Radiatively induced lepton masses

The leptonic sector is studied in the context of a scheme proposed to explain fermion mass hierarchy from radiative corrections. In the charged leptonic sector, the masses obey a pattern m_τ:m_μm:m_e ⋍ 1:γ:γ², where γ is the loop expansion parameter. A pair of isosinglet heavy fermions plays an important role in generating mass hierarchy. In the neutrino sector, ϱ_τ acquires a small mass due to the seesaw mechanism induced from the heavy fermions while ϱ_μm and ϱ_e do so from radiative corrections.     

Hierarchical quark and lepton masses in grand unified theories

A general scheme by which fermions in grand unified theories may acquire radiative hierarchical masses is suggested. The observed hierarchy of fermion masses (≈10^?3–10² GeV) appears as a direct reflection of the physics taking place in the 10¹⁴–10¹⁹ GeV energy range. ASU (10) example is shown in which quark and leptons acquire their masses by means of radiative graphs.     

Strange quark matter with dynamically generated quark masses

Bulk properties of strange quark matter (SQM) are investigated within the SU(3) Nambu–Jona-Lasinio model. In the chiral limit the model behaves very similarly to the MIT bag model which is often used to describe SQM. However, when we introduce realistic current quark masses, the strange quark becomes strongly disfavored, because of its large dynamical mass. We conclude that SQM is not absolutely stable.     

Majorana neutrino contributions to renormalization-group scaling of quark and lepton masses

It is shown that the existence of heavy Majorana neutrinos significantly affects the renormalization group scaling of quark and lepton masses with respect to the standard results.     

Diophantine collinearity and lepton masses

The combined requirements of Diophantine quantization (integral or possibly half-integral solutions of mass equations) and collinearity (with respect to a rational quantum number which need not be specified explicitly) lead to limitations on heavy lepton masses, with four allowed values in the 13.3–16.9 GeV range.     

Unifying CP violations of quark and lepton sectors

A preliminary determination of the Dirac phase in the PMNS matrix is \(\delta _\mathrm{PMNS}\approx -\frac{\pi }{2}\). A rather accurately determined Jarlskog invariant J in the CKM matrix is close to the maximum. Since the phases in the CKM and PMNS matrices will be accurately determined in the future, it is an interesting problem to relate these two phases. This can be achieved in a families-unified grand unification if the weak CP violation is introduced spontaneously à la Froggatt and Nielsen at a high energy scale, where only one meaningful Dirac CP phase appears.     

Some new symmetric relations of quark masses and prediction of fourth-generation quark masses

In this study, we discover a mass space defined by generalized Koide relations, named here as k-relations, and achieve some new symmetric relations. These relations can be further used to predict the fourth-generation quark masses in terms of dilation magnitude and angular rotation ratios in the general mass space. Thus far, no theory has been proposed that can constrain the number of generations of quarks; this theory naturally limits the number of generations of quarks.     

Unitarity boomerangs of quark and lepton mixing matrices

The most popular way to present mixing matrices of quarks (CKM) and leptons (PMNS) is the parametrization with three mixing angles and one CP-violating phase. There are two major options in this kind of parametrizations, one is the original Kobayashi–Maskawa (KM) matrix, and the other is the Chau–Keung (CK) matrix. In a new proposal by Frampton and He, a unitarity boomerang is introduced to combine two unitarity triangles, and this new presentation displays all four independent parameters of the KM parametrization in the quark sector simultaneously. In this Letter, we study the relations between KM and CK parametrizations, and also consider the quark–lepton complementarity (QLC) in the KM parametrization. The unitarity boomerang is discussed in the situation of the CK parametrization for comparison with that in the KM parametrization in the quark sector. Then we extend the idea of unitarity boomerang to the lepton sector, and check the corresponding unitarity boomerangs in the two cases of parametrizations.     

Radiatively generated parton distributions for high energy collisions

The gluon and antiquark distributions of the nucleon are generated radiatively using the assumption that at some low resolution scale the nucleon consists entirely of valence quarks and valence-like gluons. The agreement between the uniquely predicted gluon and sea distributions and the available data on deep inelastic structure functions (including also recent low-Q ² measurements) and direct-photon production is demonstrated and discussed in detail. Simple parametrizations of the resulting (positive definite!) parton distributions are presented in the range 10^?4?x≦1 and 0.2?Q ²?10⁶ GeV² as obtained according to the leading- and higher-order renormalization group evolution equations.