1. LHCb-ANA-2011-xxx
July 10, 2011
Z cross-section measurement at√
s = 7 TeV using the channel
Z → ττ.
Stephen Farry, Philip Ilten, Ronan McNulty1
1
University College Dublin, Dublin 4, Ireland.
Abstract
This note presents preliminary results for the measurement of the Z cross-section
using decays of the Z to tau final states, with up to 240 pb−1 of data taken in 2010
and 2011. One tau is identified through its decay to a muon and neutrinos; the
other through its decay to an electron or muon and neutrinos.

3. 1 Introduction
The measurement of the production cross-section for Z bosons in proton-proton collisions
constitutes an important test of the Standard Model. When performed using the different
leptonic decay modes of the Z , it allows a test of lepton universality. Since this has been
tested to better than 1% at LEP [1], any deviation observed at the LHC would be evidence
for additional channels producing final state leptons.
Unlike at LEP, where taus can be observed in a clean environment, measurements at
hadron colliders are difficult. The D0 collaboration made the first measurement [2] with a
precision of 12% in 2005. CDF performed a similar measurement [3] two years later, with
a similar precision. This year CMS made the first preliminary measurement [4] at the
LHC with an overall precision of 10%. ATLAS [5] do not currently have a measurement in
this channel, although they have reported an observation. This note reports a competitive
measurement by LHCb that has an overall uncertainty of 12%.
LHCb has already made a measurement in the channel Z → µµ [6] with a precision of
10% due to the luminosity uncertainty then available. This will be updated for the 2011
summer conferences using the full 2010 dataset and an improved luminosity estimate of
4%. Work is also progressing in the channel Z → ee [7]. This note completes the trilogy,
focusing on the final leptonic mode Z → ττ.
The identification of high energy tau decays is important in several searches at the
LHC, not least for Higgs where it can decay to tau pairs about 10% of the time for
many scenarios. Various supersymmetric particles decay preferentially into taus. For
example, in mSUGRA at high tanβ, the second-lighest neutralino decays into the LSP
and two taus 95% of the time [8]. In the constrained next-to-minimal supersymmetric
model (cNMSSM) the cascade decays of squarks and gluinos produce final states with
two taus [9]. In GMSB where the stau is the next-to-lightest supersymmetric particle it
decays to final states enriched in taus [10]. In addition, fourth generation leptons would
produce final states with taus, as well as final states with muons and electrons similar
to those searched for in this analysis [11]. Thus if a standard model measurement, such
as that described here, were to give an answer different from the theoretical expectation,
that would be an indication of new physics.
The dataset used in this analysis is described in the next section. Following that, the
procedure used to extract the Z → ττ signal is described in section 3. The calculation of
the cross-section and the evaluation of systematic uncertainties are described in section 4.
The results and comparison to theory are presented in section 5.
2 Data Sets and Trigger Configuration
This analysis uses the complete data set from 2010, corresponding to a total integrated
luminosity of 37.5±1.3 pb−1
, and all the 2011 data available in mid-June which constitutes
an additional 210.4 ± 8.4 pb−1
.
1

4. Sample ID Sample ID
Z → ττ 42100000 W → τντ + jets 42300010
Z → µµ 42112000 W → µνµ + jets 42311010
Z → ee 42122000 W → eνe + jets 42321010
W → τντ 42300000 t¯t 41900002
W → µνµ 42311000 WW, WZ, ZZ local
W → eνe 42321000
Table 1: Simulation samples used in the analyses. All official Monte Carlo was pro-
duced using Gauss v39r0 with Pythia 6.424.2. The diboson sample was produced with
Gaussv40r0 and Pythia 6.424.2.
All the data used for selecting Z → ττ have been collected using high transverse
momentum, pT , muon triggers at both L0 and HLT. These are the same triggers which
were used for selecting W and Z decays to muon final states [6] and their behaviour has
already been studied in detail.
The L0SingleMuon trigger has a pT threshold of 10 GeV. In addition, there is a global
cut requiring an SPD multiplicity below 900. The HLT1SingleMuonNoIPL0HiPt requires
a single high transverse momentum muon above 5 GeV. In addition, for 2010 runing there
were global event cuts (GEC) in the trigger requiring: IT and OT occupancies < 20%;
VELO hits < 3000; IT hits < 3000; OT hits < 10000; and number of VELO tracks < 350.
For 2011 data, the number of VELO hits must be below 10,000. HLT2SingleHighPTMuon
requires a muon with pT > 10 GeV. The GEC were implemented in order to prevent very
large events from overwhelming the trigger. Studies with W and Z decays to muons have
shown that the only requirement which reduces the physics rate is that coming from the
number of VELO hits. This has been measured with data by superimposing minimum
bias events onto W or Z events having one primary vertex in order to predict how many
events with a larger number of vertices are not triggered on account of the GEC. The
electroweak stripping requirements are defined in Reco10-Stripping13b and ask for a single
muon with pT > 20 GeV and prob(χ2
, ndf) > 0.001.
Table 1 lists the simulation samples that have been used in developing the selection
requirements and to compare with data. Each uses Pythia [12] to generate events which
are passed through the LHCb simulation. In addition we have generated dedicated diboson
events forcing the W and Z to decay to leptons. Whenever possible, the data itself was
used to define the selection criteria and to estimate efficiency and purity numbers. In
particular, the Z → µµ sample is essentially pure and is a source of muons with similar
momentum, and a source of Z decays with similar kinematics and topology. In addition,
we make use of the NoBias triggered events which have been taken with a random trigger.
2

