We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott （HPS） form. These deviations are supposed to arise entirely from a perturbation of the ma...We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott （HPS） form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary （thus maximally T-violating） and to have a strength in energy scale no greater （but perhaps smaller） than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O（（mμ/mτ）^2） ≈ 3.5 ×10^-3 from their HPS values. Assuming that （mμ/mτ）^2 can be neglected, we derive two simple constraints on the four parameters θ12,θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.展开更多
eAbstract We extend the T violating model of the paper on ＂Hidden symmetry of the CKM and neutrinomapping matrices＂ by assuming its T-violating phases X↑ and X↓ to be large and the same, with X = X↑ = X↓. In thi...eAbstract We extend the T violating model of the paper on ＂Hidden symmetry of the CKM and neutrinomapping matrices＂ by assuming its T-violating phases X↑ and X↓ to be large and the same, with X = X↑ = X↓. In this case, the model has 9 real parameters： aT, α↑,β↑,ξ↑,η↑T for the T-quark sector, α↓,β↓,ξ↓,η↓, for the sector and a common X- We examine whether these nine parameters are compatible with ten observables： the six quark masses and the four real parameters that characterize the CKM matrix （i.e., the Jarlskog invariant and three Eulerian angles）. We find that this is possible only if the T violating phase X is large, between -120^o to -135^o. In this strong T violating model, the smallness of theJarlskog invariant 3 × 10^-5 ismainly accounted for by the large heavy quark masses, with mc/mt〈ms/mb≈0.02, as well as the near completeoverlap of t and b quark, with （c｜b）=-0.04.展开更多
文摘We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott （HPS） form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary （thus maximally T-violating） and to have a strength in energy scale no greater （but perhaps smaller） than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O（（mμ/mτ）^2） ≈ 3.5 ×10^-3 from their HPS values. Assuming that （mμ/mτ）^2 can be neglected, we derive two simple constraints on the four parameters θ12,θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.
基金Supported in part by the U.S. Department of Energy (DE-FG02-92-ER40699)
文摘eAbstract We extend the T violating model of the paper on ＂Hidden symmetry of the CKM and neutrinomapping matrices＂ by assuming its T-violating phases X↑ and X↓ to be large and the same, with X = X↑ = X↓. In this case, the model has 9 real parameters： aT, α↑,β↑,ξ↑,η↑T for the T-quark sector, α↓,β↓,ξ↓,η↓, for the sector and a common X- We examine whether these nine parameters are compatible with ten observables： the six quark masses and the four real parameters that characterize the CKM matrix （i.e., the Jarlskog invariant and three Eulerian angles）. We find that this is possible only if the T violating phase X is large, between -120^o to -135^o. In this strong T violating model, the smallness of theJarlskog invariant 3 × 10^-5 ismainly accounted for by the large heavy quark masses, with mc/mt〈ms/mb≈0.02, as well as the near completeoverlap of t and b quark, with （c｜b）=-0.04.
