1. Modelling of ττ final states by embedding τ pairs in Z → μμ events
– AN –
Michał Bluj1, Armin Burgmeier2, Tomasz Früboes3,
Günter Quast2, Manuel Zeise2
CNRS/LLR­École Polytechnique
EKP, KIT, Karlsruhe
A. Sołtan Institute for Nuclear Studies

2. Overview Motivation Introduction of the embedding method
Test of the method on Monte Carlo
Absolute normalisation and systematic uncertainties
More applications

3. embedding of tau pairs is one possible solution
Motivation
determination of the shape of the invariant mass distribution coming from Z → ττ 1)
absolute normalisation of Z → ττ events
study of selection efficiencies 2)
estimation of the tau identification efficiency 2)
→ data-driven approaches to face these problems wanted
→ need ways to reduce the dependency on simulation
Z → t t
H → t t
CMS Note 2006/088
embedding of tau pairs is one possible solution
1) M. Bachtis et al., “Performance of tau reconstruction algorithms with 2010 data in CMS.”, CMS AN-2011/045
2) M. Bachtis et al., “Search for neutral Higgs boson decaying into τ pairs using 35 pb−1 at √s = 7 TeV.” CMS AN-2010/430

4. Embedding Method Two possibilities to get artificial Z → ττ
Particle Flow Level
Digitized Output Level
provides all particle flow objects, re-calculated primary vertex, beam spot and combined track collection
sufficient for most tautau analyses
easy application
trigger decision restricted to separate tautau event
no calorimeter based information
provides all possible information gathered by reconstruction algorithm
trigger decision as in the experiment
few modifications to analyses
multiple steps to produce events
very challenging technique
→ embedding with particle flow objects sufficient for the near future

5. Overview of the Method reconstructed Z → μμ event generate new
(1)
(1)
(1)
remove muons from:
track coll.
pfCandidate coll.
keep everything else
detector simulation
(2)
reconstruction
pile-up, UE etc. remain in the event
(3)
merge track and pfCandidate collections
and re-run particle flow algorithms
artificial Z → ττ event

6. Z → μμ selection VBTF baseline selection
pT>20 GeV, |η| < 2.1 for both muons
rel. comb. isolation < 0.15
common quality criteria

7. Embedding & Simulation
Z → ττ event
TAUOLA for correct modelling of spin correlations in tau decays
decay mode selection (ττ → μ + τ-jet)
cut on transverse momenta of visible decay products possible (increase of statistical precision)
detector simulation and reconstruction
no vertex smearing (vertex position from original event)
start-up conditions with beam spot from data
mixing of tracks and particle flow candidates
re-run particle flow algorithms

8. works with other final states as well!
Z → ττ selection
example: Z → ττ → μ + τhad (highest available statistics)
Event selection
Official μ + jet WP75 selection, except:
|ητ-jet| < 2.0 instead of 2.3
unprescaled single muon trigger only (no difference)
Trigger
Run Range
HLT_Mu9 …
HLT_Mu15 …
works with other final states as well!

9. Data Samples Data: muPD, Nov4th re-reco Monte-Carlo:
all samples from Fall10 with Z2 tune
Z/W samples with powheg in NLO
standard data samples

10. Quantities of the generated particles
compare simulated Z → ττ → µ+jet events with embedded events
good overall agreement
feature in eta of the muon selection (not yet corrected) are of course visible in these distributions:
isolation cut
pt cut
quality criteria
generated tau transverse momentum
generated tau pseudorapidity

11. First Look at the Result
application of the method on Monte-Carlo and on Data:
visible mass for Z → ττ → μ + τ-jet
Monte-Carlo
visible mass for Z → ττ → μ + τ-jet
Data
a first test of the products directly derived from the tau decay products
very good agreement for MC and data