5. 3 Selection of Z → ττ candidates
Z decays to two taus are characterised by two high transverse momentum narrow jets
whose composition depends on the decay mode of the tau. The purely leptonic decays
of the tau are to an electron and two neutrinos in 17% of cases and to a muon and two
neutrinos another 17% of the time. The remainder of taus decay semileptonically resulting
in one, three or five charged pions or kaons, usually accompanied by neutral pions.
In this analysis we concentrate on the final state where one tau decays to a muon and
the other decays to either an electron or a muon, referred to in this paper as the eµ and
µµ final states. Although only constituting about 9% of Z → ττ decays, the backgrounds
are much lower than for other final states. 1
The principal background comes from QCD events which contain identified leptons.
When the final state consists of two muons, there is a large background from Z/γ∗
→
µµ. Finally, isolated high transverse momentum muons and electrons can occur in top
decays and in WW, WZ and ZZ events. We now describe the identification of high
transverse momentum muons and electrons, before describing how each background source
is suppressed and evaluated. The simulation is mainly used to understand the relationship
between Z → ττ and Z → µµ events. Whenever possible, the data itself is used to
evaluate the major background sources.
3.1 Selection of high momentum muons
The LHCb Z → µµ and W → µνµ analyses [6] have shown that high transverse mo-
mentum muons can be found by requiring standard “tight” muons and insisting on good
quality tracking. The chisquared probability for track reconstruction is required to be
greater than 0.001 and TT hits are required on the tracks in order to reduce the ghost
rate. Hits are required in each of the four outermost muon stations and the summed
energy in ECAL and HCAL divided by the momentum, Etot/p is required to be below
0.2 in order to reduce the number of pions and kaons that ’punch-through’ to the muon
stations.
The effect of requiring Etot/p < 0.2 on ’punch-through’ pions can be seen in Figure 1.
The upper plot shows Etot/p < 0.2 for all muon candidates with a transverse momentum
above 20 GeV in a sample which has been enriched in QCD events by requiring that
the muon is not isolated. Two features are visible in this plot: a peak towards zero as
would be expected for genuine muons which deposit little energy in the calorimeters, and
another peak at about 0.6 suggestive of punch through. This behaviour is confirmed using
control samples. Genuine muons can be selected from the Z → µµ sample requiring the
invariant mass of the dimuon to be within 10 GeV of the Z mass. The middle plot shows
the distribution for Etot/p after scaling the momentum of the muon to match that in the
upper plot. The distribution for pions and kaons is shown in the lower plot for all tracks
1
Work is onging to perform the measurement in the channels where one tau decays to a muon and
neutrinos and the other decays semileptonically producing a tightly collimated jet of hadrons.
3

6. E/p
0 0.5 1 1.5 2
NumberofEvents
0
2000
4000
6000 =7 TeVsLHCb preliminary
E/p
0 0.5 1 1.5 2
NumberofEvents
0
1000
2000 =7 TeVsLHCb preliminary
E/p
0 0.5 1 1.5 2
NumberofEvents
0
10
20
30 =7 TeVsLHCb preliminary
Figure 1: Distributions for Etot/p in samples of: high transverse momentum muon candi-
dates where the muon is not isolated (upper plot); muons coming from selected Z → µµ
events (middle plot); high transverse momentum tracks in randomly triggered events
(lower plot).
with a momentum above 10 GeV in randomly triggered events. Requiring Etot/p < 0.2
allows the punch-through component to be reduced to a negligible level.
The composition of this muon sample can be estimated from the W → µνµ analysis:
about one third of triggered muons with pT > 20 GeV come from W and Z decay; one
third come from semi-leptonic decays of B and D mesons; and the remainder comes from
pions and kaons that decay in flight.
3.2 Selection of high momentum electrons
The same track quality requirements as for the muons are applied to candidate electrons.
Since electrons should be totally absorbed in the electromagnetic calorimeter, the ideal
response should be no energy in the HCAL, significant deposits in the PRS and a peak
around about one in the E/p distribution for the ECAL. However in LHCb the situation
for high momentum electrons is rather different, due to the saturation of the ECAL cells
at transverse energies of 10 GeV. Bremsstrahlung means that the shower may distribute
4

