Renormalization group running of neutrino parameters

Abstract

Neutrinos are the most elusive particles in our Universe. They have masses at least one million times smaller than the electron mass, carry no electric charge and very weakly interact with other particles, meaning that they are rarely captured in terrestrial detectors. Tremendous efforts in the past two decades have revealed that neutrinos can transform from one type to another as a consequence of neutrino oscillations-a quantum mechanical effect over macroscopic distances-yet the origin of neutrino masses remains puzzling. The physical evolution of neutrino parameters with respect to energy scale may help elucidate the mechanism for their mass generation.E ver since their discovery in the 1950s (ref. 1), neutrinos have continued to surprise us. In the Standard Model (SM) of elementary particle physics, neutrinos are massless particles. However, since the results from the Super-Kamiokande experiment in 1998 (ref. 2), the phenomenon of neutrino oscillations has been well established, indicating that neutrinos do have nonzero and non-degenerate masses and that they can convert from one flavour to another 3 . This important result was followed by a boom of results from several international collaborations. Certainly, these results have pinned down the values of the various neutrino parameters to an incredible precision, especially considering that neutrinos are extremely elusive particles and the corresponding experiments are extraordinarily complex 4 . Currently operating experiments and future investigations under construction are aimed at determining the missing neutrino parameters, such as the CP-violating phase (which can be important for understanding the matter-antimatter asymmetry in the Universe), the sign of the large mass-squared difference for neutrinos, and the absolute neutrino mass scale. In addition, the cubic kilometre scale neutrino telescope at the South Pole, IceCube 5 , has been successfully constructed to search for ultra-high energy astrophysical neutrinos, while a number of underground experiments are looking for neutrinoless double-beta decay (see refs 6-10) and others are waiting for neutrino bursts from galactic supernova explosions (see refs 11,12).However, the origin of neutrino masses and lepton flavour mixing remains a mystery, and calls for new physics beyond the SM. It is believed that new physics should appear somewhere above the electroweak scale (that is, L EW B10 2 GeV) but below the Planck scale (that is, L P B10 19 GeV) for the following reasons. First, the smallness of neutrino masses can be ascribed to the existence of superheavy particles, whose masses are close to the grand unified theory (GUT) scale (for example, L GUT B10 16 GeV), such as right-handed neutrinos in the canonical seesaw models [13][14][15][16][17] . Moreover, the out-of-equilibrium and CP-violating decays of

Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects

“…In the first way, starting with the RGE of κ [43,45,57], one can derive a set of RGEs for neutrino masses and flavor mixing parameters. By inspecting the structure of those RGEs, some general running behavior of neutrino masses and lepton mixing angles can be observed [43,45,57,58]. However, a further more quantitative estimation on the size of these radiative corrections becomes formidable, as the RGEs are non-linear in nature and thus difficult to solve analytically.…”

Effects of intermediate scales on renormalization group running of fermion observables in an SO(10) model

“…However, the magnitude of the RG running is what would be expected from other analyses of seesaw models (see, e.g., ref. [39] and references therein). In the SM, the angles are all larger at M Z , with the smallest difference occurring for θ ℓ 13 , which is only 3 % larger, and the largest difference for θ ℓ 23 , which is 17 % larger.…”

$$ \mu -\tau $$ μ - τ reflection symmetry embedded in minimal seesaw

“…Although σ = 0 is also predicted by the μ − τ reflection symmetry, having σ = 0 at the high energy boundary would lead to dramatic running in θ 12 . This can be seen from the following RG equation for θ 12 below the seesaw threshold [68][69][70][71]79 …”

“…This stage of RG running is below the seesaw threshold, and its impact on the lepton mixing parameters has been extensively discussed in the literature, e.g., Refs. [68][69][70][71]. In particular, the breaking of μ−τ reflection symmetry due to this stage of RG running is investigated in Refs.…”