The Search for New Physics: Identifying rare electron-to-tau conversions at the future Electron-Ion Collider

This project relates to physics at the proposed U.S. Electron-Ion Collider EIC. The EIC will collide electrons with protons (and nuclei) to explore the inner workings of protons, neutrons, and nuclei at an unprecedented level of detail. In addition, it has the potential to find “new physics”, i.e. phenomena that might exist in nature but have never been observed before. This project focuses on identifying one of these new phenomena in Monte Carlo simulations with the current design for an experiment at the EIC and distinguishing it from background events.

Charged Lepton Flavor Violation- A possible signal of New Physics

There are some quantities, like energy and momentum, that are conserved in all physics processes. Noether’s theorem states that all such conserved quantities are related to a symmetry of the physical system.

An interesting quantity to measure in an experiment is the number of charged leptons of different flavors: electron, muon, and tau. All measurements done at past and present experiment are consistent with a conversation of the number of the respective charged leptons. In other words, charged leptons keep their identity in all interactions observed so far. However, there is no known symmetry that would require this conservation. In fact, lepton flavor changes have been observed for neutral leptons, the neutrinos. Therefore, it is exciting and promising to also look for charged lepton flavor changes.

Identifying taus at the EIC would allow to search for the conversion of electrons into taus (which are heavier versions of electrons) at this facility. While the Standard Model does not explicitly forbid this process, the rates that would be consistent with the Standard Model are so low that they are way out of the reach of all past, present, and planned experiments, including the EIC. Therefore, actually measuring charged lepton flavor changes would be signal of Physics beyond the Standard Model.

But, it is challenging to identify with certainty the rare electron-proton collisions in wich the electron turns into a tau. If they occured, they would roughly constitute less than one in 100 million events recorded at the EIC.

Doing Experiments with Particle Colliders

A high-energy particle collider like the EIC accelerates charged particles to nearly the speed of light before making them collide. The collision typically creates multiple particles that fly away from the collision point.

Electron-proton collision at high energy.

Experiments at particle colliders are essentially giant cameras. They use various technologies to record the identity, energy, and direction of all the particles that come out of each collision. The design of the experiment used for this project follows the typical design of a general purpose collider experiment: It uses a tracking detector that measures the trajectory of all charged particles. In combindation with a magnetic field that bends the path of charged particles depending on their charge and momentum, this trajectory yields the electric charge and momentum of charged particles in addition to their direction. The experiment also uses so-called calorimeters to measure the direction and energy of both electrically charged and neutral particles. Calorimeters measure the energy of particles by stopping the particle (i.e. the particle deposits all its energy in the calorimeter) and returning a signal that is proportional to the deposited energy. If multiple particles can be grouped together based on the direction they are flying in, they are considered a jet. Different jet finding algorithms exist that apply differnt criteria for this grouping.

Example design of an Electron-Ion Collider experiment.

While many particles can be measured and identified directly, others decay so quickly that we can only measure their decay products. Taus are such quickly decaying particles. Even though we cannot detect them directly, we can measure their decay products and use that information to identify the original tau.

Searching for tau decays

This study aims to identify electron-to-tau conversion events in Monte Carlo simulated EIC data. We focus on taus that decay into three charged pions (and a neutral pion and a neutrino, where the latter escapes direct detection). These pions form a characteristically narrow and jet-like cone, which is typically narrower and contains fewer particles than the ubiquitous hadron jets. See the illustration below for a comparison between a typical hadron jet and a typical jet from a tau decaying into three charged pions. To identify taus, we therefore need to find an effective way to distinguish tau jets from hadron jets.

Experimental signature of a tau lepton decaying into pions.

The data

This study uses Monte Carlo simulated data for an EIC experiment. The data are generated in two steps:

Simulation of the physics process, i.e. generating all the particles that result from the collision of an electron with a proton.
Simulation of the detector response to the genreated particles, i.e. predicting what the real EIC experiment could actually measure and with what precision. This adds uncertainties reflecting the expected performance of the experiment to the simulated particles.

We use these input data files:

data/jets_lq_tau_3pi_r05_p250_e20.csv: These are the signal events. The incoming electrons convert into taus, which subsequently decay into three charged pions. Jets are created from the collision, as well as the decay of the tau.
data/jets_dis_nc_r05_p250_e20.csv: These are background events. Jets are created from the collision. The electrons keep their identity and can be detected after the collision.
data/jets_dis_cc_r05_p250_e20.csv: These are background events. Jets are created from the collision. The electron converts into a neutrino that escapes detection, which is a process well described by the Standard Model.

Each row in the data files corresponds to an identified jet. Descriptions of the individual columns are given in data/jets_column_description.xls.

The analysis

See the Jupyter notebook for this analysis eic-tau-classification.ipynb for details.

Conclusion

Using the AdaBoost decision tree classifier in scikit-learn improvoes the true positive rate of selecting tau-jets by 80% compared to an event selection based on manually chosen cuts. The false positive rate is below 1% for both methods.

Neither of these methods could reliably identify a single tau jet in a background of over 100 million hadron jets. However, in an analysis of EIC data, the tau identification is only one step of the overall event classification. In addition to finding a tau candidate, analyzing event topologies (like the angle between multiple jets found in a single electron-proton collision) will help to reduce the false positive rate, i.e. the misidentification of ‘Standard Model’ background events as ‘Beyond the Standard Model’ electron-to-tau conversion events.

Moreover, the design of the experiment and development of reconstruction algorithms are still evolving. By the time the EIC actually starts operating, the capabilities of the experiment itself to measure energies, charged tracks, and jets may have improved. This would lead to a better quality of input data for tau identification. For example, a more precise jet energy measurement by the experiment could reduce the widths of the signal and background distributions shown in the section on cut-based selection of this study. The reduced widths would improve the separation of signal and background.