7. 0 5 10 15 20 25 30 35 40
0
50
100
150
200
250
histMCmu histMCmu
Entries 15034
Mean 14.93
RMS 5.141
histMCmu
20 30 40 50 60 70 80 90 100 110 120
0
20
40
60
80
100
histCL histCL
Entries 531
Mean 76.58
RMS 11.88
histCL
Figure 2: Left: ECAL transverse energy associated to electrons in Z → ee events. Right:
Invariant mass distribution for electron pairs in Z → ee events. The points are data,
selected as described in the text. The histogram is the simulation.
over several cells; nonetheless the characteristic response in LHCb to high momentum
electrons will have thresholds at multiples of 10 GeV in transverse energy as can be seen
in the solid histogram in the left-hand plot of Figure 2 for simulated Z → ee events.
Despite this, there should still be substantial PRS deposits and no energy deposits in the
HCAL, so the identification of electrons is not too difficult. What is problematic though
is an accurate estimation of the energy: clearly the calorimeter is not reliable for this, but
neither is the tracking which will consisently underestimate the amount of energy due to
bremsstrahlung. Thus the mass peak for the Z reconstructed from di-electrons is smeared
to lower values as can be seen for simulated events in the right-hand plot of Figure 2.
The response of the calorimeters to pions and kaons can be seen in the top row of
Figure 3 which shows E/p in the ECAL, E/p in the HCAL, and the energy in the PRS,
for tracks with pT > 8 GeV in randomly triggered events. In the ECAL, the peak towards
zero shows that for many hadrons the energy deposited in the ECAL is minimal. However
there is a significant tail towards higher deposits. In the HCAL, most pions and kaons
leave significant deposits while in the PRS, the deposits are very small.
The response to simulated electrons in Z → ττ → eµνµνeντ ντ events is shown in the
middle row of Figure 3. Informed by this, the following requirements are used in order
5

8. E/p
0 0.5 1 1.5
NumberofEvents
0
500
=7 TeVsLHCb preliminary
E/p
0 0.5 1 1.5
NumberofEvents
0
20
40
60
=7 TeVsLHCb preliminary
Energy (GeV)
0 0.1 0.2 0.3
NumberofEvents
0
1000
2000
/ pECAL
E
0 0.5 1 1.5
0
50
100
150
200
250
Preliminary
LHCb
-1
= 7 TeV, L = 247 pbs
/ pHCAL
E
0 0.5 1 1.5
0
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600
800
1000
1200
1400
1600
Preliminary
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-1
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[GeV]PRS
E
0 0.1 0.2 0.3
0
50
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200
250
300
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400
450
Preliminary
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-1
= 7 TeV, L = 247 pbs
/ pECAL
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Preliminary
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/ pHCAL
E
0 0.5 1 1.5
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600
Preliminary
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-1
= 7 TeV, L = 247 pbs
0 0.05 0.1 0.15 0.2 0.25 0.3
0
50
100
150
200
250
300
350
400
histMCmu histMCmu
Entries 15034
Mean 0.1699
RMS 0.01949
histMCmu
Figure 3: Calorimeter response: ECAL energy divided by momentum (left column);
HCAL energy divided by momentum (centre column); PRS energy (right column). The
top row is for particle with pT > 8 GeV in randomly triggered data events. The middle
row is for simulated electrons in Z → ττ → eµνµνeντ ντ events. The bottom row is for
electrons in Z → ee events. The points are data and the histogram is the expectation
from simulation.
6

