Flavor structures of charged fermions and massive neutrinos

Abstract

Most of the free parameters in the Standard Model (SM) -a quantum field theory which has successfully elucidated the behaviors of strong, weak and electromagnetic interactions of all the known fundamental particles, come from the lepton and quark flavors. The discovery of neutrino oscillations has proved that the SM is incomplete, at least in its lepton sector; and thus the door of opportunity is opened to exploring new physics beyond the SM and solving a number of flavor puzzles. In this review article we give an overview of important progress made in understanding the mass spectra, flavor mixing patterns, CP-violating effects and underlying flavor structures of charged leptons, neutrinos and quarks in the past twenty years. After introducing the standard pictures of fermion mass generation, flavor mixing and CP violation in the SM extended with the presence of massive Dirac or Majorana neutrinos, we briefly summarize current experimental knowledge about the flavor parameters of quarks and leptons. Various ways of describing flavor mixing and CP violation are discussed, the renormalization-group evolution of flavor parameters is illuminated, and the matter effects on neutrino oscillations are interpreted. Taking account of possible extra neutrino species, we propose a standard parametrization of the 6 × 6 flavor mixing matrix and comment on the phenomenological aspects of heavy, keV-scale and light sterile neutrinos. We pay particular attention to those novel and essentially model-independent ideas or approaches regarding how to determine the Yukawa textures of Dirac fermions and the effective mass matrix of Majorana neutrinos, including simple discrete and continuous flavor symmetries. An outlook to the future development in unravelling the mysteries of flavor structures is also given.

A full parametrization of the $9\times 9$ active-sterile flavor mixing matrix in the inverse or linear seesaw scenario of massive neutrinos

“…( 20). If the extra neutral fermion sector is switched off (i.e., A 2 = I and R = 0), one will reproduce the exact seesaw formula of the canonical seesaw mechanism [29][30][31]. Moreover, the texture zeros F 22 = 0 and F 13 = F 31 = 0 lead us to the constraint equations…”

“…(10) and (11) have already been obtained in Refs. [29][30][31] for the canonical (type-I) seesaw mechanism. All the nine flavor mixing angles associated with A 1 , B 1 , R 1 and S 1 are very small and can at most reach the level of O(0.1) [35][36][37][38], as they describe the strength of active-sterile (or light-heavy) neutrino mixing and thus are well constrained by current neutrino oscillation data and precision measurements of various electroweak processes.…”

“…Once the extra neutral fermions are switched off (i.e., A 2 = I and R 2 = 0), Eq. ( 19) will be reduced to the canonical seesaw case [29][30][31].…”

“…[16][17][18][19][20][21][22][23][24][25][26][27][28]), a complete description of the 9×9 activesterile flavor mixing matrix for such a seesaw picture has been lacking. Following the full Euler-like parametrization of active-sterile flavor mixing in the type-I or type-(I+II) seesaw mechanism with three sterile neutrinos done previously by one of us [29][30][31], here we are going to present the first full parametrization of the 9 × 9 flavor mixing matrix in terms of 36 Euler rotation angles and 36 CP-violating phases in the inverse or linear seesaw scenario. The exact inverse or linear seesaw formula will also be derived; and possible deviations of the 3 × 3 active neutrino mixing matrix (i.e., the so-called Pontecorvo-Maki-Nakagawa-Sakata lepton flavor mixing matrix [32][33][34]) from its unitary limit will be discussed by calculating the effective Jarlskog invariants and unitarity nonagons.…”

The Structure of Flavor Mixing and Reconstruction of the Mass Matrix

“…origin of flavor mixing as famous unknown problems remain mysteries [1][2][3][4][5]. In the SM, a quark mass matrix is generated from Yukawa couplings…”