How to find mass resonances in collider experiments? How to reconstruct a colliding event from detector data?

1. Mass Reconstruction
Yuan CHAO ( 趙元 )
(National Taiwan University,
Taipei, Taiwan)
Numerical Simulation in HEP
2012/02/15

2. Outlines
Introduction
Resonances
Coordination system
Four-vector conversion
The W & Z bosons
Z-boson (Ex. 1)
Invariant mass
Missing ET
Transverse mass
W-boson (Ex. 2)
Tracks
Jets
Top reconstruction (cascade)
...
2

3. The Origin of the Universe
3

4. Goal of High Energy Physics
LHC was built for the following
purposes:
To find the origin of mass...
the Higgs boson.
Looking for the unification..
Supersymmetry as well as
other candidates of Dark
Mater & Dark energy
Investigate the mystery of
anti-matter disappearance
Physics at the early stage of
the universe: Heavy Ion
collisions and QGP
4

5. Introduction
Accelerators & detectors
LHC, CMS (hadron machine)
5

6. The Large Hadron Collider
Four major experiments at LHC
Atlas, Alice, CMS, LHCb
LHC first beam in Sep. 2008
A technical trouble occurred
10 days after the start
Physics restarted in Nov. 2009
CERN
Energy starts at 0.9 TeV
Pushed up to 2.36 TeV in Dec.
New energy record in 2010
Collision at 7 TeV on Mar. 30
Delivered data ~36/pb in 2010
Reached ~5.7/fb in 2011
To increase to 8 TeV in 2012
LHC
6

7. The Large Hadron Collider
Four major experiments at LHC
Atlas, Alice, CMS, LHCb
LHC first beam in Sep. 2008
A technical trouble occurred
10 days after the start
Physics restarted in Nov. 2009
CERN
Energy starts at 0.9 TeV
Pushed up to 2.36 TeV in Dec.
New energy record in 2010
Collision at 7 TeV on Mar. 30
Delivered data ~36/pb in 2010
Reached ~5.7/fb in 2011
To increase to 8 TeV in 2012
LHC
7

8. The Large Hadron Collider
Four major experiments at LHC
Atlas, Alice, CMS, LHCb
LHC first beam in Sep. 2008
A technical trouble occurred
10 days after the start
Physics restarted in Nov. 2009
Energy starts at 0.9 TeV
Pushed up to 2.36 TeV in Dec.
New energy record in 2010
Collision at 7 TeV on Mar. 30
13/12/11 dataset 
max L≈ 3.54x1033cm-2s-1
LP11 dataset 
EPS dataset 
Delivered data ~36/pb in 2010
Reached ~5.7/fb in 2011
To increase to 8 TeV in 2012
8

9. Atlas Detector
A Toroidal LHC Apparatus
A general purposed detector
9

10. CMS Detector
Compact Muon Solenoid
A general purposed detector
3.8
10

11. CMS Detector
Compact Muon Solenoid
A general purposed detector
3.8
11

12. Introduction
Accelerators & detectors
KEK-B, BELLE (lepton machine)
Tsukuba, Japan
Lpeak=2.1 x 1034 /cm2/s2
Aerogel
Cherenkov counter
SC solenoid
1.5T
CsI(Tl)
16X0
TOF counter
n=1.015~1.030
3.5 GeV e+
8 GeV e−
EFC
(online Lum.) Si vtx. det.
3/4 lyr. DSSD
3.5 GeV e+ on 8 GeV eWCM = M( Υ(4s) )
3km circumference
~11mrad crossing angle
BELLE
Detector
Central Drift
Chamber
small cell +He/C2H6
µ / KL detection
14/15 lyr.
RPC+Fe
12

13. Long Lived Particles
Most product of a collision decays before they reach
the detectors
Check the life-time on PDG handbook or web site:
http://pdglive.lbl.gov/
Look for the value of cτ
What we see in the detectors:
e±, μ±, γ, π±,K±, KL, n, p±
13