9. to identify electrons for this analysis: E/p > 0.1 in the ECAL; E/p < 0.05 in the HCAL;
and E > 0.05 GeV in the PRS. After these requirements, < 1% of the high momentum
tracks in randomly triggered events are retained.
The response to genuine electrons in data can be validated using a sample enriched in
Z → ee events. To select such events, both electron candidates are required to satisfy the
electron criteria above and to have pT > 20 GeV. In addition the electrons are required
to be isolated.
We define an isolation variable, Ilepton
for each lepton by
Ilepton
=
plepton
− i ptrack
i
plepton + i ptrack
i
where the sum extends over all long tracks for which (φlepton − φtrack
i )2 + (ηlepton − ηtrack
i )2 <
0.5, and p, φ, η are the momentum, azimuthal angle, and pseudorapidity of the track or
lepton as indicated by the superscript. The more isolated the lepton, the closer the value
of I is to 1.
Having required Ie
> 0.75 for both electron candidates, after which the QCD back-
ground is less than 1% (estimated using same-sign events), the invariant mass of the pair
is shown in Figure 2 for both data and Z → ee simulation. The agreement is very good
and thus provides a data sample of high transverse momentum electrons.
Returning to the three calorimeter variables used in order to identify electrons, the
bottom row of Figure 3 shows the response for electrons in data and simulation. The
good agreement with the simulation is evident for the ECAL and HCAL showing that
these variables are reliably simulated. For the PRS, the resolution is known to be under-
estimated in the simulation. Comparing these plots to the major background (top row of
Figure 3) and signal (middle row of Figure 3), the position of the electron identification
requirements is justified.
3.3 Suppression of Z/γ∗
→ µµ
When there are two muons in the final state, there is a large background due to Drell-Yan
production of dimuons. It is required that the invariant mass of the two muons is below
80 GeV which removes the Z peak. However, this does not get rid of events produced via
the photon propagator.
The first variable considered is the balance between the final state muons defined as
pbalance
T = (p
(1)
T − p
(2)
T )/(p
(1)
T + p
(2)
T ), where the superscript labels each muon. This quantity
is plotted in the left-hand plot of Figure 4 for muons in simulated Z → ττ and Z → µµ
events. The right-hand plot shows this quantity for muons in data and simulation coming
from the Z peak, confirming that the simulation reflects the behaviour in data. Based on
the simulation we require that pbalance
T > 0.2 which retains 72% of the signal and 14% of
Z → µµ.
The second variable considered is the significance of the summed signed muon impact
parameters, IPsum, which is defined as follows. The impact parameter of each muon is
7

10. BalanceTP
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
12
14
16
18
20
BalanceTP
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
12
14
16
18
20
-1
L=246pb
LHCb Preliminary
Figure 4: The variable pbalance
T for muons in: simulated Z → ττ (points) and Z → µµ
events (histogram) is shown on the left. The comparison between Z → µµ data (points)
and simulation (histogram) is shown on the right.
calculated as the distance of closest approach to the nearest primary vertex (PV). 2
It is
signed according to the sign of the angular momentum of the track around the vertex. 3
The variable IPsum is the sum of the two signed impact parameters. This variable has
the advantage that nearly all dependence on the position and resolution of the primary
vertex is removed so that only the resolution on the extrapolated track position remains.
The impact parameter resolution in the simulation is found to be 15% better than in
data so a scaling factor is applied to the simulation to bring both into agreement. The
IPsum distribution is shown in the left-hand plot of Figure 5 for muons from Z → µµ in
data and simulation. Dividing by the resolution on IPsum gives the IPsum significance.
This is plotted in the right-hand plot of Figure 5 for dimuons with an invariant mass
between 20 and 80 GeV and pbalance
T > 0.2, fitted to two templates: one comes from data
in the Z peak; the other comes from simulated Z → ττ decays. The fit is good and
2
The default PV is biased for this analysis since the muons themselves (which have a large weight on
account of their high momentum) have been used in its creation. Thus, we recalculate the PV’s in the
event, having first removed the two candidate muons.
3
This is the cross-product of the vector defined from the PV to the track’s point of closest approach,
and the track direction.
8

11. -0.2 -0.1 0 0.1 0.2
0
2
4
6
8
10
12
14
-1
L=246pb
LHCb Preliminary
Impact Parameter
0 5 10
1
10
2
10
3
10
-1
L=246pb
LHCb Preliminary
Figure 5: Left plot: The variable IPsum for dimuons with invariant mass between 80 and
100 GeV in data (points) and simulation (histogram). Right plot: The significance of
IPsum for dimuons with invariant mass between 20 and 80 GeV in data (points) fitted
to two templates describing prompt muons derived from Z → µµ data events (blue
histogram) and Z → ττ (red histogram).
allows us to estimate that above an IPsum significance of 4, the ratio of signal to prompt
background is about one-to-one.
3.4 Suppressing QCD events
QCD events can give rise to high transverse momentum electrons and muons in several
ways. Genuine electrons and muons can arise from the semileptonic decays of B and D
mesons and although the typical transverse momentum is a few GeV, significant num-
bers of events are still expected above 20 GeV. Pion and kaon decays in flight will also
produce muons. Finally, fluctuations in the energy response of the calorimeter mean that
occasionally pions and kaons will be misidentified as muons or electrons. Although the
probability for this happening may be small, the sheer number of pions and kaons present
in QCD events make this a sizeable background.
The nature of QCD means that when high energy pions or kaons are produced, they
9

