m / GeV
5.1 The τ Pair Selection
• (Kπππ)−: The four-meson final state with a total branching fraction of (0.150±0.045)% is detected via the decay τ− →K−π+π−π0ντ (0.064±0.024)% which has the largest branching fraction among the four-meson final states. The remaining channels are taken from Monte Carlo simulation.
• (Kη)−and (Kηπ)−: The final states involvingηmesons have a branching fraction of (0.027±0.006)%
and (0.029±0.009)% [66], respectively. These channels are taken from Monte Carlo simulation.
Of the multi-meson final states with open strangeness, (Kπ)−, (Kππ)− and (Kπππ)−, 93.4% of all decay channels involved are measured. The remaining 6.6% are taken from Monte Carlo simulation.
This chapter is organized as follows: First the τ selection is described. It separates theτ pair events from Z0 decays into electron pairs, muon pairs or a pair of quarks and from Bhabha scattering events and two photon background. In the second section the identification of final states with open strangeness is described and finally the invariant mass spectra are presented in Chapter 5.3.
Y
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Cen t r e o f s c r een i s ( 0 . 0000 , 0 . 0000 , 0 . 0000 )
50 GeV 20 10 5 Run : even t 4302 : 75672 Da t e 930717 T ime 225034 Ebeam 45 . 610 Ev i s 121 . 9 Emi ss - 30 . 7 V t x ( - 0 . 04 , 0 . 04 , 0 . 29 ) Bz=4 . 350 Th r us t =0 . 9993 Ap l an=0 . 0001 Ob l a t =0 . 0061 Sphe r =0 . 0006
Ct r k (N= 4 Sump= 72 . 1 ) Eca l (N= 14 SumE= 23 . 7 ) Hca l (N= 9 SumE= 46 . 4 ) Muon (N= 1 ) Sec V t x (N= 0 ) Fde t (N= 0 SumE= 0 . 0 )
Run : even t 4302 : 75672 Da t e 930717 T ime 225034 Ebeam 45 . 610 Ev i s 121 . 9 Emi ss - 30 . 7 V t x ( - 0 . 04 , 0 . 04 , 0 . 29 ) Bz=4 . 350 Th r us t =0 . 9993 Ap l an=0 . 0001 Ob l a t =0 . 0061 Sphe r =0 . 0006
Ct r k (N= 4 Sump= 72 . 1 ) Eca l (N= 14 SumE= 23 . 7 ) Hca l (N= 9 SumE= 46 . 4 ) Muon (N= 1 ) Sec V t x (N= 0 ) Fde t (N= 0 SumE= 0 . 0 )
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Cen t r e o f s c r een i s ( 0 . 0000 , 0 . 0000 , 0 . 0000 )
Fig. 5.1: Event display ofτ decay in ther−φ plane. In the upper hemisphere of the left plot, a 3-prongτ decay can be seen. The lower hemisphere is a 1-prong decay. Details are given in the text. The right plot shows a zoom of the same event to region of the primary vertex. For the 3-prong decay, a displaced vertex is observed which is due to the lifetime of theτ lepton.
clusters reconstructed in the electromagnetic calorimeter. A maximum acollinearity angle of 15◦ is allowed for these cones. The tracks and clusters considered have to fulfill the following quality criteria.
• A good trackhas to have at least 20 hits in the jet chamber in order to guarantee a proper recon-struction of the trajectory. A maximum radial distance of the first measured hit ofrmax= 75 cm from the primary vertex is allowed. The point of closest approach has to be less thand0<2 cm away from the primary vertex. Inz direction the maximum distance is|zmax| = 75 cm. A minimum transverse momentum ofpT>0.1 GeV is required for each reconstructed track.
• A good cluster has to have at least one block with a minimum energy of Emin = 100 MeV if the cluster is reconstructed in the barrel part of the detector. A minimum of two blocks with an energy sum exceedingEmin= 200 MeV is required if the cluster is in the endcaps. In that case, the most energetic block must not contain more than 99% of the total total electromagnetic energy in the cluster.
In the following the individual sources of non-τ background are discussed and the selection criteria applied to remove them are explained.
q¯qEvents:
e
¯ q
e Z0/γ q
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The Z0 decays with a branching fraction of B = (69.91±0.06)% into a pair of quarks. A typical hadronic Z0decay can be seen in the event display above. Due to the high center of mass energy this results in a final state with two back-to-back jets of high multiplicity3and significant energy deposition in the electromagnetic and hadron calorimeters. The radiation of gluons off the final state quarks would result in additional jets. To remove hadronic events, the following cuts are applied.
3The average multiplicity of a hadronic events is of the order of 15.
– A maximum of two cones with half-angle of 35◦are allowed in the event. The energy in each cone has to exceed 1% of the beam energy.
– At least one ‘good’ track per cone is required. The maximum number of tracks in the event must not exceed six.
– A maximum of ten ‘good’ clusters in the electromagnetic calorimeter is allowed in the event.