14. Long Lived Particles
Most product of a collision decays before they reach
the detectors
Check the life-time on PDG handbook or web site:
http://pdglive.lbl.gov/
Look for the value of cτ
What we see in the detectors:
e±, μ±, γ, π±,K±, KL, n, p±
Others can be found through resonances search
Resonance mass is like the finger print of particles: unique
Similar to line spectra analysis of lights
14

15. Resonance
15

16. Resonance
Short life time particles
Typical life-time of order 10-23
If flying at ~ speed of light → decay within 10-15 m
Relationship between effective cross-section σ vs. the
energy E, resonances often appear as bell-shaped
E = m c2
Natural unit: c = ħ = 1
16

17. Resonance (cont.)
Short life time particles
Typical life-time of order 10-23
If flying at ~ speed of light → decay within 10-15 m
Relationship between effective cross-section σ vs. the
energy E, resonances often appear as bell-shaped
Usually described as Breit-Wigner function
(¡=2)2
¾(E) = ¾0
(E0 ¡ E)2 + (¡=2)2
Relativistic Breit-Wigner distribution:
2
¡2 M 2
¾(m; M; ¡) = N ¢ ¢
¼ (m2 ¡ M 2 )2 + m4 (¡2 =M 2 )
Natural units: c = ħ = 1
Experimentally often use Gaussian (for detector resolution) 17

18. Coordination System
Most collider detectors built in barrel shape
Detector build along the beam line
Interesting particles have higher transverse momenta
Symmetric shape to have uniform acceptance
Special purpose detectors have different shapes
LHCb
18

19. Coordination System
Most collider detectors built in barrel shape
Detector build along the beam line
Interesting particles have higher transverse momenta
Symmetric shape to have uniform acceptance
Special purpose detectors have different shapes
Coordination convention:
Use cylindrical coordinate (r, θ, φ)
Beam direction
19

20. Coordination System (cont.)
Most collider detectors built in barrel shape
Detector build along the beam line
Interesting particles have higher transverse momenta
Symmetric shape to have uniform acceptance
Special purpose detectors have different shapes
Coordination convention:
Use cylindrical coordinate (r, θ, φ)
Adopt Lorentz invariant variable: rapidity
1
y = ln
2
µ
E + pL
E ¡ pL
¶
jpj + pL
jpj ¡ pL
¶
Pseudo-rapidity (approximation for m ≈ 0)
1
´ = ln
2
µ
·
µ ¶¸
µ
= ¡ ln tan
2
20

21. Four Vectors
The key variables: 4-vectors
Motion of particles can be described with
(px, py, pz, E) in Cartesian
More common used:
(pT, η, Φ, m0) or (pT, η, Φ, E)
q
Conversions:
px = pT cos Á
py = pT sin Á
pz = pT = tan µ = pT sinh ´
jpj = pT cosh ´
pT = p2 + p2
x
y
tan Á = py =px
Implemented in ROOT, CLHEP, ...
Will use through out the exercises
One can use TLorentzVector with helper functions
21

22. The W & Z bosons
The mediator of the weak interaction
Known as weak bosons: W & Z
A major success of Standard Model
Predicted by Glashow, Weinberg, Salam in 1968
SU(2) gauge theory
Discovery
Neutral current interaction observed in 1973
Super Proton Synchrotron (SPS) at CERN
W found Jan. 1983 at UA1 & UA2
Z was found a few months later
The four gauge bosons of electroweak: W+, W-, Z0, γ
22

23. The Z boson
Properties
Charge = 0. Spin J = 1
Elementary particle
Mass: 91.1876 ± 0.0021 GeV
Full width Γ = 2.4952 ± 0.0023 GeV
Decay modes
l+l-: 3.3658 ± 0.0023 x 10-2
Invisible: 20.00 ± 0.06 x 10-2
Hadrons: 69.91 ± 0.06 x 10-2
We'll do exercise to find Z → e+e- or μ+μ-
23

24. Ex. 1 reconstruct Z
D/L the provided sample
ROOT: http://dl.dropbox.com/u/5196749/example.tgz
Plain text: http://dl.dropbox.com/u/5196749/dump_top_cz.txt.gz
EvtInfo_RunNo,
EvtInfo_EvtNo,
Leptons_Pt, Leptons_Eta, Leptons_Phi
Leptons_Type (11: electron, 13: muon, and others)
Leptons_Charge
Identify an even:
Check the RUN#, Event#
The use of ROOT
Check ROOT website: http://root.cern.ch
Try TTree::MakeClass to generate a framework
You can also use whatever you like with the plaint text ver.
Make use of the pre-defined Lorentz vector class
Add two vectors directly
Get pT, eta, phi...
24
Calculate ΔR, ΔΦ...