12. Isolation
-1 -0.5 0 0.5 1
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1500
2000
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3000
3500
Preliminary
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-1
= 7 TeV, L = 247 pbs
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
10
20
30
40
50
60
histCLss histCLss
Entries 8249
Mean -0.1042
RMS 0.4035
histCLss
Isolation
-1 -0.5 0 0.5 1
0
10
20
30
40
50 -1
L=246pb
LHCb Preliminary
Figure 6: The least isolated lepton in the event for: Z → µµ data (points), Z → µµ
simulation (solid), and Z → ττ → µe simulation (dashed) signal events (left); same-
sign data (histogram) and opposite-sign data (points) in the eµ channel (centre); same-
sign data (histogram) and opposite-sign data (points) in the µµ channel (right), after
suppressing Z → µµ events.
are usually accompanied by other energetic hadrons. Thus the energy in a cone around
the lepton candidate is large. In contrast, for muons and electrons coming from Z → ττ,
there will be no correlated energy from the hard scatter; any hadrons in a cone around
the muon candidate will likely have come from the underlying event or from another
proton-proton interaction, and are thus quite soft.
We first require that pµ
T > 20 GeV and plepton
T > 5 GeV, the harder cut on the muon
corresponding to the stripping threshold. 4
Then the isolation variable is used both
to suppress the QCD background and to estimate the amount of contamination in the
sample. The expected shape of the least isolated lepton in Z → ττ events, as predicted
by the simulation, is shown by the dashed histogram in the left-hand plot of Figure 6.
Superimposed on this is the same distribution for Z → µµ where the points are data
and the histogram with the solid line is simulation. The close correspondence of all three
shapes allows a prediction for the shape of the data in Z → ττ events.
To estimate the shape for the QCD background events, we note that there are few
signal events below a value of 0.5, and that furthermore, those QCD events originating
from misidentification will have roughly equal numbers of same-sign and opposite-sign
events. (In the data there are 17% more opposite-sign than same-sign events below
I = 0.5, the small excess likely coming from genuine leptons in B meson decays.) The
central plot in Figure 6 shows the least isolated lepton in the eµ analysis for opposite-sign
(points) and same-sign(histogram) events, which have been normalised to the number
4
A stripping line has since been proposed with a lower threshold.
10

13. of opposite-sign events below 0.5. The agreement is good. The excess of opposite-sign
events above 0.8 is consistent with the presence of Z → ττ events. The right-hand plot
in Figure 6 shows the equivalent plot in the µµ analysis. The relative amount of QCD is
less than in the eµ analysis because the requirement on the IPsum significance has already
reduced the number of QCD events.
To select signal events, we require oppositely charged leptons with I > 0.8, where
there are 114 events for the eµ analysis and 50 events for the µµ analysis. The QCD
background is estimated from the same-sign events to be 26 events for eµ and 9 events
for µµ.
3.5 Suppression of other electroweak backgrounds
The electroweak backgrounds coming from WW,WZ,ZZ and top quark decays produce
electrons and muons which firstly, are not so strongly correlated back-to-back in the
transverse plane, and secondly, have higher invariant masses. The upper left-hand plot in
Figure 7 shows the angle, ∆φ, in the transverse plane between the muon and the lepton
for the simulated signal superimposed on Z → µµ data and simulation. All of these
show a similar peak towards π radians. The upper right-hand plot shows the simulated
distributions for top (solid histogram) and WW, WZ, ZZ (dashed histogram), which tend
to be less peaked. The lower plots in Figure 7 show the distributions for our signal events
in the eµ and µµ channels with the estimated QCD background contribution whose shape
has been taken from the same sign events after relaxing the requirements on the lepton
identification. We require that ∆φ > 2.7 radians after which the eµ analysis has 81 events
with expected backgrounds of 9.5 ± 3.0 from QCD, 0.25 ± 0.25 from top, and 2.7 ± 1.2
from dibosons, while the µµ analysis has 33 events with expected backgrounds of 1.6±1.3
from QCD, 5.5 ± 1.8 from Z/γ∗
→ µµ, and 0.0 ± 0.5 from top and dibosons.
3.6 Summary of selection
To summarise, the following requirements have been applied to extract our signals, start-
ing with all events passing the high transverse momentum muon trigger.
• Muon id: Hits in each of the four outermost muon chambers and Etot/p < 0.2.
• Electron id: EECAL/p > 0.1, EHCAL/p < 0.05, EPRS > 0.05 GeV.
• One muon with pT > 20 GeV and another oppositely signed muon or electron with
pT > 5 GeV.
• pbalance
T > 0.2 and IPsum significance > 4 and dimuon invariant mass below 80 GeV
(only for the µµ analysis).
• Ilepton
> 0.8
• ∆φ > 2.7 radians.
11

