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T. K. Kuo

Publications and source records attributed to T. K. Kuo.

At least 19 recordsLinked to original sources
arXiv2024

Hermitian Matrix Diagonalization and its Symmetry Properties

A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These equations are simple in structure and manifestly invariant in form under the symmetry operations of dilatation, translation, rephasing and permutation. When applied to the problem of neutrino oscillation in matter they produced two new ``matter invariants" which are confirmed by available data.

hep-ph↗
arXiv2022

Eigenvector-eigenvalue identities and an application to flavor physics

The eigenvector-eigenvalue identities are expanded to include general mixing parameters. Some simple relations are obtained and they reveal an intricate texture of connections between the eigenvalues and the mixing parameters. Permutation symmetry ($S_{3}\times S_{3}$) plays an indispensable role in our analysis. It is the guiding principle for the understanding of our results -- all of them are tensor equations under permutation.

hep-ph↗
arXiv2020

Rephasing invariance and permutation symmetry in flavor physics

With some modifications, the arguments for rephasing invariance can be used to establish permutation symmetry for the standard model. The laws of evolution of physical variables, which transform as tensors under permutation, are found to obey the symmetry, explicitly. We also propose to use a set of four mixing parameters, with unique properties, which may serve to characterize flavor mixing.

hep-ph↗
arXiv2020

Flavor Mixing and the Permutation Symmetry among Generations

In the standard model, the permutation symmetry among the three generations of fundamental fermions is usually regarded to be broken by the Higgs couplings. It is found that the symmetry is restored if we include the mass matrix parameters as physical variables which transform appropriately under the symmetry operation. Known relations between these variables, such as the renormalization group equations, as well as formulas for neutrino oscillations (in vacuum and in matter), are shown to be covariant tensor equations under the permutation symmetry group.

hep-ph↗
arXiv2018

Features of Neutrino Mixing

The elements (squared) of the neutrino mixing matrix are found to satisfy, as functions of the induced mass, a set of differential equations. They show clearly the dominance of pole terms when the neutrino masses "cross". Using the known vacuum mixing parameters as initial conditions, it is found that these equations have very good approximate solutions, for all values of the induced mass. The results are applicable to Long Baseline Experiments (LBL).

hep-ph↗
arXiv2017

Nucleon-anti-nucleon intruder state of Dirac equation for nucleon in deep scalar potential well

We solve the Dirac radial equation for a nucleon in a scalar Woods-Saxon potential well of depth $V_0$ and radius $r_0$. A sequence of values for the depth and radius are considered. For shallow potentials with $-1000 MeV\lesssim V_0 < 0$ the wave functions for the positive-energy states $Ψ_+(r)$ are dominated by their nucleon component $g(r)$. But for deeper potentials with $V_0 \lesssim -1500 MeV $ the $Ψ_+(r)$s begin to have dominant anti-nucleon component $f(r)$. In particular, a special intruder state enters with wave function $Ψ_{1/2}(r)$ and energy $E_{1/2}$. We have considered several $r_0$ values between 2 and 8 fm. For $V_0 \lesssim -2000 MeV$ and the above $r_0$ values, $Ψ_{1/2}$ is the only bound positive-energy state and has its $g(r)$ closely equal to $-f(r)$, both having a narrow wave-packet shape centered around $r_0$. The $E_{1/2}$ of this state is practically independent of $V_0$ for the above $V_0$ range and obeys closely the relation $E_{1/2}=\frac{\hbar c}{r_0}$.

nucl-th↗
arXiv2016

Renormalization of the Neutrino Mass Matrix

In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.

hep-ph↗
arXiv2016

Renormalization of the quark mass matrix

Using a set of rephasing-invariant variables, it is shown that the renormalization group equations for quark mixing parameters can be written in a form that is compact, in addition to having simple properties under flavor permutation. We also found approximate solutions to these equations if the quark masses are hierarchical or nearly degenerate.