Two Photon Events:
e+ e−
e+ f¯ f e− γ
γ
f ∈(e, µ, τ,q)
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In these events, a photon is radiated off each of the two initial state electrons/positrons. The interaction of these photons can produce either a leptonic or a hadronic final state. A typical two-photon event can be seen in the event display above. Since the energy of the two photons is different, the resulting final state is boosted. The event looks in general asymmetric. Furthermore, the energy of this final state is usually less than the beam energy, since the initial state particles escape undetected. The following cuts are applied to remove two-photon events.
– The maximum acollinearity angle allowed between the two cones in the event is 15◦.
– The event is removed if the visible energy in one of the cones is less than 3% of the beam energy.
– If the visible energy is in the range 3% < Evis <20%, the transverse momentum as calculated from tracks and clusters has to exceed 2 GeV.
Muon Pair Events:
e−
µ+ e+ Z0/γ
µ−
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In (3.366±0.007)% of all cases, the Z0decays into a pair of muons. The experimental signature is two high energetic (Eµ≈√
s/2 = 45.6 GeV) back-to-back tracks in the central detector, small or no energy deposition in the electromagnetic and hadron calorimeters and hits in the muon chambers which can be assigned to the tracks. A typical muon pair event can be seen in the event display above. The two muons are identified separately by requiring that at least one of the following criteria is fulfilled.
– The total energy deposited in the electromagnetic calorimeter must not exceed 2 GeV. A minimum ionizing particle on average deposits an energy ofE = 420 MeV in theOpallead glass calorimeter.
– The sum of the number of fired layers in the muon chamber and the last three layers of the HCAL must be larger than 5.
– At least two hits are found in the muon chambers.
If both muon candidates fulfill these requirements and if the sum of the energy measured in the jet chamber and in the electromagnetic calorimeter exceeds 60% of the center of mass energy, the event is identified as a muon pair.
e+e−→e+e− Events:
e−
e+ e+ Z0/γ
e−
e−
e+ e− γ
e+
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The experimental signature is two back-to-back high energetic tracks in the jet chamber with an energy close or equal to the beam energy. Since electrons are completely absorbed in the electromagnetic calorimeter, one high energetic cluster is expected per hemisphere, which can be assigned to the corresponding track. No or very little energy deposition is measured in the hadron calorimeter and no hits are expected in the muon chambers.
Two physics processes contribute to this final state. In the s-channel process, which is shown by the upper Feynman diagram, electron and positron annihilate to a Z0 or γ which then decays into an electron-positron pair. The angular distribution of the final state particles is ∝(1 + cos2Θ) like inτ pair events. In the t-channel process, where electron and positron are scattered by only a small angle via γ exchange, the angular distribution is peaking in forward direction. To remove this event type, the following cuts were applied.
– Barrel Region:
If the average|cos Θ|as calculated from tracks and the clusters in the electromagnetic calorimeter is less than 0.7 (barrel region), the average cluster energy in the event plus 30% of the average energy as calculated from the tracks has to be larger than 80% of the beam energy.
– Endcap Region:
In the endcap region the event is identified as a Bhabha event if the following criteria are not fulfilled:
∗ The average energy as calculated from the tracks is less than 80% of the beam energy and the sum of the track energy plus the average energy as measured in the electromagnetic calorimeter is less than 1.05 times the beam energy.
∗ The average energy as calculated from the tracks is greater than 80% of the beam energy and the average energy as deposited in the electromagnetic calorimeter is less than 25% of the beam energy.
Cosmic Muon Events:
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They are produced in the interaction of cosmic radiation with the atmosphere. They pass the detector from outside and leave one track in the jet chamber which will most probably be displaced from the primary vertex. For events in the central region of the detector (|cos Θ|<0.8) the information from the Time-of-Flight counter is used. Events from τ decays are required to contain at least one TOF counter that measures a time within 10 ns of that expected for a particle coming from the interaction point. In addition the time difference between the signals from two opposite4 modules is considered.
Events were rejected as cosmic rays if ∆t > 10 ns for all such pairs. If an event is not classified as being in the barrel region and does not satisfy the TOF acceptance criteria, it is required to contain at least one pair of tracks with
X|d0|<0.6 cm X|z0|<25 cm.
After the τ selection as described above, a total of 7.28% non-τ background events remain in the event sample. The Bhabha scattering events are recorded in the very forward direction (|cos Θ| > 0.9). The remaining background from µ-pairs is recorded at around |cos Θ| ≈ 0.8, which is in the overlap region between the barrel and the endcaps of the detector. The two-photon events that pass the τ selection are also predominantly in the forward direction (|cos Θ| ≥ 0.6). Since this analysis is restricted to the barrel region, their contribution is reduced to the permille level in the relevant range. The largest contribution to the non-τ background comes from q¯q events (6.28%). By requiring that in each cone the sum of the charges of all good tracks is±1 and that cones in opposite hemispheres have opposite net charge, this background is reduced to below 1%.