The document describes Longen Lan's 2014-15 summer research project developing a pseudo-top analysis in Rivet. The project aims to reproduce differential cross-section measurements of top quark kinematic quantities like transverse momentum, rapidity, and mass using Rivet. Rivet is a C++ analysis tool that allows particle-level analyses of collider data and simulations using standardized HepMC event records. The analysis will reconstruct pseudo-top quarks from decay products and compare results to ATLAS measurements to validate the Rivet implementation.

1. Developing the Pseudo-top Analysis in Rivet
(Differential t¯t cross-section measurements using pp collisions at
√
s =7 TeV in the ATLAS detector)
Longen Lan
Supervisors: K. Varvell K. Finelli A. Saavedra
ARC Centre of Excellence for Particle Physics at the Terascale
School of Physics, University of Sydney
2014-15 Summer Research
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 1 / 1

2. Why do we study top quarks?
It is the heaviest quark in the Standard Model (SM).
The LHC provides an excellent opportunity to study its decay
modes with a high degree of sensitivity
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 2 / 1

3. Why do we study top quarks?
It is the heaviest quark in the Standard Model (SM).
The LHC provides an excellent opportunity to study its decay
modes with a high degree of sensitivity
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 2 / 1

4. t¯t production mode
g
¯t
t
Figure: gg → t¯t
Gluon-gluon fusion from the pp collisions can result in top-antitop
quark production as shown above.
At the LHC, this is the production mode
1 80% of the time at
√
s = 7 TeV
2 90% of the time at
√
s = 14 TeV
The other main production mode is from quark anti-quark
annihilation.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 3 / 1

5. t¯t production mode
g
¯t
t
Figure: gg → t¯t
Gluon-gluon fusion from the pp collisions can result in top-antitop
quark production as shown above.
At the LHC, this is the production mode
1 80% of the time at
√
s = 7 TeV
2 90% of the time at
√
s = 14 TeV
The other main production mode is from quark anti-quark
annihilation.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 3 / 1

6. t¯t production mode
g
¯t
t
Figure: gg → t¯t
Gluon-gluon fusion from the pp collisions can result in top-antitop
quark production as shown above.
At the LHC, this is the production mode
1 80% of the time at
√
s = 7 TeV
2 90% of the time at
√
s = 14 TeV
The other main production mode is from quark anti-quark
annihilation.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 3 / 1

7. t¯t decay mode
Figure: Single-lepton t¯t decay mode
While there are other modes of t¯t decay, this study concerns
the mode shown above.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 4 / 1

8. t¯t decay mode
Figure: Single-lepton t¯t decay mode
While there are other modes of t¯t decay, this study concerns
the mode shown above.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 4 / 1

9. t¯t decay mode
Figure: t¯t decay results in light (u-,d-,s-) jets and b-jets
The collective group of high-speed quarks collimate into jets.
b-jets have slightly off-centre vertices from pp collisions due to
the lifetime of heavy-flavoured b-hadrons
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 5 / 1

10. t¯t decay mode
Figure: t¯t decay results in light (u-,d-,s-) jets and b-jets
The collective group of high-speed quarks collimate into jets.
b-jets have slightly off-centre vertices from pp collisions due to
the lifetime of heavy-flavoured b-hadrons
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 5 / 1

11. Event selection - objects
In this study, only electrons and muons are considered as leptons.
1 Exactly 1 muon or electron, four or more jets of which at least
two are b-jets
2 Exactly 1 muon or electron neutrino, although some tau
neutrinos may be allowed
3 Emiss
T > 30 GeV and transverse W mass mT (W ) > 35 GeV
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 6 / 1

12. Event selection - objects
In this study, only electrons and muons are considered as leptons.
1 Exactly 1 muon or electron, four or more jets of which at least
two are b-jets
2 Exactly 1 muon or electron neutrino, although some tau
neutrinos may be allowed
3 Emiss
T > 30 GeV and transverse W mass mT (W ) > 35 GeV
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 6 / 1

13. Event selection - objects
In this study, only electrons and muons are considered as leptons.
1 Exactly 1 muon or electron, four or more jets of which at least
two are b-jets
2 Exactly 1 muon or electron neutrino, although some tau
neutrinos may be allowed
3 Emiss
T > 30 GeV and transverse W mass mT (W ) > 35 GeV
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 6 / 1

