arXiv subjects

Hisakazu Minakata

Publications and source records attributed to Hisakazu Minakata.

At least 19 recordsLinked to original sources

arXiv2025

eV-scale sterile neutrino: A window open to non-unitarity?

An excess observed in the accelerator neutrino experiments in the $ν_μ \rightarrow ν_{e}$ channel at high confidence level (CL) has been interpreted as due to eV-scale sterile neutrino(s). But, it has been suffered from the problem of ``appearance-disappearance tension'' at the similarly high CL because the measurements of the $ν_μ \rightarrow ν_μ$ channel do not observe the expected event number depletion corresponding to the sterile contribution in the appearance channel. We suggest non-unitarity as a simple and natural way of resolving the tension, which leads us to construct the non-unitary $(3+1)$ model. With reasonable estimation of the $α$ parameters governing non-unitarity, which we argue growing when more sterile states added, we perform an illustrative analysis to illuminate if the tension can be resolved in this model. We have found the unique solution with $\sin^2 2θ_{14} \approx 0.3$, which is consistent with the (reactors + Ga) data and is stable against variation of the appearance signature. This solution bridges between the two high CL signatures, BEST and LSND-MiniBooNE, and implies a large neutrino-antineutrino asymmetry, given the much less anomaly indicated in the antineutrino sector.

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arXiv2025

Sterile-active resonance: A global qualitative picture

In the $ν$SM extended by adding an eV-scale sterile state, the $(3+1)$ model, the sterile-active level crossing entails the MSW resonance, here referred as the sterile-active (SA) resonance. In this paper, we construct an effective theory of SA resonance which involves only the sterile-active mixing angles and $Δm^2_{41}$, thanks to the given environment of high matter potential which freezes the $ν$SM oscillations. We give our first attempt at an analytic treatment of the effective theory to illuminate the global picture of the SA resonance at a glance. We formulate a perturbative framework in which the structure of ``texture zeros'' of the $S$ matrix in the flavor space and the suppression by the small parameters $\sin θ_{j 4}$ ($j=1,2,3$) allows us to reveal the flavor$-$event-type hierarchy of the resonance-effect strength in the probabilities. We have shown that the cascade events dominantly comes from the three paths through $P(ν_{e} \rightarrow ν_{e})$, $P(\barν_{e} \rightarrow \barν_{e})$, and $P(\barν_μ \rightarrow \barν_τ)$, and a three-component fit is suggested to disentangle the SA resonance generation mechanisms.

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arXiv2024

Neutrino amplitude decomposition, $S$ matrix rephasing invariance, and reparametrization symmetry

The $S$ matrix rephasing invariance is one of the fundamental principles of quantum mechanics that originates in its probabilistic interpretation. For a given $S$ matrix which describes neutrino oscillation, one can define the two different rephased amplitudes $S_{αβ}^{ \text{Reph-1} } \equiv e^{ i (λ_{1} / 2E) x} S_{αβ}$ and $S_{αβ}^{ \text{Reph-2} } \equiv e^{ i (λ_{2} / 2E) x} S_{αβ}$, which are physically equivalent to each other, where $λ_{k} / 2E$ denotes the energy eigenvalue of the $k$-th mass eigenstate. We point out that the transformation of the reparametrization (Rep) symmetry obtained with ``Symmetry Finder'' maps $S_{αβ}^{ \text{Reph-1} }$ to $S_{αβ}^{ \text{Reph-2} }$, and vice versa, providing a local and manifest realization of the $S$ matrix rephasing invariance by the Rep symmetry of the 1-2 state exchange type. It is strongly indicative of quantum mechanical nature of the Rep symmetry. The rephasing and Rep symmetry relation, though its all-order treatment remains incomplete, is shown to imply absence of the pure 1-3 exchange symmetry in Denton~{\it et al.}~perturbation theory. It then triggers a study of convergence of perturbation series.

