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Akira Takamura

Publications and source records attributed to Akira Takamura.

18 recordsLinked to original sources
arXiv2024

New CP Phase and Exact Oscillation Probabilities of Dirac Neutrino derived from Relativistic Equation

We present a new formulation for deriving neutrino oscillation probabilities relativistically, based not on the Schrödinger equation but on the Dirac equation. In the context of two generations, we calculate the oscillation probabilities precisely in a scenario where only the Dirac mass term is present. Our analysis reveals the emergence of two new features in the oscillation probabilities derived from the Dirac equation. The first feature is that the oscillation probabilities depend on the absolute value of the neutrino mass. While it has generally been assumed that oscillation probabilities depend solely on mass squared differences, we show that they also depend on the absolute mass. The second feature is the emergence of a new CP phase. If interactions exist that can distinguish the flavors of right-handed neutrinos in physics beyond the Standard Model, we could potentially observe this new CP phase even in the two-generation model. We discuss the feasibility of detecting the contributions of these features through neutrino oscillations at atomic scales. In contrast, these effects are negligible in conventional short- and long-baseline experiments, and no contradictions arise with previous findings.

hep-ph↗
arXiv2024

Unification of Neutrino-Neutrino and Neutrino-Antineutrino Oscillations

In the case of two-generation Majorana neutrinos, we derive the oscillation probabilities for $ν\leftrightarrow ν$, $ν^c \leftrightarrow ν^c$, and $ν\leftrightarrow ν^c$ within a unified framework using a relativistic equation. We demonstrate that the Majorana phase arises not from lepton number violation but from chirality change. Additionally, we verify the conservation of unitarity. Notably, we find that the oscillation probabilities for $ν\leftrightarrow ν^c$ derived in this paper differ significantly from previous results, particularly in the absence of zero-distance effects and direct CP violation.

hep-ph↗
arXiv2021

Natural Understanding of Sterile Neutrino by Relativistic Equation

We derive the neutrino oscillation probabilities including sterile neutrinos by using the Dirac equation. If neutrinos have both the Dirac and the Majorana mass terms, left-handed neutrino $ν_L$ and right-handed anti-neutrino $ν_R^c$ enter the same multiplet and can transfer each other. Sterile neutrinos have been introduced by hand as the fourth generation neutrino in many papers, however, we can understand sterile neutrinos naturally in the framework of three generations. We also point out that the oscillations into sterile neutrinos strongly suggest the existence of both the Dirac and the Majorana mass terms, and for neutrinos to be the Majorana particles.

hep-ph↗
arXiv2021

Exact Oscillation Probabilities of Neutrinos in Three generations derived from Relativistic Equation

In three generations or more, we derive the oscillation probabilities of both Dirac and Majorana neutrinos relativistically by using the Dirac equation. We present various oscillation probabilities for including wrong-helicity neutrinos, right-handed neutrinos, and anti-neutrinos. We summarize the relations between these probabilities. As neutrinos have finite mass, there are two components for each chirality corresponding to positive and negative helicities. We show that the probability is different for each component even if neutrinos have the same chirality. The probabilities derived by the relativistic equation depend on not only the mass squared differences but also the absolute masses of neutrinos. Besides, the new CP phases appear in the probabilities of oscillations with chirality-flip. These new CP phases are equivalent to the Majorana CP phases in the case of Majorana neutrinos. We investigate the CP dependence of oscillation probabilities in vacuum. There are no direct CP violation in $ν_α\leftrightarrow ν_β^c$ oscillations even if the flavors, $α$ and $β$, are different as in the same as two generations. In other words, the difference between the CP-conjugate probabilities vanishes. However, in three generations or more, the sine terms of new CP phases appear in the probabilities in addition to the cosine terms. This is different from the result obtained in two generations. Furthermore, the zero-distance effect does not appear in our formulation.

hep-ph↗
arXiv2011

Supernova neutrino signals by liquid Argon detector and neutrino magnetic moment

We study electron-neutrino and electron-antineutrino signals from a supernova with strong magnetic field detected by a 100 kton liquid Ar detector. The change of neutrino flavors by resonant spin-flavor conversions, matter effects, and neutrino self-interactions are taken into account. Different neutrino signals, characterized by neutronization burst event and the total event numbers of electron-neutrinos and electron-antineutrinos, are expected with different neutrino oscillation parameters and neutrino magnetic moment. Observations of supernova neutrino signals by a 100 kton liquid Ar detector would constrain oscillation parameters as well as neutrino magnetic moment in either normal and inverted mass hierarchies.

astro-ph.HE↗
arXiv2008

Effect of Leptonic CP Phase in nu_mu --> nu_mu Oscillations

In the case of large 1-3 mixing angle as sin^2(2theta13 > 0.03, we investigate the possibility for measuring the leptonic CP phase by using only nu_mu --> nu_mu oscillations independently of nu_mu --> nu_e oscillations. As the result, we find that the CP phase can be measured best around the energy E=0.43 GeV and the baseline length L=5000km without strongly depending on the uncertainties of other parameters. In this region, the CP phase effect remains even after averaging over neutrino energy. We also find that there is the CP sensitivity even in the short baseline length L < 1000 km if Delta m_{31}^2 is determined with the uncertainty of about 0.1 . In the T2KK experiment, we explore the possibility for determining Delta m_{31}^2 by using one baseline from Tokai to Korea and then measuring the CP phase by using the baseline to Kamioka. As the result, we find that some information of the CP phase can be obtained from both measurements.