14. Figure 8 shows the distribution for the invariant mass of the two leptons in each
analysis after the above requirements. The estimated background contribution is also
shown. The electroweak backgrounds have been taken from the simulation. The shape
of the QCD background has been obtained by relaxing the requirements on the lepton
identification and using the same-sign events. For the dimuon analysis, the shape of the
contribution from Zγ∗
has been obtained by removing the invariant mass requirement,
requiring IPsum < 1, and normalising to the number of events above 80 GeV.
4 Cross-section Determination
The cross-section, σ, has been calculated from the number of selected events, N, through
σ =
N − Nbkg
2A LBR(τ → eνeντ )BR(τ → µνµντ )
for the eµ analysis and from
σ =
N − Nbkg
A LBR(τ → µνµντ )2
for the dimuon analysis, where Nbkg is the estimated number of background events re-
maining in the final sample, is the overall efficiency for selecting signal events, L is
the effective luminosity, A is an acceptance correction which relates the finite acceptance
of LHCb to the kinematic region in which the cross-section is quoted, and BR is the
branching ratio of the tau into the given final state. Each of these quantities is now
discussed.
4.1 Efficiency
The total efficiency can be broken up into the following components:
= trigger
µ
track
l
track
µ
id
l
id sel
where trigger is the efficiency for triggering on events that pass the offline selection, track
is the efficiency for reconstructing a long track given that the truth track is within the
LHCb fiducial region, id is the efficiency for identifying the long track as a muon or
electron, and sel is the efficiency of the selection criteria.
The trigger used for this analysis is the same as that used for the 2010 W → µν and
Z → µµ analyses so we use the same number for the single trigger efficiency in 2010 data.
This was evaluated in Z → µµ events from the number of events where both muons fired
the trigger, to the number where only one fired the trigger, and found to be 0.781±0.006.
The global event cut imposed on the number of VELO hits lower this by 6% for 2010
data. The overall trigger efficiency for the µµ final state is higher than for eµ since either
muon could have fired the trigger.
12

15. The tracking efficency for muons above 20 GeV has been determined for the W and
Z analyses of 2010 data using a tag-and-probe of muons coming from Z → µµ. It was
found to be flat with pT > 20 GeV and gives a value of 0.84 ± 0.01. Comparison of the
tracking efficiency for muons in J/ψ events [13] (where pT > 1 GeV) showed no difference
to muons from Z, within the statistical uncertainty of the comparison of 2%, which is
taken as a systematic in our measurement.
The tracking efficiency for electrons has not yet been measured in data. Consequently,
we use the value obtained in the simulation scaled by the ratio of the muon tracking
efficiency in data to the muon tracking efficiency in the simulation. As a systematic we
assign half the difference between the muon tracking efficiency in 2010 data and simulation.
This gives a value of e
track = 0.80 ± 0.3.
The muon identification efficiency has been determined in 2010 data using a tag-and-
probe technique for the Z → µµ analysis, to be 0.991 ± 0.002. We assume the same
efficiency for 2011 data.
The electron identification efficiency has been determined in 2010 data with the Z →
ee selection requirements, from the ratio of di-electron events with two identified electrons
to the number of events with one identified electron [7], as shown in Figure 9. The amount
of background in each sample has been determined from template fits using minimum bias
data with no identified electrons to describe the background shape, and simulated Z → ee
for the signal. A value of 0.962 ± 0.004 was obtained and as a systematic we take the
difference of 0.01 to the corresponding number in the simulation.
The selection efficiency in the eµ analysis has been determined from the Z → ττ
simulation corrected using the agreement between Z → µµ data and simulation. Thus,
Z→ττ
sel (MC) as determined in the simulation is scaled by Z→µµ
sel (data)/ Z→µµ
sel (MC) where
the same selection requirements have been imposed on Z → µµ data and simulation. A
value of 0.46 ± 0.03 is found. The systematic uncertainty is calculated by combining
in quadrature the differences for each cut between efficiencies calculated using Z → µµ
events in data and simulation. The largest disagreement occurs in the isolation variable
as can be seen in Figure 6, which is a result of the different number of pile-up events
and the imperfect description of the underlying event. Only the latter is a true source
of uncertainty, so the systematic from this source is calculated from the difference in
efficiency between data and simulation in events which have precisely one PV.
The µµ analysis has additional requirements on pbalance
T and IPsum significance after
which the selection efficiency is 0.172. However, since these cuts are designed to remove
Z → µµ events, it is not possible to use the remaining number of Z → µµ in data and
simulation to calculate a systematic. Consequently, for both these variables, anti-cuts
are applied to the control sample requiring pbalance
T < 0.2 and IPsum significance < 1.
The difference between the efficiencies in Z → µµ data and simulation for each selection
variable are added in quadrature resulting in a selection efficiency of 0.172 ± 0.014.
13