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arXiv2023

Comparative study of the 1-2 exchange symmetries in neutrino frameworks with global and local validities

A new picture ``one-resonance - one-symmetry'' has been proposed recently to reveal nature of the reparametrization symmetry in neutrino oscillation in matter and where it resides: Symmetry of $i \leftrightarrow j$ state-exchange type exists at around a resonance with $i$ and $j$ being the states which participate in the level crossing. Consistently, the 1-2 and 1-3 state exchange symmetries are identified at around the solar and atmospheric resonances, respectively, in the locally-valid frameworks. On the other hand, the Denton {\it et al.} (DMP) perturbation theory, a globally-valid framework, has the 1-2 exchange symmetry which is akin to the one in the aforementioned solar-resonance perturbation (SRP) theory. In our picture, the symmetry must be associated with the resonance, not the framework, and if so these two 1-2 symmetries must be identical to each other. We conduct a comparative study of the 1-2 symmetries possessed by SRP and DMP to confirm their identity. An almost identity is verified, but in a highly nontrivial way.

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arXiv2023

Symmetry in neutrino oscillation in matter with non-unitarity

Recently we have developed a method called ``Symmetry Finder'' (SF) for hunting the reparametrization symmetry in the three-neutrino system in matter. Here, we apply SF to the Denton {\it et al.} (DMP) perturbation theory extended by including unitarity violation (UV), a possible low-energy manifestation of physics beyond the $ν$SM. Implementation of UV into the SF framework yields the additional two very different constraints, which nonetheless allow remarkably consistent solutions, the eight DMP-UV symmetries. Treatment of one of the constraints, the genuine non-unitary part, leads to the key identity which entails the UV $α$ parameter transformation only by rephasing, which innovates the invariance proof of the Hamiltonian. The quantum mechanical nature of the symmetry dictates the both $ν$SM and UV variables to transform jointly, through which the response of the two sectors are related to reveal their interplay. Thus, the symmetry can serve for a tool for diagnostics, probing the interrelation between the $ν$SM and a low-energy description of new physics. Problem of SF symmetry in vacuum is revisited to complete eight symmetries akin to DMP's.

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arXiv2022

Symmetry in neutrino oscillation in matter: New picture and the $ν$SM -- non-unitarity interplay

We update and summarize the present status of our understanding of the reparametrization symmetry with $i \leftrightarrow j$ state exchange in neutrino oscillation in matter. We introduce a systematic method called ``Symmetry Finder'' (SF) to uncover such symmetries, demonstrate its efficient hunting capability, and examine their characteristic features. Apparently they have a local nature: The 1-2 and 1-3 state exchange symmetries exist at around the solar- and atmospheric-resonances, respectively, with the level-crossing states exchanged. However, this view is not supported, to date, in the globally valid Denton et al. (DMP) perturbation theory, which possesses the 1-2 exchange symmetry but not the 1-3. It is probably due to lack of our understanding, and we find a clue for a larger symmetry structure than that we know. In the latter part of this article, we introduce non-unitarity, or unitarity violation (UV), into the $ν$SM neutrino paradigm, a low-energy description of beyond $ν$SM new physics at high (or low) scale. Based on the analyses of UV extended versions of the atmospheric-resonance and the DMP perturbation theories, we argue that the reparametrization symmetry has a diagnostics capability for the theory with the $ν$SM and UV sectors. A speculation is given on the topological nature of the identity which determines the transformation property of the UV $α$ parameters.

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arXiv2022

Toward diagnosing neutrino non-unitarity through CP phase correlations

We discuss correlations between the $ν$SM CP phase $δ$ and the phases that originate from new physics which causes neutrino-sector unitarity violation (UV) at low energies. This study is motivated to provide one of the building pieces for a machinery to diagnose non-unitarity, our ultimate goal. We extend the perturbation theory of neutrino oscillation in matter proposed by Denton {\it et al.}~(DMP) to include the UV effect expressed by the $α$ parametrization. By analyzing the DMP-UV perturbation theory to first order, we are able to draw a completed picture of the $δ$ - UV phase correlations in the whole kinematical region covered by the terrestrial neutrino experiments. There exist the two regions with the characteristically different patterns of the correlations: (1) the chiral-type $[e^{- i δ} α_{μe}, ~e^{ - i δ} α_{τe}, ~α_{τμ}]$ (PDG convention) correlation in the entire high-energy region $\vert ρE \vert \gsim 6~(\text{g/cm}^3)$ GeV, and (2) (blobs of the $α$ parameters) - $e^{ \pm i δ}$ correlation in anywhere else. Some relevant aspects for measurement of the UV parameters, such as the necessity of determining all the $α_{βγ}$ elements at once, are also pointed out.

