Finding Unexpected Non-Helical Tracks

Abstract

Many theories of physics beyond the Standard Model predict particles with non-helical trajectories in a uniform magnetic field, but standard tracking algorithms assume helical paths and so are incapable of discovering non-helical tracks. While alternative algorithms have been developed for specific trajectories, unforeseen physics could lead to unanticipated behavior, and such unexpected tracks are largely invisible to current algorithms, despite being potentially striking to the naked eye. A model-agnostic tracking algorithm is presented, capable of reconstructing a broad class of smooth non-helical tracks without requiring explicit specification of particle trajectories, instead defining the target trajectories implicitly in the training sample. The network exhibits strong performance, even outside of the trajectories defined by the training sample. This proof-of-principle study takes the first step towards searches for unexpected tracks which may await discovery in current data.

Figures (10)

• Figure 1: Trajectories (blue) and hits (red) for tracks with 1 (top left), 2 (top right), 4 (bottom left), or 25 (bottom right) Fourier modes, where the 25-mode track follows a Schwartz function to ensure smoothness. Shown are the $x-y$ (top) and $r-z$ projections.
• Figure 2: An example of a Schwartz function (red), which enforces a falling upper limit on amplitude as frequency grows, guaranteeing smoothness if amplitudes are selected (green dots) below the upper limit.
• Figure 3: Shown are the distributions of number of hits per generated track depending on the number of frequency modes used in the trajectory generation.
• Figure 4: Visualization of tracks generated in disjoint spaces defined by three example Schwartz functions A,B,and C. In green are Fourier coefficients generated under the red curve. In yellow are the coefficients generated between the blue and red curves. The two resulting tracks cannot have the same Fourier representation, and must be different.
• Figure 5: Examples of tracks generated in the 6-5 space defined in the text.