Momentum and angular resolution

The position of the first chamber and distance between two chambers are determined by optimizing two factors: angular resolution due to the drift chamber position resolution and the multiple scattering. As a result, the two chambers are placed at 50 cm upstream and 50 cm downstream from the first order focal plane (235 cm downstream from the dipole exit).

Table 8 shows the materials assumed in the simulation. >From the target to the exit of the dipole vacuum chamber (just before the first chamber) is vacuum.

The simulation was performed in following procedures:

1. A GEANT simulation was performed with idealistic wire chambers (resolution = 0) without any multiple scattering effects.
2. In order to construct the function which associates the kaon momentum and chamber hit positions, the generated events were fitting with a code based on the principal component analysis (ERIKA).
3. The GEANT simulation was carried out with finite wire chamber resolution and/or with multiple scattering effects. The chamber hit positions were associated with the particle's momentum by the functions obtained from the fitting of the idealistic events. Using the obtained momentum and the known initial momentum, since the generator code produced, were compared to estimate the resolution affected by the simulated effects.

Figures 12 and 13 show respectively the wire chamber resolution (per plane) dependences of the HKS momentum resolution and angular resolution obtained by the simulation. A finite resolution is obtained even for idealistic chambers without multiple scattering events, because the principal component analysis takes only finite number of terms. The result is summarized in table 9.

表 8: List of materials and their properties used in the simulation

Item	$t$	$\rho$	$X_0$	thickness (/radiation length)
	(cm)	(g/cm$^3$)	(g/cm$^2$)
Dipole Exit Window
Kevlar(C$_{14}$N$_2$O$_2$H$_{10}$)	0.02	0.74	55.2	2.68 ${\times}10^{-4}$
Mylar(C$_{10}$O$_4$H$_8$)	0.01+0.0025	1.39	39.95	4.35 ${\times}10^{-4}$
HDC1
Mylar	0.012	1.39	39.95	4.18 ${\times}10^{-4}$
Ar gas	5.08	1.78 ${\times}10^{-3}$	19.55	4.63 ${\times}10^{-4}$
HDC1-HDC2 gap
He gas	100	1.79 ${\times}10^{-4}$	94.32	1.68 ${\times}10^{-4}$
HDC2
Mylar	0.012	1.39	39.95	4.18 ${\times}10^{-4}$
Ar gas	5.08	1.78 ${\times}10^{-3}$	19.55	4.63 ${\times}10^{-4}$

表 9: Momentum and Angular resolution

Materials	Chamber resolution	$dP$	$d(dx/dz)$	$d(dy/dz)$
	($\mu$m/plane)	(keV/$c$)	(mr)	(mr)
None	0	51	0.04	0.2
He bag only		52	0.05	0.4
DC Ar only		68	0.11	1.1
DC window only	0	65	0.11	1.0
Dipole window only		82	0.15	1.7
Full		97	0.23	2.4
Full	200	112	0.28	2.9

The simulation shows a momentum resolution of 2 $\times 10^{-4}$ FWHM ($\sigma$ = 110 keV/$c$) and an angular resolution of 0.3 mr (horizontal) and 3 mr (vertical) for the chamber position resolution of 200 $\mu$m (rms) per plane.