Muon decay and imaging

The decay rate of a muon in muonic hydrogen is taken to be the same as that of a free muon ( s^-1), ignoring the small nuclear capture rate ( s^-1 [210]). When muon decay is selected as the reaction, an imaging routine is called to simulate the MWPC response.

Two MWPC planes (instead of three as in the actual experiment), as well as the copper thermal heat shield and stainless steel vacuum window, were defined in the program. The electron was generated isotropically (within a cone containing the MWPC planes) from the muon decay position, and passed through the shield and the window, where multiple scattering deflected the electron angle according to a Gaussian distribution with a width given by

where p, are the momentum and velocity of the electron, and x/X₀ is the medium thickness in radiation lengths [211]. The electron energy spectrum is approximated by

with MeV (normalization arbitrary). This is half of a Gaussian with FWHM of 50 MeV, displaced by 53 MeV, which is sufficiently close to the real spectrum for our purposes. When the electron track intersected with the ith MWPC at [x_i, y_i, z_i], the position was smeared in y-z plane by a Gaussian with a distribution of standard deviation , characterizing the finite resolution of MWPCs. The new positions [x_i, y'_i, z'_i] were fitted with a straight line, and extrapolated back to the perpendicular plane bisecting the target, similar to the way the real data was analyzed.