Reconstructing the rest frame of systems
Transcript of Reconstructing the rest frame of systems
Reconstructing the rest frame of τ+ τ- systems
P e t e r R o s e n d a h lT h o m a s B u r g e s s
B j a r n e S t u g u
I F T U n i v e r s i t y o f B e r g e n
Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Motivation
We want to study resonances decaying to a pair of taus.
Unfortunately, some observables are best defined the rest frame of τ pairs, especially variables for studying the τ polarisation
At LHC, Z and Higgs bosons are produced with high boost
Due to neutrinos in the τ decays, no trivial way exists to reconstruct the resonance rest frame
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Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Idea
For resonances at the Z mass or above, the τ-jets are collinear.
In resonance rest frame, the visible τ-jets are nearly back-to-back.
Proposed method:
Reconstruct rest frame by finding boost that makes τ-jets back-to-back
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τ-jet
τ-jet
Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
z-Boost Reconstruction
We define acollinarity, α, as the deviation from being back-to-back
Z and Higgs bosons at LHC are produced with a predominantly longitudinal boost
Search for the boost along the z-axis, βz, that minimises α between the τ-jets
zβ
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
α0.0
0.5
1.0
1.5
2.0
2.5
3.0
|<0.1zβ|
<0.1tβ|<0.1,
zβ|
>0.3tβ|<0.1,
zβ|
<0.7zβ0.5<
<0.1tβ<0.7,
zβ0.5<
>0.3tβ<0.7,
zβ0.5<
>0.9zβ
<0.1tβ>0.9,
zβ
>0.3tβ>0.9,
zβ
α as function of βz
Easy to minimise since α always has single minimum - can be found with a
simple binary search
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Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Full Boost Reconstruction
Method can easily be extended to search for the full boost - not only along the z-axis.
First find βz
Estimate transverse direction by summing up τ-jets pT and ETmiss
Finally, search for minimum along transverse direction to find βT
[rad.]RFα0.0 0.2 0.4 0.6 0.8 1.0
rate
(Nor
mal
ised
)0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035-τ +τ → Z
Gen. RF
Reco.(Z) RF
Reco.(XYZ) RF
Lab. Frame
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Z →τ+τ- Pythia8 + Tauola simulation
In many cases reconstructing βz will be sufficient
Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Performance
Performance studied on Z→ τ- τ+ Pythia8+Tauola simulations
Rest frame is nicely found for all generated boost values
Better performance in full boost method,
However needs accurate transverse direction as input
|Recoβ - Genβ|0.0 0.1 0.2 0.3 0.4 0.5 0.6
rate
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)
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Z-method
XYZ-method
MeansZ-method 0.149XYZ-method 0.076
Note: Log scale
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Reconstructed vs generated boost
Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Applications
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Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Polarisation studyDecays of τ-leptons carry information about polarisation
Effect strongest in τ→πν
Looking at E(π-)/MZ
Effects washed out in detector frame (▲)
Almost fully recovered in reconstructed frame (△)
Z/ Mvis2 E0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
rate
(Nor
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)0.00
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0.06 Gen. h= 1Gen. h=-1Reco. h= 1Reco. h=-1Lab. h= 1Lab. h=-1
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τ→πν decays from Pythia8 + Tauola simulation
Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Spin Reconstruction
Polarisation configuration depends on the boson spin
Spin information can be extracted by studying the polarisation correlation of τ+ vs. τ-
rate
(Nor
mal
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)
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2
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-610×
H / M- 2 E0 0.2 0.4 0.6 0.8 1
H /
M+
2 E
0
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0.8
1
rate
(Nor
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)
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-610×
Z / M- 2 E0 0.2 0.4 0.6 0.8 1
Z /
M+
2 E
0
0.2
0.4
0.6
0.8
1Z (spin 1) H (spin 0)
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Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
In detector frame In recon. frame
0.23 0.47
Sensitivity to spinFrom these distributions a likelihood function can be created
and a sensitivity to spin defined as
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logL-0.4 -0.2 0.0 0.2 0.4 0.6
Ent
ries/
0.01
0
2
4
6
8
10
12
14
16
Z
Mean 1.47e-01RMS 1.33e-02
HiggsMean -1.64e-01RMS 1.60e-02
Sensitivity 0.47
The Evis distributions for single ⇡ decay modes shown in figure 7 for the generated
and reconstructed heavy boson RFs show that the true correlations are partly recovered
in the reconstructed RF using the XYZ-method proposed in section 2. Furthermore, it is
shown that these correlations are much weakened in the laboratory frame.
4.1 Analysis of the sensitivity to spin
Conservation of angular momentum leads to distinctly di↵erent helicity configurations when
comparing the final states of Z0 and H decays in their rest frames. While the spin compo-
nents along the direction of flight of the ⌧+ must add up to ±1 for the Z0, the sum must
be 0 for the H decays. Thus the spin e↵ects can be studied by looking at the correlations
in Evis of the two ⌧ -leptons as shown in figure 8.
rate
(Nor
mal
ised
)
1
2
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4
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-610×
H / M- 2 E0 0.2 0.4 0.6 0.8 1
H /
M+
2 E
0
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0.6
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(a) Spin 0 (H sample).
rate
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)
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-610×
Z / M- 2 E0 0.2 0.4 0.6 0.8 1
Z /
M+
2 E
0
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0.4
0.6
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1
(b) Spin 1 (Z0sample).