12. Absolute Normalisation & Systematic Uncertainties

13. = ηµ Z → µµ Systematics in this step pTµ
not reachable via Z → µµ selection
Z → µµ
reachable via Z → µµ selection
(pT >20, |η|<2.1)
yellow area exaggerated (~1-2%)
Systematics in this step
phase space
lepton
universality
pTµ =
compensate for kinematic selection
correct for different efficiencies on data ητ
all Z → ττ events
Z → ττ
phase space
pTτ
Tasks
determine absolute normalisation
study systematic effects
study ττ via
monte-carlo
study ττ via
embedding

14. Systematics Roadmap MC Systematic Effects embedding
yes luminosity no
yes pile-up no
yes jet energy scale no
yes tau-jet energy scale yes
No (in principle) statistical uncertainty yes
yes trigger systematics yes
no radiation yes
yes tau reconstruction efficiency yes
no Z → mumu selection impurities yes
list is probably not complete
MC and embedding have orthogonal systematic errors
some of the big uncertainties are correct by construction in embedding method

15. Pile-Up in data vs. Monte Carlo
even small pile-up has a significant impact on the results of the Z → ττ → µ + jet analysis
compare Z → ττ data with Z → ττ Monte-Carlo (normalized to same integrated luminosity)
visible mass distribution, ττ sample
Z → ττ from data vs. MC
visible mass distribution, ττ sample
Z → ττ from data vs. MC with PU

16. Pile-Up in data vs. Monte Carlo
the correct modelling of pile-up is inherent to the method
compare embedded Z → ττ events from data with Z → ττ Monte-Carlo (normalized to same integrated luminosity)
visible mass distribution, ττ sample
Embedded Z → ττ data vs. MC with PU
Embedded Z → ττ data vs. MC

17. Results from high statistics Monte Carlo sample

18. Absolute normalization of embedded sample
absolute normalization desired (equivalent to a tau id efficiency measurement)
use Z → µµ acceptance from W/Z group as base for all correction factor and assume lepton universality (i.e. BR(Z→µµ) = BR(Z→ττ))
correct for...
branching ratio of ττ → µ + jet
reconstruction efficiency for Z → µµ with respect to acceptance
data-driven correction factors for Z → µµ reconstruction efficiency
cut into ττ phase space (e.g. events outside of the µµ acceptance)
muon Isolation efficiency in ττ → µ + jet
for data: inaccurate description of single muon HLT in simulation wrt. to data

19. Results on MC after Z → ττ → μ + τ-jet selection
muon transverse momentum
tau transverse momentum
even tails well described

20. Results on MC after Z → ττ → μ + τ-jet selection
missing transverse energy
transverse mass
distributions well described

21. Results on MC after Z → ττ → μ + τ-jet selection
visible mass
secondary vertex fit mass
complex kinematic fit on the whole event
very good agreement

22. Cut into ττ phase space
Z → µµ selection imposes an implicit cut on ττ (i.e. pT>20 and |η|<2.1)
about 1.5% of the events from non-reachable phase space pass the ττ → µ+jet selection (including other Z → ττ events mimicing ττ → µ + jet)
Is this just a scaling factor or are the relevant distributions distorted?
compare some crucial distributions for the different regions in phase space with simulated Z → ττ events
1.5% of the selected events
reconstructed tau transverse momentum
ττ→µ+jet selection cut on pTτ>20 GeV
reconstructed muon transverse momentum
ττ→µ+jet selection cut on pTµ>15 GeV

23. Cut into ττ phase space II
missing transverse energy distribution
after ττ→µ+jet selection
svfit mass distribution
after ττ→µ+jet selection
distributions are identical within statistical uncertainties

24. Cut into ττ phase space III
the effect of the non-reachable phase space is small and can be absorbed into a single scaling factor
binomial error as statistical uncertainty on the scaling factor (can be decreased if needed)
systematical error estimated by comparing with a pythia sample

25. Effect of muon isolation
→ 0.978
→ 0.993
Discrepancy in efficiency of muon isolation cut in ττ → µ + jet
Non-embedded events are cleaner despite isolation requirement in Z → µµ selection
Treat as systematic uncertainty
muon isolation distribution, ττ sample
ττ→µ+jet after all cuts except muon isolation

