Abstract
As is well known, the smallest neutrino mass turns out to be vanishing in the minimal seesaw model, since the effective neutrino mass matrix Mν is of rank two due to the fact that only two heavy right-handed neutrinos are introduced. In this paper, we point out that the one-loop matching condition for the effective dimension-five neutrino mass operator can make an important contribution to the smallest neutrino mass. By using the available one-loop matching condition and two-loop renormalization group equations in the supersymmetric version of the minimal seesaw model, we explicitly calculate the smallest neutrino mass in the case of normal neutrino mass ordering and find m1 ∈ [10−8, 10−10] eV at the Fermi scale ΛF = 91.2 GeV, where the range of m1 results from the uncertainties on the choice of the seesaw scale ΛSS and on the input values of relevant parameters at ΛSS.
Highlights
JHEP11(2021)101 where κ = YνMR−1YνT is in general a 3 × 3 complex and symmetric matrix
As is well known, the smallest neutrino mass turns out to be vanishing in the minimal seesaw model, since the effective neutrino mass matrix Mν is of rank two due to the fact that only two heavy right-handed neutrinos are introduced
We point out that the one-loop matching between the full theory and the effective theory can generate a nonzero mass of the lightest neutrino in the minimal seesaw model
Summary
To scrutinize the type-I seesaw model [19] at a superhigh-energy scale with precision measurements at low energies, one may follow the approach of effective field theories [20]. Starting with the initial values of physical parameters in the effective theory at the matching scale, one implements the RG equations to run those parameters to the threshold of the heavy particle N1 Such a procedure can be continued until the relevant energy scale of low-energy observations is reached, such as the Fermi scale ΛF ≡ MZ = 91.2 GeV. The matching and running of physical parameters in the type-I seesaw model have been extensively studied in the literature [21,22,23,24,25,26,27,28,29,30] we apply the aforementioned strategy to the MSM in the MSSM framework.1 In this case, the superpotential relevant for lepton masses and flavor mixing can be written as.
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