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Register a new userReal and Imaginary Elements of Fermion Mass Matrices
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Prompted by the recent better determination of the angles of the unitarity triangle, we re-appraise the problem of finding simple fermion mass textures, possibly linked to some symmetry principle and compatible with grand unification. In particular, the indication that the angle alpha is close to rectangle turns out to be the crucial ingredient leading us to single out fermion mass textures whose elements are either real or purely imaginary. In terms of the five parameters ascribed to the quark sector, these textures reproduce the eight experimental data on quark mass ratios and mixings within 1 sigma. When embedded in an SU(5) framework, these textures suggest a common origin for quark and lepton CP violations, also linked to the spontaneous breaking of the gauge group.
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We study a flavor model that the quark sector has the $S_3$ modular symmetry,while the lepton sector has the $A_4$ modular symmetry. Our model leads to characteristic quark mass matrices which are consistent with experimental data of quark masses, mixing angles and the CP violating phase. The lepton sector is also consistent with the experimental data of neutrino oscillations. We also study baryon and lepton number violations in our flavor model.
We present empirical relations that connect the dimensionless ratios of fermion masses for the charged lepton, up-type quark and down-type quark sectors. Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, beta=Arg(2 - exp^{-i*gamma}). According to this relation, the measured value of beta is close to the maximum value that can be reached. Finally, the particular mass relations with the charged lepton sector find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.
We propose a model that all quark and lepton mass matrices have the same zero texture. Namely their (1,1), (1,3) and (3,1) components are zeros. The mass matrices are classified into two types I and II. Type I is consistent with the experimental data in quark sector. For lepton sector, if seesaw mechanism is not used, Type II allows a large $ u_mu - u_tau$ mixing angle. However, severe compatibility with all neutrino oscillation experiments forces us to use the seesaw mechanism. If we adopt the seesaw mechanism, it turns out that Type I instead of II can be consistent with experimental data in the lepton sector too.
Grand Unified Theories predict relationships between the GUT-scale quark and lepton masses. Using new data in the context of the MSSM, we update the values and uncertainties of the masses and mixing angles for the three generations at the GUT scale. We also update fits to hierarchical patterns in the GUT-scale Yukawa matrices. The new data shows not all the classic GUT-scale mass relationships remain in quantitative agreement at small to moderate tan beta. However, at large tan beta, these discrepancies can be eliminated by finite, tan beta-enhanced, radiative, threshold corrections if the gluino mass has the opposite sign to the wino mass.
By employing QCD inequalities, we discuss appearance of the pion condensate for both real and imaginary isospin chemical potentials, taking also into account imaginary quark chemical potential. We show that the charged pion can condense for real isospin chemical potential, but not for imaginary one. Furthermore, we evaluate the expectation value of the neutral-pion field for imaginary isospin chemical potential by using framework of the twisted mass. As a result, it is found that the expectation value becomes zero for the finite current-quark mass, whereas the Banks-Casher relation is obtained in the massless limit.
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