arXiv subjects
Publications and source records attributed to T. K. Kuo.
The renormalization evolution of all parameters in the neutrino mass matrix depends only on one variable, the energy scale. This fact, coupled with rephasing considerations, leads to a set of renormalization invariants, correlating the evolution of physical parameters. For the general three flavor case, we obtain these invariants explicitly and discuss their implications.
In the Standard Model (and MSSM), renormalization effects on neutrino mixing are generally very small and the attractive fixed points are at vanishing neutrino mixing. However for multi-higgs extensions of the Standard Model, renormalization effects on neutrino mixing can be large and nontrivial fixed points are possible. Here we examine a simple two-higgs model. For two flavors, maximal mixing is an attractive infrared fixed point. For three flavors, the neutrino mass matrix evolves towards large off-diagonal elements at low energies. The experimentally suggested bimaximal neutrino mixing pattern is one possible attractive infrared fixed point.
The renormalization group equations for the general 2 by 2, complex, neutrino mass matrix are shown to have exact, analytic solutions. Simple formulas are given for the physical mixing angle, complex phase and mass ratio in terms of their initial values and the energy scales. We also establish a (complex) renormalization invariant relating these parameters. The qualitative features of the physical parameters' renormalization are clearly illustrated in vector field plots. In both the SM and MSSM, maximal mixing is a saddle point.
In the seesaw model with hierarchical Dirac masses, the neutrino mixing angle exhibits the behavior of a narrow resonance. In general, the angle is strongly suppressed, but it can be maximal for special parameter values. We delineate the small regions in which this happens, for the two flavor problem. On the other hand, the physical neutrino masses are hierarchical, in general, except in a large part of the region in which the mixing angle is sizable, where they are nearly degenerate. Our general analysis is also applicable to the RGE of neutrino mass matrix, where we find analytic solutions for the running of physical parameters, in addition to a complex RGE invariant relating them. It is also shown that, if one mixing angle is small, the three neutrino problem reduces to two, two flavor problems.
The parameter imbedding method for the Fredholm equation converts it into an initial value problem in its parameter $λ$. We establish the method for general operator equations of the form $[I + \hat{f}(λ)]ψ= ϕ$. It is particularly useful for studying spontaneous symmetry breaking problems, such as contained in the nonlinear Schwinger-Dyson equation.
We derive a condition for a nontrivial solution of the Schwinger-Dyson equation to be accompanied by a Goldstone bound state. It implies that, for quenched planar QED, although chiral symmetry breaking occurs when there is a cutoff, the continuum limit fails to exist.
For two flavors, the seesaw matrix can be identified with a two dimensional representation of the Lorentz group. This analogy facilitates the computation of physical neutrino parameters, while giving an intuitive understanding of the results. It is found that the induced mixing angle exhibits resonance behavior. For maximal mixing, we derive a precise relation among the right-handed mixing angle, the Majorana mass ratio, and their phase.
We provide a complete and systematic analysis of hermitian, hierarchical quark mass matrices with four texture zeros. Using triangular mass matrices, each pattern of texture zeros is readily shown to lead to a definite relation between the CKM parameters and the quark masses. Nineteen pairs are found to be consistent with present data, and one other is marginally acceptable. In particular, no parallel structure between the up and down mass matrices is found to be favorable with data.
We give a general analysis of neutrino mixing in the seesaw mechanism with three flavors. Assuming that the Dirac and u-quark mass matrices are similar, we establish simple relations between the neutrino parameters and individual Majorana masses. They are shown to depend rather strongly on the physical neutrino mixing angles. We calculate explicitly the implied Majorana mass hierarchies for parameter sets corresponding to different solutions to the solar neutrino problem.
Possible outcomes of neutrino events at both Super-Kamiokande and SNO for a type-II supernova are analyzed considering the uncertainties in SN neutrino spectra (temperature) at emission, which may complicate the interpretation of the observed events. With the input of parameters deduced from the current solar and atmospheric experiments, consequences of direct-mass hierarchy $m_{ν_τ} \gg m_{ν_μ} > m_{ν_{e}}$ and inverted-mass hierarchy $m_{ν_{e}} > m_{ν_μ} \gg m_{ν_τ}$ are investigated. Even if the $ν$ temperatures are not precisely known, we found that future experiments are likely to be able to separate the currently accepted solutions to the solar neutrino problem (SNP): large angle MSW, small angle MSW, and the vacuum oscillation, as well as to distinguish between the direct and inverted mass hierarchies of the neutrinos.
