1. LHC Physics GRS PY 898 B8 Lecture #7
Tulika Bose
March 2nd, 2009
Taus and Jets

2. Taus @ LHC Standard model processes Z -> tt, W -> tn
Useful for validation, tuning of the algorithms, calibration
Searches
Many discovery channels involve tau leptons in the final state:
MSSM Higgs (A/H, H+)
A/H -> tt, H+-> tn
SM Higgs
qqH->qqtt, ttH->tttt

3. Tau characteristics ct ~= 87mm, mt=1.78 Gev/c2 Leptonic decays
t-> e(m) n n : ~ 35.2 %
Identification done through the final lepton
Hadronic decays (~65%)
1 prong
t -> nt + p+/- + n(po) : 49.5 %
3 prongs
t -> nt + 3p+/- + n(po) : 15.2 %
“t-jet” is produced
Tau decay branching ratios

4. Tau characteristics Tau-jets at LHC: Very collimated
90% of the energy is contained in a ‘cone’ of radius R=0.2 around the jet direction for ET>50 GeV
Low charged track multiplicity
One, three prongs
Hadronic, EM energy deposition
Charged pions
Photons from po
Often taus are produced in pairs: 42% of final states contain two “tau-jet”

5. Tau identification tau tagging basic ingredients
Calorimetric isolation and shape variables
Charged tracks isolation
Other tau characteristics suitable for tagging:
Impact parameter
Decay length
Invariant Mass
Main backgrounds for taus
QCD jets
Electron that shower late or with strong bremstrahlung
Muons interacting in the calorimeter
Only hadronic tau decays are considered since the leptonic tau decays produce standard electrons/muons
Identification through the final lepton

6. ATLAS tau algorithms TauRec Calorimeter + inner detector are used
Energy from calorimeter is calibrated
Tracks+clusters are associated
Several suitable variables are computed
Likelihood or variable cut used for tau-id
Tau1P3P
Intended for studies of low mass Higgs
Visible tau hadronic energy GeV
Identify a leading track
Single prong (Tau1P) or three-prong (Tau3P) candidate
Compute set of discriminating variables
Apply set of basic cut for tau-id or use Multi-variate classification technique

7. ATLAS: tauRec Calorimeter-based tau reconstruction
Start from >15 GeV Cluster in region Δη X Δφ = 0.1 X 0.1
Tau candidate reconstruction
Collimated Calorimeter cluster
small number of associated charged tracks
Preliminary requirements:
abs(h)<2.5
Collimated Calorimeter Clusters (ET>15 GeV)
One or three associated “good” charged tracks
PT>2GeV
DR(track,cluster center)<0.3

8. ATLAS: tauRec Calorimeter Isolation
j runs over all cells within 0.1 <ΔR < 0.2
i runs over all cells within ΔR < 0.4
EM-radius
i runs over all cells in cluster (n total cells) 8
Iso fraction

9. ATLAS: tauRec Track multiplicity
pT > 2 GeV
Powerful for high ET discrimination between jets and taus
Tau charge
Sum of charges of all associated tracks
Transverse energy width in η strip layer

10. ATLAS: tauRec

11. ATLAS:tauRec performance
Though the likelihood is formed in bins of ET, it still shows some ET dependence. Cuts used in analysis should therefore depend on ET.
88.5 < pT < 133.5
likelihood
Likelihood built with the previously described variables
Cut on likelihood depend on ET
pT < 28.5 GeV
Neural Network and cut-based
approaches are also supported.

12. ATLAS: Tau1P3P Track-based reconstruction
Start with a seed track with pT > 9 GeV
Create candidates with up to 5 tracks (3 quality tracks)
Tau candidates preselection
“Good” hadronic leading track PT>9 GeV
0 or 2 nearby-track: PT>2GeV, DR<0.2
DR(track-direction,jet-direction)<0.2
Require isolation in ring 0.2< DR<0.4
Calculate several discriminant variables like in TauRec case

13. ATLAS Tau1P3P: multivariate analysis
Signal and background samples are used to combine the observables to a single one, called “discriminant”
It is possible to cut on discriminant to separate signal from background
Better background rejection is obtained with the same signal efficiency
Tau1P results

