**Abstract**

**Abstract**

** neutrinos** has been known for nearly a century, yet the

**Introduction**

**Neutrinos oscillate between different flavors as they propagate.**

Neutrinos have 3 flavor states and 3 mass states. Each flavor state \(\lvert \nu_\alpha \rangle \) can be written in terms of the 3 mass states \(\lvert \nu_i \rangle \),

\(\lvert \nu_\alpha \rangle = \sum_i U_{\alpha i} \lvert \nu_i \rangle \),

where \(\alpha = e, \mu, \tau \) and \(i = 1, 2, 3 \). The matrix \(U\) is unitary and is at the center of the traditional neutrino propagation model.

**Current and future experiments that measure neutrino oscillations can be modeled.**

\(\bar{P}_{\alpha \beta} = \left( \int_{E_i}^{E_f} dE \frac{d\Phi}{dE} \sigma(E) P_{\alpha \beta}(E) \right) \Big / \left(\int_{E_i}^{E_f} dE \frac{d\Phi}{dE} \sigma(E) \right)\)

The average transition probability \(\bar{P}_{\alpha \beta}\) from flavor \(\alpha\) to \(\beta\) is modeled by calculating the fraction of detected neutrinos with oscillations over that without oscillations.

**Two experiments that can model these oscillations are Tokai-to-Kamioka (T2K) and the Jiangmen Underground Neutrino Observatory (JUNO)**

The T2K experiment measures the average \(\mu\)-to-\(e\) neutrino oscillations over the entire energy spectrum of incoming neutrinos. JUNO is expected to measure electron neutrino survival (\(e\)-to-\(e\)) probabilities over a range of energies.

The expected number of detection events (flux times cross section) was estimated using the curves provided by the T2K [1] and JUNO [2] collaborations. The baseline distances for neutrino travel are 295 km (T2K) and 53 km (JUNO).

**Results from T2K**

**This non-unitary model can explain current data on neutrinos from the Tokai-to-Kamioka experiment.**

**Results from JUNO**

**References**

[1] Hayato, Y. et al. 2003, Letter of Intent: Neutrino Oscillation Experiment at JHF, Tech. rep.

[2] An, F., et al. 2016, Jour. Phys. G. Nucl. Part. Phys., 43.

[3] Berryman, J. M., de GouvĂȘa, A., HernĂĄndez, D., & Oliveira, R. L. 2015, Phys. Let. B, 742, 74.

[4] AbrahĂŁo, T., Minakata, H., Nunokawa, H., & Quiroga, A. A. 2015, Jour. High Energy Phys., 2015, 1.

[5] Coloma, P., & Peres, L. 2017. arXiv:1705.03599[hep-ph]

**Acknowledgments**

This material is based upon work supported by the National Science Foundation under Grant No. AST-1757792, a Research Experiences for Undergraduates (REU) grant awarded to CIERA at Northwestern University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

email: santos30 [at] purdue.edu