arXiv subjects

Yoshitaka Okumura

Publications and source records attributed to Yoshitaka Okumura.

At least 19 recordsLinked to original sources

arXiv2011

Quark/lepton mass and mixing in S_3 invariant model and CP-violation of neutrino

Weak bases of flavors (u, c), (d,s), (e, μ), (ν_e,ν_μ) are assumed as the S_3 doublet and t, b, τ, {ν_τ} are the S_3 singlet and further there are assumed S_3 doublet Higgs (H_1, H_2) and S_3 singlet Higgs H_S. We suggest an S_3 invariant model in which the Yukawa interactions constructed from these S_3 doublets and singlets are S_3 invariant. In this model, we can explain the quark sector mass hierarchy, quark mixing V_{CKM} and measure of CP violation naturally. In the leptonic sector, neutrino masses are assumed to be constructed through the see-saw mechanism from the Majorana mass. The tri-bimaximal-like character of neutrino mixing V_{MNS} can be explained dynamically without any other symmetry restrictions. It is predicted that a quasi-degenerate mass spectroscopy of neutrino is favorable, and values of |V_{MNS}|_{13}, CP violation invariant measure J and the effective Majorana mass | | in neutrino-less double beta decay are not so tiny.

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arXiv2006

Generalized Covariant Derivative on Extra Dimension and Weinberg-Salam Model

The generalized covariant derivative on 5-dimen-sional space including 1-dimensional extra compact space is defined, and, by use of it, the Weinberg-Salam model is reconstructed. The spontaneous breakdown of symmetry takes place owing to the extra dimension under the settings that the Higgs field exists in the extra dimensional space depending on the argument $y$ of this extra space, whereas the gauge and fermion fields do not depend on $y$. Both Yang-Mills-Higgs and fermion Lagrangians in Weinberg-Salam model are correctly reproduced.

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arXiv2005

Noncommutative gauge theory with the symmetry $U(n\otimes m)*$ and standard-like model with fractional charges

$U(n\otimes m)\ast$ gauge field theory on noncommutative spacetime is formulated and the standard-like model with the symmetry ${\text{U}(3_c\otimes 2\otimes 1_{\text{\scriptsize$Y$}})\ast}$ is reconstructed based on it. $\text{U}(n+m)\ast$ gauge group reduces to $\text{U}(n+m)$ on the commutative spacetime which is not ${\text{U}}(N), (N=n+m)$ but isomorphic to $\text{SU}(n)\times\text{SU}(m)\times \text{U}(1)$ in this article. On the noncommutative spacetime, the representation that fields belong to is fundamental, adjoint or bi-fundamental. For this reason, one had to construct the standard model by use of bi-fundamental representations. However, we can reconstruct the standard-like model with only fundamental and adjoint representation and without using bi-fundamental representations. It is well known that the charge of fermion is 0 or $\pm1$ in the U(1) gauge theory on noncommutative spacetime. Thus, there may be no room to incorporate the noncommutative U(1) gauge theory into the standard model because the quarks have fractional charges. However, it is shown in this article that there is the noncommutative gauge theory with arbitrary charges which symmetry is for example $\text{U}(3\otimes 1)\ast$. This type of gauge theory emerges from the spontaneous breakdown of the noncommutative U(4)$\ast$ gauge theory in which the gauge field contains the 0 component $A_μ^0(x,θ)$. The standard-like model in this paper also has fermion fields with fractional charges. Thus, the noncommutative gauge theory with fractional U(1) charges can not exist alone, but it must coexist with noncommutative nonabelian gauge theory.

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arXiv2004

A Dynamical Interpretation of Connes' Unimodularity Condition in Standard Model and Majorana Neutrino

Standard model is minimally extended using the unitary group $G'=U(3)\times SU(2)\times U(1)$ of Connes' color-flavor algebra. In place of Connes' unimodularity condition an extra Higgs is assumed to spontaneously break $G'$ down to standard model gauge group. It is shown that the theory becomes anomaly-free only if right-handed neutrino is present in each generation. It is also shown that the extra Higgs gives rise to large Majorana mass of right-handed neutrino and the model contains new vectorial neutral current.

