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Kentaro Kojima

Publications and source records attributed to Kentaro Kojima.

At least 19 recordsLinked to original sources
arXiv2026

SU(9) grand unified model with rank-reducing discrete boundary conditions on $T^2/\mathbb Z_4$

We study a six-dimensional SU(9) grand unified model with rank-reducing discrete boundary conditions and continuous Wilson line phases on the orbifold $T^2/\mathbb Z_4$. We show that the model can realize grand unification of the Standard Model gauge interactions and electroweak symmetry breaking via the Hosotani mechanism. The model has several attractive features. Two Higgs doublets arise as zero modes of the extra-dimensional components of the gauge field, and the leptons and quarks in each generation are separately embedded into two bulk multiplets, in the ${\bf 36}$ and ${\bf 84}$ representations of SU(9), respectively, without exotic matter. Furthermore, proton decay processes mediated by the gauge bosons in the bulk are absent, because the leptons and quarks belong to different bulk multiplets.

hep-ph↗
arXiv2025

Models with rank-reducing discrete boundary conditions on $T^2/{\mathbb Z}_4$

We study six-dimensional $SU(n)$ gauge models with rank-reducing discrete boundary conditions on the orbifold $T^2/{\mathbb Z}_4$, without and with continuous Wilson line phases. For the latter case, we find that a minimal model can describe the breakdown of the electroweak symmetry based on an $SU(6)$ gauge group. This model possesses excellent features that two Higgs doublets come from the zero modes of the extra-dimensional gauge field, and the quarks in each generation can be unified into one multiplet, without exotic quarks, as the zero modes of a bulk field in the $\boldsymbol{15}$ representation of $SU(6)$. There exists a vacuum where the electroweak symmetry is slightly broken by the Hosotani mechanism, with the addition of suitable bulk fields. %adding suitable bulk fields, and Interestingly, quadratic divergences are not reintroduced into the Higgs masses from the tadpole terms of the field strength localized on fixed points, not only at one-loop level but also at higher orders.

hep-ph↗
arXiv2024

Chained computerized adaptive testing for the Force Concept Inventory

Although conceptual assessment tests are commonly administered at the beginning and end of a semester, this pre-post approach has inherent limitations. Specifically, education researchers and instructors have limited ability to observe the progression of student conceptual understanding throughout the course. Furthermore, instructors are limited in the usefulness of the feedback they can give to the students involved. To address these challenges, we propose an alternative approach that leverages computerized adaptive testing (CAT) and increasing the frequency of CAT-based assessments during the course, while reducing the test length per administration, thus keeping or decreasing the total number of test items administered throughout the course. The feasibility of this idea depends on how far the test length per administration can be reduced without compromising the test accuracy and precision. Specifically, the overall test length is desired to be shorter than when the full assessment is administered as a pretest and subsequent post-test. To achieve this goal, we developed a CAT algorithm that we call Chain-CAT. This algorithm sequentially links the results of each CAT administration using collateral information. We developed the Chain-CAT algorithm using the items of the Force Concept Inventory (FCI) and analyzed the efficiency by numerical simulations. We found that collateral information significantly improved the test efficiency, and the overall test length could be shorter than the pre-post method. Without constraints for item balancing and exposure control, simulation results indicated that the efficiency of Chain-CAT is comparable to that of the pre-post method even if the length of each CAT administration is only 5 items and the CAT is administered 9 times throughout the semester. (To continue, see text.)

physics.ed-ph↗
arXiv2024

Vacuum structure of an eight-dimensional $SU(3)$ gauge theory on a magnetized torus

We analyze the vacuum structure of an eight-dimensional non-abelian gauge theory with a compactified four-dimensional torus as the extra dimensions. As a non-trivial background configuration of the gauge field of an $SU(n)$ gauge group, we suppose a magnetic flux in two extra dimensions, and continuous Wilson line phases are also involved. We introduce matter fields and calculate the mass spectrum of low-energy modes appearing in a four-dimensional effective theory in an $SU(3)$ model as an explicit example. As expected, potentially tachyonic states in four-dimensional modes appear from extra-dimensional gauge fields that couple to the flux background since the gauge group is simply connected. The Wilson line phases give a non-vanishing contribution to their masses, and we have a low-energy mass spectrum without tachyonic states, given that these phases take an appropriate value. To verify the validity of the values of the Wilson line phases, we examine the one-loop effective potential for these phases and explicitly show the contribution from each type of field present in our model. It is clarified that, although there seems to be no local minimum in the potential for the Wilson line phases in the pure Yang-Mills case, by including matter fields, we could find a vacuum configuration where tachyonic states disappear.