26. Absolute normalization1) 1) 1) 1) 1)
these numbers are used for the closure test...
1) only in data

27. coll. approx. mass distribution svfit mass distribution
Closure test on MC
coll. approx. mass distribution
svfit mass distribution

28. Normalisation on 2010 Data
apply above normalisation procedure to real data
method is able to make an perfect absolute prediction of Z → ττ events from measured Z → μμ events on data

29. Study of Selection Efficiencies
embedded ττ sample was also used to study the efficiencies of cuts
compare embedded events from data with simulated sample
variation of cut reveals potential problems in the description of the studied process
integration
variation
good agreement,
only small deviations …

30. Study of Selection Efficiencies
the approach is also applicable to cuts on additional objects in the event (as everything except the Z → ττ comes directly from data!)
study the combination of the transverse mass cut, the opposite sign requirement and the second lepton veto
Result:
systematic uncertainty
on the studied cuts

31. Tau Identification Efficiency
assuming lepton universality and the knowledge of the branching ratios BR(Z → ττ) and BR(Z → μμ)
solve formula for tau id (instead of NZ → ττ)
described in detail in AN-2011/045 (“Performance of tau reconstruction algorithms with 2010 data in CMS”)

32. first version of the AN published last week
Conclusion and plans
introduction of the embedding method
tests of embedding on Monte-Carlo successful
absolute normalisation possible
systematic uncertainties understood
study of selection efficiencies
embedding method ready for tau analyses, e.g. ττ → μμ, ττ → e + τ-jet, ττ → μ + τ-jet
first version of the AN published last week
comments are welcome!
CMS AN-11/020

33. Backup Slides

34. svfit mass distribution collinear approx. mass distribution
Radiation effects
Z → µµ events can suffer from bremsstrahlung
define radiation as particle flow photon from the Z → μμ event in a ΔR=0.5 cone around τ → μ with pTγ >1 GeV
limited impact on embedded events (~1%)
svfit mass distribution
collinear approx. mass distribution

35. Dimuon Invariant Mass Cut
dimuon invariant mass cut introduces a bias in the pT spectrum
reason: no comparable cut for Z → ττ
solution: no cut on invariant dimuon mass
muon transverse momentum in Z → μμ
scaled to unity
generated tau transverse momentum
after embedding and selection

36. https://twiki.cern.ch/twiki/bin/view/CMS/MuonTauReplacementWithPFlow
Documentation
introduction, code, comments...

37. Cut on ΣpTvis of tau decay products
cut on ΣpTvis allows an increase in statistical precision
constraint of the phase space is absorbed into an event weight
results are invariant under this cut as long as it is loose enough to not interfere with the analysis
visible mass distribution
for embedded Z → ττ
svfit mass distribution
for embedded Z → ττ

38. Embedding with ττ → μμ channel: LL variables
Alexei Raspereza and Agni Bethani
dimuon pseudo-rapidity
ratio of the dimuon pT to the
scalar sum of muons' pT
relative particle flow isolation for
positive muon
azimuthal angle between negative muon
momentum and missing transverse momentum
azimuthal angle between negative muon
momentum and missing transverse momentum
azimuthal angle between negative muon
momentum and missing transverse momentum

39. Embedding with ττ → μμ channel: dimuon mass
Alexei Raspereza and Agni Bethani
ττ → µµ search, uses log likelihood
details:
dimuon mass shape comparisons of ττ MC and embedding:
dimuon visible mass after preselection
dimuon visible mass after final selection

40. Embedding with ττ → μμ channel: isolation
Alexei Raspereza and Agni Bethani
muons: relative pf-isolation and distance-of-closest approach
relative particle flow isolation for
negative muon
muons' distance-of-closest
approach significance
Good agreement within present statistical errors

41. Decay Mode and Z → µµ selection
Z → µµ selection efficiency within acceptance (statistical error negligible, but systematic errors from VBTF group)
correction factors are determined with tag&probe from data
usual Z → µµ selection included in embedding modules in CMSSW
selection of tau decay and MC preselection are supported
restrict ττ decay to ττ → µ + jet
gain in statistical precision
BR(Z → ττ → µ + jet) = 0.226