3 –Tevatron -> LHC Physics

FNAL Academic Lectures – May, 2006 1

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 Width

Pt of W and Z

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

0)(/1 2 QCDs

2 2 2( ) [12 /(33 2 )]/ ln( / )]s f QCDQ n Q

fmGeVQCD 1~2.0~

2

2

2

((1 ) ) 0.55

((10 ) ) 0.23

( ) 0.15

S

S

S Z

GeV

GeV

M

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

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

d/dPT ~ 1/PT3 so

(>) ~ 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


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 cB cb


Weak Decay WidthsWeak Decay WidthsWeak Decay WidthsWeak Decay Widths

t -> W b

2 5 3

2 4

5

/192

~ ( / )

2

W W

G m

m M m

m scaling for q and l

except t below body threshold

3

2

/ 8 2

~ /16( / )

,

t t

W t W t

Gm

m M m

fast decays no toponium

G2

m W

ee

2 2~| | ~A G

2[ ] 1/ , [ ]G M M 2 5~ G m

( )eW e

5 3 2/ ~ [ / ]Q t W Q t Wm m M

Fermi theory

Standard Model

2 5 3/192G m

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


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

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

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 GeV

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

2 22 , ~ 80W W WM M GeV

, ,ee

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

~ 9 ( )

e W W

W e

W e M GeV

W e

2( ) [ / 24][ / cos ] ~ 0.16W Z WZ M GeV

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 M

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 that 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 respectively, for massless quanta. The propagator for massless bosons can be thought of as the Fourier transform of the Coulomb interaction potential. The propagator for fermions follows 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

2 2( ) 0

( ) 0

P M

P M

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

2 2 2

2

2

cos (1 )

~ [3 ( / ) ] /16

[11 tan / 24 ]ln( / )

W Z W

t W t W

H W W H W

M M

m M

M M

tWtWW dmMmdM )/)(16/3(

2/ [ 11 tan / 48 ]( / )W W W W H HdM M dM M


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

165 170 175 180 18580.2

80.25

80.3

80.35

80.4

80.45

80.5MW vs Mt for 100, 300, 1000 GeV Higgs

Mt (GeV)

MW

(G

eV)

MH=100MH=300MH=1000


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.

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3 –Tevatron -> LHC Physics