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arXiv2003

Lorentz covariant field theory on noncommutative spacetime based on DFR algebra

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arXiv2003

Noncommutative gauge theory with arbitrary U(1) charges

It is well-known that the charge of fermion is 0 or $\pm1$ in the U(1) gauge theory on noncommutative spacetime. Since the deviation from the standard model in particle physics has not yet observed, and so there may be no room to incorporate the noncommutative U(1) gauge theory into the standard model because the quarks have fractional charges. However, it is shown in this article that there is the noncommutative gauge theory with arbitrary charges which symmetry is for example SU(3+1)$\ast$. This enveloping gauge group consists of elements $\exp i {\sum_{a=0}^8 T^a α^a(x,θ)\ast+ Q β(x,θ)\ast} $ with $Q=\text{diag}(e,e,e,e') $ and the restriction $\lim_{θ\to0}α^0(x,θ)=0.$ This type of gauge theory is emergent from the spontaneous breakdown of the noncommutative SU(N)$\ast$ or SO(N)$\ast$ gauge theory in which the gauge field contains the 0 component $A_μ^0(x,θ)$. $A_μ^0(x,θ)$ can be eliminated by gauge transformation. Thus, the noncommutative gauge theory with arbitrary U(1) charges can not exist alone, but it must coexist with noncommutative nonabelian gauge theory. This suggests that the spacetime noncommutativity requires the grand unified theory which spontaneously breaks down to the noncommutative standard model with fractionally charged quarks.

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arXiv2003

Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory

It is shown that the one-loop two-point amplitude in {\it Lorentz-invariant} non-commutative (NC) $ϕ^3$ theory is finite after subtraction in the commutative limit and satisfies the usual cutting rule, thereby eliminating the unitarity problem in Lorentz-non-invariant NC field theory in the approximation considered.

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arXiv2003

Lorentz invariant nonabelian gauge theory on noncommutative space-time and BRST symmetry

Lorentz covariance is the fundamental principle of every relativistic field theory which insures consistent physical descriptions. Even if the space-time is noncommutative, field theories on it should keep Lorentz covariance. In this paper, the nonabelian gauge theory on noncommutative spacetime is defined and its Lorentz invariance is maintained based on the idea of Carlson, Carone and Zobin. The deviation from the standard model in particle physics has not yet observed, and so any model beyond standard model must reduce to it in some approximation. Noncommutative gauge theory must also reproduce standard model in the limit of noncommutative parameter $θ^{μν}\to0$. Referring to Jur$\check{\text{c}}$o {\it et. al.}, we will construct the nonabelian gauge theory that deserves to formulate standard model. BRST symmetry is very important to quantize nonabelian gauge theory and construct the covariant canonical formulation. It is discussed about the fields in noncommutative gauge theory without considering those components. Scale symmetry of ghost fields is also discussed.

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arXiv2002

Lorentz-Invariant Non-Commutative Space-Time Based On DFR Algebra

It is argued that the familiar algebra of the non-commutative space-time with $c$-number $θ^{μν}$ is inconsistent from a theoretical point of view. Consistent algebras are obtained by promoting $θ^{μν}$ to an anti-symmetric tensor operator ${\hatθ}^{μν}$. The simplest among them is Doplicher-Fredenhagen-Roberts (DFR) algebra in which the triple commutator among the coordinate operators is assumed to vanish. This allows us to define the Lorentz-covariant operator fields on the DFR algebra as operators diagonal in the 6-dimensional $θ$-space of the hermitian operators, ${\hatθ}^{μν}$. It is shown that we then recover Carlson-Carone-Zobin (CCZ) formulation of the Lorentz-invariant non-commutative gauge theory with no need of compactification of the extra 6 dimensions. It is also pointed out that a general argument concerning the normalizability of the weight function in the Lorentz metric leads to a division of the $θ$-space into two disjoint spaces not connected by any Lorentz transformation so that the CCZ covariant moment formula holds true in each space, separately. A non-commutative generalization of Connes' two-sheeted Minkowski space-time is also proposed. Two simple models of quantum field theory are reformulated on $M_4\times Z_2$ obtained in the commutative limit.

