| Summary: | 碩士 === 國立臺灣大學 === 物理學研究所 === 106 === The Belle experiment at the KEKB collider in Tsukuba, Japan is a B meson factory designed to operate at a center-of-mass energy of 10.58 GeV, the mass value of Υ(4S). It is undergoing an upgrade that will boost its instantaneous luminosity to 8×10^35 cm^−2 s^−1 (40 times higher than before), whereas the maximum acceptable event rate for the data acquisition system is only 30kHz. Most of the detector responses arise from the scattered particles with other particles in the accelerated bunch, or with the residual gas molecules in the vacuum beam pipe. Furthermore, only a few percent of the total number of e+ e− collisions correspond to Υ, B or τ events. The rest are considered backgrounds and must be either suppressed or prescaled in real time without losing too many signal events. To achieve this goal, a hardware-based online trigger system with good background suppression, high efficiency, low latency and no dead time is indispensable.
In experimental particle physics, tracking refers to the pattern recognition process that searches for the trajectories of charged particles by analyzing the traces they leave on the detector. Once the trajectory, or the track, is reconstructed, the momentum and the charge is also determined. High-precision tracking provides crucial information for telling signals from backgrounds, since most background events don''t produce charged particles with enough transverse momenta near the collision point. As a result, the track trigger in Belle II is redesigned to accommodate the dramatic increase of luminosity and background rate.
The track trigger starts from relating adjacent wire hits in space and in time from a drift chamber, grouping them into maximally 9 segments of a track. Out of the 9 segment hits, 5 are groups of sense wires parallel to the beam axis, and thus their positions contain information of the track projected onto the 2-dimensional plane perpendicular to the beam axis. The track trigger then detects the coincidence of several axial track segments by transforming their radial and angular positions to a parameter space with a conformal map followed by a Hough map, and looking for their intersections there. Each segment in one layer of the detector cylinder contributing to the track is extracted. Afterwards, it fits these positions with the drift length, and reconstructs the track''s projection in the plane perpendicular to the beam axis. Finally, by combining the 2D track information with the remaining track segments which contains the information of longitudinal position, the vertex position along the beam axis is reconstructed. Each of these steps is a separate module in the track trigger system. This thesis focus on implementing the steps of finding and reconstructing the 2D track using an algorithm developed by our collaborator.
The 2D tracker module is implemented on 4 printed circuit boards with field programmable gate array (FPGA) and 10 Gbps optical I/O connection to both upstream and downstream modules. It has a latency of 11 data clocks (352 ns) excluding the transmission time. The lower bound of the 1-σ confidence interval of its tracking efficiency is measured to be more than 98% for cosmic ray tracks with radial impact parameters smaller than 1 cm, pt > 0.5 GeV, with at least 4 track segment hits, and coming from regions with expected track segment finding efficiency.
This thesis also outlines the implementation of the 2D fitter, which involves fitting an arc to the positions of the axial track segment hits corrected by their drift lengths. As the fitting contains many fixed-point arithmetic operations implemented as look-up tables, it is crucial to reduce the usage of the block RAM while maintaining similar arithmetic precision. Composite look-up tables, which increase the precision in the worst-performing part of the arithmetic function''s range by sacrificing the unnecessary precision in other parts, are developed to meet the requirement. Lastly, several improvements are made to stabilize the buildup process of the optical transmission data flow. In particular, an automatic way to reset different optical transceivers on the same side of the die, separated with an adjustable time interval, is tested to make the buildup more stable at the full 10 Gbps lane rate.
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