10.2 Material Effect

We studied the effect of the detector material to the muon detector. Table 10.1 summarizes the amount of material of the standard JLC detector in front of the return yoke and in the return yoke itself at $\theta = 90^{\circ }$. The muon momentum is required to be more than 2.2 GeV to reach the return yoke, and to be more than 5.2 GeV to fully penetrate the return yoke.

 

Table 10.1: Material thickness of the detector at $\theta = 90^{\circ }$. Those in front of the return yoke, in the return yoke itself, and the total thickness are listed.

	In front	Return Yoke	Total
Weight	1.09 kg/cm2	1.51 kg/cm2	2.60 kg/cm2
Radiation length	158 X0	109 X0	267 X0
Interaction length	5.6 $\lambda_0$	11.2 $\lambda_0$	16.8 $\lambda_0$

Multiple scattering due to the material in front of the muon detector is simulated by JIM [2], the full simulation program of the JLC detector. In the simulation, muons are generated at the interaction point with a momentum of (p_x , 0, 0) where the +z direction is along the electron beam. The hit positions at the inner surface of the return yoke (x=500 cm) are recorded.

  

Figure 10.2: Distributions of the z-coordinate at the return yoke surface (a) $p_{\mu }=5$ GeV, (b)  $p_{\mu }=10$ GeV, (c)  $p_{\mu }=20$ GeV, and (d)  $p_{\mu }=50$ GeV.

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Figure 10.3: (a) The standard deviation of the z-coordinate at the return yoke surface as a function of the muon momentum, and (b) the distribution of the muon momentum in the b-quark pair production at s=500 GeV.

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Fig. 10.2 shows the distributions of the z-coordinate for muons with initial momentum of 5, 10, 20, and 50 GeV. The distributions of the y-coordinate are very similar to those of the z-coordinate. Fig. 10.3(a) shows the standard deviation of the z-coordinate ($\sigma_z$) due to multiple scattering as a function of the muon momentum. This result is similar to that obtained for the TESLA detector [3]. Fig. 10.3(b) shows the momentum distribution of muons in the b-quark pair production at $\sqrt {s}=500$ GeV. As seen in this histogram the majority of muons have momentum below 50 GeV, for which $\sigma_z$ is larger than 1 cm. We thus conclude that the position resolution of about 1 cm is sufficient for the muon tracking device.