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 quirks

.

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:

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:

**All the hits lie on a plane**: Like planetary motions, angular momentum conservation implies that the quirky motions will be planar!**Magnetic fields and detector interactions are small**: magnetic fields and detector effects can in principle cause the quirks' motion to be non-planar. However, a quick computation shows that these effects are insignificant.

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

*d*_{cm} 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 *d*_{cm} is between 0.01mm to 1m, which corresponds to the interesting regime where the distance scale is measurable by the detector.