arXiv subjects

Junpei Harada

Publications and source records attributed to Junpei Harada.

At least 19 recordsLinked to original sources

arXiv2025

Exact vacuum solution with Hopf structure in general relativity

An exact solution to the vacuum Einstein equations is presented, whose structure is based on the Hopf fibration. The solution employs a geodesic null vector field that defines a twisting congruence and appears in the metric in Kerr-Schild form. This solution is of Petrov type D and involves two parameters. Remarkably, the resulting spacetime is regular, with no curvature singularities. Both the Kretschmann scalar and the Chern-Pontryagin scalar are nonzero and remain finite throughout the spacetime. In addition, the Newman-Penrose Weyl scalar $\Psi_2$ possesses both nonzero real and imaginary parts, reflecting the topologically nontrivial nature of the gravitational field. The spacetime also admits two Killing vector fields and a Killing-Yano tensor, which induces an associated Killing tensor, revealing its hidden symmetry. The derivation is simple and self-contained, offering a transparent and geometrically guided approach to finding new exact solutions in general relativity.

gr-qc↗

arXiv2024

Gauge-invariant formulation for the gravitational wave equations

A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization with helicity $\pm 2$, Yang's theory with three modes of polarization with helicity $\pm 2$ and $0$, and so-called "general metric theories" with six modes of polarization with helicity $\pm 2$, $\pm 1$, and two $0$'s. To identify the polarizations of gravitational waves, it is explicitly demonstrated how the gauge-invariant approach reproduces the earlier results.

gr-qc↗

arXiv2023

Dark energy in conformal Killing gravity

The Friedmann equation, augmented with an additional term that effectively takes on the role of dark energy, is demonstrated to be an exact solution to the recently proposed gravitational theory named "conformal Killing gravity." This theory does not explicitly incorporate dark energy. This finding suggests that there is no necessity to postulate the existence of dark energy as an independent physical entity. The dark energy derived from this theory is characterized by a specific equation of state parameter, denoted as $\omega$, which is uniquely determined to be $-5/3$. If this effective dark energy is present, typically around 5% of the total energy density at the present time, and under the assumption of density parameters for matter and the cosmological constant, $\Omega_{\rm m}\sim 0.25$ and $\Omega_\Lambda \sim 0.7$, respectively, the expansion of the universe at low redshifts ($z < 1.5$) can exceed expectations, while the expansion at $z > 1.5$ remains unchanged. This offers a potential solution to the Hubble tension problem. Alternatively, effective dark energy could be a dominant component in the present-day universe. In this scenario, there is also the potential to address the Hubble tension, and furthermore, it resolves the coincidence problem associated with the cosmological constant.

gr-qc↗

arXiv2023

Gravity at cosmological distances: Explaining the accelerating expansion without dark energy

Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. Existing theories, including general relativity, do not simultaneously fulfill all three criteria. To address this, a new gravitational field equation is proposed that satisfies these criteria. From this equation, a spherically symmetric exact solution is derived, which is a generalization of the Schwarzschild solution. It incorporates three terms: the Schwarzschild term, the de Sitter term, and a newly discovered term, which is proportional to $r^4$ in a radial coordinate, that becomes significant only at large distances. The equation is further applied to cosmology, deriving an equation for the scale factor. It then presents a solution that describes the transition from decelerating to accelerating expansion in a matter-dominated universe. This is achieved without the need for negative pressure as dark energy or the positive cosmological constant. This provides a novel explanation for the current accelerating expansion of the universe.

gr-qc↗

arXiv2022

Cotton gravity and 84 galaxy rotation curves

Recently, as a generalization of general relativity, a gravity theory has been proposed in which gravitational field equations are described by the Cotton tensor. That theory allows an additional contribution to the gravitational potential of a point mass that rises linearly with radius as $\Phi = -GM/r + \gamma r/2$, where $G$ is the Newton constant. The coefficients $M$ and $\gamma$ are the constants of integration and should be determined individually for each physical system. When applied to galaxies, the coefficient $\gamma$, which has the dimension of acceleration, should be determined for each galaxy. This is the same as having to determine the mass $M$ for each galaxy. If $\gamma$ is small enough, the linear potential term is negligible at short distances, but can become significant at large distances. In fact, it may contribute to the extragalactic systems. In this paper, we derive the effective field equation for Cotton gravity applicable to extragalactic systems. We then use the effective field equation to numerically compute the gravitational potential of a sample of 84 rotating galaxies. The 84 galaxies span a wide range, from stellar disk-dominated spirals to gas-dominated dwarf galaxies. We do not assume the radial density profile of the stellar disk, bulge, or gas; we use only the observed data. We find that the rotation curves of 84 galaxies can be explained by the observed distribution of baryons. This is due to the flexibility of Cotton gravity to allow the integration constant $\gamma$ for each galaxy. In the context of Cotton gravity, "dark matter" is in some sense automatically included as a curvature of spacetime. Consequently, even galaxies that have been assumed to be dominated by dark matter do not need dark matter.