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arXiv2021

Measuring tau neutrino appearance probability via unitarity

We propose a {\em unitarity method} for determining $τ$ neutrino appearance probability $P(ν_μ \rightarrow ν_τ)$ in long-baseline (LBL) accelerator experiments and atmospheric neutrino observations. When simultaneous in situ measurements of $P(ν_μ \rightarrow ν_μ)$ and $P(ν_μ \rightarrow ν_{e})$ proceed, as is typical in the LBL experiments, one can use unitarity to "measure" $P(ν_μ \rightarrow ν_τ)$. A theorists' toy analysis for the model-independent determination of $P(ν_μ \rightarrow ν_μ)$ and $P(ν_μ \rightarrow ν_{e})$ is presented by using the NOvA data. It is shown in our analysis that $\lsim$5\% (8\%) measurement of $τ$ neutrino appearance probability in neutrino (antineutrino) mode is possible in the peak region $1.5 \lesssim E_ν\lesssim 2.5$ GeV. The $ν$SM-independent nature of determination of the probabilities is emphasized.

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arXiv2021

Symmetry Finder applied to the 1-3 mass eigenstate exchange symmetry

In a previous paper, Symmetry Finder (SF) method is proposed to find the reparametrization symmetry of the state-exchange type in neutrino oscillation in matter. It has been applied successfully to the 1-2 state exchange symmetry in the DMP perturbation theory, yielding the eight symmetries. In this paper, we apply the SF method to the atmospheric-resonance perturbation theory to uncover the 1-3 state relabeling symmetries. The pure 1-3 state symmetry takes the unique position that it is practically impossible to formulate in vacuum under the conventional choice of the flavor mixing matrix. In contrast, our SF method produces the sixteen 1-3 state exchange symmetries in matter. The relationship between the symmetries in the original (vacuum plus matter) Hamiltonian and the ones in the diagonalized system is discussed.

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arXiv2021

Symmetry Finder: A method for hunting symmetry in neutrino oscillation

Symmetry in neutrino oscillation serves for a better understanding of the physical properties of the phenomenon. We present a systematic way of finding symmetry in neutrino oscillation, which we call Symmetry Finder (SF). By extending the known framework in vacuum into a matter environment, we derive the SF equation, a powerful machinery for identifying symmetry in the system. After learning lessons on symmetry in the Zaglauer-Schwarzer system with a matter equivalent of the vacuum symmetry, we apply the SF method to the Denton et al. (DMP) perturbation theory to first order. We show that the method is so powerful that we uncover the eight reparametrization symmetries with the $1 \leftrightarrow 2$ state exchange in DMP, denoted as IA, IB, $\cdot \cdot \cdot$, IVB, all new except for IA. The transformations consist of the both fundamental and dynamical variables, indicating their equal importance. It is also shown that all the symmetries discussed in this paper can be understood as the Hamiltonian symmetries, which ensures their all-order validity and applicability to varying density matter.

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arXiv2021

Neutrino amplitude decomposition in matter

Observation of the interference between the atmospheric-scale and solar-scale oscillations is one of the challenging and tantalizing goals of the ongoing and upcoming neutrino experiments. An inevitable first step required for such analyses is to establish the way of how the oscillation $S$ matrix can be decomposed into the atmospheric and solar waves, the procedure dubbed as the amplitude decomposition. In this paper, with use of the perturbative framework proposed by Denton et al. (DMP), we establish the prescription for amplitude decomposition which covers the whole kinematical region of the terrestrial neutrino experiments. We analyze the limits to the atmospheric- and solar-resonance regions to argue that the dynamical two modes of the DMP decomposition can be interpreted as the matter-dressed atmospheric and solar oscillations. The expressions of the oscillation probability, which are decomposed into the non-interference and interference terms, are derived for all the relevant flavor oscillation channels. Through construction of the DMP decomposition, we reveal the nature of $ψ$ ($θ_{12}$ in matter) symmetry as due to the $S$ matrix rephasing invariance. A new picture of the DMP perturbation theory emerged, a unified perturbative framework for neutrino oscillation in earth matter.

