Majorana physics through the Cabibbo Haze

Abstract

We present a model in which the Supersymmetric Standard Model is augmented by the family symmetry Z 7 ⋊ Z 3 . Motivated by SO(10), where the charge twothirds and neutral Dirac Yukawa matrices are related, we propose, using family symmetry, a special form for the seesaw Majorana matrix; it contains a squared correlated hierarchy, allowing it to mitigate the severe hierarchy of the quark sector. It is reproduced naturally by the invariant operators of Z 7 ⋊ Z 3 , with the hierarchy carried by familon fields. In addition to relating the hierarchy of the ∆I w = 1/2 to the ∆I w = 0 sector, it contains a Gatto-Sartori-Tonin like relation, predicts a normal hierarchy for Tri-bimaximal and Golden Ratio mixings, and gives specific values for the light neutrino masses.

Modulated bimaximal neutrino mixing

“…(46)] by tuning the former to θ C . Perhaps, this is not just a mere numerical coincidence and one finds the related discussion in the "Cabibbo Haze" based theories [77,78].…”

θ13 and the flavor ring

“…Such a relationship is natural in minimal SU (5), where the Yukawa coupling ψχH d to a5 Higgs predicts,…”

“…In a previous work [5], we investigated the relation between the up-quark and seesaw sectors of the Flavor Ring within the framework of a (Z 7 ⋊ Z 3 ) flavor symmetry [6]. In this paper, we close the ring by presenting the results of a numerical study of the interplay between the CKM parameters, charged lepton masses, and neutrino mixing angles.…”

“…In a previous publication [5] we addressed the seesaw sector of the Flavor Ring. We assumed that the form of the Majorana matrix M was determined by the family symmetry (Z 7 ⋊ Z 3 ), the smallest non-Abelian discrete subgroup of SU (3) that is not a subgroup of SO(3) or SU (2); it contains 21 elements and only 3,3, 1 ′ ,1 ′ and 1 representations.…”

“…5 Another possible output to check is m b /mτ . However, upon performing the search, we found no solutions with a GJ insertion in the (33) entry, implying that, up to small Cabibbo corrections, m b ≈ mτ at unification.…”