16. 4.2 Luminosity
The luminosity has been calculated for the events which were analysed using the standard
LHCb luminosity tool. Values of 37.5 ± 1.3pb−1
were obtained for the 2010 dataset and
210.4 ± 8.4(208.9 ± 7.3)pb−1
for the eµ(µµ) analyses using 2011 data.
4.3 Acceptance
In order to compare directly to LHCb’s measurement of the Z cross-section in the channel
Z → µµ, we choose to quote the result in the same kinematic region, requiring both
leptonic products of the Z (in this case taus) to be within pseudorapidities of 2 and 4.5,
to have transverse momenta above 20 GeV, and an invariant mass between 60 and 120
GeV. Because we actually measure the decay products of the taus and do not detect them
directly, we require an acceptance factor, A, in order to correct from the kinematic range
in which the final states can be observed. Specifically, A is defined as the number of
Z → ττ → µlνµνlντ ντ events where one muon has a transverse momentum above 20 GeV
and a pseudorapidity between 2 and 4.5 and the other lepton has a transverse momentum
above 5 GeV and a pseudorapidity between 2 and 4.5 divided by the number of events
where both taus have transverse momenta above 20 GeV and pseudorapidities between
2 and 4.5. This number has been evaluated to be 0.25 ± 0.002 for the eµ analysis and
0.39 ± 0.009 for the µµ, using PYTHIA and HERWIG with the difference between the
generators taken as an estimate of the uncertainty.
5 Results and comparison to theory
Table 2 summarises the number of selected Z events, estimated backgrounds, efficiencies
and acceptance, together with their uncertainties. These lead to measurements of the Z
cross-section times branching ratio to taus of
σ(Z → ττ; pτ
T > 20 GeV; 2 < ητ
< 4.5); 60 < mZ < 120 GeV) = 78 ± 9 ± 7 ± 3 pb
σ(Z → ττ; pτ
T > 20 GeV; 2 < ητ
< 4.5); 60 < mZ < 120 GeV) = 87 ± 15 ± 10 ± 3 pb
in the eµ and µµ final states respectively, where the first uncertainty is statistical, the
second is systematic, and the third is due to the luminosity.
Both results are consistent with each other and are combined assuming independent
uncertainties on the number of signal events, and correlated uncertainties for the back-
grounds, efficiencies, acceptance and luminosity that are in common between the analyses.
This gives a combined result of
σ(Z → ττ; pτ
T > 20 GeV; 2 < ητ
< 4.5); 60 < mZ < 120 GeV) = 80 ± 8 ± 7 ± 3 pb
The dominant uncertainty is currently due to the statistics, while the largest systematic
effect comes from the determination of the selection efficiency. The measurement is com-
patible with the measurement in the Z → µµ analysis of 73 ± 4 ± 7 pb. The latter, at
14