14. Event selection - kinematic ranges
1 Leptons and jets have a pT > 25 GeV and |η| < 2.5.
2 Events are discarded (vetoed) if
1 ∆R ≤ 0.4 between a lepton and jet
2 ∆R ≤ 0.5 between two jets
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 7 / 1

15. Event selection - kinematic ranges
1 Leptons and jets have a pT > 25 GeV and |η| < 2.5.
2 Events are discarded (vetoed) if
1 ∆R ≤ 0.4 between a lepton and jet
2 ∆R ≤ 0.5 between two jets
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 7 / 1

16. Classifying the b-jets
Figure: b-jets have higher mass and higher charged track multiplicity
and are distinguished from the other jets.
The b1-jet has the smallest angular separation (∆R) from
the leptons and the b2-jet is the remaining jet.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 8 / 1

17. Pseudo-top-quarks (ˆt)
are top-quark proxies that can be defined in terms of reconstructed
detector objects (in this study) or stable particles (future studies).
They are defined by the W boson decays:
1 Leptonic pseudo-top object (ˆtl ): constructed from the lepton
(l), leptonic neutrino (νl ) characterised by the missing
transverse energy (Emiss
T ) and the b1-jet such that:
p
ˆtl
= pl
+ pνl
+ pb1
2 Hadronic pseudo-top object (ˆth): constructed from the
remaining two highest pT jets (j1, j2) and the b2-jet such that:
p
ˆth
= pj1
+ pj2
+ pb2
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 9 / 1

18. Pseudo-top-quarks (ˆt)
are top-quark proxies that can be defined in terms of reconstructed
detector objects (in this study) or stable particles (future studies).
They are defined by the W boson decays:
1 Leptonic pseudo-top object (ˆtl ): constructed from the lepton
(l), leptonic neutrino (νl ) characterised by the missing
transverse energy (Emiss
T ) and the b1-jet such that:
p
ˆtl
= pl
+ pνl
+ pb1
2 Hadronic pseudo-top object (ˆth): constructed from the
remaining two highest pT jets (j1, j2) and the b2-jet such that:
p
ˆth
= pj1
+ pj2
+ pb2
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 9 / 1

19. Pseudo-top-quarks (ˆt)
are top-quark proxies that can be defined in terms of reconstructed
detector objects (in this study) or stable particles (future studies).
They are defined by the W boson decays:
1 Leptonic pseudo-top object (ˆtl ): constructed from the lepton
(l), leptonic neutrino (νl ) characterised by the missing
transverse energy (Emiss
T ) and the b1-jet such that:
p
ˆtl
= pl
+ pνl
+ pb1
2 Hadronic pseudo-top object (ˆth): constructed from the
remaining two highest pT jets (j1, j2) and the b2-jet such that:
p
ˆth
= pj1
+ pj2
+ pb2
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 9 / 1

20. ATLAS truth MC plots
The previous study produced its results explored t¯t decay products
at the particle-level to allow a more direct connection to the
measured objects by the detector.
Figure: An ATLAS truth MC plot from the previous study
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 10 / 1

21. Kinematic quantities
The study[1] will focus on three kinematic quantities:
top-quark transverse momentum (pT )
rapidity (y)
mass (m)
Differential cross-section measurements dependent on the above
quantities will then be reproduced by Rivet with the objective to
match the ATLAS truth MC plots as closely as possible.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 11 / 1

22. What is Rivet?
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 12 / 1

23. What is Rivet?
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 13 / 1

24. What is Rivet?
Rivet is a C++ class library[2] with in-built methods and classes
for particle-level analyses from high energy collider experiments.
Figure: Methods within the FourMomentum class
Code Documentation (Doxygen) and other information about
Rivet can be found on http://rivet.hepforge.org.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 14 / 1

25. Why use Rivet?
1 Publicly accessible: Rivet uses HepMC[3] (an object-oriented
event record) which is de facto used by most HEP users
2 Versatile: It does not matter what made the generator
events, e.g. ATLAS (real data), POWHEG + PYTHIA
(simulated data)
3 Easy to use: classes and methods are named after HEP
properties and processes for clean analysis codes
4 Templates: The core team and developers are constantly
working on analysis codes for common HEP experiments (e.g.
ATLAS, Belle) which can be fine-tuned later by the researcher
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 15 / 1

