My favorite research project at UC Berkeley. I developed a new algorithm that can extract a small signal — involving 16
hits— hidden in a sea of thousands of
hits. The algorithm was published in Physical Review , and solved a long standing problem on how to detect new hypothetical particles called
One of the main goals of fundmental physics is to discovery new particles and forces. To this end, physicists collide protons and study what comes out, in hopes of catching a glimpse of new particles. However, there are many plausible ways new particles and forces and manifest in an experiment and some are particularly difficult to detect.
Quirks are one such example: they are heavy hypothetical particles that interact with each other (but not to ordinary particles) through a new strong and long-range force. When produced, quirks come in a quirk and an anti-quirk pair. The pair of quirks is connected by an invisible quantum mechanical string, which tugs and pulls the quirks at the end, leading to an intricate and quirky dance. Such quirky behavior makes them difficult to detect in a experiment, as traditional detection methods rely on the assumptions that particles move in a helicial track under a magnetic field.
Here's what quirks might look like:
The animation shows the trajectories of quirks, produced when two beams of protons collide (coming from the top and bottom). The concentric cylinders depict an sample set of particle detectors. The length scale of the figure is roughly 1m x 1m, and 1s animation time corresponds to 1ns lab time.
A simulated proton-proton collision event at the ATLAS experiment. The full particle trajectories are not directly measured; rather, particles pass through the cylindrical detectors and individual
hits are recorded. The colored dots represent random hits due to production of un-interesting particles. The black dots represent hits from the quirks. There is no simple way to distinguish which hits come from which particles!
Particle detectors track particles by having layers of materials (such as Silicon) that particles can pass through. Each time a particle hits the detector, a
hit (essentially a point in space) is registered. Typically only charged particles can be tracked, and these particles follow helices under a static magnetic fields. Thus, particle trajectories are obtained by fitting helices to hits. Unfortunately, quirks do not follow helical paths! and they will simply result in un-fitted hits, which will be discarded and ignored. A pair of quicks going through a few layers will typically only leave a handful of hits. So then, how do we find efficient algorithms for reconstructing the motions of quirks when there are thousands of unfitted hits in a typical proton-proton collision event?
The crux of solving the problem, it turns out, is to not try to fit the quirks' trajectories, but rather understand and extract the hit-patterns using physics principles. The two key observations are:
Then, mathematically, the problem of finding the trajectories of quirks becomes finding hits that lie on the same plane. In proton collisions, the collision point is fairly well measured, thus the
origin of the plane can be defined. As shown in my paper, the problem of plane-fitting can be translated to finding eigenvalues of a simple 3x3 matrix. Thus, quirks tracking is reduced to solving many matrix eigenvalue problems. Still, some adaptive strategy is needed, as one does not know in advance which hits belong to the quirks, and most of the hits are simply noise. A brute force method would require looping through all possible hit combinations, which will be very computationally intensive. By observing that the quirks-pair tends to be close to each other and follow a straight line on average, I showed that a fast adaptive plane-fitting algorithm can be implemented to run on O(N) time, a substantial reduction in computational complexity. Such a technique is similar to edge detection algorithms in image-processing.
After implementing our simulations (using python and Mathematica), I applied my adaptive plane-fitting algorithm, and showed that the algorithm can indeed find the plane of the quirks' motions
The plot shows the distribution of the residuals (a measure of goodness-of-fit) of my adaptive plane-fitting algorithm. A requirement of having at least 15 hits in 8 layers of detector is imposed. The resolution of a tracking detector is roughly 0.01cm, and the purple and red line show that for two sample signals, my algorithm can find a suitable plane with a small residual. The green and blue lines show the results for running the algorithm for background samples. The residuals here are much larger as backgrounds mostly lead to random hits that do not lie closely on a plane. Requiring a small residual can effectively remove all backgrounds.
The figure illustrates the theory space of a basic quirk model, where (anti)quirks have charge +1 (-1). The x-axis is the mass of the quirk, while the y-axis is the strength of the hidden quirky force (larger value means stronger). dcm shows contours of the average width of the quirks motions. The left of the light red (purple) line indicates regions where quirks may be discovered (excluded) in the near future by the ATLAS experiment. My algorithm works when dcm is between 0.01mm to 1m, which corresponds to the interesting regime where the distance scale is measurable by the detector.