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arXiv2021

Neutrino Oscillations at JUNO, the Born Rule, and Sorkin's Triple Path Interference

We argue that neutrino oscillations at JUNO offer a unique opportunity to study Sorkin's triple-path interference, which is predicted to be zero in canonical quantum mechanics by virtue of the Born rule. In particular, we compute the expected bounds on triple-path interference at JUNO and demonstrate that they are comparable to those already available from electromagnetic probes. Furthermore, the neutrino probe of the Born rule is much more direct due to an intrinsic independence from any boundary conditions, whereas such dependence on boundary conditions is always present in the case of electromagnetic probes. Thus, neutrino oscillations present an ideal probe of this aspect of the foundations of quantum mechanics.

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arXiv2020

Neutrino amplitude decomposition: Toward observing the atmospheric - solar wave interference

Observation of the interference between the atmospheric and solar oscillation waves with the correct magnitude would provide another manifestation of the three-generation structure of leptons. As a prerequisite for such analyses we develop a method for decomposing the oscillation $S$ matrix into the atmospheric and solar amplitudes. Though the similar method was recently proposed successfully in vacuum, once an extension into the matter environment is attempted, it poses highly nontrivial problems. Even for an infinitesimal matter potential, inherent mixture of the atmospheric and solar oscillation waves occurs, rendering a simple extension of the vacuum definition untenable. We utilize general kinematic structure as well as analyses of the five perturbative frameworks, in which the nature of matter-dressed atmospheric and solar oscillations are known, to understand the origin of the trouble, how to deal with the difficulty, and to grasp the principle of decomposition. Then, we derive the amplitude decomposition formulas in these frameworks, and discuss properties of the decomposed probabilities. We mostly discuss the $ν_μ \rightarrow ν_{e}$ channel, but a comparison with the $ν_μ \rightarrow ν_τ$ channel reveals an interesting difference.

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arXiv2020

Constraining visible neutrino decay at KamLAND and JUNO

We study visible neutrino decay at the reactor neutrino experiments KamLAND and, JUNO. Assuming the Majoron model of neutrino decay, we obtain constraints on the couplings between Majoron and neutrino as well as on the lifetime/mass of the most massive neutrino state i.e., $τ_{3} / m_{3}$ or $τ_{2} / m_{2}$, respectively, for the normal or the inverted mass orderings. We obtain the constraints on the lifetime $τ_{2} / m_{2} \geq 1.4 \times 10^{-9}~\rm{s/eV}$ in the inverted mass ordering for both KamLAND and JUNO at 90% CL. In the normal ordering in which the bound can be obtained for JUNO only, the constraint is milder than the inverted ordering case, $τ_{3} / m_{3} \geq 1.0 \times 10^{-10}~\rm{s/eV}$ at 90% CL. We find that the dependence of lightest neutrino mass ($=m_{\rm{lightest}}$), $m_1 (m_3)$ for the normal (inverted) mass ordering, on the constraints for the different types of couplings (scalar or pseudo-scalar) is rather strong, but the $m_{\rm{lightest}}$ dependence on the lifetime/mass bound is only modest.

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arXiv2020

Physics of parameter correlations around the solar-scale enhancement in neutrino theory with unitarity violation

