Related papers: New Perspective on Fermion Mass Matrices
For any $n\ge 2$ and fixed $k\ge 1$, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring $\mathbb{M}_n(\mathbb{F})$ to be written as a sum of an invertible matrix $U$ and a nilpotent matrix…
The observed hierarchy in the fermion masses, which imply a set of small mass ratios, is not naturally small regarding 't Hooft's criteria. In this work, in a model independent approach, we introduce a set of conditions by which fermion…
One can always write the mass matrix for Weyl spinors so that it is symmetric. However this is often not a good idea. It is usually incompatible with irreducibility of the fermion representations. As a result, a symmetrized mass term hides…
The crossing matrix of a braid on $N$ strands is the $N\times N$ integer matrix with zero diagonal whose $i,j$ entry is the algebraic number (positive minus negative) of crossings by strand $i$ over strand $j$ . When restricted to the…
A parameter free, model independent analysis of quark mass matrices is carried out. We find a representation in terms of a diagonal mass matrix for the down (up) quarks and a suitable matrix for the up (down) quarks, such that the mass…
If neutrinos have masses, why are they so tiny? Are these masses of the Dirac type or of the Majorana type? We are already familiar with the mechanism of how to obtain a tiny Majorana neutrino mass by the famous see-saw mechanism. The…
The Large N expansion in gauge models with an NJL mechanism is discussed in view of the resulting fermionic mass matrix. A hidden symmetry model is introduced.
We show that the four-zero texture of Hermitian quark mass matrices can survive current experimental tests: it is able to yield sufficiently large predictions for the flavor mixing parameter $|V_{ub}/V_{cb}|$ and the CP-violating parameter…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
A microscopic theory is presented for identifying shape-phase structures and transitions in interacting fermion systems. The method provides a microscopic description for collective shape-phases, and reveals detailed dependence of such…
Symmetries in neutrino physics are explored using analogies to fermion pairing in many-body systems. In particular, the SO(5) symmetry of the most general neutrino mass Hamiltonian with both Dirac and Majorana mass terms as well as the…
In this talk we survey some of the recent promising developments in the search for the theory behind neutrino mass and mixing, and indeed all fermion masses and mixing. The talk is organized in terms of a neutrino mass models decision tree…
We propose a neutrino mass matrix texture bearing a suitable correlation $m_{22}=-2\,m_{13}$ and study its phenomenological implications. In light of both normal and inverted hierarchies, the texture imposes specific bounds on some…
In this and subsequent papers, one dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the…
State symmetries are defined as permutations which act on vector spaces of column vectors and square matrices, resulting in isotropy groups for specific vector spaces. A large number of properties for such objects is shown, to provide a…
After an Introduction briefly describing the rise and fall of the three-zero texture of the Zee model, we discuss still-allowed two-zero textures for the Majorana three-neutrino mass matrix. Finally, a model with two right-handed neutrinos…
The analogues of elementary particles have been extensively searched for in condensed matter systems because of both scientific interests and technological applications. Recently massless Dirac fermions were found to emerge as low energy…
We study the implications of the simultaneous existence of a texture zero and a vanishing minor in the neutrino mass matrix. There are thirty six possible texture structures of this type, twenty one of which reduce to two texture zero cases…
We carry out a complete and systematic study of all the possible one-zero textures for the neutrino mass matrix in light of the recent neutrino oscillation data which hint to a relatively large non-vanishing value for the smallest mixing…
We study all possible texture zeros in the Majorana neutrino mass matrix which are allowed from neutrino oscillation as well as cosmology data when the charged lepton mass matrix is assumed to take the diagonal form. In case of one-zero…