Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userClassification of lepton mixing matrices from finite residual symmetries
97
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
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.
It has been suggested that residual symmetries in the charged-lepton and neutrino mass matrices can possibly reveal the flavour symmetry group of the lepton sector. We review the basic ideas of this purely group-theoretical approach and discuss some of its results. Finally, we also list its shortcomings.
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.
Contrary to the quark mixing matrix, the lepton mixing matrix could be symmetric. We study the phenomenological consequences of this possibility. In particular, we find that symmetry would imply that |U_{e3}| is larger than 0.16, i.e., above its current 2 sigma limit. The other mixing angles are also constrained and CP violating effects in neutrino oscillations are suppressed, even though |U_{e3}| is sizable. Maximal atmospheric mixing is only allowed if the other observables are outside their current 3 sigma ranges, and sin^2 theta_{23} lies typically below 0.5. The Majorana phases are not affected, but the implied values of the solar neutrino mixing angle have some effect on the predictions for neutrinoless double beta decay. We further discuss some formal properties of a symmetric mixing matrix.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
