The smallest neutrino mass revisited

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.

The µ–τ reflection symmetry of Majorana neutrinos *

“…In this case the seesaw threshold effects play a critical role, but the numerical output of m 1 (or m 3 ) strongly depends on the numerical inputs of those unknown Yukawa coupling matrix elements. If the evolution of neutrino flavor parameters simply starts from M min , the so-called seesaw scale where the heavy degrees of freedom have been integrated out and the unique dimension-five Weinberg operator is responsible for the origin of three active neutrino masses [138], then a nonzero value of m 1 (or m 3 ) at Λ EW cannot be generated from m 1 = 0 (or m 3 = 0) at M min unless the two-loop RGE running behaviors are taken into account [139][140][141][142]. In the latter case the resulting mass of the lightest Majorana neutrino ν 1 or ν 3 is typically of O(10 −13 ) eV or smaller-such a vanishingly small neutrino mass and the associated Majorana CP-violating phase do not cause any seeable effects in neutrino physics.…”

Renormalization group effects for a rank degenerate Yukawa matrix and the fate of the massless neutrino

“…This result for the 3-2 model is the one-loop renormalization group equations and treelevel matching. However, the result has been shown to not hold for one-loop matching in supersymmetry [25] and two-loop renormalization group equation for the Weinberg operator coefficient κ [26]. Inclusion of all two-loop renormalization group equations [27,28] and complete one-loop level matching in the Standard Model could be interesting.…”

“…For the 3-2 seesaw model the neutrino Dirac mass matrix is a 3 by 2 matrix and its rank is two. The 3-2 seesaw model has been previously studied sometimes under the name the minimal Type-I seesaw model [10,[19][20][21][22][23][24][25]. For the model with three right-handed neutrinos, we assume a texture of the neutrino Dirac mass terms to reduce the rank of the matrix to two.…”

“…Then we determine the matrix rank of the effective neutrino mass matrix. The renormalization group running of neutrino masses has been studied previously in literature with the rank of the 3-2 seesaw model being considered for the one loop matching approximation [25] and two loop renormalization group effects [26]. However, we believe the stability of the 3-3 seesaw model with a matrix of rank two has not been examined against renormalization group effects.…”

“…Then, for example, to have I 0 = 0 any of the eigenvalues can equal zero, but the other two eigenvalues must remain non-zero to have I 1 and I 2 as non-zero. [10,[19][20][21][22][23][24][25]. This version introduces two new right-handed neutrinos to the Standard Model that we label as N 1 and N 2 following Eq.…”