arXiv subjects

Makoto Sakamoto

Publications and source records attributed to Makoto Sakamoto.

At least 37 records · Page 2Linked to original sources

arXiv2018

Dynamical generation of fermion mass hierarchy in an extra dimension

We propose a new mechanism to produce a fermion mass hierarchy dynamically in a model with a singlet generation of fermions. A five dimensional gauge theory on an interval with point interactions (zero-width branes) takes responsibility for realizing three generations and each massless zero mode localizes at boundaries of the segments on the extra dimension. An extra-dimension coordinate-dependent vacuum expectation value of a scalar field makes large differences in overlap integrals of the localized zero modes and then an exponential fermion mass hierarchy can appear. The positions of the point interactions control the magnitude of the fermion mass hierarchy and are determined by the minimization condition of the Casimir energy. As a result of the minimization of the Casimir energy, an exponential mass hierarchy appears dynamically. We also discuss the stability of the extra dimension.

hep-th↗

arXiv2017

Supersymmetry in 6d Dirac Action

We investigate a 6d Dirac fermion on a rectangle. It is found that the 4d spectrum is governed by $N=2$ supersymmetric quantum mechanics. Then we demonstrate that the supersymmetry is very useful for classifying all the allowed boundary conditions and to expand the 6d Dirac field in Kaluza-Klein modes. A striking feature of the model is that even though the 6d Dirac fermion has non-vanishing bulk mass, the 4d mass spectrum can contain degenerate massless chiral fermions, which may provide a hint to solve the problem of the generation of quarks and leptons. It is pointed out that zero-energy solutions are not affected by the presence of the boundaries, while the boundary conditions work well for determining the positive-energy solutions. We also provide a brief discussion on possible boundary conditions in the general case, especially those on polygons.

hep-th↗

arXiv2017

6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum

We classify possible boundary conditions of a 6d Dirac fermion $Ψ$ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i) 4d-chirality positive components being zero at the boundaries and (ii) 2d-chirality positive components being zero at the boundaries. In the case of (i), twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameter $θ$. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. The emergence of the angle parameter $θ$ originates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii), this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.

hep-th↗

arXiv2017

Spectral intertwining relations in exactly solvable quantum-mechanical systems

In exactly solvable quantum-mechanical systems, ladder and intertwining operators play a central role because, if they are found, the energy spectra can be obtained algebraically. In this paper, we propose the spectral intertwining relation as a unified relation of ladder and intertwining operators in a way that can depend on the energy eigenvalues. It is shown that the spectral intertwining relations can connect eigenfunctions of different energy eigenvalues belonging to two different Hamiltonians, which cannot be obtained by previously known structures such as shape invariance. As an application, we find new spectral intertwining operators for the Hamiltonians of the hydrogen atom and the Rosen--Morse potential.

quant-ph↗

arXiv2017

Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz rule

N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kinetic terms have nontrivial quantum corrections.

hep-lat↗

arXiv2017

Polyakov Loop in Non-covariant Operator Formalism

We discuss a Polyakov loop in non-covariant operator formalism which consists of only physical degrees of freedom at finite temperature. It is pointed out that although the Polyakov loop is expressed by a Euclidean time component of gauge fields in a covariant path integral formalism, there is no direct counterpart of the Polyakov loop operator in the operator formalism because the Euclidean time component of gauge fields is not a physical degree of freedom. We show that by starting with an operator which is constructed in terms of only physical operators in the non-covariant operator formalism, the vacuum expectation value of the operator calculated by trace formula can be rewritten into a familiar form of an expectation value of Polyakov loop in a covariant path integral formalism at finite temperature for the cases of axial and Coulomb gauge.

hep-th↗

arXiv2016

Comprehensive Analysis of Yukawa Hierarchies on $T^2/Z_N$ with Magnetic Fluxes

Based on the result of classification in our previous work, we exhaustively investigate Yukawa sector of $U(8)$ model on magnetized orbifolds $T^{2}/Z_{2}$, $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$ by evaluating ratios of the mass eigenvalues of the three states in all the possible configurations with one and two Higgs pairs where three generations are realized in fermions. Because of smearing effect via kinetic mixing, one can realize a hierarchy such as $10^{-2}$-$10^{-3}$, but it is very difficult to achieve the mass ratio between the up and top quarks ($m_{\text{up}}/m_{\text{top}} \sim 10^{-5}$) on the complicated magnetized orbifolds $T^{2}/Z_{N}\,(N=3,4,6)$.

