arXiv subjects

Zhi-zhong Xing

Publications and source records attributed to Zhi-zhong Xing.

At least 19 recordsLinked to original sources

arXiv2026

Parameter degeneracy and information loss in inverse flavor mapping for high-energy astrophysical neutrinos

Given a high-energy astrophysical neutrino flux, its source flavor ratios $η= \{η^{}_e, η^{}_μ, η^{}_τ\}$ are correlated with the ones $f = \{f^{}_e, f^{}_μ, f^{}_τ\}$ measured at a neutrino telescope via $f = P η$, where the elements of $P$ consist of four lepton flavor mixing parameters. But realistic {\it inverse} flavor mapping $η= P^{-1} f$ encounters unavoidable parameter degeneracy and information loss, especially in or near the $\det P = 0$ limit allowed by current neutrino oscillation data. In this work we explore the parameter correlation condition for $\det P = 0$ including the $μ$-$τ$ reflection symmetry case, formulate the corresponding constraints on $f^{}_e$ and $f^{}_μ$ versus $η^{}_e$ and $η^{}_μ$, and illustrate to what extent the source flavor distribution can be mapped by using the recent IceCube all-sky neutrino flux data ranging from 5 TeV to 10 PeV under the assumption that the relevant sources have a common flavor composition.

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arXiv2026

Neutrino cuboid for normal mass ordering and tribimaximal flavor mixing

Given the latest JUNO implication for normal neutrino mass ordering, we parametrize three neutrino masses in a flavor cuboid: $m^{}_1 = m^{}_0 \sinξ$, $m^{}_2 = m^{}_0 \cosξ\sinζ$ and $m^{}_3 = m^{}_0 \cosξ\cosζ$. We find that this cuboid is able to accommodate both neutrino mass degeneracy and tribimaximal flavor mixing in its cubic limit with $ξ^{}_* = \arctan\left(1/\sqrt{2}\right) \simeq 35.26^\circ$ and $ζ^{}_* = 45^\circ$. Assuming $θ^{}_{12} = ξ$ and $θ^{}_{23} = ζ$ for the two large angles of neutrino oscillations and expanding them around $ξ^{}_*$ and $ζ^{}_*$, we propose a viable ansatz which predicts a normal but nearly degenerate neutrino mass spectrum and a nearly tribimaximal neutrino mixing pattern. Testing the achieved correlation among $ξ^{}_* - θ^{}_{12}$, $ζ^{}_* - θ^{}_{23}$ and $Δm^2_{21}/Δm^2_{31}$ will provide a smoking gun for the validity of this ansatz.

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arXiv2026

Family-separated seesaw relations of Majorana neutrinos

Given the canonical seesaw mechanism as a most natural extension of the standard model in its neutrino sector, we find out a special but brand new solution to the exact seesaw equation: $m^{}_i/M^{}_i = - R^2_{αi}/U^2_{αi}$ for the masses and flavor mixing matrix elements of light and heavy Majorana neutrinos of the $i$-th family (for $i = 1, 2, 3$ and $α= e, μ, τ$). This family-separated seesaw scenario allows us to establish simple relations between the original seesaw parameters and the active degrees of freedom, and thus offers a number of testable predictions in neutrino phenomenology.

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arXiv2026

Potential divergence in tracing $μ$ and $τ$ flavors of astrophysical neutrinos

We derive general formulas for three flavor fractions $(η^{}_e , η^{}_μ, η^{}_τ)$ of the high-energy neutrinos originating from a remote astrophysical source by using their flavor ratios $(f^{}_e , f^{}_μ, f^{}_τ)$ observed at a neutrino telescope, and diagnose a potential divergence associated with $η^{}_μ$ and $η^{}_τ$ as an unavoidable consequence of the $μ$-$τ$ interchange symmetry exhibiting in the $3\times 3$ lepton flavor mixing matrix $U$. We present a complete set of analytical expressions for $(η^{}_e , η^{}_μ, η^{}_τ)$ as functions of two typical $μ$-$τ$ symmetry breaking parameters in the standard parametrization of $U$, and apply it to the recent IceCube all-sky neutrino flux data ranging from 5 TeV to 10 PeV in the assumption that the relevant sources have a common flavor composition. We also explain why only $η^{}_e$ and $η^{}_μ+ η^{}_τ$ can be extracted from a precision measurement of $f^{}_e$ and $f^{}_μ= f^{}_τ$ in the exact $μ$-$τ$ flavor symmetry limit.