gr-qc↗

arXiv2021

Emergence of the Cotton tensor for describing gravity

It is shown that the Cotton tensor can describe the effects of gravity beyond general relativity. Any solution of the Einstein equations with or without the cosmological constant satisfies the field equations described by the Cotton tensor. It implies that the cosmological constant is an integration constant. A vacuum of a theory is represented by the vanishing of the Cotton tensor, rather than the vanishing of the Ricci tensor. An exact Schwarzschild-like solution for a static and spherically symmetric source is discovered. Although the field equations involve the third order of derivative, it is found that they reduce to the second-order differential equations due to a variational principle.

gr-qc↗

arXiv2020

Connection independent formulation of general relativity

A connection-independent formulation of general relativity is presented, in which the dynamics does not depend on the choice of connection. The gravity action in this formulation includes one additional scalar term in addition to the Einstein-Hilbert action. No conditions on the connection are imposed. Nevertheless, this formulation yields the Einstein equations, without adding the Gibbons-Hawking-York term even when a manifold has a boundary. Furthermore, this formulation yields a unified description of general relativity, teleparallel gravity, and symmetric teleparallel gravity.

gr-qc↗

arXiv2016

Gauge coupling unification with extra Higgs doublets

Gauge coupling unification is studied within the framework where there are extra Higgs doublets and $E_6$ exotic fields. Supersymmetric models and nonsupersymmetric models are investigated, and a catalog of models with gauge coupling unification is presented.

hep-ph↗

arXiv2015

Neutrino mixing and CP violation from Dirac-Majorana mixing

We consider a minimal condition that predicts the 1-3 lepton mixing angle $θ_{13} \simeq θ_{\rm C}/\sqrt{2}$ with $θ_{\rm C}$ the Cabibbo angle, and give the improved prediction of $θ_{13}$. In the case of normal mass ordering, the theoretical value of $θ_{13}$ is predicted as $θ_{13}=8.6^\circ$, which is in good agreement with the current global best fit. In the case of inverted mass ordering, the theoretical value is predicted as $θ_{13}=9.7^\circ$, which is far from the current global best fit. We also study the leptonic CP violation. We show that any values of the leptonic Dirac CP phase $δ_{\rm CP}$ can be obtained by fine tuning. Without fine tuning, $|\sinδ_{\rm CP}|$ should be very small, typically of ${\cal O}(λ^2)$ where $λ\equiv \sinθ_{\rm C}$. Furthermore, a model-independent measure of CP violation is proposed, which is applicable to any flavor models.

hep-ph↗

arXiv2013

Non-maximal θ_{23}, large θ_{13} and tri-bimaximal θ_{12} via quark-lepton complementarity at next-to-leading order

We show that the next-to-leading order corrections in the quark-lepton complementarity are important to explain the observed pattern of neutrino mixing. In particular, the next-to-leading order corrections 1) lead to a deviation of θ_{23} from maximal mixing, 2) reduce the predicted value of $\sin^2 2θ_{13}$ by 9.8%, 3) provide the same value of $\sin^2 θ_{12}$ as that of the tri-bimaximal mixing. This is shown by calculating $\sin^2 2θ_{ij} (i,j=1,2,3)$ to ${\cal O}(λ^6)$ in the framework in which the product of the CKM and PMNS matrices is bimaximal.

hep-ph↗

arXiv2009

Roton energy gap and spontaneous symmetry breaking

We study elementary excitations in superfluid helium-4 employing an approach based on the spontaneous symmetry breaking. In particular, we calculate the roton energy gap at zero temperature $Δ(0)$. The relation that we have derived is $Δ(0) / k_B T_λ= 4$. The theoretical value of $Δ(0)/k_B$ is 8.707 K, which is significantly close to the experimental value of 8.712 K. The deviation between the theoretical and experimental values is less than 0.1%.

cond-mat.other↗

arXiv2007

Spontaneous Symmetry Breaking in Superfluid Helium-4

We derive an analytical expression for a critical temperature of spontaneous symmetry breaking in a repulsive hard-core interacting Bose system. We show that the critical temperature of spontaneous symmetry breaking in a hard-core interacting Bose system is determined by the three physical parameters: the density of Bose liquid at absolute zero (rho_0), the mass (m) and the hard sphere diameter (sigma) of a boson. The formula that we have derived is Tc = rho_0 pi hbar^2 sigma / m^2 kB. We report Tc of liquid helium-4 is 2.194 K, which is significantly close to the lambda temperature of 2.1768 K. The deviation between the predicted and experimental values of the lambda temperature is less than 1%.

cond-mat.other↗

arXiv2006

Neutrino mixing and CP violation from Dirac-Majorana bimaximal mixture and quark-lepton unification