hep-ph↗

arXiv2016

Active Dirac Neutrinos via $SU(2)_L$ Doublets in 5d

We propose a new mechanism to generate minuscule active neutrino masses in a five-dimensional~(5d) spacetime of an interval without introducing $SU(2)_L$ singlet neutrinos. Under asymmetric boundary conditions on the two end points, a bulk mass for a 5d fermion allows a Dirac particle with a tiny mass eigenvalue. Implementing this mechanism, which provides us a new tool for building neutrino mass models, to the standard model gauge structure is possible when all the gauge bosons and the Higgs boson are localized on one of the branes.

hep-ph↗

arXiv2015

Classification of three-generation models on magnetized orbifolds

We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on $T^2/Z_2$, $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$ with allowing nonzero discretized Wilson line phases and Scherk-Schwarz phases. We also analyze two actual examples with nonzero phases leading to one-pair Higgs and five-pair Higgses and discuss the difference from the results without nonzero phases studied previously.

hep-ph↗

arXiv2014

Operator analysis of physical states on magnetized $T^{2}/Z_{N}$ orbifolds

We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try to examine properties of the physical states on (complicated) magnetized orbifolds $T^{2}/Z_{3}$, $T^{2}/Z_{4}$, $T^{2}/Z_{6}$ (and would be in other cases on higher-dimensional torus) and could be an essential tool for actual realistic model construction based on these geometries.

hep-th↗

arXiv2014

Realization of the Lepton Flavor Structure from Point Interactions

We investigate a 5d gauge theory on $S^1$ with point interactions. The point interactions describe extra boundary conditions and provide three generations, the charged lepton mass hierarchy, the lepton flavor mixing and tiny degenerated neutrino masses after choosing suitable boundary conditions and parameters. The existence of the restriction in the flavor mixing, which appears from the configuration of the extra dimension, is one of the features of this model. Tiny Yukawa couplings for the neutrinos also appears without the see-saw mechanism nor symmetries in our model. The magnitude of CP violation in the leptons can be a prediction and is consistent with the current experimental data.

hep-ph↗

arXiv2014

Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry

We propose a lattice model of supersymmetric complex quantum mechanics which realizes the non-renormalization theorem on a lattice. In our lattice model, the Leibniz rule in the continuum, which cannot hold on a lattice due to a no-go theorem, is replaced by the cyclic Leibniz rule (CLR) for difference operators. It is shown that CLR allows two of four supercharges of the continuum theory to preserve while a naive lattice model can realize one supercharge at the most. A striking feature of our lattice model is that there are no quantum corrections to potential terms in any finite order of perturbation theory. This is one of characteristic properties of supersymmetric theories in the continuum. It turns out that CLR plays a crucial role in the proof of the non-renormalization theorem. This result suggests that CLR grasps an essence of supersymmetry on a lattice.

hep-lat↗

arXiv2014

Realization of lepton masses and mixing angles from point interactions in an extra dimension

We investigate a model on an extra dimension $S^1$ where plenty of effective boundary points described by point interactions (zero-thickness branes) are arranged. After suitably selecting the conditions on these points for each type of five-dimensional fields, we realize the tiny active neutrino masses, the charged lepton mass hierarchy, and lepton mixings with a CP-violating phase, simultaneously. Not only the quark's but also the lepton's configurations are generated in a unified way with acceptable accuracy, with neither the see-saw mechanism nor symmetries in Yukawa couplings, by suitably setting the model parameters, even though their flavor structures are dissimilar each other. One remarkable point is that a complex vacuum expectation value of the five-dimensional Higgs doublet in this model becomes the common origin of the CP violation in both quark and lepton sectors. The model can be consistent with the results of the precision electroweak measurements and Large Hadron Collider experiments.