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arXiv2026

Leptonic first-row correlation and unitarity waiting for further JUNO tests

We conjecture that there exists a remarkable correlation among the three elements in the first row of the $3\times 3$ lepton flavor mixing matrix $U$: $|U^{}_{e1}|^2 = 2 \left(|U^{}_{e2}|^2 + |U^{}_{e3}|^2\right)$, which holds even though $U$ is non-unitary in the canonical seesaw mechanism. This ``first-row correlation" is fully consistent with $\sin^2θ^{}_{12} = \left(1 - 2\tan^2θ^{}_{13}\right)/3$ in the unitarity limit of $U$, as supported by the latest JUNO and Daya Bay precision measurements at a confidence level close to $1σ$.

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arXiv2025

Towards a detection of reactor $\overlineν^{}_e \to \overlineν^{}_μ$ and $\overlineν^{}_e \to \overlineν^{}_τ$ oscillations with possible CP violation

We propose an unprecedented detection of reactor $\overlineν^{}_e \to \overlineν^{}_μ$ and $\overlineν^{}_e \to \overlineν^{}_τ$ oscillations by using elastic antineutrino-electron scattering processes $\overlineν^{}_α+ e^- \to \overlineν^{}_α+ e^-$ (for $α= e, μ, τ$), among which the $\overlineν^{}_e$ events can be singled out by accurately measuring the $\overlineν^{}_e$ flux via the inverse beta decay $\overlineν^{}_e + p \to e^+ + n$. A proof-of-concept study shows that such measurements will not only be able to test the conservation of probability for reactor antineutrino oscillations, but also offer a new possibility to probe leptonic CP violation at the one-loop level.

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arXiv2025

New rephasing invariants and CP violation built from the trios of the CKM or PMNS matrix elements

Given the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) quark flavor mixing matrix $V$, we define a new set of rephasing invariants in terms of the "trios" of its nine elements: $\lozenge^{ijk}_{αβγ} \equiv (V^{}_{αi} V^{}_{βj} V^{}_{γk})/\det V$ with $α\neq β\neq γ$ and $i \neq j \neq k$ running respectively over $(u, c, t)$ and $(d, s, b)$. We find that ${\rm Im} \lozenge^{ijk}_{αβγ} = - {\cal J}$ holds, where ${\cal J}$ is the well-known Jarlskog invariant of weak CP violation. Analogous rephasing invariants $\blacklozenge^{ijk}_{αβγ} \equiv (U^{}_{αI} U^{}_{βj} U^{}_{γk})/\det U$ can be defined for the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton flavor mixing matrix $U$, where $α\neq β\neq γ$ and $i \neq j \neq k$ run respectively over $(e, μ, τ)$ and $(1, 2, 3)$. Taking into account small non-unitarity of $U$ based on the canonical seesaw mechanism for neutrino mass generation, we calculate ${\rm Im} \blacklozenge^{ijk}_{αβγ}$ with the help of a full Euler-like block parametrization of the seesaw flavor structure and demonstrate that their leading terms converge to a universal invariant ${\cal J}^{}_ν$ in the unitarity limit of $U$.

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arXiv2025

Quantum-entangled B mesons and CP violation: a brief overview

This paper is intended to provide a brief overview of the quantum-entangled production of neutral meson-antimeson pairs, and to highlight the first discovery of a clean physical CP-violating phase in coherent neutral-$B$ decays as a smoking gun of the Kobayashi-Maskawa mechanism of CP violation in the standard model of particle physics.

