## Random Mass Matrix Model and Lepton Flavor Mixing in Neutrinos

When matter is divided into smaller and smaller pieces, it eventually reaches a point where it can no longer be divided, and what remains is a particle. The Standard Model identifies 12 elementary particles, which are made up of quarks and leptons, each with six different flavors. The flavors are grouped into three generations, with charged and neutral leptons forming different particles such as electron, muon, and tau neutrinos. The masses of these neutrinos are represented by a three-by-three matrix in the Standard Model.

A team led by Professor Naoyuki Haba from Osaka Metropolitan University Graduate School of Science analyzed the neutrino mass matrix, focusing on the leptons that make it up. Neutrinos have less mass difference between generations than other elementary particles, so the research team considered them roughly equal in mass between generations. Using a random mass matrix model, they analyzed the matrix by randomly assigning each element. Their findings, published in Progress of Theoretical and Experimental Physics, showed that lepton flavor mixings are large in the random mass matrix model.

Professor Haba emphasized that understanding the properties of elementary particles is crucial for exploring the universe and ultimately answering the grand question of our origins. He also noted that there is a vast realm of physics beyond the mysteries of the Standard Model.

This study sheds light on the fundamental properties of neutrinos and their mass matrix, which can aid in developing more comprehensive models of the universe. The findings of this study may contribute to advancing our understanding of particle physics and cosmology and provide a foundation for further research in this field.

## Explaining Neutrino Mass Hierarchy with Random Matrix Theory

The neutrino mass hierarchy has been a long-standing mystery in particle physics, and various models have been proposed to explain it. In a recent study, researchers focused on the anarchy approach to neutrino mass hierarchy in the Dirac neutrino, seesaw, and double seesaw models. They found that the measure of the matrix should obey the Gaussian distribution for the anarchy approach to work.

The research team considered several models of light neutrino mass, where the matrix is composed of the product of multiple random matrices. They were able to prove, to the best of their ability at this stage, why the calculation of the squared difference of the neutrino masses is closest to experimental results in the case of the seesaw model with random Dirac and Majorana matrices.

According to Professor Haba, the study shows that the neutrino mass hierarchy can be mathematically explained using random matrix theory. However, the proof is not yet mathematically complete and is expected to be rigorously proven as random matrix theory continues to develop.

The research highlights the importance of studying the fundamental properties of elementary particles, such as neutrinos, to understand the universe’s origins fully. The findings of this study may contribute to advancing our understanding of particle physics and cosmology and provide a foundation for further research in this field.

Moving forward, the research team plans to continue their efforts to elucidate the three-generation copy structure of elementary particles. This essential nature is still entirely unknown, both theoretically and experimentally. Further research in this area could lead to a better understanding of the universe’s building blocks and its evolution.

## Contributions of Random Matrix Theory in Understanding Neutrino Mass Hierarchy

Random matrix theory has been a valuable tool in understanding the properties of elementary particles, particularly neutrinos. The recent study led by Professor Naoyuki Haba and his team provides further evidence that random matrix theory can explain the neutrino mass hierarchy. This finding has significant implications for both the field of particle physics and our understanding of the universe.

The study’s results may help us gain a deeper understanding of the fundamental properties of elementary particles, such as their mass and charge, which are crucial in developing more accurate models of the universe’s evolution. This could lead to new discoveries about the origins of the universe and its fundamental building blocks.

Moreover, the study’s findings could contribute to advancements in technology, particularly in the fields of energy and communication. Neutrinos, being one of the most abundant particles in the universe, could be harnessed for practical applications, such as energy generation and data transmission.

In summary, the study’s contribution to random matrix theory provides new insights into neutrino mass hierarchy and helps us better understand the fundamental properties of elementary particles. The findings have significant implications for our understanding of the universe and could lead to practical applications in technology.

### Deep Dive

- Beringer, J. et al. (2012). Review of Particle Physics (PDF). Physical Review D. 86 (1). https://doi.org/10.1103/PhysRevD.86.010001
- Giunti, C. and Kim, C.W. (2007). Fundamentals of Neutrino Physics and Astrophysics. Oxford University Press. ISBN: 9780198508717.
- Haba, N., Shimizu, Y. and Terao, H. (2021). Large flavor mixing from random mass matrix. Progress of Theoretical and Experimental Physics. 2021 (5). https://doi.org/10.1093/ptep/ptab042
- Langacker, P. (2010). The Standard Model and Beyond (2nd ed.). CRC Press. ISBN: 9781420082458.
- Mohapatra, R.N. and Pal, P.B. (2004). Massive Neutrinos in Physics and Astrophysics. World Scientific Publishing. ISBN: 9789812388321.

Quotation: https://phys.org/news/2023-04-random-matrix-theory-approaches-mystery.html

Original Article: https://academic.oup.com/ptep/article/2023/2/023B07/6992884