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arXiv2000

A Field-Theoretic Approach to Connes' Gauge Theory on $M_4\times Z_2$

Connes' gauge theory on $M_4\times Z_2$ is reformulated in the Lagrangian level. It is pointed out that the field strength in Connes' gauge theory is not unique. We explicitly construct a field strength different from Connes' one and prove that our definition leads to the generation-number independent Higgs potential. It is also shown that the nonuniqueness is related to the assumption that two different extensions of the differential geometry are possible when the extra one-form basis $χ$ is introduced to define the differential geometry on $M_4\times Z_2$. Our reformulation is applied to the standard model based on Connes' color-flavor algebra. A connection between the unimodularity condition and the electric charge quantization is then discussed in the presence or absence of $ν_R$.

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arXiv1999

BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry

Noncommutative geometry(NCG) on the discrete space successfully reproduces the Higgs mechanism of the spontaneously broken gauge theory, in which the Higgs boson field is regarded as a kind of gauge field on the discrete space. We could construct the generalized differential geometry(GDG) on the discrete space $M_4\times Z_N$ which is very close to NCG in case of $M_4\times Z_2$. GDG is a direct generalization of the differential geometry on the ordinary manifold into the discrete one. In this paper, we attempt to construct the BRST invariant formulation of spontaneously broken gauge theory based on GDG and obtain the BRST invariant Lagrangian with the t'Hooft-Feynman gauge fixing term.

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arXiv1999

Generalized Chern-Simons Form and Descent Equation

We present the general method to introduce the generalized Chern-Simons form and the descent equation which contain the scalar field in addition to the gauge fields. It is based on the technique in a noncommutative differential geometry (NCG) which extends the $N$-dimensional Minkowski space $M_N$ to the discrete space such as $M_N\times Z_2$ with two point space $Z_2$. However, the resultant equations do not depend on NCG but are justified by the algebraic rules in the ordinary differential geometry.

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arXiv1998

Lagrangian Formulation of Connes' Gauge Theory

It is shown that Connes' generalized gauge field in non-commutative geometry is derived by simply requiring that Dirac lagrangian be invariant under local transformations of the unitary elements of the algebra, which define the gauge group. The spontaneous breakdown of the gauge symmetry is guaranteed provided the chiral fermions exist in more than one generations as first observed by Connes-Lott. It is also pointed out that the most general gauge invariant lagrangian in the bosonic sector has two more parameters than in the original Connes-Lott scheme.

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arXiv1998

Gauge Theories Coupled to Fermions in Generation

Gauge theories coupled to fermions in generation are reformulated in a modified version of extended differential geometry with the symbol $χ$. After discussing several toy models, we will reformulate in our framework the standard model based on Connes' real structure. It is shown that for the most general bosonic lagrangin which is required to also reconstruct N=2 super Yang-Mills theory Higgs mechanism operates only for more than one generation as first pointed out by Connes and Lott.

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arXiv1997

An estimation of the Higgs boson mass in the two loop approximation in a noncommutative differential geometry

In the two loop approximation, a renormalization group analysis of the Higgs boson mass is performed based on the condition $g^2=(5/3)g'^2=4λ$ for SU(2)_L, U(1)_Y gauge and the Higgs quartic coupling constants, respectively. This condition is introduced in the new scheme of our noncommutative differential geometry (NCG) for the reconstruction of the standard model. However, contrary to SU(5) GUT without supersymmetry, the grand unification of coupling constants is not realized in this scheme. The physical mass of the Higgs boson depends strongly on the top quark mass $m_{top}$ through the Yukawa coupling of the top quark in the $β$ functions.The two loop effect lowers the numerical value calculated within the one loop approximation by several GeV. The Higgs boson mass varies from 150.25GeV to 167.15GeV corresponding to 169.34GeV< m_{top}<181.02GeV. We find the Higgs boson mass m_H=158.18GeV for m_{top}=175.04GeV and $m_H=166.12GeV for m_{top}=180.34GeV.