The hierarchical structure in the quark masses and mixings allows its ten physical parameters to be most conveniently encoded in mass matrices of the upper triangular form. We classify these matrices in the hierarchical, minimal parameter basis where the mismatch between the weak and mass eigenstates involves only small mixing angles. Ten such pairs are obtained for the up and down quarks. This analysis can be used to classify texture zeros of general mass matrices. For hermitian mass matrices with five texture zeros, this method yields immediately five pairs of textures with simple, analytic predictions for the quark mixings. Comparison with data indicates that, of the five pairs, three are disfavored, one is marginally acceptable, while the fifth fits well.
Exotic explanations are considered for atmospheric neutrino observations. Our analysis includes matter effects and the mixing of all three neutrinos under the simplifying assumption of only one relevant mixing scale. Constraints from accelerator, reactor and solar neutrinos are included. We find that the proposed mixing mechanisms based on violations of Lorentz invariance or on violations of the equivalence principle cannot explain the recent observations of atmospheric neutrino mixing. However the data still allow a wide range of energy dependences for the vacuum mixing scale, and also allow large electron-neutrino mixing of atmospheric neutrinos. Next generation long baseline experiments will constrain these possibilities.
The hierarchical quark masses and small mixing angles are shown to lead to a simple triangular form for the U- and D-type quark mass matrices. In the basis where one of the matrices is diagonal, each matrix element of the other is, to a good approximation, the product of a quark mass and a CKM matrix element. The physical content of a general mass matrix can be easily deciphered in its triangular form. This parameterization could serve as a useful starting point for model building. Examples of mass textures are analyzed using this method.
In this Brief Report, a non-standard solution to the solar neutrino problem is revisited. This solution assumes that neutrino flavors could have different couplings to gravity, hence, the equivalence principle is violated in this mechanism. The gravity induced mixing has the potential of accounting for the current solar neutrino data from several experiments even for massless neutrinos. We fit this solution to the total rate of neutrino events in the SuperKamiokande detector together with the total rate from other detectors and also with the most recent results of the SuperKamiokande results for the recoil-electron spectrum.
We study the effect of including flavor changing neutral currents (FCNC) in the analysis of the neutrino signal of a supernova burst. When we include the effect of the FCNC which are beyond the standard model (SM) in the study of the MSW resonant conversion, we obtain dramatic changes in the Δm^2-sin^2(2θ) probability contours for neutrino detection.
We show that the current bounds on the leptoquark couplings imply that if leptoquarks are produced in e p collisions, a significant fraction of them could form a leptoquark-quark bound state. The decay of the bound state has a distinct event shape with rapidity gap. A possible application of this observation in the leptoquark search at HERA is discussed.
A supersymmetric $Sp_{L}(6) \times U_{Y}(1)$ model (SUSY $Sp(6)$) is proposed as an extension of the standard electroweak model. The model is applied in a phenomenological study of $B^{0}_{d} \bar{B}^{0}_{d}$ mixing. It is found that the supersymmetric (SUSY) partner $\tilde{z}^{\prime}$ of the extra $Z^{\prime}$ can significantly cancel the other contributions to bring the mixing parameter $x_{d}$ within the experimentally allowed range $0.57 \stackrel{<}{\sim} x_{d} \stackrel{<}{\sim} 0.77$ for a top mass of $158 \stackrel{<}{\sim} m_{t} \stackrel{<}{\sim} 194$ Gev. Other interesting and possibly novel features of flavor changing neutral currents (FCNC) in SUSY theories with horizontal gauge symmetries are pointed out.
We extend our previous work on the precision electroweak tests in the Sp(6)_L X U(1)_Y family model to include for the first time the important Z->b b-bar vertex corrections encoded in a new variable epsilon_b, utilizing all the latest LEP data. We include in our analysis the one loop EW radiative corrections due to the new bosons in terms of epsilon_1, epsilon_b and $ΔΓ_Z$. We find that the correlation between epsilon_1 and epsilon_b makes the combined constraint much stronger than the individual ones. The model is consistent with the recent CDF result of $m_t=174\pm 10^{+13}_{-12}\GeV$, but it can not accomodate $m_t\gsim 195\GeV$.