hep-ph↗
arXiv2023

Mass spectrum in a six-dimensional $SU(n)$ gauge theory on a magnetized torus

We examine six-dimensional $SU(n)$ gauge theories compactified on a two-dimensional torus with a constant magnetic flux background to obtain a comprehensive low-energy mass spectrum. We introduce general background configurations including the magnetic flux and continuous Wilson line phases, consistent with classical equations of motion. Under the standard gauge fixing procedure, the complete mass spectrum in low-energy effective theory for the $SU(n)$ case is newly presented without imposing restrictions on the gauge fixing parameter. Our analysis confirms the inevitable existence of tachyonic modes, which neither depend on the background configurations of Wilson line phases nor are affected by the gauge fixing parameter. Masses for some low-energy modes exhibit dependence on the gauge fixing parameter, and these modes are identified as would-be Goldstone bosons that are absorbed by massive four-dimensional vector fields. We discuss the phenomenological implications associated with stabilization or condensation of the tachyonic states. Various mass spectra and symmetry-breaking patterns are expected with flux backgrounds in the $SU(n)$ case. They are helpful for constructing phenomenologically viable models beyond the standard model, such as gauge-Higgs unification and grand unified theories.

hep-th↗
arXiv2023

Grand Gauge-Higgs Unification on $T^2/{\mathbb Z}_3$ via Diagonal Embedding Method

We study a novel six-dimensional gauge theory compactified on the $T^2/{\mathbb Z}_3$ orbifold utilizing the diagonal embedding method. The bulk gauge group is $G\times G\times G$, and the diagonal part $G^{\rm diag}$ remains manifest in the effective four-dimensional theory. Further spontaneous breaking of the gauge symmetry occurs through the dynamics of the zero modes of the extra-dimensional components of the gauge field. We apply this setup to the $SU(5)$ grand unified theory and examine the vacuum structure determined by the dynamics of the zero modes. The phenomenologically viable models are shown, in which the unified symmetry $G^{\rm diag}\cong SU(5)$ is spontaneously broken down to $SU(3)\times SU(2)\times U(1)$ at the global minima of the one-loop effective potential for the zero modes. This spontaneous breaking provides notable features such as a realization of the doublet-triplet splitting without fine tuning and a prediction of light adjoint fields.

hep-ph↗
arXiv2022

On representation matrices of boundary conditions in $SU(n)$ gauge theories compactified on two-dimensional orbifolds

We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in $SU(n)$ or $U(n)$ gauge theories compactified on the orbifolds $T^2/{\mathbb Z}_N$ ($N = 2, 3, 4, 6$). We suppose that the theory has a global $G' = U(n)$ symmetry. Using constraints, unitary transformations and gauge transformations, we examine whether the representation matrices can simultaneously become diagonal or not. We show that at least one diagonal representative necessarily exists in each equivalence class on $T^2/{\mathbb Z}_2$ and $T^2/{\mathbb Z}_3$, but the representation matrices on $T^2/{\mathbb Z}_4$ and $T^2/{\mathbb Z}_6$ can contain not only diagonal matrices but also non-diagonal $2 \times 2$ ones and non-diagonal $3 \times 3$ and $2 \times 2$ ones, respectively, as members of block-diagonal submatrices. These non-diagonal matrices have discrete parameters, which means that the rank-reducing symmetry breaking can be caused by the discrete Wilson line phases.

hep-th↗
arXiv2022

Early Dark Energy from a Higher-dimensional Gauge Theory

The Hubble constant estimated from the CMB measurements shows large disagreement with the locally measured value. This inconsistency is called the Hubble tension and is vastly studied in recent years. Early Dark Energy (EDE) gives a few percent contribution to the total energy density of the universe only at an epoch before the recombination, and it is considered as a promising solution to the tension. A simple realization of EDE is given by dynamics of a scalar field, called the EDE scalar, and models including the EDE scalar are extensively studied in the literature. In this paper, we present a novel EDE scenario based on higher-dimensional gauge theories. An extra component of gauge fields associated with a compact extra dimension behaves as the EDE scalar at low-energy and has a periodic potential, which has a similar form as potentials for pseudo Nambu-Goldstone bosons (PNGB). In a five-dimensional U(1) gauge theory, we show that a scalar field that originates from the gauge field can give EDE through its dynamics in a PNGB type potential with a suitable choice of parameters in the theory. We focus on the scenario where EDE is explained by the scalar field and clarify constraints on the fundamental parameters of the gauge theory, such as the gauge coupling, the compactification scale, and the mass parameters for matter fields. We also find that a sufficient dilution of EDE requires non-trivial relations among U(1) charges of matter fields. With specific matter contents, we numerically solve the time evolution of the scalar field and confirm that its energy density behaves as an EDE. In our scenario, the parameters of the gauge theory and predicted properties of EDE are related to each other. Thus, the cosmological restrictions on the EDE properties provide insights into higher-dimensional gauge theories.