14. ATLAS Tau1P3P: Performance
Neural Net performance

15. CMS: Ecal isolation
Signal efficiency of about 80% with a bkg rejection of ~5 for QCD jets with pT>80 GeV

16. CMS: Tracker isolation
Isolation based on the number of tracks inside the isolation cone (RI) is applied.
Only good tracks are considered:
Associated to the Primary Vertex
PT of the Leading Track (i.e. highest pT track) must exceed a few GeV/c
Leading Track must be found inside the Matching cone
RM : calo jet - leading track matching cone
pTLT : cut on pT of the leading track in matching cone
RS : signal cone around leading track
RI : isolation cone (around jet axis or leading track)
pTi : cut on pT of tracks in the isolation cone

17. CMS: tau jets and QCD jets efficiency
Single Tau
(30<ET<150 GeV)
QCD jets
50<ET<170 GeV
In the order of decreasing efficiency
symbols correspond to decreasing MC ET intervals
Cuts used:
8 hits per track, Norm. Chi2 < 10
PtLT > 6 GeV/c, RM = 0.1, RI = , PTI > 1 GeV, |Dz| < 2mm

18. CMS: other tagging methods
Tracker isolation is a primary requirement for the tau jet identification
All the following tagging methods are applied to jets which preliminarly pass the Tracker Isolation:
Tagging with IP
Tagging with decay length
Mass tag
I.P. distribution
Tau
1 prong
QCD
1 track
Transverse I.P. efficiency

19. CMS: tagging with decay length
The lifetime of the tau lepton (ct = 87 mm) allows for the reconstruction of the secondary vertex for the 3 (and 5) prongs decay
Events are required to pass tracker isolation, only tracks inside signal cone are used in the vertex fitter
Fake vertices in the pixel
material removed by
cutting on the transverse
flight distance (< 4 cm)
3D decay length
Both “Transverse” decay length and 3D decay length considered

20. Tau Jet energy scale Use particle flow (PF)
Both Atlas and CMS apply energy scale corrections
Tau jets need softer corrections to their energy, wrt QCD jets.
At the same transverse energy, pions in Tau jets have harder transverse momentum than pions in QCD jets
In Tau jets there is a larger amount of electromagnetic energy (due to the presence of p0)
CMS
Use particle flow (PF)
Essentially reconstruction and identification of every constituent particle inside the tau
Electrons, photons, p±, po, neutral hadrons

21. Jets

22. LHC
Gluon jets from parton scattering
Mostly in lower pt QCD processes
Quark jets from parton scattering
Higher pT QCD processes
Dominant prompt photon channel, Z+jet…
Final state in extra dimensions models with graviton force mediator
Quark jets from decays
Wjj in ttbar decays
End of long decay chains in SUSY and other exotic particle production
Jets needed for both precision and discovery physics in wide range of energies

23. Jet Finding After the hard interaction, partons hadronize into stable
particles
Stable particles interact with
the detectors
Jet algorithms cluster energy
deposits in the EM and HAD
calorimeter, or more generally
four-vectors
Jet algorithm provides a good
correspondence between what
is observed and the hard
interaction

24. Jet Finding Particle Jet
a spread of particles running roughly in the same direction as the parton after hadronization

25. Jet Finding Calorimeter Jet
jet is a collection of energy deposits with a cone R:
Cone direction maximizes the total ET of the jet
Various clustering algorithms

26. Algorithm Considerations
Initial considerations
Jets define the hadronic final state of basically all physics channels
Jet reconstruction essential for signal and background definition
Applied algorithms not necessarily universal for all physics scenarios
Mass spectroscopy Wjj in ttbar needs narrow jets
Generally narrow jets preferred in busy final states like SUSY
Increased resolution power for final state composition
QCD jet cross section measurement prefers wider jets
Important to capture all energy from the scattered parton
Which jet algorithms to use ?
Use theoretical and experimental guidelines collected by the Run II Tevatron Jet Physics Working Group
J. Blazey et al., hep-ex/ v2

27. Theoretical Considerations
Infrared safety
Soft particles in between jets should not change jets
Artifical split due to absence of gluon radiation between two partons/particles

28. Theoretical Considerations
Infrared safety
Soft particles in between jets should not change jets
Collinear safety
Particles split into two with same total energy should not change results
Minimize sensitivity due to ET ordering of seeds

