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Ryo Takahashi

Publications and source records attributed to Ryo Takahashi.

At least 145 records · Page 8Linked to original sources
arXiv2015

Hierarchy problem, gauge coupling unification at the Planck scale, and vacuum stability

From the point of view of the gauge hierarchy problem, introducing an intermediate scale in addition to TeV scale and the Planck scale ($M_{\rm Pl} = 2.4 \times 10^{18}\,{\rm GeV}$) is unfavorable. In that way, a gauge coupling unification (GCU) is expected to be realized at $M_{\rm Pl}$. We explore possibilities of GCU at $M_{\rm Pl}$ by adding a few extra particles with TeV scale mass into the standard model (SM). When extra particles are fermions and scalars (only fermions) with the same mass, the GCU at $M_{\rm Pl}$ can (not) be realized. On the other hand, when extra fermions have different masses, the GCU can be realized around $\sqrt{8 π} M_{\rm Pl}$ without extra scalars. This simple SM extension has two advantages that a vacuum becomes stable up to $M_{\rm Pl}$ ($\sqrt{8 π} M_{\rm Pl}$) and a proton lifetime becomes much longer than an experimental bound.

hep-ph↗
arXiv2015

The dimension of a subcategory of modules

Let R be a commutative noetherian local ring. As an analogue of the notion of the dimension of a triangulated category defined by Rouquier, the notion of the dimension of a subcategory of finitely generated R-modules is introduced in this paper. We found evidence that certain categories over nice singularities have small dimensions. When R is Cohen-Macaulay, under a mild assumption it is proved that finiteness of the dimension of the full subcategory consisting of maximal Cohen-Macaulay modules which are locally free on the punctured spectrum is equivalent to saying that R is an isolated singularity. As an application, the celebrated theorem of Auslander, Huneke, Leuschke and Wiegand is not only recovered but also improved. The dimensions of stable categories of maximal Cohen-Macaulay modules as triangulated categories are also investigated in the case where R is Gorenstein, and special cases of the recent results of Aihara and Takahashi, and Oppermann and Stovicek are recovered and improved. Our key technique involves a careful study of annihilators and supports of Tor, Ext and \underline{Hom} between two subcategories.

math.AC↗
arXiv2015

Blowup behavior for a degenerate elliptic sinh-Poisson equation with variable intensities

In this paper, we provide a complete blow-up picture for solution sequences to an elliptic sinh-Poisson equation with variable intensities arising in the context of the statistical mechanics description of two-dimensional turbulence, as initiated by Onsager. The vortex intensities are described in terms of a probability measure defined on the interval. Under Dirichlet boundary conditions we establish the exclusion of boundary blowup points, we show that the concentration mass does not have residual L1-terms and we determine the location of blowup points in terms of Kirchhoff's Hamiltonian. We allow the measure to be a general Borel measure, which could be "degenerate." Our main results are new for the standard sinh-Poisson equation as well.

math.AP↗
arXiv2015

Higgs inflation and Higgs portal dark matter with right-handed neutrinos

We investigate the Higgs inflation and the Higgs portal dark matter with the right-handed neutrino. The dark matter and the right-handed neutrino in the Higgs inflation play important roles in explaining the recent experimental results of the Higgs and top masses, and the cosmic microwave background by BICEP2 at the same time. This inflation model predicts $805~{\rm GeV} \lesssim m_{\rm DM} \lesssim1220~{\rm GeV}$ for the DM mass, $1.05 \times10^{14}~{\rm GeV} \lesssim M_R \lesssim 2.04 \times10^{14}~{\rm GeV}$ for the right-handed neutrino mass, and $8.42 \lesssim ξ\lesssim 12.4$ for the non-minimal coupling within $m_H=125.6 \pm 0.35~{\rm GeV}$ for the Higgs and $M_t=173.34 \pm 0.76~{\rm GeV}$ for the top masses.

hep-ph↗
arXiv2015

Annihilation of cohomology and strong generation of module categories

The cohomology annihilator of a noetherian ring that is finitely generated as a module over its center is introduced. Results are established linking the existence of non-trivial cohomology annihilators and the existence of strong generators for the category of finitely generated modules. Exploiting this link, results of Popescu and Roczen, and Wang concerning cohomology annihilators of commutative rings, and also results of Aihara and Takahashi, Keller and Van den Bergh, and Rouquier on strong finite generation of the corresponding bounded derived category, are generalized to cover excellent local rings and also rings essentially of finite type over a field.

math.AC↗
arXiv2015

Annihilation of cohomology, generation of modules and finiteness of derived dimension

Let $(R,\m,k)$ be a commutative noetherian local ring of Krull dimension $d$. We prove that the cohomology annihilator $\ca(R)$ of $R$ is $\m$-primary if and only if for some $n\ge0$ the $n$-th syzygies in $\mod R$ are constructed from syzygies of $k$ by taking direct sums/summands and a fixed number of extensions. These conditions yield that $R$ is an isolated singularity such that the bounded derived category $\db(R)$ and the singularity category $\ds(R)$ have finite dimension, and the converse holds when $R$ is Gorenstein. We also show that the modules locally free on the punctured spectrum are constructed from syzygies of finite length modules by taking direct sums/summands and $d$ extensions. This result is exploited to investigate several ascent and descent problems between $R$ and its completion $\widehat R$.

