Lepton flavors6/5/2023 Even in the condensed version of the PDG booklet, such listings run to more than 170 pages. A quick look at the Particle Data Group (PDG) booklet, with its long lists of the decays of B mesons, D mesons, kaons and other hadrons, gives an impression of the breadth and depth of the field. Today, flavour physics is a major field of activity. The ν̅ τ in b → cτ –ν̅ τ can also be replaced by a right-handed neutrino, which is not part of the Standard Model. Possible new contributions to this process include exchanges of new colour-singlet states (middle), or new coloured states coupling simultaneously to quarks and leptons (right). The semileptonic decay of the b quark in the Standard Model (left). In other words, the gauge forces, such as the electroweak force, are flavour-universal in the SM, while the exchange of a Higgs particle is not. The Higgs field, on the other hand, distinguishes between fermions of different flavours and endows them with different masses – sometimes strikingly so. It directly follows from the assumption that the SM gauge group, SU(3) × SU(2) × U(1), is one and the same for all three generations of fermions. This “flavour universality” is deeply ingrained in the symmetry structure of the Standard Model (SM) and applies to both the electroweak and strong forces (though the latter is irrelevant for leptons). The three flavours of charged leptons – electron, muon and tau – are the same in many respects. These 12 elementary fermions are grouped into three generations of increasing mass. A similar picture evolved for the leptons: the electron and the muon were joined by the unexpected discovery of the tau lepton at SLAC in 1975 and completed with the three corresponding neutrinos. From the three types known at the time – up, down and strange – the list of quark flavours grew to six. In 1971, at a Baskin-Robbins ice-cream store in Pasadena, California, Murray Gell-Mann and his student Harald Fritzsch came up with the term “flavour” to describe the different types of quarks. If the effect strengthens as more data are gathered, possible explanations range from new gauge forces to leptoquarks. "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.Recent experimental results hint that some electroweak processes are not lepton-flavour independent, contrary to Standard Model expectations. 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 this study, we showed that the neutrino mass hierarchy can be mathematically explained using random matrix theory. Having considered several models of light neutrino mass where the matrix is composed of the product of several random matrices, the research team was able to prove, as best they could at this stage, why the calculation of the squared difference of the neutrino masses are closest with the experimental results in the case of the seesaw model with the random Dirac and Majorana matrices. "Beyond the remaining mysteries of the Standard Model, there is a whole new world of physics."Īfter studying the neutrino mass anarchy in the Dirac neutrino, seesaw, double seesaw models, the researchers found that the anarchy approach requires that the measure of the matrix should obey the Gaussian distribution. "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. They showed theoretically, using the random mass matrix model that the lepton flavor mixings are large. They analyzed the neutrino mass matrix by randomly assigning each element of the matrix. Neutrinos are known to have less difference in mass between generations than other elementary particles, so the research team considered that neutrinos are roughly equal in mass between generations. A research team led by Professor Naoyuki Haba from the Osaka Metropolitan University Graduate School of Science, analyzed the collection of leptons that make up the neutrino mass matrix.
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