hep-ph↗
arXiv2013

Properties of the Neutrino Mixing Matrix

For neutrino mixing we propose to use the parameter set $X_{i}$ $(=|V_{ei}|^{2})$ and $Ω_{i}$ $(=ε_{ijk}|V_{μj}|^{2}|V_{τk}|^{2})$, with two constraints. These parameters are directly measurable since the neutrino oscillation probabilities are quadratic functions of them. Physically, the set $Ω_{i}$ signifies a quantitative measure of $μ-τ$ asymmetry. Available neutrino data indicate that all the $Ω_{i}$'s are small $(\lesssim O(10^{-1}))$, but with large uncertainties. The behavior of $Ω_{i}$ as functions of the induced neutrino mass in matter are found to be simple, which should facilitate the analyses of long baseline experiments.

hep-ph↗
arXiv2011

Rephasing invariance and the neutrino mu-tau symmetry

The vacuum neutrino mixing is known to exhibit an approximate $μ-τ$ symmetry, which was shown to be preserved for neutrino propagating in matter. This symmetry reduces the neutrino transition probabilities to very simple forms when expressed in a rephasing invariant parametrization introduced earlier. Applications to long baseline experiments are discussed.

hep-ph↗
arXiv2010

Rephasing invariance and neutrino mixing

A rephasing invariant parametrization is introduced for three flavor neutrino mixing. For neutrino propagation in matter, these parameters are shown to obey evolution equations as functions of the induced neutrino mass. These equations are found to preserve (approximately) some characteristic features of the mixing matrix, resulting in solutions which exhibit striking patterns as the induced mass varies. The approximate solutions are compared to numerical integrations and found to be quite accurate.

hep-ph↗
arXiv2010

Neutrino mixing in matter

Three-neutrino mixing in matter is studied through a set of evolution equations which are based on a rephasing invariant parametrization. Making use of the known properties of measured neutrino parameters, analytic, approximate, solutions are obtained. Their accuracy is confirmed by comparison with numerical integration of these equations. The results, when expressed in the elements squared of the mixing matrix, exhibit striking patterns as the matter density varies.

hep-ph↗
arXiv2009

Mass Matrices and Their Renormalization

We obtain explicitly the renormalization group equations for the quark mass matrices in terms of a set of rephasing invariant parameters. For a range of assumed high energy values for the mass ratios and mixing parameters, they are found to evolve rapidly and develop hierarchies as the energy scale decreases. To achieve the experimentally observed high degree of hierarchy, however, the introduction of new models with specific properties becomes necessary.

hep-ph↗
arXiv2006

Probing neutrino mass hierarchies and $ϕ_{13}$ with supernova neutrinos

We investigate the feasibility of probing the neutrino mass hierarchy and the mixing angle $ϕ_{13}$ with the neutrino burst from a future supernova. An inverse power-law density $ρ\sim r^{n} $ with varying $n$ is adopted in the analysis as the density profile of a typical core-collapse supernova. The survival probabilities of $ν_{e}$ and $\barν_{e}$ are shown to reduce to two-dimensional functions of $n$ and $ϕ_{13}$. It is found that in the $n-\sin^{2} ϕ_{13}$ parameter space, the 3D plots of the probability functions exhibit highly non-trivial structures that are sensitive to the mass hierarchy, the mixing angle $ϕ_{13}$, and the value of $n$. The conditions that lead to observable differences in the 3D plots are established. With the uncertainty of $n$ considered, a qualitative analysis of the Earth matter effect is also included.

hep-ph↗
arXiv2005

Rephasing Invariance and Hierarchy of the CKM Matrix

We identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of $λ^2$, from $λ^2$ to $λ^8$. It is shown that, at the present level of accuracy, only the first three parameters are needed to fit all available data on flavor physics.

hep-ph↗
arXiv2005

Rephasing Invariant Parametrization of Flavor Mixing Matrices

The three-flavor mixing matrix can be parameterized by the rephasing invariants Gamma_{ijk} = V_{1i} V_{2j} V_{3k}. This formulation brings out the inherent symmetry of the problem and has some appealing features. Examples illustrating the parametrization and applications to quark mixing are presented.

hep-ph↗
arXiv2002

Lorentz transformation and vector field flows

The parameter changes resulting from a combination of Lorentz transformation are shown to form vector field flows. The exact, finite Thomas rotation angle is determined and interpreted intuitively. Using phase portraits, the parameters evolution can be clearly visualized. In addition to identifying the fixed points, we obtain an analytic invariant, which correlates the evolution of parameters.

math-ph↗