ) 0

P M

P M

φψ

− =− =

Klein-Gordon

Dirac

W mass shift due to top (m) and Higgs (M)


What is MWhat is MHH and How Do We Measure It? and How Do We Measure It?What is MWhat is MHH and How Do We Measure It? and How Do We Measure It?

• The Higgs mass is a free parameter in the current “Standard Model” (SM).

• Precision data taken on the Z resonance constrains the Higgs mass. Mt = 176 +- 6 GeV, MW = 80.41 +- 0.09 GeV. Lowest order SM predicts that MZ = MW/cosW.. Radiative corrections due to loops.

Note the opposite signs of contributions to mass from fermion and boson loops. Crucial for SUSY and radiative stability.

W

W

W

W

b

t

H

W

tWtWW dmMmdM )/)(16/3( πα=

2/ [ 11 tan / 48 ]( / )W W W W H HdM M dM Mα π= −


CDF D0 Data Favor a Light HiggsCDF D0 Data Favor a Light HiggsCDF D0 Data Favor a Light HiggsCDF D0 Data Favor a Light Higgs

1 6 5 1 7 0 1 7 5 1 8 0 1 8 5

8 0 . 2

8 0 . 2 5

8 0 . 3

8 0 . 3 5

8 0 . 4

8 0 . 4 5

8 0 . 5

M W vs M t fo r 1 0 0 , 3 0 0 , 1 0 0 0 G e V H i g g s

M t ( G e V )

M W ( G e V )

M H = 1 0 0

M H = 3 0 0

M H = 1 0 0 0


Top and W Mass and HiggsTop and W Mass and HiggsTop and W Mass and HiggsTop and W Mass and Higgs

1 s.d contours:

all precision EW data

A light H mass seems to be weakly favored.

High P T Hadron Collider Physics

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