29. Theoretical Considerations
Infrared safety
Soft particles in between jets should not change jets
Collinear safety
Particles split into two with same total energy should not change results
Minimize sensitivity due to ET ordering of seeds
Invariance under boost
Same jets in lab frame of reference as in collision frame
Order independence
Same jet from partons, particles, detector signals

30. Experimental Considerations
Detector technology independence
Jet efficiency should not depend on detector technology
Final jet calibration and corrections ideally unfold all detector effects
Stability within environment
(Electronic) detector noise should not affect jet reconstruction within reasonable limits
Energy resolution limitation
Avoid energy scale shift due to noise
Stability with changing (instantaneous) luminosity
Control of underlying event and pile-up signal contribution
“Easy” to calibrate
Small algorithm bias for jet signal
High reconstruction efficiency
Identify all physically interesting jets from energetic partons
Efficient use of computing resources
Balance physics requirements with available computing

31. Jet Algorithms: Cone
Cone-based algorithms have been traditionally used at hadron colliders
Particles above certain pT threshold are seeds
1) for each seed, all particles within ΔR < R are added to the seed to form a new jet
2) if (η|ϕ) of the seed coincide with the jet axis (Δη|Δϕ < 0.05), jet is considered stable, otherwise new jet axis is used for the direction of the new seed and algorithm returns to point 1)
If final jet shares more than a fraction f of energy of higher ET jet, jets are merged, otherwise shared particles are are assigned to the closest jet

32. Steps in a Clustering Algorithm
Start from a collection of four-vectors, highest ET acts as seed
Sum all four-vectors within cone to form a proto-jet
Repeat until proto-jet is stable (axis of proto-jet aligns with the sum of four-vectors within the cone) or reach maximum iterations
Repeat until all towers are used
Apply splitting/merging algorithm to ensure four-vectors
are assigned to only one proto-jet
→ Left with list of all stable jets

33. Algorithm Flow Charts
Clustering Algorithm
Merging/Splitting Algorithm

34. Problems with Cone-based Clustering Algorithms
Seed based cone algorithms are typically “infrared unsafe”
Addition of an an infinitismally soft particle can lead to new stable jet configurations → sensitive to hadronization model and order of perturbative QCD calculation
Problems arise when comparing to higher order p-QCD calculations
The addition of a threshold to the seed towers makes the algorithm “collinear unsafe”

35. Variants of Cone jet finders
Simplified algorithm (iterative cone)
Once stable jet is found remove its constituents from the input list and start again…
Fast and therefore typically used in the trigger
Collinear and infrared unsafe
MidPoint algorithm places additional seeds in between doublets (or triplets ) of initial seeds
Reduced infrared sensitivity; collinear unsafe
Seedless cone works without any seeds but is very CPU intensive
SISCone
fast seedless implementation is now available (collinear safe)
Infrared safe

36. SISCone

37. SISCone

38. SISCone
SISCone is Infrared safe

39. Jet Algorithms: kT Iterative procedure to cluster pairs
of particles based on “closeness”
For each pair calculate:
Find minimum of all dii, dij
If dii, call it jet
If dij, combine particle I and j
Iterate until only jets left
Parameter D controls the
termination of the merging
and characterizes the size of the resulting jet

40. Variants of kT
Iterative and seedless procedure makes it infrared and collinear safe
Different distance measures available
KT (p=1)
Aachen/Cambridge(p=0)
Inverse or anti-kT (p=-1)
Different distance measures behave differently in terms of hadronisation corrections, pile-up
However, slow to execute
Recently a faster version has been made available….

41. Fast KT

42. Performance of Different Jet Algorithms
Midpoint
JetClu
Used by CDF
Different jet algorithms find different jets
kT Clustering
Midpoint leaves unclustered towers
Dark Towers
kT has jets with poorly defined
boundaries

43. Jets

44. Jet Finding Efficiency

45. Response

46. Response

47. Jet calibration strategy

48. Jet Corrections Correct Jet Energy to the particle level
With corrections (MCJet) derived entirely from the Monte Carlo simulation, CaloJets can be corrected to GenJets using “MC truth” information
Being replaced by the factorized corrections

49. Jet Corrections

50. Underlying Event

51. Offset correction
Pile-up of multiple proton-proton collisions and electronic noise in the detector produce an energy offset
Offset correction subtracts, on average, the unwanted energy from the jet
Estimate using noise-only and minimum bias MC events