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arXiv2025

Rephasing invariants of CP violation for heavy and light Majorana neutrinos

In the canonical seesaw mechanism, the strengths of charged-current interactions for light and heavy Majorana neutrinos are described respectively by the $3\times 3$ matrices $U$ and $R$ that are correlated with each other via the exact seesaw relation and the unitarity condition. We write out the Majorana-type invariants of CP violation of $R$ and $U$, which are insensitive to redefining the phases of three charged-lepton fields; and the Dirac-type invariants of CP violation of $R$ and $U$ that are insensitive to the rephasing of both the charged-lepton fields and the neutrino fields. Such invariants are explicitly calculated with the help of a full Euler-like block parametrization of the seesaw flavor structure containing nine active-sterile flavor mixing angles and six independent CP-violating phases, and their corresponding roles in the CP-violating asymmetries of three heavy Majorana neutrino decays and in the flavor oscillations of three light Majorana neutrinos are briefly discussed. We point out that similar rephasing invariants arising from the interplay between $R$ and $U$ may also manifest themselves in a variety of lepton-flavor-violating and lepton-number-violating processes.

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arXiv2025

Confronting the seesaw mechanism with neutrino oscillations: a general and explicit analytical bridge

With the help of a full Euler-like block parametrization of the flavor structure for the canonical seesaw mechanism, we present the first general and explicit analytical calculations of the two neutrino mass-squared differences, three flavor mixing angles and the effective Dirac CP-violating phase responsible for the primary behaviors of neutrino oscillations. Such model-independent results will pave the way for testing the seesaw mechanism at low energies.

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arXiv2025

Neutrino Theory in the Precision Era

This document summarises discussions on future directions in theoretical neutrino physics, which are the outcome of a neutrino theory workshop held at CERN in February 2025. The starting point is the realisation that neutrino physics offers unique opportunities to address some of the most fundamental questions in physics. This motivates a vigorous experimental programme which the theory community fully supports. \textbf{A strong effort in theoretical neutrino physics is paramount to optimally take advantage of upcoming neutrino experiments and to explore the synergies with other areas of particle, astroparticle, and nuclear physics, as well as cosmology.} Progress on the theory side has the potential to significantly boost the physics reach of experiments, as well as go well beyond their original scope. Strong collaboration between theory and experiment is essential in the precision era. To foster such collaboration, \textbf{we propose to establish a CERN Neutrino Physics Centre.} Taking inspiration from the highly successful LHC Physics Center at Fermilab, the CERN Neutrino Physics Centre would be the European hub of the neutrino community, covering experimental and theoretical activities.

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arXiv2025

Emergent large flavor mixing from canonical and inverse seesaws?

While the canonical seesaw mechanism provides a most natural qualitative interpretation of tiny masses for the three active neutrinos, it offers no explanation for their large flavor mixing effects. The latter can be regarded as an emergent consequence of this mechanism, in which case we are left with an intriguing cross seesaw framework in the mass basis of all the six Majorana neutrinos. To lower the mass scales of heavy neutrinos, one is motivated to invoke the inverse seesaw mechanism but has to pay the price for a fine-tuned cancellation between its two sets of new degrees of freedom, in which case the largeness of active flavor mixing is an emergent phenomenon as well. A comparison between the approximate seesaw relations in the flavor basis and those exact ones in the mass basis is also made.

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arXiv2024

Lepton flavor physics: some theoretical aspects

A brief and personal overview of some theoretical aspects of lepton flavor physics is presented, with a focus on the canonical seesaw mechanism and Majorana nature of massive neutrinos.