math.AC↗
arXiv2015

Search for new physics via photon polarization of $b \rightarrow s γ$

We suggest a discriminant analysis of new physics beyond the standard model through a detection of photon polarization in a radiative B meson decay. This analysis is investigated in SUSY SU(5) GUT with right-handed neutrino and left-right symmetric models. New physics search via CP asymmetry in the same process are also evaluated in each model for comparison. We show that new physics can be found via detecting the photon polarization in a parameter space of TeV energy scale.

hep-ph↗
arXiv2015

Gravitational effects on vanishing Higgs potential at the Planck scale

We investigate gravitational effects on the so-called multiple point criticality principle (MPCP) at the Planck scale. The MPCP requires two degenerate vacua, whose necessary conditions are expressed by vanishing Higgs quartic coupling $λ(M_{\rm Pl})=0$ and vanishing its $β$ function $β_λ(M_{\rm Pl})=0$. We discuss a case that a specific form of gravitational corrections are assumed to contribute to $β$ functions of coupling constants although it is accepted that gravitational corrections do not alter the running of the standard model (SM) couplings. To satisfy the above two boundary conditions at the Planck scale, we find that the top pole mass and the Higgs mass should be $170.8\,{\rm GeV} \lesssim M_t\lesssim 171.7\,{\rm GeV}$ and $M_h=125.7\pm0.4\,{\rm GeV}$, respectively, as well as include suitable magnitude of gravitational effects (a coefficient of gravitational contribution as $|a_λ| > 2$). In this case, however, since the Higgs quartic coupling $λ$ becomes negative below the Planck scale, two vacua are not degenerate. We find that $M_h \gtrsim 131.5\,{\rm GeV}$ with $M_t \gtrsim 174\,{\rm GeV}$ is required by the realization of the MPCP. Therefore, the MPCP at the Planck scale cannot be realized in the SM and also the SM with gravity since $M_h \gtrsim 131.5\,{\rm GeV}$ is experimentally ruled out.

hep-ph↗
arXiv2015

Active and reactive power in stochastic resonance for energy harvesting

A power allocation to active and reactive power in stochastic resonance is discussed for energy harvesting from mechanical noise. It is confirmed that active power can be increased at stochastic resonance, in the same way of the relationship between energy and phase at an appropriate setting in resonance.

physics.soc-ph↗
arXiv2015

Extension closedness of syzygies and local Gorensteinness of commutative rings

We refine a well-known theorem of Auslander and Reiten about the extension closedness of n-th syzygies over noether algebras. Applying it, we obtain the converse of a celebrated theorem of Evans and Griffith on Serre's condition (S_n) and the local Gorensteiness of a commutative ring in height less than n. This especially extends a recent result of Araya and Iima concerning a Cohen-Macaulay local ring with canonical module to an arbitrary local ring.

math.AC↗
arXiv2015

$ν_R$ dark matter-philic Higgs for 3.5 keV X-ray signal

We suggest a new model of 7 keV right-handed neutrino dark matter inspired by a recent observation of 3.5 keV X-ray line signal in the XMM-Newton observatory. It is difficult to derive the tiny masses with a suitable left-right mixing of the neutrino in a framework of ordinary simple type-I seesaw mechanism. We introduce a new Higgs boson, a dark matter-philic Higgs boson, in which the smallness of its vacuum expectation value can be achieved. We investigate suitable parameter regions where the observed dark matter properties are satisfied. We find that the vacuum expectation value of dark matter-philic Higgs boson should be about 0.17 GeV.

hep-ph↗
arXiv2015

Security of Power Packet Dispatching Using Differential Chaos Shift Keying

This paper investigates and confirms one advantageous function of a power packet dispatching system, which has been proposed by authors' group with being apart from the conventional power distribution system. Here is focused on the function to establish the security of power packet dispatching for prohibiting not only information but also power of power packet from being stolen by attackers. For the purpose of protecting power packets, we introduce a simple encryption of power packets before sending them. Encryption scheme based on chaotic signal is one possibility for this purpose. This paper adopts the Differential Chaos Shift Keying (DCSK) scheme for the encryption, those are partial power packet encryption and whole power packet encryption.

cs.IT↗
arXiv2014

Maximal Cohen-Macaulay approximations and Serre's condition

This paper studies the relationship between Serre's condition $(\R_n)$ and Auslander--Buchweitz's maximal Cohen--Macaulay approximations. It is proved that a Gorenstein local ring satisfies $(\R_n)$ if and only if every maximal Cohen--Macaulay module is a direct summand of a maximal Cohen--Macaulay approximation of a (Cohen--Macaulay) module of codimension $n+1$.

math.AC↗
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

Building modules from the singular locus

A finitely generated module over a commutative noetherian ring of finite Krull dimension can be built from the prime ideals in the singular locus by iteration of three procedures: taking extensions, direct summands, and cosyzygies. In 2003 Schoutens gave a bound on the number of iterations required to build any module, and in this note we determine the exact number. This building process yields a stratification of the module category, which we study in detail for local rings that have an isolated singularity.

math.AC↗