26. Why use Rivet?
1 Publicly accessible: Rivet uses HepMC[3] (an object-oriented
event record) which is de facto used by most HEP users
2 Versatile: It does not matter what made the generator
events, e.g. ATLAS (real data), POWHEG + PYTHIA
(simulated data)
3 Easy to use: classes and methods are named after HEP
properties and processes for clean analysis codes
4 Templates: The core team and developers are constantly
working on analysis codes for common HEP experiments (e.g.
ATLAS, Belle) which can be fine-tuned later by the researcher
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 15 / 1

27. Why use Rivet?
1 Publicly accessible: Rivet uses HepMC[3] (an object-oriented
event record) which is de facto used by most HEP users
2 Versatile: It does not matter what made the generator
events, e.g. ATLAS (real data), POWHEG + PYTHIA
(simulated data)
3 Easy to use: classes and methods are named after HEP
properties and processes for clean analysis codes
4 Templates: The core team and developers are constantly
working on analysis codes for common HEP experiments (e.g.
ATLAS, Belle) which can be fine-tuned later by the researcher
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 15 / 1

28. Why use Rivet?
1 Publicly accessible: Rivet uses HepMC[3] (an object-oriented
event record) which is de facto used by most HEP users
2 Versatile: It does not matter what made the generator
events, e.g. ATLAS (real data), POWHEG + PYTHIA
(simulated data)
3 Easy to use: classes and methods are named after HEP
properties and processes for clean analysis codes
4 Templates: The core team and developers are constantly
working on analysis codes for common HEP experiments (e.g.
ATLAS, Belle) which can be fine-tuned later by the researcher
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 15 / 1

29. Why use Rivet?
1 Publicly accessible: Rivet uses HepMC[3] (an object-oriented
event record) which is de facto used by most HEP users
2 Versatile: It does not matter what made the generator
events, e.g. ATLAS (real data), POWHEG + PYTHIA
(simulated data)
3 Easy to use: classes and methods are named after HEP
properties and processes for clean analysis codes
4 Templates: The core team and developers are constantly
working on analysis codes for common HEP experiments (e.g.
ATLAS, Belle) which can be fine-tuned later by the researcher
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 15 / 1

30. Producing Rivet plots
1 An ATLAS t¯t template analysis code was obtained from the
Rivet website as the foundation of the source code
2 The code was fine-tuned to the requirements of the study:
1 adding new functions to calculate kinematic quantities
2 declaring and establishing pseudo-top and jet objects
3 flow control statements to implement event selection criteria
3 The code is repeatedly fine-tuned such that its plots agrees
with the ATLAS truth MC plots as closely as possible to be
uploaded to Hepforge (Rivet)
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 16 / 1

31. Producing Rivet plots
1 An ATLAS t¯t template analysis code was obtained from the
Rivet website as the foundation of the source code
2 The code was fine-tuned to the requirements of the study:
1 adding new functions to calculate kinematic quantities
2 declaring and establishing pseudo-top and jet objects
3 flow control statements to implement event selection criteria
3 The code is repeatedly fine-tuned such that its plots agrees
with the ATLAS truth MC plots as closely as possible to be
uploaded to Hepforge (Rivet)
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 16 / 1

32. Producing Rivet plots
1 An ATLAS t¯t template analysis code was obtained from the
Rivet website as the foundation of the source code
2 The code was fine-tuned to the requirements of the study:
1 adding new functions to calculate kinematic quantities
2 declaring and establishing pseudo-top and jet objects
3 flow control statements to implement event selection criteria
3 The code is repeatedly fine-tuned such that its plots agrees
with the ATLAS truth MC plots as closely as possible to be
uploaded to Hepforge (Rivet)
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 16 / 1

33. Results
: Leptonic : Hadronic
Figure: Particle-level Pseudo-top Transverse Momentum
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 17 / 1

34. Results
: Leptonic : Hadronic
Figure: Particle-level Pseudo-top Mass
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 18 / 1

35. Results
: Leptonic : Hadronic
Figure: Particle-level Pseudo-top Rapidity
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 19 / 1

36. Results
: Pseudorapidity : Azimuthal Angle
Figure: Particle-level Leptonic Component Results
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 20 / 1

