NeuroTrigger Goals

Motivation
The motivation for the trigger proposed here is to drastically increase the precision of the z-vertex. A typical resolution of around 1-2 cm would be required to reject more than 80% of the non-vertex background events (see Fig. 1).

Distribution of the z-position of reconstructed vertices in Belle[1].

Figure 1. Distribution of the z-position of reconstructed vertices in Belle [1]. The z-axis is parallel to the beam. The peak at z = 0 cm corresponds to signal decays, the wide background is due to the Touschek effect and beam-gas interactions. The second peak at z ≈ −10 cm is an artifact of the bunch structure of the beam.

This target precision, however, must be reached at the first trigger level. This means that the proposed trigger must be executed in a pipelined deadtime-free manner within the required latency of the first trigger level, i.e. within a maximum of 3 \mus. The crucial step forward in the proposed approach is to use also the drift time in addition to the topological information of the priority wire in the track segments. This is naturally suited to increase the space point precision by roughly an order of magnitude. Neural networks are good candidates for the implementation of the trigger in hardware, but other possibilities will be explored as well.

Benefits
As is shown in Fig. 1, the dominant fraction of the triggered events in Belle indeed comes from regions outside the collision point. These events have passed the first trigger level due to their signatures which are in accordance with the “wanted” physics events. While at later trigger stages with more detailed track reconstruction such events can be clearly rejected to avoid the spamming of the data storage, the problem of the background triggered at the first level (L1) lies in the fact that by technological limitations this rate cannot exceed certain bounds. For example, the first trigger level for Belle II has to be limited to an output rate of about 30 kHz. If this bound is exceeded, the trigger conditions have to be tightened, which risks cutting strongly in certain physics channels. The channels most in danger of being lost in Belle II are described in physics validation. Another aspect of excessive background passing L1 is the increased deadtime for the experiment, reducing the useful luminosity. Note that deadtime starts as soon as L1 is asserted. Depending on the readout time of the detector, the overall deadtime may increase drastically when the L1 rate becomes too high. Both these effects, lowering the thresholds to open up for physics, and reducing the deadtime as much as possible to optimally use the luminosity provided by the machine, are usually mutually exclusive. The best way to master this dilemma is to optimize L1 to reduce the background already at this first deadtime-free level as much as possible. For the case of Belle II, a straightforward calculation using the drift times of the axial and stereo wires of the CDC shows that a vertex resolution of 1-2 cm can be reached, sufficient to reject most of the non-vertex background. Another interesting application of our new track trigger concept is the identification of secondary vertices in an event. Such a scheme would be extremely useful for the LHC detectors. Secondary vertices from heavy quark decays provide unique signatures for certain classes of new (or even old) physics, such as top and Higgs production, or of new heavy states decaying into long-lived SM particles. In either case, triggering on a clear (transverse) offset of the secondary vertex from the primary greatly reduces the background from “uninteresting” QCD events. For the LHC application, however, the precision of the silicon detectors would be needed. While at present, semiconductor technology is not yet in a position to provide fast signals for the first trigger level, there are new ways on the horizon (“3D technology”) which could eventually be used in future upgrades of the silicon systems in the LHC detectors.

Main Goal
The main goals to be accomplished in this research project are to develop algorithms that find the relevant sectors in a given event and to establish a hardware realization for this “sector finder” and the subsequent (neural or otherwise) computational machinery which guarantees the fixed latency required for L1, in conjunction with a sufficient precision of the estimated z-vertex. Although we have shown that neural networks for this kind of machinery are up to this task in principle, we intend to explore also other approaches in order to find an optimal solution within the constraints of performance and financial viability. The research strategy for identifying and implementing possible solutions will be presented in the following.

Sector finding
Sector finding is the first part of the z-vertex trigger. Dividing the phase space into sectors is necessary to limit the number of input channels for the vertex reconstruction method to a manageable level. We determine the geometrical parameters of the tracks in the event
and then for each track select the appropriate sector. Using information from the 3D finder is impossible, as there is no time for additional computation within the L1 latency. The starting point will therefore be the existing 2D track finder of the CDC, which performs a conformal transformation, followed by a Hough transform track finder using the axial layers of the CDC. Since it is far from obvious that the track parameters produced by the Hough transform are sufficiently precise, we will evaluate its performance and explore possible improvements if necessary. In the next step, the stereo wires have to be matched to the 2D track candidates, producing estimates of the polar angles of the tracks. We will explore several approaches to this problem, which could be based for example on pre-computed neighborhood relations. In a final step, the tracks are sorted into the predefined sectors according to their track parameters. The definition of the sectors will depend critically on the resolution of the track parameters and the method chosen for the reconstruction of the z-vertex.

