Narrow Results

We discuss mass matrices with four texture zeros for the quarks and leptons. The three mixing angles for the quarks and leptons are functions of the fermion masses. The results agree with the experimental data. The ratio of the masses of the first two neutrinos is given by the solar mixing angle. The neutrino masses are calculated: $m_1\approx 0.004\mathrm{\text{eV}}$, $m_2\approx 0.010\mathrm{\text{eV}}$ and $m_3\approx 0.070\mathrm{\text{eV}}$.

In this paper, we propose a simple model based on the S₃ flavor symmetry, in which a perturbation ansatz is suggested that the flavor symmetry is explicitly broken down via S₃$\to$Z₂$\to \varnothing$ in the up-quark sector and via S₃$\to$Z₃$\to \varnothing$ in the down-quark sector. Our model is successful in obtaining the strong hierarchy of mass matrices of both up-type quarks and down-type quarks, but unsuccessful in obtaining the realistic mixing between the third generation and the first two, as in other models based on S₃ flavor symmetry proposed in the literature. Through detailed analysis, we find the reason for the unsuccesses in our model which is related to the reducibility of the three-dimensional representation of the S₃ group. We conclude that any perturbations in mass matrices preserving the partial symmetry of S₃ cannot help getting realistic mixing between the third generation and first two without fine-tuning.

The flavor mixing of the quarks is described by the CKM matrix, which is parametrized by three mixing angles and one phase parameter. We discuss a new texture for the two mass matrices of the six quarks. The three flavor mixing angles can be calculated — they are functions of the ratios of the quark masses. The third mixing angle is given by the CKM matrix element $\left|V_{cb}\right|$. We find: $\left|V_{cb}\right|\simeq 2(m_s/m_b)$. The calculated mixing angles agree with the mixing angles, measured in many experiments.

I give an overview of some basic properties of massive neutrinos. The first part of this talk is devoted to three fundamental questions about three known neutrinos and to their flavor issues — the mass spectrum, mixing pattern and CP violation. The second part of this talk is to highlight a few hot topics at the frontiers of neutrino physics and neutrino astrophysics, including the naturalness and testability of TeV seesaw mechanisms at the LHC, effects of nonstandard interactions on neutrino oscillations, flavor distributions of ultrahigh-energy cosmic neutrinos at neutrino telescopes, collective flavor oscillations of supernova neutrinos, flavor effects in thermal leptogenesis, the GSI anomaly and Mössbauer neutrino oscillations, and so on. I finally make some concluding remarks for the road ahead.

The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle in particle physics, and it must be highly correlated with the hierarchy of quark flavor mixing. This chapter is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP-violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.

In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are nonsingular in $𝜀=p^2-m_n^2$, where $p$ is the external four-momentum and $m_n$ is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.

In the light of several recent analyses pointing toward texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and simplified structure of texture specific quark mass matrices in a generalized “$u$-diagonal” basis within the Standard Model framework using the unitarity of CKM matrix and the observed hierarchies in quark mass spectra and mixing angles. It is observed that the measured $1\sigma$ values of the three physical parameters namely $m_u$, $m_d$ and $s_{12}$ naturally lead to the vanishing of (11) element in the down type quark mass matrix and that the single measurable CP violating phase ${\delta }_{13}$ in the CKM matrix is sufficient enough in $M_d^{\prime }$ to explain the observed mixing pattern in a suitable basis. The leading order as well as exact analytic phenomenological solutions are addressed for the modest pattern of quark mass matrices derived from CKM matrix and precision measurements of mixing parameters.

The fermion flavor structure is investigated by bilinear decomposition of the mass matrix after EW symmetry breaking, and the roles of factorized matrices in flavor mixing and mass generation are explored. On a new Yukawa basis, the minimal parameterization of flavor mixing is realized containing two relative phases and two free $\mathrm{\text{SO}}{(2)}_L$ rotation angles. It is shown that flavor mixing can be addressed from four independent parameters. The validity of the flavor mixing structure is checked in both the lepton and quark sectors. Under the decomposition of flavor mixing, fermion mass matrices are reconstructed in the hierarchy limit. A flat mass matrix with all elements equal to 1 arises naturally from the requirement that homology exists between up-type and down-type fermion mass matrices. Some hints of a flat matrix and flavor breaking are also discussed.

The possible formation of tensor condensates originated from a tensor-type interaction between quarks is investigated in the three-flavor Nambu–Jona–Lasinio model including the Kobayashi–Maskawa–’t Hooft interaction, which leads to flavor mixing. It is shown that independent two tensor condensates appear and a tensor condensate related to the strange quark easily occurs by the effect of the flavor mixing compared with one related to light quarks. Also, it is shown that the tensor condensate related to the strange quark appears at a slightly smaller chemical potential if the Kobayashi–Maskawa–’t Hooft interaction is included, due to the flavor mixing effect. It is also shown that the two kinds of tensor condensates may coexist in a certain quark chemical potential due to the flavor mixing.

To obtain the equation of state of quark matter and construct hybrid stars, we calculate the thermodynamic potential in the three-flavor Nambu–Jona-Lasinio model including the tensor-type four-point interaction and the Kobayashi–Maskawa–’t Hooft interaction. To construct the hybrid stars, it is necessary to impose the $\beta$ equilibrium and charge neutrality conditions on the system. It is shown that tensor condensed phases appear at large chemical potential. Under the possibility of the existence of the tensor condensates, the relationship between the radius and mass of hybrid stars is estimated.