37. Results
: Muon Channel : Electron Channel
Figure: Particle-level Leptonic Transverse Momentum Results
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 21 / 1

38. Results
: Muon Channel : Electron Channel
Figure: Particle-level Missing Transverse Energy
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 22 / 1

39. Did you just make that up?
How was the z-component of the neutrino’s momentum obtained
from the transverse plane?
The pz,ν was in fact calculated as a solution to the following
quadratic equation:
(El + Eν)2
− (px,l + pxν )2
− (py,l + pyν )2
− (pz,l + pzν )2
= m2
W
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 23 / 1

40. Did you just make that up?
How was the z-component of the neutrino’s momentum obtained
from the transverse plane?
The pz,ν was in fact calculated as a solution to the following
quadratic equation:
(El + Eν)2
− (px,l + pxν )2
− (py,l + pyν )2
− (pz,l + pzν )2
= m2
W
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 23 / 1

41. Results
: Muon Channel : Electron Channel
Figure: Azimuthal Angle of the Leading Jet
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 24 / 1

42. Results
: Muon Channel : Electron Channel
Figure: Particle-level t¯t mass
The muon and electron channel both have very similar results.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 25 / 1

43. Results
: Rapidity : Transverse Momentum
Figure: Particle-level t¯t Results
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 26 / 1

44. Discussion
Most Rivet plots agreed with their respective ATLAS truth MC
plots quite well. Where there were significant discrepancies
between the two graphs,
We may not have completely understood Rivet and what
some of its methods exactly do
There are certain limitations in the Rivet source code subject
to future development
There weren’t as many events for the larger kinematic
quantities which led to higher statistical uncertainties and
deviations
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 27 / 1

45. Discussion
Most Rivet plots agreed with their respective ATLAS truth MC
plots quite well. Where there were significant discrepancies
between the two graphs,
We may not have completely understood Rivet and what
some of its methods exactly do
There are certain limitations in the Rivet source code subject
to future development
There weren’t as many events for the larger kinematic
quantities which led to higher statistical uncertainties and
deviations
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 27 / 1

46. Discussion
Most Rivet plots agreed with their respective ATLAS truth MC
plots quite well. Where there were significant discrepancies
between the two graphs,
We may not have completely understood Rivet and what
some of its methods exactly do
There are certain limitations in the Rivet source code subject
to future development
There weren’t as many events for the larger kinematic
quantities which led to higher statistical uncertainties and
deviations
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 27 / 1

47. Discussion
Most Rivet plots agreed with their respective ATLAS truth MC
plots quite well. Where there were significant discrepancies
between the two graphs,
We may not have completely understood Rivet and what
some of its methods exactly do
There are certain limitations in the Rivet source code subject
to future development
There weren’t as many events for the larger kinematic
quantities which led to higher statistical uncertainties and
deviations
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 27 / 1

48. Conclusion
It is worthwhile for HEP researchers to familiarise themselves with
Rivet to write analysis codes.
Rivet has the potential to be universally used in future HEP
studies, especially for experimental physicists.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 28 / 1

49. Conclusion
It is worthwhile for HEP researchers to familiarise themselves with
Rivet to write analysis codes.
Rivet has the potential to be universally used in future HEP
studies, especially for experimental physicists.
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 28 / 1

50. Acknowledgements
Dr. Kevin Finelli and Dr. Aldo Saavedra
Associate Professor Kevin Varvell
Goncalo Borges and Andrew Bakich
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 29 / 1

51. References I
W. Bell et al.
Differential top-antitop cross-section measurements as a
function of multi-object variables constructed from final-state
particles using pp collisions at
√
s = 7 TeV in the ATLAS
detector, Version 1.3, 2013
Andy Buckley et al.
Rivet user manual version 2.2.0,
http://rivet.hepforge.org/rivet-manual.pdf, 2014
Alberto Ribon, CERN PH/SFT
HepMC, Linear Collider Software Workshop, CERN, 28 May
2009 https://indico.cern.ch/event/58717/session/0/
contribution/0/material/slides/0.pdf
Longen Lan , Supervisors: K. Varvell, K. Finelli, A. Saavedra Developing the Pseudo-top Analysis in Rivet 30 / 1