We discuss physics of the three neutrino flavor transformation with non-unitary mixing matrix, with particular attention to the correlation between the $ν$SM- and the $α$ parameters which represent effect of unitarity violating (UV) new physics. Toward the goal, a new perturbative framework is created to illuminate the effect of non-unitarity in region of the solar-scale enhanced oscillations. We refute the skepticism about the physical reality of the $ν$SM CP $δ$ - $α$ parameter phase correlation by analysis with the SOL convention of $U_{\text{\tiny MNS}}$ in which $e^{ \pm i δ}$ is attached to $s_{12}$. Then, a comparative study between the solar- and atmospheric-scale oscillation regions allowed by the framework reveals a dynamical $δ-$(blobs of the $α$ parameters) correlation in the solar oscillation region, in sharp contrast to the ``chiral'' type phase correlation $[e^{- i δ} \barα_{μe}, e^{ - i δ} \barα_{τe}, \barα_{τμ}]$ in the PDG convention seen in the atmospheric oscillation region. An explicit perturbative calculation to first order in the $ν_μ \rightarrow ν_{e}$ channel allows us to decompose the UV related part of the probability into the unitary evolution part and the genuine non-unitary part. We observe that the effect of non-unitarity tends to cancel between these two parts, as well as between the different $α_{βγ}$ parameters.

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arXiv2020

Standard versus Non-Standard CP Phases in Neutrino Oscillation in Matter with Non-Unitarity

We formulate a perturbative framework for the flavor transformation of the standard three active neutrinos but with non-unitary flavor mixing matrix, a system which may be relevant for leptonic unitarity test. We use the $α$ parametrization of the non-unitary matrix and take its elements $α_{βγ}$ ($β,γ= e,μ,τ$) and the ratio $ε\simeq Δm^2_{21} / Δm^2_{31}$ as the small expansion parameters. Qualitatively new two features that hold in all the oscillation channels are uncovered in the probability formula obtained to first order in the expansion: (1) The phases of the complex $α$ elements always come in into the observable in the particular combination with the $ν$SM CP phase $δ$ in the form $[e^{- i δ} \barα_{μe}, ~e^{ - i δ} \barα_{τe}, ~\barα_{τμ}]$ under the PDG convention of unitary $ν$SM mixing matrix. (2) The diagonal $α$ parameters appear in particular combinations $\left( a/b - 1 \right) α_{ee} + α_{μμ}$ and $α_{μμ} - α_{ττ}$, where $a$ and $b$ denote, respectively, the matter potential due to CC and NC reactions. This property holds only in the unitary evolution part of the probability, and there is no such feature in the genuine non-unitary part, while the $δ$ - $α$ parameter phase correlation exists for both. The reason for such remarkable stability of the phase correlation is discussed.

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arXiv2020

Interference between the Atmospheric and Solar Oscillation Amplitudes

We propose to detect the interference effect between the atmospheric-scale and solar-scale waves of neutrino oscillation, one of the key consequences of the three-generation structure of leptons. In vacuum, we show that there is a natural and general way of decomposing the oscillation amplitude into these two oscillation modes. The nature of the interference is cleanest in the $\barν_e$ disappearance channel since it is free from the CP-phase $δ$. We find that the upcoming JUNO experiment offers an ideal setting to observe this interference with more than $4\,σ$ significance, even under conservative assumptions about the systematic uncertainties.

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arXiv2019

Using low energy atmospheric neutrinos for precision measurement of the mixing parameters

Use of low energy atmospheric neutrinos is considered for precision measurement of neutrino mixing parameters. At around energy $E \simeq$ a few $\times$100 MeV and baseline $L$ of a few $\times$1000 km, CP phase effect is $\sim$10 times larger than that of the conventional LBL accelerator neutrino experiments. We report here a few progresses: (1) To analyze physics in the region, a new perturbative framework at around the solar-scale enhancement is developed. (2) To know the characteristic features of CP $δ$ dependence of the atmospheric neutrinos at low energies, we plot the ratio of the $ν_{e}$ and $\barν_{e}$ fluxes $F(δ)/F(δ=0)$ for $δ=\pm \fracπ{2}$ and $π$ as a function of $E$ using the Honda {\it et al.} flux. Interestingly, it shows $δ$ dependence of $\simeq$5-10\% level, with positive (negative) sign for $ν_{e}$ ($\barν_{e}$). (3) To reduce the flux systematic errors, measurement of muon energy distribution around $\sim$1 GeV at high altitude may be useful. Water Cherenkov or muon range detectors may be the options with advantage in the latter if it is magnetized in view of the $δ$ dependence of the flux.

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