At the core of matter lies the indivisible component known as the particle. To date, 12 distinct fundamental particles have been identified, consisting of quarks and leptons in six unique varieties. These variations are organized into three tiers—each featuring one charged and one neutral lepton—that give rise to diverse particles such as electron, muon, and tau neutrinos. The neutrino masses for these three strata are portrayed by a three-by-three matrix in the Standard Model.

A team of scientists, investigated the collection of leptons that make up the neutrino mass matrix. The mass discrepancies between neutrino generations are known to be significantly smaller than those of other fundamental particles. Consequently, the researchers postulated that the masses of neutrinos across generations are approximately equivalent. They scrutinized the neutrino mass matrix by arbitrarily assigning each element within it. Their theoretical analysis, using the random mass matrix model, demonstrated that the lepton flavor mixings are substantial. These findings were published in the journal Progress of Theoretical and Experimental Physics.

Professor Haba elucidated that understanding the characteristics of elementary particles propels the investigation of the cosmos, ultimately delving into the profound question of our origins. “Beyond the remaining enigmas of the Standard Model lies an entirely new realm of physics.” The study group investigated the disorder in neutrino mass for Dirac neutrinos, as well as in the seesaw and double seesaw models. They found that, when using the chaos method, the matrix measurement must follow a Gaussian distribution. After examining multiple light neutrino mass models, which involve the creation of a matrix through the multiplication of several random matrices, the researchers managed to offer an initial justification for the squared discrepancy in neutrino masses. Their findings are consistent with experimental data when using the seesaw model featuring random Majorana and Dirac matrices.

“In this investigation, we demonstrated that random matrix theory can be employed to mathematically rationalize the neutrino mass hierarchy. However, this evidence is not yet mathematically definitive and is anticipated to be rigorously validated as random matrix theory advances,” stated Professor Haba. “Moving forward, we will persist in our pursuit to demystify the three-tiered replica structure of elementary particles, the fundamental nature of which remains utterly enigmatic from both theoretical and experimental perspectives.”