The Neural Network First-Level Hardware Track Trigger of the Belle II Experiment

We describe the principles and performance of the first-level ("L1") hardware track trigger of Belle II, based on neural networks. The networks use as input the results from the standard Belle II trigger, which provides "2D" track candidates in the plane transverse to the electron-positron beams. The networks then provide estimates for the origin of the 2D track candidates in direction of the colliding beams ("$z$-vertex"), as well as their polar emission angles $\theta$. Given the $z$-vertices of the "neural" tracks allows identifying events coming from the collision region ($z \approx 0$), and suppressing the overwhelming background from outside by a suitable cut $d$. Requiring $|z| < d$ for at least one neural track in an event with two or more 2D candidates will set an L1 trigger. The networks also enable a minimum bias trigger, requiring a single 2D track candidate validated by a neural track with a momentum larger than 0.7 GeV in addition to the $|z|$ condition. The momentum of the neural track is derived with the help of the polar angle $\theta$.