Speaker
Description
Mathematical methods for reconstructing the spatial resolution of multilayer position-sensitive detectors designed to register fast charged particles are considered. It is assumed that reference detectors with known resolution are not available. Therefore, it is necessary to obtain measurement errors from measurements with unknown errors.
Typically, the assumption of equal resolutions is used, as in Refs. [1,2] and many others. This approach greatly simplifies the calculation, but prevents a more detailed study of the detectors.
A more sophisticated approach is proposed in Ref. [3]. It allows one to find layer resolutions individually, even if they are different, but does not work for detectors with less than five detecting layers. However, there are many experiments, including one planned at PNPI [4], with detectors consisting of fewer layers.
A more general approach presented in this report uses track fitting with arbitrary weights of hits and uses not only variances of residuals but also covariances of residuals. Although no solution has been found to obtain individual resolutions of four fixed layers, many useful values can be obtained. The exact average resolution of four layers (that is the square root of the average of four variances of layer resolutions) can be obtained for four-layer detectors with symmetric gaps between layers. The exact average resolutions of two outer and two internal layers can also be obtained in this case. If the detector is not symmetric, one can find approximate averages described above. If the resolutions of outer layers are close to each other, one can also obtain the approximate individual resolutions of two internal layers with very good precision.
Moreover, if the layers can be rearranged or moved, individual resolutions of all detecting layers of four-layer and three-layer detectors can be obtained.
The recently proposed geometric mean method, see Ref. [5] and some other publications, does not provide any additional information.
References
- G. Charpak et al., Nucl. Instr. Meth. 167 (1979) 455.
- F. Piuz et al., Nucl. Instr. Meth. 196 (1982) 451.
- R. Fruhwirth, Nucl. Instr. Meth. A243 (1986) 173.
- A.A. Vorbyev, Phys. Part. Nucl. Lett., 16 (2019) 524.
- R.K. Carnegie et al., Nucl. Instr. and Meth. A 538 (2005) 372.
