Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRoots of unity and lepton mixing patterns from finite flavour symmetries
120
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
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.
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 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 prove that the triviality of the Galois action on the suitably twisted odd-dimensional etale cohomogy group of a smooth projective varietiy with finite coefficients implies the existence of certain primitive roots of unity in the field of definition of the variety. This text was inspired by an exercise in Serres Lectures on the Mordell--Weil theorem.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