25. Ex. 1 reconstruct Z
Loop through all the leptons
Find two leptons with the same flavor, opposite charge
Sum up the four-vector and calculate the mass
Draw a plot of the mass, pT, eta, phi... distribution for all
combinations
Check the result plot
Where is the peak position? (try a fit!)
How to improve the S/N? (re-fine the cuts)
What's the width?
Comparing with lifetime?
Compare ee vs. mu mu
25

26. The W boson
Properties
Charge = ±1 e. Spin J = 1
Elementary particle
Mass: 80.399 ± 0.023 GeV
Full width Γ = 2.085 ± 0.042 GeV
Decay modes
l+-nu: 10.80 ± 0.09 x 10-2
Hadrons: 67.60 ± 0.27 x 10-2
We'll do exercise to find W → e±ν or μ±ν
26

27. How to find the invisibles?
Neutrino detection at colliders
No direct method due to its low interaction nature
Relies on the knowledge of the whole event
Basic idea: energy & momentum conservation
To find the missing part
Sum up all the particles
→ Transverse energy (calorimeter), momentum (tracks)
Calculate the "miss ET" as negative of the sum
Longitudinal component not considered: loss & background
27

28. The Transverse Mass
Definition
For the lack of longitudinal information of nu
2
MT = (ET;` + ET;º )2 ¡ (~T;` + ~T;º )2
p
p
= 2jpT;` jjpT;º j[1 ¡ cos(¢Á`;º )]
MissET is the key here
Relies on robust calorimeter detectors
Usually poorer than direct measurements
28

29. Ex. 2 reconstruct W
Use the same provided sample
There's a special entry for computed MissET (type: 0)
Go through all the leptons and MissET
Find the best lepton to combine with MissET
Calculate the transverse mass
Draw a plot of the combinations
Check the result plot
Where is the peak position? (try a fit!)
How to improve the S/N? (re-fine the cuts)
Do you see the cut-off?
29

30. Tracks
Charged particles can be detected as “tracks"
So called "tracking system"
Silicon, wired chamber, gas tubes...
Magnetic filed for the momentum
Curving direction for charge sign
Parameterization
Helix parameters
30

31. Calorimeters
Calorimeter for energy measurement
ElectroMagnetic Calorimeter
Hadron Calorimeter
To fully absorb the particle
Heavy material
Showers (see Chin-chen's)
Convert into counts or light
Granularity
Used for electron & neutral particle detection
Better energy resolution at very high pT
Usually worse spatial resolution
31

32. Calorimeters
EM Calorimeter
ElectroMagnetic interactions
Detecting e±, γ
Showering
Bremsstrahlung (low E: compton)
Pair production
Pair annihilation
Shower size
Moliere radius
RM = 0:0265X0(Z + 1:2)
Radiation length
Shower length
X = X0
ln(E0 =Ec )
ln 2
32

33. Jets
Jets are products of out-going partons
Including quarks and gluons
Hadronization as strong interaction
Particles pulled out of vacuum for colorless
Detecting Jets
Bunches of particles
Including kaons, pions, leptons...
Usually detected with "calorimeters"
Various types and clustering algorithms
33

34. Jets in Hadron Machines
TrackJet
Charged Tracks are used for clustering
Good for early data study
CaloJet
Uses ECal/HCal towers for clustering
JPT (Jet Plus Tracks)
Replace the avg. calo response with
individual charged hadrons measured
in tracker system
Zero Supp. offset correction
Correction for in-calo-cone tracks
Adding out-of-calo-cone tracks
Correction for track eff. & muons
PFJet (Particle Flow Jet)
New approach in CMS
JME-09-002
34

