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Dimuon events

A sample of e⁺e^- $\rightarrow$ Z⁰(n$\gamma$), Z⁰ $\rightarrow$ $\mu^{+}_{}$$\mu^{-}_{}$ events was also selected to study the probability of having off-energy electrons in VSAT. In this study the 1998 data² was used and the selection criteria was optimised with the help of a KORALZ4.2 [4] Monte Carlo sample³.

To suppress the background, which was mainly due to cosmic muons, it was required that:

1. Two muons were found, one positive and one negative, with no other particles in the event. The muons should be identified as ``very loose'' or better.
   
2. The energy of each muon should be 10 < E_$\mu^{\pm}$ < 125 GeV.
   
3. The azimuthal angles were required to fulfil ||$\phi_{\mu ^+}^{}$ - $\phi_{\mu ^-}^{}$| - 180⁰| < 3⁰.
   
4. Both muons should come from the primary vertex ( Q(LPV+4)=0 ).
   
5. The transverse momentum of the muons should have p^T_gt > 35 GeV/c , where p^T_gt $\equiv$ max(p^T_$\mu^{+}$, p^T_$\mu^{-}$).

Figure 7: Distributions of E_tot, $\theta_{\mu ^-}^{}$ and $\phi_{\mu ^-}^{}$ . Points represent data and the hatched histograms represent MC. The top row of plots shows events which fulfil conditions 1, 2 and 3 and the bottom row those fulfilling conditions 4 as well.

The upper three plots in Figure 7 show the distributions of E_tot, $\theta_{\mu ^-}^{}$ and $\phi_{\mu ^-}^{}$ after conditions 1, 2 and 3 were satisfied. At this stage 4741 events remained, with 495 expected. The angular distributions had broad peaks at $\theta$ $\approx$ 90⁰ and around $\phi$ = $\pm$90⁰ which were not predicted by Monte Carlo. The reason is of course the large contamination of cosmic muons. Many of the cosmic events can be rejected by the requirement on the primary vertex (condition 4). The bottom three plots in Figure 7 depict the distributions of E_tot, E_$\mu^{+}$ and p^T_gt  after the vertex cut. 800 events remained in the data with an unchanged number of expected events.

The last cut on p^T_gt removes softer muons coming from e⁺e^- $\rightarrow$ $\gamma^{*}_{}$(n$\gamma$),$\gamma^{*}_{}$ $\rightarrow$ $\mu^{+}_{}$$\mu^{-}_{}$, $\gamma$$\gamma$ collisions or Z⁰ $\rightarrow$ $\tau^{+}_{}$$\tau^{-}_{}$  events. After this cut 369$\pm$19 events remained in the data, with 408$\pm$7$\pm$3 expected from the Monte Carlo study (the second error is due to the uncertainty in the cross section). Good agreement between data and predictions was obtained, as can be seen in Figure 8, which shows different angular distributions such as the polar angle of each muon ( $\theta_{\mu^\pm}^{}$ ), the sum of polar angles ( $\theta_{\mu ^+}^{}$ + $\theta_{\mu ^-}^{}$ ) and the difference in azimuthal angles ( |$\phi_{\mu ^+}^{}$ - $\phi_{\mu ^-}^{}$| ). The total energy ( E_tot = E_$\mu^{+}$ + E_$\mu^{-}$ ) and invariant mass of the muons ( W = $\sqrt{{E_{tot}}^2 - (\vec{p}_{\mu^+}+\vec{p}_{\mu^-})^2}$) are also presented in Figure 8. The overall impression from the data-Monte Carlo comparison is that the efficiency is somewhat too high in the simulation and that the energies are slightly high.

Figure: 8 Distributions of polar angle ( $\theta_{\mu ^+}^{}$ and $\theta_{\mu ^-}^{}$ ), the sum of polar angles ( $\theta_{\mu ^+}^{}$ + $\theta_{\mu ^-}^{}$ ), the difference of azimuthal angles ( |$\phi_{\mu ^+}^{}$ - $\phi_{\mu ^-}^{}$| ), and the total energy of the muons (E_tot ) and their invariant mass (W ).

Out of the 417 selected events, only 18 had an electron in the VSAT. In all of these events, only one module scored a hit. The energy measured by VSAT was corrected using the offline VSAT programs. The total probability and probabilities for each module derived from this sample are shown in Table 3.

Figure: 9 Distributions of E_tot, $\theta_{\mu }^{}$ and $\phi_{\mu }^{}$  for events fulfilling conditions 1-4.

Table 4: The probability of an off-energy electron with energy greater than E_min in the four different VSAT modules. The measurement was done with cosmic muon events.

Emin [GeV]	NVSAT	$\cal {P}$ [%]	$\cal {P}$1[%]	$\cal {P}$2[%]	$\cal {P}$3[%]	$\cal {P}$4[%]
15	113	2.1 $\pm$ 0.2	0.9 $\pm$ 0.1	0.15 $\pm$ 0.05	0.9 $\pm$ 0.1	0.11 $\pm$ 0.05
50	94	1.7 $\pm$ 0.2	0.7 $\pm$ 0.1	0.09 $\pm$ 0.04	0.8 $\pm$ 0.1	0.11 $\pm$ 0.05
60	84	1.6 $\pm$ 0.2	0.7 $\pm$ 0.1	0.04 $\pm$ 0.03	0.8 $\pm$ 0.1	0.09 $\pm$ 0.04
70	75	1.4 $\pm$ 0.2	0.6 $\pm$ 0.1	0.04 $\pm$ 0.03	0.7 $\pm$ 0.1	0.08 $\pm$ 0.04
80	31	0.6 $\pm$ 0.1	0.19 $\pm$ 0.06	-	0.35 $\pm$ 0.08	0.04 $\pm$ 0.03