Vertex reconstruction
Once the sectors associated to the track candidates have been found, the z-positions of their respective point of origin (vertex) have to be estimated. The estimation algorithm has to respect the timing constraints and must be suited to an implementation on specialized hardware . Statistically optimal methods such as least-squares estimation are too slow, and a compromise between precision and speed will have to be found. Preliminary studies have shown that there are promising candidate algorithms based on MLPs (see Proof of Principle).
The basic principle of the actual reconstruction of the z-vertex is to feed the drift times of all relevant priority wires within a given sector into the multivariate method of choice. This will require extensive optimization work and training of a large number of MLPs or similar estimation machines. As the training relies on simulated data sets, validation and robustness will be a major concern. Some preliminary work on the robustness has already been done and can serve as a starting point for further studies [8]. In addition to the z-coordinate of the vertex, the z-vertex trigger should also provide a quality indicator. Track candidates with poor quality should then get less weight in the final decision whether to issue a veto or not. The optimization and the final evaluation of the various approaches with respect to performance and timing is a critical part of the work. The robustness against the assumptions made in the simulation will be confirmed by appropriate sensitivity studies.

Proof of Principle
In order to show that a sufficiently precise z-vertex reconstruction is possible at L1, we have adopted a neural network approach applied to single tracks. We use a multi-layer perceptron (MLP) with an input layer of typical size 20, one hidden layer of typical size 60, and a single output node yielding the value of the “reconstructed” z-vertex of the track. The priority wires of the “firing” TSs from the 9 superlayers are arranged topologically in the input layer, with the individual drift times as the input values. We have trained networks with single tracks taken from narrow regions in polar and azimuth angle (\theta and \phi) as well as in a limited region of transverse momentum (p_T). A region defined by (\theta, \phi, p_T) is called a “sector”. The priority wires used in the training were taken from the chosen sector. Trainings with simulated tracks in various sectors showed that the required z-vertex resolution can indeed be achieved [7] by this method (see Fig. 5).

possible z vertex resolution

Figure 5. Achieved z-vertex resolution [7] with MLPs for charged single track events in a small sector constrained by the track parameters \phi \in [0, 1]^{\circ}. Left plot: low momentum tracks with transverse momentum p_T = 0.2 GeV, right plot: high momentum tracks with p_T = 7 GeV.

The generalization of this proof of concept to the full acceptance region of the detector requires a pre-processing that can select the correct sector for each track in the event.

Physics validation
The purpose of the z-vertex trigger is to suppress background events, which typically have a small number of tracks. It will therefore not be activated for events in which the number of tracks is above a certain threshold. Below this threshold, it has to be guaranteed that physics topologies with a small number of tracks are not rejected. One of these topologies is the very interesting decay \tau \rightarrow \mu \gamma [9], where the other \tau decay contains only one charged track, leaving us with only two tracks in the full event. Another topology in the B physics sector is the decay of a B meson into two neutrinos [10], while the other one decays via B \rightarrow D^{*+} l^- \nu with D^{*+} \rightarrow D^0 \pi^+ and D^0 \rightarrow K^+ \pi^- . The pion of the D^{*+} decay will often not be recognized in the CDC due its low momentum, so that only three tracks remain. The two neutrino decay of the B meson is of moderate physics interest itself, but is selected as a test case as a conservative mimic of decays with just one charged track like B \rightarrow h \nu \nu [11], B \rightarrow l^+ \nu [12, 13], and others. Other channels with few tracks will be studied if they are of interest to the physics program of Belle II.

Maintenance and Monitoring
The z-vertex trigger is intended to operate for the entire lifetime of the experiment, i.e., at least until 2022. Due to the increasing luminosity, we have to anticipate changing beam and background conditions. The performance of the CDC may also change, for better or worse, during the data taking periods. It is therefore crucially important to develop user-friendly tools that allow physicists who do not belong to the development team to quickly adapt the trigger to the actual circumstances and conditions. If a neural machinery is adopted, fast retraining of a large number MLPs has to be possible. Equally important are monitoring tools that allow a fast assessment of the trigger performance. The development and commissioning of these tools will be a significant part of the software aspect of the project.