Abstract
In this chapter, details of the analysis are described in order. The missing mass of the \(\pi ^-p \rightarrow K^-X\) reaction is calculated by reconstructing particle tracks in both the beam and SKS spectrometers. The missing-mass resolution for the \(\varTheta ^+\) was estimated to be \(2.13\pm 0.15\) MeV (FWHM). Using the \(\varSigma ^{\pm }\) production data and the beam-through data, the absolute scale of the missing mass for the \(\varTheta ^+\) production data was calibrated with an uncertainty of 1.4 MeV/\(c^2\). Thus, it is demonstrated that we are able to observe a sharp missing-mass peak and determine the mass and, possibly, width with a good precision, if the \(\varTheta ^+\) is produced. The cross section was calculated by correcting the data for the experimental efficiency and acceptance with an uncertainty of 7 %. The measured differential cross sections of the \(\pi ^{\pm }p \rightarrow K^+\varSigma ^{\pm }\) reactions were in good agreement with the past experimental data.
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- 1.
This value is the one obtained after applying the momentum scale calibration described in Sect. 3.6.3.
- 2.
The zeroth order coefficient of the function was not used for the correction because it corresponds to the absolute momentum scale which should be calibrated later in Sect. 3.6.3.
- 3.
The covariance between a and b (\(-1.39 \times 10^{-5}\)) was also taken into account.
- 4.
The scattering angle term was negligibly small in previous hypernuclear experiments using SKS because of the large target mass M; however, the term is not negligible in hadron production reactions.
- 5.
In the region near the pole edge and the coil of the SKS magnet, the calculated field value deviated from the measured value in \(10^{-2}\), whereas the deviation was within \(10^{-3}\) in the central region [9].
- 6.
\(\theta _\mathrm{SKS}\) is almost the same as the scattering angle and does not depend on the beam direction.
- 7.
The inner (outer) track corresponds to the events scattered to left (right) at the target in Fig. 2.6.
- 8.
The differential cross sections in the c.m. frame are presented in Appendix D.
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Moritsu, M. (2016). Data Analysis. In: Search for the Pentaquark Θ+ via the π−p → K−X Reaction at J-PARC. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-0012-6_3
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DOI: https://doi.org/10.1007/978-981-10-0012-6_3
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