hep-ph↗
arXiv2006

Measuring the Leptonic CP Phase in $ν_μ \to ν_μ$ Oscillations

In $ν_μ \to ν_μ$ oscillations, we find that the effect of the CP phase $δ$ becomes large in the region $E<2$ GeV and $L>2000$ km. In this region, the change of the probability in this channel reaches about 0.4 due to the CP phase effect beyond our expectation in the case of large 1-3 mixing angle. Furthermore, the CP phase effect have almost same sign over the region $E>0.5$ GeV so that one may find the signal of CP violation by measuring the total rate only. As an example, we use an experimental setup and demonstrate that the allowed region is limited to one by combined analysis of $ν_e$ and $ν_μ$ events although there remain three allowed regions by the analysis of $ν_e$ events alone.

hep-ph↗
arXiv2006

New Index of CP Phase Effect and $θ_{13}$ Screening in Long Baseline Neutrino Experiments

We introduce a new index of the leptonic CP phase dependence $I_{\rm CP}$ and derive the maximal condition for this index in a simple and general form. $I_{\rm CP}\simeq 100%$ may be realized even in the JPARC experiment. In the case that the 1-3 mixing angle can be observed in the next generation reactor experiments, namely $\sin^2 2θ_{13}>0.01$, and nevertheless $ν_e$ appearance signal cannot be observed in the JPARC experiment, we conclude that the CP phase $δ$ becomes a value around $135^{\circ}$ $(45^{\circ})$ for $Δm^2_{31}>0$ $(Δm^2_{31}<0)$ without depending the uncertainties of solar and atmospheric parameters.

hep-ph↗
arXiv2005

Large Non-perturbative Effects of Small Δm^2_{21}/Δm^2_{31} and \sin θ_{13} on Neutrino Oscillation and CP Violation in Matter

In the framework of three generations, we consider the CP violation in neutrino oscillation with matter effects. At first, we show that the non-perturbative effects of two small parameters, Δm_{21}^2/Δm_{31}^2 and \sin θ_{13}, become more than 50% in certain ranges of energy and baseline length. This means that the non-perturbative effects should be considered in detailed analysis in the long baseline experiments. Next, we propose a method to include these effects in approximate formulas for oscillation probabilities. Assuming the two natural conditions, θ_{23}=45^\circ and the fact that the matter density is symmetric, a set of approximate formulas, which involve the non-perturbative effects, has been derived in all channels.

hep-ph↗
arXiv2005

Enhancement of CP Violating terms for Neutrino Oscillation in Earth Matter

We investigate the $ν_e \to ν_μ$ oscillation in the framework of three generations when neutrinos pass through the earth. The oscillation probability is represented by the form, $P(ν_e \to ν_μ)=A\cos δ+B\sin δ+C$ in arbitrary matter profile by using the leptonic CP phase $δ$. We compare our approximate formula in the previous paper with the formula which includes second order terms of $α=Δm_{21}^2/Δm_{31}^2$ and $s_{13}=\sin θ_{13}$. Non-perturbative effects of $α$ and $s_{13}$ can be taken into account in our formula and the precision of the formula is rather improved around the MSW resonance region. Furthermore, we compare the earth matter effect of $A$ and $B$ with that of $C$ studied by other authors. We show that the magnitude of $A$ and $B$ can reach a few ten % of $C$ around the main three peaks of $C$ in the region $E>1$ GeV by numerical calculation. We give the qualitative understanding of this result by using our approximate formula. The mantle-core effect, which is different from the usual MSW effect, appears not only in $C$ but also in $A$ and $B$, although the effect is weakened.

hep-ph↗
arXiv2004

Proposal of a Simple Method to Estimate Neutrino Oscillation Probability and CP Violation in Matter

We study neutrino oscillation within the framework of three generations in matter. We propose a simple method to approximate the coefficients A, B and C which do not depend on the CP phase δin the oscillation probability P(ν_e \to ν_μ)=A\cos δ+ B\sin δ+C. An advantage of our method is that an approximate formula of the coefficients A, B and C in arbitrary matter {\it without the usual first order perturbative calculations} of the small parameter Δm_{21}^2/Δm_{31}^2 or \sin θ_{13} can be derived. Furthermore we show that all the approximate formulas for low, intermediate and high energy regions given by other authors in constant matter can be easily derived from our formula. It means that our formula is applicable over a wide energy region.

