Simulation of the Calibration Procedure

Simulated events are used to test the calibration method. The simulation take account of target physics processes, spectrometer optics and detector resolution.

The simulation of target processes is based on SIMC, a physics simulation program for Hall C basic equipment experiment, adapted for HKS experiment. The ionization energy loss, Bremsstrahlung, multiple scattering and beam spread effects are included in the simulation. The simulation uses 5mm thick CH$_2$ target and 0.1 g/cm$^2$ Carbon target.

Simulated events from target are send through The spectrometers. RAYTRACE is used to simulate events in the electron arm. Since Raytrace data card is not available for the Kaon arm, the events are transfered from target to HKS focal plane by a 5-variable ($xtar$, $xptar$, $ytar$,$yptar$,$\delta p$), 6-order forward matrix. Only optical properties (no physical processes) are considered in this step.

At focal plane of the spectrometers, the positions and angles are smeared according to detector resolution and multiple scattering. For Enge, the resolutions ($\sigma$) are: 86 $\mu$m (x), 0.7 mr(xp), 210 $\mu$m(y), 2.8 mr(yp). For HKS, they are: 160 $\mu$m (x and y), 0.33 mr (xp and yp).

The simulated focal plane events are then reconstructed back to the target using backward reconstruction matrix. The beam energy and particle momentum are corrected by the average energy loss in the target. The corrections are 0.4923 MeV (beam energy), 0.6015 MeV (e' momentum), 0.4890 MeV (Kaon momentum) for CH$_2$ target, 0.0820 MeV (beam energy), 0.1026 MeV (e' momentum), 0.0866 MeV (Kaon Momentum) for Carbon target.

The simulated $\Lambda$, $\Sigma ^0$ and $^{12}_\Lambda$B missing mass spectra are shown in fig.3. The predicted $1^-$ state of $^{12}_\Lambda$B at 2.73 MeV is also included in the simulation for comparison. The quasi-free carbon background on CH$_2$ target is simulated with $\Lambda$ and $\Sigma ^0$ events by a assumed S/B ratio of 6:1 under $\Lambda$ peak. The $^{12}_\Lambda$B GS has a missing mass resolution of 397 KeV (FWHM) with correct optics.

The simulated Enge focal plane sieve slit correlation patterns are shown in fig.4. Fig.5 shows the yfp vs. xfp correlations for each X-column of sieve slit holes.

The simulated HKS focal plane sieve slit patterns are shown in fig.6.

Figure 3: Simulated $\Lambda$, $\Sigma ^0$ and $^{12}_\Lambda$B missing mass spectra with Carbon QF background from CH$_2$ target

Figure 4: Simulated Enge focal plane sieve slit correlation and hole patterns.

Figure 5: Simulated Enge focal plane $yfp$ vs. $xfp$ correlations for each X-column of sieve slit holes.

Figure 6: Simulated HKS focal plane sieve slit correlation and hole patterns.