Abstract
We construct a texture where the Seesaw matrix is diagonalized by the TriBiMaximal (TBM) matrix with a phase. All CKM and PMNS angles are within their pdg values, and the mass relations of quarks and charged leptons extrapolated to GUT scale are satisfied, including the Gatto relation. The novel ingredient is the asymmetry of the down-quark and charged lepton Yukawa matrices. Explaining the reactor angle requires a $\require{cancel} \cancel {CP}$ phase in the TBM matrix, resulting in the Jarlskog-Greenberg invariant at $|J|=0.028$, albeit with an undetermined sign. While $SO(10)$ restrains the right-handed neutrino Majorana matrix, the neutrino masses are left undetermined.
Highlights
The Standard Model evocates simplicity at a smaller scale, both in gauge couplings and in the mass patterns of down quarks and charged leptons
TBM simplicity comes at a cost: the reactor angle θ13 generated from the seesaw is zero
Our objective is to search for asymmetric Yukawa matrices that satisfy all experimental constraints: the Cabibbo-Kobayashi-Mapskffiaffiffiwffiffiffiffiaffiffiffiffi(ffiffiCffi KM) matrix, the Gatto relation [9] tanθC 1⁄4 md=ms ≈ λ where θC is the Cabibbo angle and λ is a Wolfenstein parameter, and the down-quark and charged lepton mass relations at the grand unified theory (GUT) scale using the renormalization group [10] mb 1⁄4 mτ, md 1⁄4 3me, ms 1⁄4 mμ=3 together with the values of the three lepton mixing angles [11]
Summary
The Standard Model evocates simplicity at a smaller scale, both in gauge couplings (grand-unified theories) and in the mass patterns of down quarks and charged leptons. The Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton mixing matrix is an overlap of seesaw and charged lepton mixing matrices The latter, derived from the charged lepton Yukawa matrix, may generate enough “Cabibbo haze” [5] to explain the data, but symmetric Yukawa matrices with TBM diagonalization underestimate the reactor angle [6]. Our objective is to search for asymmetric Yukawa matrices that satisfy all experimental constraints: the Cabibbo-Kobayashi-Mapskffiaffiffiwffiffiffiffiaffiffiffiffi(ffiffiCffi KM) matrix, the Gatto relation [9] tanθC 1⁄4 md=ms ≈ λ where θC is the Cabibbo angle and λ is a Wolfenstein parameter, and the down-quark and charged lepton mass relations at the GUT scale using the renormalization group [10] mb 1⁄4 mτ, md 1⁄4 3me, ms 1⁄4 mμ=3 together with the values of the three lepton mixing angles [11]. The uniqueness of the asymmetry in explaining the data is extensively discussed in the Appendices
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