52. Offset correction
Calorimeter tower threshold ET > 0.5 GeV suppresses pile-up
Offset due to electronic noise is found to be negligible
Offset due to a single pile-up event is small: <ET>= GeV
Offset will increase with number of pile-up events
Estimated using zero-bias data; data triggered on in the presence of bunch crossings but vetoing hard interactions; minimum-bias triggered events

53. Relative Response Correction
Jet response varies as a function of jet h for a fixed jet pT
h dependent corrections make the response flat as a function of h
Correction can be determined from MC truth and later on from QCD dijet events in collision data

54. Relative Response Correction
Use pT balance in back-to-back dijet events
One jet in the central control region (barrel jet)
Other jet (probe jet) with arbitrary h
Use dedicated calibration triggers to collect dijet events

55. Absolute Correction
Calorimeter energy response to a particle level jet is smaller than unity and varies as a function of jet pT
pT dependent corrections remove these variations and make the response equal to unity

56. Absolute Correction (data)

57. Absolute Correction (data)

58. EMF Correction
Fraction of jet energy deposited in the EM Calorimeter (EMF) provides additional information that can be used to improve the jet energy resolution
Optional correction; can be used for analyses requiring optimal jet energy resolution
DpT = GenJet pT – corr. CaloJet pT

59. Flavor Correction
Corrects a jet to the particle level assuming the jet originated from a specific parton flavor (as opposed to the QCD dijet mixture of parton flavors used previously)
E.g. light quarks have higher response than gluons since they fragment into higher momentum particles
=> g/Z+jets samples will have higher response than QCD dijet
Corrections can be obtained from MC truth and ttbar data
QCD dijet

60. Flavor Correction

61. Multiple Interactions
Data-based correction

62. Parton Corrections These take the jet back to the corresponding parton
GenJet response to an input parton depends on the parton flavor
Gluons radiate more than light quarks have a lower GenJet response (since more final state radiation falls outside the jet)
GenJet response depends on the size of the jet with the response increasing with cone size (or D)
Can be determined from dijet MC events

63. Jet Energy Corrections at startup
Jet energy correction and its systematic uncertainty depend on the underlying calibration of the ECAL and HCAL
Calorimeter workflow
ECAL calibration
Use isolated p->gg events for uniform azimuthal response
Use Z->ee and W->en events for absolute EM scale
HCAL calibration
Use zero-bias and minimum bias events to equalize tower-to-tower response in azimuth (f); separately for barrel, endcap and forward
Use single isolated tracks to calibrate calorimeter towers in HB and HE with respect to the momentum measurement in the tracker
Use dijet events to achieve tower response uniformity in h

64. Jet Energy Corrections
Jet Energy Correction Worklow
Derive MC truth based jet energy corrections using realistic MC simulation
Do not include jet energy corrections in the trigger level
Apply a simple factor of 0.7 to HF towers to flatten the calorimeter response over eta
Also take data for a few fills without any correction factors to study possible biases
Extract ECAL and HCAL calibrations from data; reprocess data
Derive offset, eta-dependent, pT dependent corrections from data using dijet pT balance
Reprocess data…

65. Corrected Dijet Mass
Reconstructed dijet mass distribution for Z’ events
GenJet: clustered stable particles,
does not include detector effects,
includes neutral particles
CaloJet: clustered calorimeter
jets, uncorrected
Corrected CaloJet: jet corrections
applied to the calorimeter jets
Jet energy scale will be a dominant experimental systematic uncertainty for dijet resonance searches
Even a small amount of data (<100pb^-1 at 10 TeV) would be sufficient to surpass the Tevatron sensitivity

67. Jet Resolution

69. Energy vs Momentum Resolution
Can use tracking information to improve jet resolution
For: n=100, B=1T, L=1m, σ=250μm
» 250 GeV/c we can’t reliably measure the charge of the particle at the 3σ level
Jet+Tracks (JPT) corrections are available (see WorkBook)
Calorimeter energy resolution becomes better as E increases while the tracker’s momentum resolution becomes worse
Exercise: Find momentum at which tracker resolution equals calorimeter resolution

70. Offset correction

71. Jet reconstruction: noise (incoherent) in ATLAS

72. Jet reconstruction: noise (coherent) in ATLAS