Trigger

The total cross sections and trigger rates at the goal luminosity of cm$^{-2}$s$^{-1}$ for various physical processes of interest are listed in Table . We need to accumulate samples of Bhabha and events to measure the luminosity and to calibrate the detector responses, but, since their rates are very large, these trigger rates must be prescaled by a factor $\sim$100. Because of their distinct signatures, this should not be difficult. Although the cross section for physics events of interest is reasonably small, they can be triggered by appropriately restrictive conditions.

Because of the high beam current, high beam backgrounds are expected. Based on simulation studies, we expect $\sim$100 Hz from beam-related backgrounds which are dominated by spent electrons and positrons. Since the rates are very sensitive to actual accelerator conditions, it is difficult to make a reliable estimate. Therefore, the trigger system is required to be robust against unexpectedly high beam background rates. The trigger conditions should be flexible so that background rates are kept within the tolerance of the data acquisition system (max. 500 Hz), while the efficiency for physics events of interest is kept high. It is important to have redundant triggers to keep the efficiency high even for varying conditions. The Belle trigger system has been designed and developed to satisfy these requirements.

The Belle trigger system consists of the Level-1 hardware trigger and the Level-3 software trigger. The latter has been designed to be implemented in the online computer farm. Fig.  shows the schematic view of the Belle Level-1 trigger system [83]. It consists of the sub-detector trigger systems and the central trigger system called the Global Decision Logic (GDL). The sub-detector trigger systems are based on two categories: track triggers and energy triggers. CDC and TOF are used to yield trigger signals for charged particles. CDC provides $r$-$\phi$ and $r$-$z$ track trigger signals. The ECL trigger system provides triggers based on total energy deposit and cluster counting of crystal hits. These two categories allow sufficient redundancy. The KLM trigger gives additional information on muons and the EFC triggers are used for tagging two photon events as well as Bhabha events. The sub-detectors process event signals in parallel and provide trigger information to GDL, where all information is combined to characterize an event type. Information from SVD has not been implemented in the present trigger arrangement.

Figure: The Level-1 trigger system for the Belle detector.

Considering the ultimate beam crossing rate of 509 MHz ($\sim$2 ns interval) with the full bucket operation of KEKB [5], a "fast trigger and gate" scheme is adopted for the Belle trigger and data acquisition system. The trigger system provides the trigger signal with the fixed time of 2.2 $\mu$s after the event occurrence. The trigger signal is used for the gate signal of the ECL readout and the stop signal of TDC for CDC, providing $T_0$. Therefore, it is important to have good timing accuracy. The timing of the trigger is primarily determined by the TOF trigger which has the time jitter less than 10 ns. ECL trigger signals are also used as timing signals for events in which the TOF trigger is not available. In order to maintain the 2.2 $\mu$s latency, each sub-detector trigger signal is required to be available at the GDL input by the maximum latency of 1.85 $\mu$s. Timing adjustments are done at the input of GDL. As a result, GDL is left with the fixed 350 ns processing time to form the final trigger signal. In the case of the SVD readout the TOF trigger also provides the fast Level-0 trigger signal with a latency of $\sim$0.85 $\mu$s. The Belle trigger system, including most of the sub-detector trigger systems, is operated in a pipelined manner with clocks synchronized to the KEKB accelerator RF signal. The base system clock is 16MHz which is obtained by subdividing 509MHz RF by 32. The higher frequency clocks, 32MHz and 64MHz, are also available for systems requiring fast processing.

The Belle trigger system extensively utilizes programmable logic chips, Xilinx Field Programmable Gate Array (FPGA) and Complex Programmable Logic Device (CPLD) chips [84], which provide the large flexibility of the trigger logic and reduce the number of types of hardware modules.

Table: Total cross section and trigger rates with $L$ = 10$^{34}$ cm$^{-2}$s$^{-1}$ from various physics processes at $\Upsilon$(4S). Superscript indicates the values pre-scaled by a factor 1/100 and superscript indicates the restricted condition of 0.3 GeV/c.

Physics process	Cross section (nb)	Rate (Hz)
$\Upsilon$(4S) $B\bar{B}$	1.2	12
Hadron production from continuum	2.8	28
+	1.6	16
Bhabha ( $\geq$ 17$^o$)	44	4.4
( $\geq$ 17$^o$)	2.4	0.24
2$\gamma$ processes ( $\geq$ 17$^o$, 0.1 GeV/c)	$\sim$ 15	$\sim$ 35
Total	$\sim$ 67	$\sim$ 96