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arXiv2024

On the orthogonal matrix in the Casas-Ibarra parametrization for the Yukawa interactions of Majorana neutrinos

The Casas-Ibarra (CI) parametrization of the Yukawa coupling matrix of Majorana neutrinos is generalized by considering the exact seesaw relation and including non-unitarity of the $3 \times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) flavor mixing matrix. With the help of a full $6 \times 6$ Euler-like block description of the flavor structure for the seesaw mechanism, we find that the orthogonal matrix $\mathbb{O}$ in the CI parametrization can be expressed as $\mathbb{O}^{}_{ij} = \sqrt{M^{}_j/m^{}_i} \hspace{0.05cm} F^{}_{ij}$ with $m^{}_i$ and $M^{}_j$ being the masses of light and heavy Majorana neutrinos and $F^{}_{ij}$ consisting of the PMNS and active-sterile flavor mixing parameters (for $i, j = 1, 2, 3$). Assuming a specific pattern of $\mathbb{O}$ is therefore equivalent to imposing some special conditions on the seesaw parameter space.

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arXiv2024

Mapping the sources of CP violation in neutrino oscillations from the seesaw mechanism

We present the first complete calculation of the Jarlskog invariant, a working measure of the strength of CP violation in the flavor oscillations of three light neutrino species, with the help of a full Euler-like block parametrization of the flavor structure in the canonical seesaw mechanism. We find that this invariant depends on 240 linear combinations of the 6 original phase parameters that are responsible for CP violation in the decays of three heavy Majorana neutrinos in 27 linear combinations as a whole, and thus provides the first model-independent connection between the microscopic and macroscopic matter-antimatter asymmetries.

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arXiv2024

A new Wolfenstein-like expansion of lepton flavor mixing towards understanding its fine structure

Taking the tri-bimaximal flavor mixing pattern as a particular basis, we propose a new way to expand the $3\times 3$ unitary Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton flavor mixing matrix $U$ in powers of the magnitude of its smallest element $ξ\equiv \left|U^{}_{e 3}\right| \simeq 0.149$. Such a Wolfenstein-like parametrization of $U$ allows us to easily describe the salient features and fine structures of flavor mixing and CP violation, both in vacuum and in matter.

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arXiv2023

First determination of the Jarlskog invariant of CP violation from the moduli of the CKM matrix elements

We find that the precision and accuracy of current experimental data on the moduli of nine Cabibbo-Kobayashi-Maskawa (CKM) quark flavor mixing matrix elements allow us to numerically determine the it correct size of the Jarlskog invariant of CP violation from four of them in eight different ways for the first time without making any special assumptions. This observation implies a remarkable self-consistency of the correlation between CP-conserving and CP-violating quantities of the CKM matrix as guaranteed by its unitarity.

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arXiv2023

A Pythagoras-like theorem for CP violation in neutrino oscillations

The probabilities of $ν^{}_μ \to ν^{}_{e}$ and $\overlineν^{}_μ \to \overlineν^{}_{e}$ oscillations in vacuum are determined by the CP-conserving flavor mixing factors ${\cal R}^{}_{ij} \equiv {\rm Re} (U^{}_{μi} U^{}_{e j} U^{*}_{μj} U^{*}_{e i})$ and the universal Jarlskog invariant of CP violation ${\cal J}^{}_ν \equiv (-1)^{i+j} \; {\rm Im} (U^{}_{μi} U^{}_{e j} U^{*}_{μj} U^{*}_{e i})$ (for $i, j = 1, 2, 3$ and $i < j$), where $U$ is the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix. We show that ${\cal J}^{2}_ν = {\cal R}^{}_{12} {\cal R}^{}_{13} + {\cal R}^{}_{12} {\cal R}^{}_{23} + {\cal R}^{}_{13} {\cal R}^{}_{23}$ holds as a natural consequence of the unitarity of $U$. This Pythagoras-like relation may provide a novel cross-check of the result of ${\cal J}^{}_ν$ that will be directly measured in the next-generation long-baseline neutrino oscillation experiments. Indirect non-unitarity effects and terrestrial matter effects on ${\cal J}^{}_ν$ and ${\cal R}^{}_{ij}$ are also discussed.

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