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Register a new userClassification of lepton mixing patterns from finite flavour symmetries
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Flavour symmetries have been used to constrain both quark and lepton mixing parameters. In particular, they can be used to completely fix the mixing angles. For the lepton sector, assuming that neutrinos are Majorana particles, we have derived the complete list of mixing patterns achievable in this way, as well as the symmetry groups associated to each case. Partial computer scans done in the past have hinted that such list is limited, and this does indeed turn out to be the case. In addition, most mixing patterns are already 3-sigma excluded by neutrino oscillation data.
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The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem.
Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level.
We investigate the possibility that the first column of the lepton mixing matrix U is given by u_1 = (2,-1,-1)^T/sqrt{6}. In a purely group-theoretical approach, based on residual symmetries in the charged-lepton and neutrino sectors and on a theorem on vanishing sums of roots of unity, we discuss the finite groups which can enforce this. Assuming that there is only one residual symmetry in the Majorana neutrino mass matrix, we find the almost unique solution Z_q x S_4 where the cyclic factor Z_q with q = 1,2,3,... is irrelevant for obtaining u_1 in U. Our discussion also provides a natural mechanism for achieving this goal. Finally, barring vacuum alignment, we realize this mechanism in a class of renormalizable models.
We perform a model-independent global fit to $bto sell^+ell^-$ observables to confirm existing New Physics (NP) patterns (or scenarios) and to identify new ones emerging from the inclusion of the updated LHCb and Belle measurements of $R_K$ and $R_{K^*}$, respectively. Our analysis, updating Refs. [1,2] and including these new data, suggests the presence of right-handed couplings encoded in the Wilson coefficients ${cal C}_{9mu}$ and ${cal C}_{10mu}$. It also strengthens our earlier observation that a lepton flavour universality violating (LFUV) left-handed lepton coupling (${cal C}_{9mu}^{rm V}=-{cal C}_{10mu}^{rm V}$), often preferred from the model building point of view, accommodates the data better if lepton-flavour universal (LFU) NP is allowed, in particular in ${cal C}_{9}^{rm U}$. Furthermore, this scenario with LFU NP provides a simple and model-independent connection to the $bto ctau u$ anomalies, showing a preference of $approx 7,sigma$ with respect to the SM. It may also explain why fits to the whole set of $bto sell^+ell^-$ data or to the subset of LFUV data exhibit stronger preferences for different NP scenarios. Finally, motivated by $Z^prime$ models with vector-like quarks, we propose four new scenarios with LFU and LFUV NP contributions that give a very good fit to data. We provide also an addendum collecting our updated results after including the data for the $Bto K^*mumu$ angular distribution released in 2020 by the LHCb collaboration.
We look for predictive flavour patterns of the effective Majorana neutrino mass matrix that are compatible with current neutrino oscillation data. Our search is based on the assumption that the neutrino mass matrix contains equal elements and a minimal number of parameters, in the flavour basis where the charged lepton mass matrix is diagonal and real. Three unique patterns that can successfully explain neutrino observables at the $3sigma$ confidence level with just three physical parameters are presented. Neutrino textures described by four and five parameters are also studied. The predictions for the lightest neutrino mass, the effective mass parameter in neutrinoless double beta decays and the CP-violating phases in the leptonic mixing are given.
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