Conditions of general Z2 symmetry and TM1,2 mixing for the minimal type-I seesaw mechanism in an arbitrary basis

نویسندگان

چکیده

In this paper, using a formula for the minimal type-I seesaw mechanism by LDLT (or generalized Cholesky) decomposition, conditions of general Z2-invariance neutrino mass matrix m are obtained in an arbitrary basis. The found to be (M22ai+−M12bi+)(M22aj−−M12bj−)=−det⁡Mbi+bj− Z2-symmetric and -antisymmetric part Yukawa Yij±≡(Y±TY)ij/2≡(aj±,bj±) right-handed Mij. other words, symmetric antisymmetric bi must proportional those quantity a˜i≡ai−M12M22bi. They equivalent condition that is block diagonalized eigenvectors generator T. These results applied three Z2 symmetries, μ−τ symmetry, TM1 mixing, magic symmetry which predicts TM2 mixing. For case TM1,2, become M222a˜1TBMa˜2TBM=−det⁡Mb1TBMb2TBM M222a˜1,2TBMa˜3TBM=−det⁡Mb1,2TBMb3TBM with components a˜iTBM biTBM TBM basis v1,2,3. particular, (anti-)symmetric S2Y=±Y phenomenologically excluded because it m2=0 or m1,m3=0. where not (anti-)symmetric, singular values displayed without root sign.

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ژورنال

عنوان ژورنال: Nuclear Physics B

سال: 2022

ISSN: ['1873-1562', '0550-3213']

DOI: https://doi.org/10.1016/j.nuclphysb.2022.115893