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Register a new userFlavor Mixing of Quarks and Neutrinos
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Authors
Harald Fritzsch
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The texture zero mass matrices for the quarks and leptons describe very well the flavor mixing of the quarks and leptons. We can calculate the angles of the unitarity triangle. We expect the angle alpha of the unitarity triangle to be 90 degrees. The masses of the neutrinos can be calculated - they are very small, the largest neutrino mass is 0.05 eV. We calculated the matrix element of the mixing matrix, relevant for the reactor mixing angle. It can be measured in the near future in the DAYA BAY experiment.
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We discuss a new mass matrix with specific texture zeros for the quarks. The three flavor mixing angles for the quarks are functions of the quark masses and can be calculated. The following ratios among CKM matrix elements are given by ratios of quark masses: |Vtd/Vts| q md /ms and |Vub/Vcb| p mu/mc . Also we can calculate two CKM matrix elements: |Vcb| |Vts| 2 (ms/mb ). This relation as well as the relation |Vtd/Vts| q md /ms are in good agreement with the experimental data. There is a problem with the relation |Vub/Vcb| p mu/mc , probably due to wrong estimates of the quark masses mu and m
Starting with high scale mixing unification hypothesis, we investigate the renormalization group evolution of mixing parameters and masses for Dirac type neutrinos. Following this hypothesis, the PMNS mixing angles and phase are taken to be identical to the CKM ones at a unifying high scale. Then, they are evolved to a low scale using renormalization-group equations. The notable feature of this hypothesis is that renormalization group evolution with quasi-degenerate mass pattern can explain largeness of leptonic mixing angles even for Dirac neutrinos. The renormalization group evolution naturally results in a non-zero and small value of leptonic mixing angle $theta_{13}$. One of the important predictions of this work is that the mixing angle $theta_{23}$ is non-maximal and lies only in the second octant. We also derive constraints on the allowed parameter range for the SUSY breaking and unification scales for which this hypothesis works. The results are novel and can be tested by present and future experiments.
We discuss the reconstruction of neutrino flavor neutrino at a distant source in the very high en- ergy regime. This reconstruction procedure is relevant to the confirmation of detecting cosmogenic neutrinos, for example. To facilitate such a reconstruction, it is imperative to achieve effective flavor discriminations in terrestrial neutrino telescopes. We note that, for energies beyond few tens of PeV, a tau-lepton behaves like a track similar to a muon. Hence, while it is rather challenging to separate { u}{mu} from { u}{tau} in this case, one can expect to isolate { u}e from the rest by a distinctive shower signature. We present the result of flavor ratio reconstruction given the anticipated accuracies of flavor measurement in neutrino telescopes and current uncertainties of neutrino mixing parame- ters. It is shown that the further separation between { u}{mu} and { u}{tau} events does not improve the flavor reconstruction due to the approximate { u}{mu} - { u}{tau} symmetry.
Light sterile neutrinos can be probed in a number of ways, including electroweak decays, cosmology and neutrino oscillation experiments. At long-baseline experiments, the neutral-current data is directly sensitive to the presence of light sterile neutrinos: once the active neutrinos have oscillated into a sterile state, a depletion in the neutral-current data sample is expected since they do not interact with the $Z$ boson. This channel offers a direct avenue to probe the mixing between a sterile neutrino and the tau neutrino, which remains largely unconstrained by current data. In this work, we study the potential of the DUNE experiment to constrain the mixing angle which parametrizes this mixing, $theta_{34}$, through the observation of neutral-current events at the far detector. We find that DUNE will be able to improve significantly over current constraints thanks to its large statistics and excellent discrimination between neutral- and charged-current events.
We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter $a equiv 2sqrt{2} G^{}_{rm F} N^{}_e E$ to be an arbitrary scale-like variable with $N^{}_e$ being the net electron number density and $E$ being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix $V$ and the effective neutrino masses $widetilde{m}^{}_i$ (for $i = 1, 2, 3$). Given the standard parametrization of $V$, the RGEs for ${widetilde{theta}^{}_{12}, widetilde{theta}^{}_{13}, widetilde{theta}^{}_{23}, widetilde{delta}}$ in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial $mu$-$tau$ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of $V$ are also obtained as a by-product.
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