Monte Carlo parameter determination

In order to make a comparison with data, some parameters in the SMC code need to be determined, including (a) muon beam distribution, and (b) wire chamber position resolution. This was achieved using a pure H₂ layer. We have already discussed (a) in the context of determining the effective thicknesses (Section 6.1), where the beam distribution was determined from the MWPC image of the target region in the Ydirection. For the present analysis, a flat-top Gaussian beam distribution with a flat top radius R_flat of 10 mm and Gaussian FWHM_g of 10 mm (noted 1010 mm) was used.

 Because the target is extended in the Y direction, the Y image is rather insensitive to the wire chamber resolution parameter . We therefore used the Z image to determine $\sigma ^{WC}_{z}$ and assumed that had a comparable value. Note that we need not know too precisely because the Ydistribution is already broad and the Y image is not affected much by the choice of .

    

Figure 7.3: Determination of MWPC resolution parameters.

We have performed iterative fits of the Monte Carlo calculations to the data to find the best value for $\sigma ^{WC}_{z}$(Fig. 7.3). Plotted with error bars in Fig. 7.3 (a) is a Z image of MWPC system for a pure H₂ target, from which one expects no muonic atom emission except at very low energies [216]. A time cut of s (t₀being muon entrance time) is applied to eliminate the background from muon stopping in heavy elements in the target frames. The data was fitted in the interval shown in the figure with a Monte Carlo assuming $\sigma ^{WC}_{z} = 1.3$ mm with a beam parameter of mm (histogram). The normalization factor being the only free parameter, the fit gave DOF of 1.62 (10.3% confidence level).

Figure 7.3 (b) shows the result of an iterative fit, varying for two different beam parameters. Thus we conclude that the best value for the MWPC resolution parameters is mm with only a small dependence of the beam parameters.