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
FNAL Academic Lectures – May, 2006 2
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
FNAL Academic Lectures – May, 2006 3
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
FNAL Academic Lectures – May, 2006 4
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.
FNAL Academic Lectures – May, 2006 5
CDF Run II – Data ReachCDF Run II – Data ReachCDF Run II – Data ReachCDF Run II – Data Reach
FNAL Academic Lectures – May, 2006 6
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)
FNAL Academic Lectures – May, 2006 7
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.
FNAL Academic Lectures – May, 2006 8
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.
FNAL Academic Lectures – May, 2006 9
““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
FNAL Academic Lectures – May, 2006 10
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
FNAL Academic Lectures – May, 2006 11
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
FNAL Academic Lectures – May, 2006 12
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-->+
FNAL Academic Lectures – May, 2006 13
COMPHEP – Tree OnlyCOMPHEP – Tree OnlyCOMPHEP – Tree OnlyCOMPHEP – Tree Only
Tevatron, 2 TeV
||<1, ET>10 GeV
FNAL Academic Lectures – May, 2006 14
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
FNAL Academic Lectures – May, 2006 15
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.
FNAL Academic Lectures – May, 2006 16
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
FNAL Academic Lectures – May, 2006 17
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
FNAL Academic Lectures – May, 2006 18
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
FNAL Academic Lectures – May, 2006 19
Jet Spectroscopy - TopJet Spectroscopy - Top
CDF - Lepton + jets (Si or lepton tags)
t-->Wb so 2 b’s in the eventb c
FNAL Academic Lectures – May, 2006 20
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
FNAL Academic Lectures – May, 2006 21
Top Mass @ FNALTop Mass @ FNALTop Mass @ FNALTop Mass @ FNALRun I Run II
FNAL Academic Lectures – May, 2006 22
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?
FNAL Academic Lectures – May, 2006 23
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.
FNAL Academic Lectures – May, 2006 24
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
FNAL Academic Lectures – May, 2006 25
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.
FNAL Academic Lectures – May, 2006 26
Run II – DY High MassRun II – DY High MassRun II – DY High MassRun II – DY High Mass
FNAL Academic Lectures – May, 2006 27
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.
FNAL Academic Lectures – May, 2006 28
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
FNAL Academic Lectures – May, 2006 29
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;
FNAL Academic Lectures – May, 2006 30
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.
FNAL Academic Lectures – May, 2006 31
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
FNAL Academic Lectures – May, 2006 32
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.
FNAL Academic Lectures – May, 2006 33
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
FNAL Academic Lectures – May, 2006 34
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
FNAL Academic Lectures – May, 2006 35
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.
FNAL Academic Lectures – May, 2006 36
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 )
FNAL Academic Lectures – May, 2006 37
W Mass - All MethodsW Mass - All MethodsW Mass - All MethodsW Mass - All Methods
Direct
Precision EW measurements
FNAL Academic Lectures – May, 2006 38
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
FNAL Academic Lectures – May, 2006 39
COMPHEP - PCOMPHEP - PTWTWCOMPHEP - PCOMPHEP - PTWTW
Basic 2 --> 2 behavior, 1/PT
3. . Gluon radiation from either initial quark.
FNAL Academic Lectures – May, 2006 40
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).
FNAL Academic Lectures – May, 2006 41
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.
FNAL Academic Lectures – May, 2006 42
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.
FNAL Academic Lectures – May, 2006 43
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.
FNAL Academic Lectures – May, 2006 44
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.
FNAL Academic Lectures – May, 2006 45
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.
FNAL Academic Lectures – May, 2006 46
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
FNAL Academic Lectures – May, 2006 47
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.
FNAL Academic Lectures – May, 2006 48
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)
FNAL Academic Lectures – May, 2006 49
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
FNAL Academic Lectures – May, 2006 50
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