Any material can be broken down into smaller and smaller parts until it can no longer be divided further, at which point it is reduced to a single particle. There are currently 12 different types of elementary particles known, which are composed of quarks and leptons, each of which has six distinct flavours. To create various particles, such as the electron, muon, and tau neutrinos, these flavours are divided into three generations, each having a charged and a neutral lepton. A three-by-three matrix is used in the Standard Model to represent the masses of the three generations of neutrinos.
Scientists from the Osaka Metropolitan University Graduate School of Science, under the direction of Professor Naoyuki Haba, examined the assortment of leptons that make up the neutrino mass matrix.
The research team assumed that neutrinos are roughly identical in mass between generations because neutrinos are known to exhibit less variation in mass between generations than other elementary particles. By allocating each component of the neutrino mass matrix at random, they examined it. They demonstrated theoretically that the lepton flavour mixings are substantial using the random mass matrix model. Progress of Theoretical and Experimental Physics reported their findings.
“Clarifying the properties of elementary particles leads to the exploration of the universe and ultimately to the grand theme of where we came from,” Professor Haba explained. “Beyond the remaining mysteries of the Standard Model, there is a whole new world of physics.”
Researchers discovered that the anarchy approach necessitates that the matrix’s measure adhere to the Gaussian distribution after researching the neutrino mass anarchy in the Dirac neutrino, seesaw, and double seesaw models. The research team was able to demonstrate, as best they could at this point, why the calculation of the squared difference of the neutrino masses is closest to the experimental results in the case of the seesaw model with the random Dirac and Majorana matrices after taking into account several models of light neutrino mass where the matrix is composed of the product of several random matrices.
“In this study, we showed that the neutrino mass hierarchy can be mathematically explained using random matrix theory. However, this proof is not mathematically complete and is expected to be rigorously proven as random matrix theory continues to develop,” said Professor Haba. “In the future, we will continue with our challenge of elucidating the three-generation copy structure of elementary particles, the essential nature of which is still completely unknown both theoretically and experimentally.”