hep-ph↗
arXiv2002

Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density

We investigate neutrino oscillations in constant matter within the context of the standard three neutrino scenario. We derive an exact and simple formula for the oscillation probability applicable to all channels. In the standard parametrization, the probability for $ν_e$ $\to$ $ν_μ$ transition can be written in the form $P(ν_e \to ν_μ)=A_{eμ}\cosδ+B_{eμ}\sinδ+C_{eμ}$ without any approximation using CP phase $δ$. For $ν_μ$ $\to$ $ν_τ$ transition, the linear term of $\cos 2δ$ is added and the probability can be written in the form $P(ν_μ \to ν_τ)=A_{μτ}\cosδ+B_{μτ} \sinδ+C_{μτ}+D_{μτ}\cos 2δ$. We give the CP dependences of the probability for other channels. We show that the probability for each channel in matter has the same form with respect to $δ$ as in vacuum. It means that matter effects just modify the coefficients $A$, $B$, $C$ and $D$. We also give the exact expression of the coefficients for each channel. Furthermore, we show that our results with respect to CP dependences are reproduced from the effective mixing angles and the effective CP phase calculated by Zaglauer and Schwarzer. Through the calculation, a new identity is obtained by dividing the Naumov-Harrison-Scott identity by the Toshev identity.

hep-ph↗
arXiv2002

Overall Feature of CP dependence for Neutrino Oscillation Probability in Arbitrary Matter Profile

We study the CP dependence of neutrino oscillation probability for all channels in arbitrary matter profile within three generations. We show that an oscillation probability for ν_e \to ν_μcan be written in the form P(ν_e \to ν_μ) =A_{eμ} cos δ+ B_{eμ} sin δ+ C_{eμ} without any approximation using the CP phase δ. This result holds not only in constant matter but also in arbitrary matter. Another probability for ν_μ\to ν_τcan be written in the form P(ν_μ\to ν_τ)= A_{μτ} cos δ+ B_{μτ} sin δ + C_{μτ} + D_{μτ} cos 2δ+ E_{μτ} sin 2δ. The term which is proportional to sin 2δdisappear, namely E_{μτ}=0, in symmetric matter. It means that the probability reduces to the same form as in constant matter. As for other channels, probabilities in arbitrary matter are at most the quadratic polynomials of sin δand cos δas in the above two channels. In symmetric matter, the oscillation probability for each channel reduces to the same form with respect to δas that in constant matter.

hep-ph↗
arXiv1998

Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model

We algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. For this purpose, we derive the raising and lowering operators which increase and decrease eigenvalues of pseudomomenta. The operators exchanging eigenvalues of two pseudomomenta have been known. All the eigenstates are systematically produced by starting from the ground state and multiplying these operators to it.

solv-int↗
arXiv1995

New $I=J$ Rules for the Baryon Vertices in $1/N_c$ Expansion

We apply the $1/N_c$ expansion in QCD to the baryon vertices. We find new model independent properties for the isoscalar and isovector baryon vertices from the view point of $1/N_c$ expansion in QCD. One of these results, $I=J$ rule, have been already found. The other properties, new $I=J$ rules, are the rules about the isospin and strangeness dependence for the baryon vertices.

hep-ph↗
arXiv1995

Finite $N_c$ Results for $F/D$ Ratios of the Baryon Vertices and $I=J$ Rule

We calculate the $F/D$ ratios of spin-nonflip baryon vertex for an arbitrary number of color degrees of freedom $N_c$ both in the non-relativistic quark model with the $SU(6)$ spin-flavor symmetry and in the chiral soliton model with $SU(3)$ flavor symmetry. We find that the spin-nonflip $F/D$ ratio tends to $-1$ in the limit of $N_c \to \infty$. We show that this leading value $F/D= -1$ of spin-nonflip baryon vertex in the $1/N_c$ expansion corresponds to the isoscalar dominance while the well known leading value $F/D=1/3$ of the spin-flip vertex corresponds to the isovector dominance. We discuss origins of the dominance of isovector in spin-flip and isoscalar in spin-nonflip baryon vertices, referred to as the $I=J$ rule. \par In terms of the matrix elements of the operator which transform as the generator $λ^8$ of the $SU(3)$ symmetry we derive the model independent isoscalar formula for baryon vertices and apply this to the mass formula and the isoscalar part of the baryon magnetic moments. The same Okubo-Gell-Mann mass relation and its refined relation among the octet baryons as the one for the case $N_c=3$ is derived model independently for arbitrary color degrees of freedom $N_c$. Contrary to $λ^8$,

hep-ph↗
arXiv1994

The F/D Ratios of Spin-flip Baryon Vertex in 1/N_c Expansion

We calculate the $F/D$ ratios of spin 1/2 baryon vertex for both the non-relativistic quark model and the chiral soliton model with arbitrary number of color degrees of freedom $N_c$ and examine the results in terms of the consistency condition approach for the baryon vertices recently developed by Dashen, Jenkins and Manohar from the viewpoint of QCD. We show that the $1/N_c$ corrections have two different origins, i.e. one is from the baryon states or baryon wave functions and the other from the vertex operators. Although in the limit of $N_c \to \infty$ the $F/D$ tends to 1/3 in all models, the $1/N_c$ expansion of $F/D$ ratio does not converge for $N_c=3$ in the chiral soliton model in contrast to the non-relativistic quark model.

hep-ph↗