Figure 8. Energy correlations in the reconstructed RF using the XYZ-method of a ⌧+⌧� pair withboth ⌧ -leptons decaying to h± ⌫⌧ . To avoid e↵ects coming from the mass di↵erences all energiesare scaled with the mass of the decaying boson.
To quantify the observed di↵erence between spin 0 and spin 1 particles, the Z0 and H
samples were split into training and test samples. Probability density functions for both
spins, P0
(E⌧� , E⌧+) and P1
(E⌧� , E⌧+), were constructed as the fraction of events in a bin
of (E⌧� , E⌧+) in the corresponding training sample. From this a likelihood, L, is created
for N events from both training samples by
logL =NX
i=0
�log(P i
1
)� log(P i0
)�/N (4.1)
The test samples of Z0 and H events are divided in sub-samples of N events and the
likelihood is calculated for each sub-sample. The distribution of logL when N = 1000 and
when both ⌧ -lepton decays to h± ⌫⌧ is shown in figure 9.
Inspired by [15], a sensitivity, S, is defined such that the number of standard deviations
between the means of the two distributions, n�, is given by
n� = SpN (4.2)
– 10 –
The Evis distributions for single ⇡ decay modes shown in figure 7 for the generated
and reconstructed heavy boson RFs show that the true correlations are partly recovered
in the reconstructed RF using the XYZ-method proposed in section 2. Furthermore, it is
shown that these correlations are much weakened in the laboratory frame.
4.1 Analysis of the sensitivity to spin
Conservation of angular momentum leads to distinctly di↵erent helicity configurations when
comparing the final states of Z0 and H decays in their rest frames. While the spin compo-
nents along the direction of flight of the ⌧+ must add up to ±1 for the Z0, the sum must
be 0 for the H decays. Thus the spin e↵ects can be studied by looking at the correlations
in Evis of the two ⌧ -leptons as shown in figure 8.
rate
(Nor
mal
ised
)
1
2
3
4
5
6
7
-610×
H / M- 2 E0 0.2 0.4 0.6 0.8 1
H /
M+
2 E
0
0.2
0.4
0.6
0.8
1
(a) Spin 0 (H sample).
rate
(Nor
mal
ised
)
1
2
3
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-610×
Z / M- 2 E0 0.2 0.4 0.6 0.8 1
Z /
M+
2 E
0
0.2
0.4
0.6
0.8
1
(b) Spin 1 (Z0sample).
Figure 8. Energy correlations in the reconstructed RF using the XYZ-method of a ⌧+⌧� pair withboth ⌧ -leptons decaying to h± ⌫⌧ . To avoid e↵ects coming from the mass di↵erences all energiesare scaled with the mass of the decaying boson.
To quantify the observed di↵erence between spin 0 and spin 1 particles, the Z0 and H
samples were split into training and test samples. Probability density functions for both
spins, P0
(E⌧� , E⌧+) and P1
(E⌧� , E⌧+), were constructed as the fraction of events in a bin
of (E⌧� , E⌧+) in the corresponding training sample. From this a likelihood, L, is created
for N events from both training samples by
logL =NX
i=0
�log(P i
1
)� log(P i0
)�/N (4.1)
The test samples of Z0 and H events are divided in sub-samples of N events and the
likelihood is calculated for each sub-sample. The distribution of logL when N = 1000 and
when both ⌧ -lepton decays to h± ⌫⌧ is shown in figure 9.
Inspired by [15], a sensitivity, S, is defined such that the number of standard deviations
between the means of the two distributions, n�, is given by
n� = SpN (4.2)
– 10 –
Sensitivity
Likelihoods for Z and Higgs
Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
[GeV]0 20 40 60 80 100 120 140 160 180 200
rate
(Nor
mal
ised
)0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045hτhτ → 0 Z
° > 170jetsφΔ
Z-method
Alternative Mass Estimation
Neutrinos in the τ decay makes reconstruction the mass of a resonance non-trivial
In the resonance rest frame, the leading τ-jet energy will accumulate towards half the resonance mass
As a simple approximation the kinematic edge can be found at the steepest slope in the leading τ-energy distribution
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Mass can be extrapolated similarly to W mass measurements
Z →τ+τ- Pythia8 + Tauola simulation
2E1
Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Comparison to other methods
Both methods can be applied on all events
Methods currently used at the LHC, only works for a fraction of suitable event topologies
In the region where the Coll. Approx. breaks down, this method can be applied without using ETmiss
Method is extremely fast and simple
more 1000x faster than likelihood method currently used by CMS and ATLAS
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Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012
Summary and Outlook
A way of reconstructing rest frame of τ pair resonances and its applications have been presented
Method and its applications are published atarxiv:1105.6003 (recently accepted in JHEP)
Suitable to all τ decay channels and not necessarily specific to τ pairs
No detector effects have been included in plots shown
However, we are investigating use of the method in ATLAS
C++ code available on request
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Peter Rosendahl, University of Bergen Spaatind - 05 jan 2012 14
Thank you for your attention