astro-ph.CO↗
arXiv2019

Polynomial solutions of $q$-Heun equation and ultradiscrete limit

We study polynomial-type solutions of the $q$-Heun equation, which is related with quasi-exact solvability. The condition that the $q$-Heun equation has a non-zero polynomial-type solution is described by the roots of the spectral polynomial, whose variable is the accessory parameter $E$. We obtain sufficient conditions that the roots of the spectral polynomial are all real and distinct. We consider the ultradiscrete limit to clarify the roots of the spectral polynomial and the zeros of the polynomial-type solution of the $q$-Heun equation.

math.CA↗
arXiv2017

The Standard Model Gauge Symmetry from Higher-Rank Unified Groups in Grand Gauge-Higgs Unification Models

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on $S^1/Z_2$. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and $E_6$ models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.

hep-ph↗
arXiv2016

Gauge Symmetry Breaking Patterns in an SU(5) Grand Gauge-Higgs Unification

We study gauge symmetry breaking patterns of the five-dimensional $SU(5)$ grand gauge-Higgs unification compactified on an orbifold $S^1/{\mathbb Z}_2$ with the Hosotani mechanism in the framework of the diagonal embedding method. We find matter contents that lead to the $SU(3)\times SU(2)\times U(1)$ gauge symmetry on the global minimum of the effective potential and also present examples of matter content for which each regular subgroup of $SU(5)$ is realized as vacuum configuration. The finite temperature phase transitions for the models with the gauge symmetry of the standard model at zero temperature and also for supersymmetric models are studied. We show in a certain model with supersymmetry that the vacuum of the standard model selected dynamically before the inflation continues to stay there up to the present.

hep-ph↗
arXiv2011

Grand Gauge-Higgs Unification

We propose a novel way to break grand unified gauge symmetries via the Hosotani mechanism in models that can accommodate chiral fermions. Adjoint scalar fields are realized through the so-called diagonal embedding method which is often used in the heterotic string theory. We calculate the one-loop effective potential of the adjoint scalar field in a five dimensional model compactified on an S^1/Z_2 orbifold, as an illustration. It turns out that the potential is basically the same as the one in an S^1 model, and thus the results in literatures, in addition to the chiral fermions, can be realized easily.

hep-ph↗
arXiv2011

Cascade Textures and SUSY SO(10) GUT

We give texture analyses of cascade hierarchical mass matrices in supersymmetric SO(10) grand unified theory. We embed cascade mass textures of the standard model fermion with right-handed neutrinos into the theory, which gives relations among the mass matrices of the fermions. The related phenomenologies, such as the lepton flavor violating processes and leptogenesis, are also investigated in addition to the PMNS mixing angles.

hep-ph↗
arXiv2010

Cascade Hierarchy in SUSY SU(5) GUT

We study cascade hierarchy in supersymmetric SU(5) grand unified theory. The neutrino Dirac mass matrix of the cascade form can lead to the tri-bimaximal generation mixing at the leading order in the seesaw mechanism while the down quark mass matrix of a hybrid cascade form naturally gives the CKM structure. We embed such experimentally favored mass textures into supersymmetric SU(5) GUT, which gives a relation between the down quark and charged lepton mass matrices. Related phenomenologies, such as lepton flavor violating processes and leptogenesis, are also investigated in addition to lepton mixing angles.

hep-ph↗
arXiv2009

Probing neutrino masses and tri-bimaximality with lepton flavor violation searches

We examine relation between neutrino oscillation parameters and prediction of lepton flavor violation, in light of deviations from tri-bimaximal mixing. Our study shows that upcoming experimental searches for lepton flavor violation process can provide useful implications for neutrino mass spectrum and mixing angles. With simple structure of heavy right-handed neutrino and supersymmetry breaking sectors, the discovery of tau \to mu gamma decay determines neutrino mass hierarchy if large (order 0.1) reactor angle is established.

hep-ph↗
arXiv2008

Multi-Higgs Mass Spectrum in Gauge-Higgs Unification

We study an SU(2) supersymmetric gauge model in a framework of gauge-Higgs unification. Multi-Higgs spectrum appears in the model at low energy. We develop a useful perturbative approximation scheme for evaluating effective potential to study the multi-Higgs mass spectrum. We find that both tree-massless and massive Higgs scalars obtain mass corrections of similar size from finite parts of the loop effects. The corrections modify multi-Higgs mass spectrum, and hence, the loop effects are significant in view of future verifications of the gauge-Higgs unification scenario in high-energy experiments.

hep-ph↗
arXiv2007

Probing flavor structure in unified theory with scalar spectroscopy

The flavor structure in unified theory is probed with superparticle mass spectrum observed in future particle experiments. A key ingredient is the generation dependence of scalar mass non-degeneracy. The observed non-degeneracy in low-energy regime is shown to provide a direct imprint of flavor structure in high-energy fundamental theory. The implication from flavor-violating rare process is also discussed.

hep-ph↗