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arXiv1997

Left-right symmetric gauge model in a noncommutative geometry on $M_4\times Z_4$

The left-right symmetric gauge model with the symmetry of $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)$ is reconstructed in a new scheme of the noncommutative differential geometry (NCG) on the discrete space $M_4\times Z_4$ which is a product space of Minkowski space and four points space. The characteristic point of this new scheme is to take the fermion field to be a vector in a 24-dimensional space which contains all leptons and quarks. Corresponding to this specification, all gauge and Higgs boson fields are represented in $24\times 24$ matrix forms. We incorporate two Higgs doublet bosons $h$ and $SU(2)_R$ adjoint Higgs $ξ_R$ which are as usual transformed as $(2,2^\ast,0)$ and $(1,3,-2)$ under $SU(2)_L\times SU(2)_R\times U(1)$, respectively. Owing to the revise of the algebraic rules in a new NCG, we can obtain the necessary potential and interacting terms between these Higgs bosons which are responsible for giving masses to the particles included. Among the Higgs doublet bosons, one CP-even scalar boson survives in the weak energy scale and other four scalar bosons acquire the mass of the $SU(2)_R\times U(1)$ breaking scale, which is similar to the situation in the standard model. $ξ_R$ is responsible to spontaneously break $SU(2)\ma{R} \times U(1)$ down to $U(1)\ma{Y}$ and so well explains the seesaw mechanism. Up and down quarks have the different masses through the vacuum expectation value of $h$.

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arXiv1996

Renormalization group analysis of the Higgs boson mass in a noncommutative differential geometry

Within one loop approximation, the renormalization group analysis of the Higgs boson mass is performed with an initial condition induced by $m_{_H}=\sqrt{2}m_{_W}$ which is presented in the new scheme of our noncommutative differential geometry for the reconstruction of the standard model. This initial condition holds at energy derived from $g^2=(5/3)g'^2$ with the running SU(2)$_{_L}$ and U(1)$_{_Y}$ gauge coupling constants. $\sin^2θ_{_W}=3/8$ is obtained under same conditions. However, contrary to ${\rm SU(5)}$ GUT without supersymmetry, the grand unification of coupling constant is not realized in this scheme. The physical mass of the Higgs boson considerably depends on the top quark mass $m_{top}$ since the top quark Yukawa coupling constants gives a large negative contribution to $β$ function of the Higgs quartic coupling constant in wide range. The Higgs boson mass varies from 153.42GeV to 191.94GeV corresponding to $168{\rm GeV}\leq m_{top}\leq 192{\rm GeV}$. We find $m_{_H}=164.01$GeV for $ m_{top}=175$GeV and $m_{_H}=171.92$GeV for $ m_{top}=180$GeV.

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arXiv1996

Non-Commutative Differential Geometry on Discrete Space $M_4\times Z\ma{N}$ and Gauge Theory

The algebra of non-commutative differential geometry (NCG) on the discrete space $M_4\times Z\ma{N}$ previously proposed by the present author is improved to give the consistent explanation of the generalized gauge field as the generalized connection on $M_4\times Z\ma{N}$. The nilpotency of the generalized exterior derivative ${\mbf d}$ is easily proved. The matrix formulation where the generalized gauge field is denoted in matrix form is shown to have the same content with the ordinary formulation using {\mbf d}, which helps us understand the implications of the algebraic rules of NCG on $M_4\times Z\ma{N}$. The Lagrangian of spontaneously broken gauge theory which has the extra restriction on the coupling constant of the Higgs potential is obtained by taking the inner product of the generalized field strength. The covariant derivative operating on the fermion field determines the parallel transformation on $M_4\times Z\ma{N}$, which confirms that the Higgs field is the connection on the discrete space. This implies that the Higgs particle is a gauge particle on the same footing as the weak bosons. Thus, it is expected that the mass relation $m\ma{H}=\frac{4}{\sqrt{3}}m\ma{W}\sinθ\ma{W}$ proposed by the present author holds without any correction in the same way as the mass relation $m\ma{W}=m\ma{Z}\cosθ\ma{W}$. The Higgs kinetic and potential terms are regarded as the curvatures on $M_4\times Z\ma{N}$.

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