hep-ph↗

arXiv2014

Cyclic Leibniz rule: a formulation of supersymmetry on lattice

For the purpose of constructing supersymmetric(SUSY) theories on lattice, we propose a new type relation on lattice -cyclic Leibniz rule(CLR)- which is slightly different from an ordinary Leibniz rule. Actually, we find that CLR can enlarge the number of SUSYs and construct more Nicolai mappings in a quantum-mechanical model. In this model, the exact mass degeneracy between fermion and boson is shown.

hep-lat↗

arXiv2014

$Z_N$ twisted orbifold models with magnetic flux

We propose new backgrounds of extra dimensions to lead to four-dimensional chiral models with three generations of matter fermions, that is $T^2/Z_N$ twisted orbifolds with magnetic fluxes. We consider gauge theory on six-dimensional space-time, which contains the $T^2/Z_N$ orbifold with magnetic flux, Scherk-Schwarz phases and Wilson line phases. We classify all the possible Scherk-Schwarz and Wilson line phases on $T^2/Z_N$ orbifolds with magnetic fluxes. The behavior of zero modes is studied. We derive the number of zero modes for each eigenvalue of the $Z_N$ twist, showing explicitly examples of wave functions. We also investigate Kaluza-Klein mode functions and mass spectra.

hep-th↗

arXiv2013

$CP$ phase from twisted Higgs vacuum expectation value in extra dimension

We propose a new mechanism for generating a CP phase via Higgs a vacuum expectation value originating from geometry of an extra dimension. A twisted boundary condition is the key to produce an extra-dimension coordinate-dependent vacuum expectation value, which contains a CP phase degree of freedom and can be a new source of a CP phase in higher-dimensional gauge theories. As an illustrative example, we apply our mechanism to a five-dimensional gauge theory with point interactions and show that our mechanism can dynamically produce a nontrivial CP-violating phase with electroweak symmetry breaking, even though the five-dimensional model does not include any CP-violating phases of Yukawa couplings in the five-dimensional Lagrangian because of a single generation of five-dimensional fermions. We apply our mechanism to a model with point interactions, which has no source of CP-violating phases in the couplings of the higher-dimensional action, and show that a nontrivial CP phase dynamically appears.

hep-ph↗

arXiv2013

17P/Holmes: Contrast in activity between before and after the 2007 outburst

A Jupiter-family comet, 17P/Holmes, underwent outbursts in 1892 and 2007. In particular, the 2007 outburst is known as the greatest outburst over the past century. However, little is known about the activity before the outburst because it was unpredicted. In addition, the time evolution of the nuclear physical status has not been systematically studied. Here we study the activity of 17P/Holmes before and after the 2007 outburst through optical and mid-infrared observations. We found that the nucleus highly depleted its near-surface icy component before but became activated after the 2007 outburst. Assuming a conventional 1-um-sized grain model, we derived a surface fractional active area of 0.58% +- 0.14% before the outburst whereas it was enlarged by a factor of ~50 after the 2007 outburst. We also found that large (>=1 mm) particles could be dominant in the dust tail observed around aphelion. Based on the size of the particles, the dust production rate was >=170 kg/s at the heliocentric distance rh = 4.1 AU, suggesting that the nucleus still held active status around the aphelion passage. The nucleus color was similar to that of the dust particles and average for a Jupiter-family comet but different from most Kuiper Belt objects, implying that the color may be inherent to icy bodies in the solar system. On the basis of these results, we concluded that more than 76 m surface materials were blown off by the 2007 outburst.

astro-ph.EP↗

arXiv2013

CP phase from Higgs's boundary condition

We propose a new mechanism to generate a CP phase originating from a non-trivial Higgs vacuum expectation value in an extra dimension. A twisted boundary condition for the Higgs doublet can produce an extra dimensional coordinate-dependent vacuum expectation value containing a CP phase degree of freedom. With this mechanism, we construct a phenomenological model on S^{1} which can simultaneously and naturally explain the origins of the fermion generations, the quark mass hierarchy and the structure of the Cabibbo-Kobayashi-Maskawa matrix with the CP phase.

hep-ph↗