17. eµ µµ
2010 data 2011 data 2010 data 2011 data
Number of events 10 71 4 29
Estimated background 1.9 ± 0.5 10.6 ± 2.7 1.1 ± 0.3 6.1 ± 2.0
trigger 0.73 ± 0.01 0.78 ± 0.01 0.81 ± 0.01 0.86 ± 0.01
µ
track 0.84 ± 0.02 0.84 ± 0.02
e
track 0.80 ± 0.03 - -
µ
id 0.991 ± 0.002 0.991 ± 0.002
e
id 0.962 ± 0.01 - -
sel 0.46 ± 0.03 0.172 ± 0.014
0.215 ± 0.010 0.230 ± 0.011 0.097 ± 0.005 0.103 ± 0.005
Acceptance 0.25 ± 0.002 0.39 ± 0.009
Luminosity (pb−1
) 37.5 ± 1.3 210.4 ± 8.4 37.5 ± 1.3 208.9 ± 7.3
Branching Ratio 0.062 0.030
Cross-section (pb) 78 ± 9 ± 7 ± 3 87 ± 15 ± 10 ± 3
Table 2: Summary of numbers and cross-section.
the time, was dominated by a large uncertainty on the luminosity determination and is
due to be updated shortly. Nonetheless, this means that currently the total uncertainty
in both these measurements is roughly equal. The ratio of these two numbers allows a
comparison of the Z coupling to taus and muons, and gives a value of
Γ(Z → ττ)
Γ(Z → µµ)
= 1.10 ± 0.14
consistent with lepton universality.
References
[1] ALEPH, DELPHI, L3, OPAL, SLD Collaborations, Precision Electroweak Measure-
ments on the Z Resonance. Physics Reports, 427 Nos. 5-6 (2006) 257.
[2] D0 Collaboration, Measurement of σ(pp → Z).BR(Z → ττ) at
√
s = 1.96TeV.,
Phys. Rev. D71 (2005) 072004.
[3] CDF Collaboration, Measurement of σ(pp → Z).BR(Z → ττ) at
√
s = 1.96TeV.,
Phys. Rev. D75 (2007) 092004.
[4] CMS Collaboration, hep-ex/0227764.
[5] ATLAS Collaboration, ATLAS-CONF-2011-045.
[6] W and Z production at
√
s = 7 TeV with the LHCb experiment, LHCb-CONF-2011-
12.
15

18. [7] David Ward, Electroweak meeting, April 15th, 2011.
https://indico.cern.ch/getFile.py/access?contribId=2&resId=1&
materialId=slides&confId=134788
[8] F. Heinemann, Discovery potential of the second lightest neutralino in mSUGRA in
the tau channel at high tan beta at the LHC, hep-ex/0406056.
[9] U. Ellwagger, A. Florent, D. Zerwas, Discovering the constrained NMSSM with tau
leptons at the LHC, JHEP1101:103, (2011).
[10] D. Ludwig, Expected performance of the ATLAS detector in GMSM models with tau
final states, arXiv:1002.0944v1 hep-ex.
[11] L. Carpenter, A. Rajaramar, O. Whiteson, Search for fourth generation charged lep-
tons, arXiV:1010.1011v1 hep-ph.
[12] T. Sj ostrand et al., Comp. Phys. Commun. 135 (2001) 238.
[13] Michel de Cian, Tracking and Alignment Meeting, Feb 17, 2011.
https://indico.cern.ch/getFile.py/access?contribId=0&resId=0&
materialId=slides&confId=120872
16

19. /e)µ,µ(φ∆
0 1 2 3
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Preliminary
LHCb
-1
= 7 TeV, L = 247 pbs
/e)µ,µ(φ∆
0 1 2 3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Preliminary
LHCb
-1
= 7 TeV, L = 247 pbs
0 0.5 1 1.5 2 2.5 3
0
2
4
6
8
10
12
14
16
18
20
histCLos histCLos
Entries 68
Mean 2.684
RMS 0.5734
histCLos
)µ,µ(φ∆
1 1.5 2 2.5 3
0
2
4
6
8
10
-1
L=246pb
LHCb Preliminary
Figure 7: The upper left-hand plot shows the acoplanarity of the two leptons in Z →
µµ events, (the points being data and the solid histogram being simulation) and the
estimation for Z → ττ → eµνµνeντ ντ from simulation (dashed histogram). The upper
right-hand the acoplanarity of the leptons in simulated top events (solid histogram) and
WW, WZ and ZZ events (dashed). The lower left-hand plot shows the acoplanarity of
the two leptons in the eµ analysis for data (points) while the solid histograms show the
estimated contribution coming from QCD. The lower right plot shows the acoplanarity
of the two leptons in the µµ analysis while the solid histogram is the estimated QCD
contribution.
17

20. [GeV]eµm
50 100
0
2
4
6
8
10
12
14
16
18
20
Preliminary
LHCb
-1
= 7 TeV, L = 247 pbs
[GeV]µµM
20 40 60 80 100
0
2
4
6
8
10
12
-1
L=246pb
LHCb Preliminary
Figure 8: Invariant mass of the dileptons in the eµ (left) and µµ (right) analyses. The
points are data while the solid histograms show the estimated background contributions.
Only events below 80 GeV are used to calculate the cross-section in the µµ analysis.
Figure 9: Invariant mass of events with isolated tracks having pT > 20 GeV where one
of the tracks has been identified as an electron (left) and both are identified (right). The
points are data, the light histogram is Z → ee simulation, while the dark histogram comes
from minimum bias events with no electron identification.
18