35. Jets at LHC
Several jet clustering algorithm available in CMS:
Jet is the energy sum of a cluster
p
Cone algorithm: R = ¢´2 + ¢Á2 ' 0:5
Iterative cone, midpoint cone, SISCone
2p
2p
Pairing distance: dij = min kT i ; kT j
´¢
ij
D
Kt: p=1, CA: p=0, Anti-Kt: p=-1
CMS uses FastJet package http://fastjet.fr
Algorithm consideration
Infrared & colinear safe
Good performance (Energy, position ...)
Robust to Piled-ups & UE
CPU efficient: O( N2 ln(N) ) : O( N ln(N) )
G. Salam, “Jetography"
Sequential recombination: ³
Priority needed on various jet algorithms
Good to have many for cross checking
The default jet algorithm is Anti-Kt
35

36. Resonance from Jets
36

37. The CDF Anomaly
37

38. Ways of Improvement
Constrained Mass
Using constraints to refine the distribution
38

39. Ways of Improvement
Constrained Mass
Using constraints to refine the distribution
Re-fit on vertex, ex. Λ (cτ = 7.89 cm)
¤ ! p¼
39

40. Ways of Improvement
Constrained Mass
Using constraints to refine the distribution
Re-fit on vertex
Mass constraints in cascaded decays, ex. ψ(2s) → J/ψ
Ã(2s) ! J=Ã + ¼ + ¼ ¡ ; J=Ã ! e+ e¡
40

41. Ways of Improvement
Constrained Mass
Using constraints to refine the distribution
Re-fit on vertex
Mass constraints in cascaded decays
Energy constraint from accelerator info
Mbc
q
2
= Ebeam ¡ p2
B
41

42. Ways of Improvement
Constrained Mass
Using constraints to refine the distribution
Re-fit on vertex
Mass constraints in cascaded decays
Energy constraint from accelerator info
Be aware: could also destroy the shape...
42

43. Top Reconstruction
Properties
Charge = 2/3. Spin J = 1/2
Elementary particle
Mass: 172.9 ± 1.5 GeV
Full width Γ = 2.0 ± 0.7 GeV
Decay modes
Wb 0.99 ± 0.09
Lifetime so short (5 x 10-25) that no hadron forms before it
decays: bare quark
Theory: 1973 (K&M), Discovery 1995
Search
Semi-leptonic
¹
pp ! tt ! W (qq )b; W (`0 º 0 )¹
¹
b
Di-leptonic
¹
pp ! tt ! W (`º)b; W (`0 º 0 )¹
b
Di-jet
¹
pp ! tt ! W (qq )b; W (q q )¹
¹
¹b
43

44. Top Reconstruction
Semi-leptonic search:
Higher branching fraction
Fully reconstruct by assigning W mass constraint
p
pz =
2
pz` (px` pxº + py` pyº + MW =2) § E`
Di-leptonic search:
2
2
2
(px` pxº + py` pyº + MW =2)2 ¡ ET º (E` ¡ p2 )
z`
2 ¡ p2
E`
z`
Very clean mode as no extra jets
Suffer from low branching fraction
Cannot fully reconstructed due to two neutrinos
An upper mass bound on mass combinations:
h
i
(1)
(2)
mT 2 (minvis ) = min max[mT (minvis ; pT ); mT (minvis ; pT )]
(1)
(2)
pT ;pT
q
vis invis ¡ pvis ¢ pinvis )
mT (minvis ; pinvis ) = m2 + m2
T
vis
invis + 2(ET ET
T
T
44

45. Summary
Introduced the experiments
Motivation & goals
Accelerators & detectors
Basics on data analysis
The four-vector
Mass reconstruction
Missing ET
Advance techniques
More on detectors
Constrained fits
Cascaded decays
Summary & conclusions
Q&A
45

46. 以上
Thank YOU!
謝謝
Remercie de Votre
Attention

47. Higgs Limits on σ/σSM (CLs)
95% CL: obs. 127-600, exp: 117-543 GeV
47