We demonstrate that only two ansatz can produce the features of the neutrino mixing angles. The first ansatz comes from the quark-lepton grand unification; $ν_{Di} = V_{CKM} ν_α$ is satisfied for left-handed neutrinos, where $ν_{Di}$ are the Dirac mass eigenstates and $ν_α$ are the flavour eigenstates. The second ansatz comes from the assumption; $ν_{Di} = U_{bimaximal} ν_{i}$ is satisfied between the Dirac mass eigenstates $ν_{Di}$ and the light Majorana neutrino mass eigenstates $ν_{i}$, where $U_{bimaximal}$ is the bimaximal mixing matrix. By these two ansatz, the Maki-Nakagawa-Sakata matrix is given by $U_{MNS} = V_{CKM}^\dagger U_{bimaximal}$. We find that in this model the novel relation $θ_{sol} + θ_{13} = π/4$ is satisfied, where $θ_{sol}$ and $θ_{13}$ are solar and CHOOZ angle respectively. This "Solar-CHOOZ Complementarity" relation indicates that only if the CHOOZ angle $θ_{13}$ is sizable, the solar angle $θ_{sol}$ can deviate from the maximal mixing. We also infer the CP violation in neutrino oscillations. The leptonic Dirac CP phase $δ_{MNS}$ is predicted as $\sin δ_{MNS} \simeq A λ^2 η$, where $A, λ, η$ are the CKM parameters in Wolfenstein parametrization. Furthermore, we remark that the ratio of the Jarlskog CP violation factor for quarks and leptons is important, because the large uncertainty on $η$ is cancelled out in the ratio, $R_J \equiv J_{CKM}/J_{MNS} \simeq 4\sqrt{2} A λ^3 \simeq 5 \times 10^{-2}$.

hep-ph↗

arXiv2004

Application of heavy-quark effective theory to lattice QCD: II. Radiative corrections to heavy-light currents

We apply heavy-quark effective theory to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this approach, the inverse heavy-quark mass and the lattice spacing are treated as short distances, and their effects are lumped into short-distance coefficients. We show how to use this formalism to match lattice gauge theory to continuum QCD, order by order in the heavy-quark expansion. In this paper, we focus on heavy-light currents. In particular, we obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of heavy-light decay constants, and heavy-to-light transition form factors. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.

hep-lat↗

arXiv2002

Perturbative calculation of O(a) improvement coefficients

We compute several coefficients needed for O(a) improvement of currents in perturbation theory, using the Brodsky-Lepage-Mackenzie prescription for choosing an optimal scale q*. We then compare the results to non-perturbative calculations. Normalization factors of the vector and axial vector currents show good agreement, especially when allowing for small two-loop effects. On the other hand, there are large discrepancies in the coefficients of O(a) improvement terms. We suspect that they arise primarily from power corrections inherent in the non-perturbative methods.

hep-lat↗

arXiv2002

Phenomenological approach to symmetry breaking pattern of democratic mass matrix

We investigate the symmetry breaking pattern of the democratic mass matrix model, which leads to the small flavor mixing in quark sector and bi-large mixing in lepton sector. We present the symmetry breaking matrices in quark sector which are determined by alternative ways instead of conventional ansatz. These matrices might be useful for understanding the origin of democratic symmetry and its breaking.

hep-ph↗

arXiv2002

Heavy quark action on the anisotropic lattice

We investigate the $O(a)$ improved quark action on anisotropic lattice as a potential framework for the heavy quark, which may enable precision computation of hadronic matrix elements of heavy-light mesons. The relativity relations of heavy-light mesons as well as of heavy quarkonium are examined on a quenched lattice with spatial lattice cutoff $a_σ^{-1} \simeq$ 1.6 GeV and the anisotropy $ξ=4$. We find that the bare anisotropy parameter tuned for the massless quark describes both the heavy-heavy and heavy-light mesons within 2% accuracy for the quark mass $a_σm_Q < 0.8$, which covers the charm quark mass. This bare anisotropy parameter also successfully describes the heavy-light mesons in the quark mass region $a_σm_Q \leq 1.2$ within the same accuracy. Beyond this region, the discretization effects seem to grow gradually. The anisotropic lattice is expected to extend by a factor $ξ$ the quark mass region in which the parameters in the action tuned for the massless limit are applicable for heavy-light systems with well controlled systematic errors.

hep-lat↗

arXiv2001

Application of heavy-quark effective theory to lattice QCD: III. Radiative corrections to heavy-heavy currents

We apply heavy-quark effective theory (HQET) to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this paper we focus on flavor-changing currents that mediate transitions from one heavy flavor to another. We stress differences in the formalism for heavy-light currents, which are discussed in a companion paper, showing how HQET provides a systematic matching procedure. We obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of zero-recoil form factors for the semileptonic decays $B\to D^{(*)}lν$. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.

hep-lat↗