Neutrino Theory

Abstract

The possible manifestations of New Physics beyond that predicted by the Standard Theory, which can be related to the existence of non-zero neutrino masses and neutrino mixing, are briefly discussed. The phenomenology of 3-neutrino mixing, the present status of our knowledge about the 3-neutrino mixing parameters, including the absolute neutrino mass scale, and of the Dirac and Majorana CP violation in the lepton sector, are summarised. The current theoretical ideas about the origins i) of neutrino masses and of the enormous disparity between their values and the values of the charged lepton and quark masses, and ii) of the pattern of neutrino mixing revealed by the neutrino oscillation experiments, are reviewed, with the non-Abelian discrete symmetry approach considered in somewhat greater detail. The possibilities to test these ideas are also briefly discussed.-In the Majorana nature of massive neutrinos, and total lepton charge non-conservation, L = const.-In the existence of new particles, e.g., at the TeV scale: heavy Majorana neutrinos N j , doubly and singly charged scalars, H −− , H − , etc. -In the existence of new (flavour changing and/or flavour conserving but flavour non-symmetric) nonstandard neutrino interactions (NSI) [6,7] (for recent discussions see, e.g., [8,9,10]). -In the existence of charged lepton flavour violating (ChLFV) processes, µ → e + γ and µ → 3e decays, µe conversion on nuclei, etc., having rates close to the existing stringent upper limits. -In the existence of unforeseen new phenomena.Apart obviously from the last item, the indicated possible manifestations of New Physics were extensively discussed at this Conference.There can be more than 3 massive neutrinos, n > 3, for example, if there exist sterile righthanded (RH) neutrinos νl R and left-handed (LH) antineutrinosνl L (described by SU (2) ×U (1) Y W singlet RH neutrino fields νl R (x)), which posses a Majorana mass term and couple via a Dirac mass term to the active flavour LH neutrinos ν lL and RH antineutrinosν lR (LH flavour neutrino fields ν lL (x)). In what concerns the masses of the additional massive neutrino states ν 4 , ν 5 ,..., m 4 , m 5 ,..., there are a few possibilities. i) They can be at the eV scale, m 4 , m 5 , ... ∼ 1 eV. In this case active-sterile neutrino oscillations, ν e(µ) → ν s (≡νl L ) are possible. At present we have hints that such oscillations might take place from LSND and MiniBooNE experiments, re-analyses of short baseline (SBL) reactor neutrino oscillation data ("reactor neutrino anomaly") and data of radioactive source calibration of the solar neutrino SAGE and GALLEX experiments "Gallium anomaly") (see, e.g., [11]). However, as recent analyses have shown [11,12], the global fits of the relevant data -positive evidence and negative results -have an extremely low quality, indicating the existence of inconsistencies between the different data sets.

Fermion mass hierarchies, large lepton mixing and residual modular symmetries

“…5,2 are available. In this case the spectrum follows a (1, , 4 ) pattern, without a massless fermion (see section 3.4.1).…”

“…Resorting to (3.26), one finds that the spectrum is hierarchical, with (m 3 , m 2 , m 1 ) ∼ (1, , 4 ).…”

“…We have considered the T -diagonal basis for A 5 . One can explicitly check that, at leading order in = |q|, the components of 4 , with q = exp (2πiτ /5) and a common normalisation N . The power structure matches that of eq.…”

“…In almost all phenomenologically viable flavour models based on modular invariance constructed so far the hierarchy of the charged-lepton and quark masses is obtained by finetuning some of the constant parameters present in the models. 4 Perhaps, the only notable exceptions are refs. [100,101], in which modular weights are used as Froggatt-Nielsen charges, and additional scalar fields of non-zero modular weights play the role of flavons.…”

“…The hierarchical pattern of charged-lepton masses can most naturally be understood within the Froggatt-Nielsen mechanism based on the U(1) FN flavour symmetry [2] and its extensions. The enormous disparity between the neutrino masses and the masses of the charged leptons and quarks can be understood within the seesaw or radiative models of neutrino mass generation or else employing the Weinberg effective operator idea [3] (for a concise review see, e.g., [4]). All these approaches lead naturally to massive Majorana neutrinos.…”