arXiv subjects

Zhi-zhong Xing

Publications and source records attributed to Zhi-zhong Xing.

At least 37 records · Page 2Linked to original sources

arXiv2023

CP violation in light neutrino oscillations and heavy neutrino decays: a general and explicit seesaw-bridged correlation

With the help of a block parametrization of the canonical seesaw flavor textures in terms of the Euler-like rotation angles and CP-violaing phases, we derive a general and explicit expression for the Jarlskog invariant of CP violation in neutrino oscillations and compare it with the CP-violating asymmetries of heavy Majorana neutrino decays within the minimal seesaw framework which contains two right-handed neutrino fields. Two simplified scenarios are discussed to illustrate how direct or indirect the correlation between these two types of CP violation can be.

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arXiv2023

The $μ$-$τ$ reflection symmetry of Majorana neutrinos

The observed pattern of lepton flavor mixing and CP violation strongly indicates the possible existence of a simple flavor symmetry in the neutrino sector -- the effective Majorana neutrino mass term keeps invariant when the three left-handed neutrino fields transform as $ν^{}_{e \rm L} \to (ν^{}_{e \rm L})^c$, $ν^{}_{μ\rm L} \to (ν^{}_{τ\rm L})^c$ and $ν^{}_{τ\rm L} \to (ν^{}_{μ\rm L})^c$. A direct application of such a $μ$-$τ$ reflection symmetry to the canonical seesaw mechanism can help a lot to constrain the flavor textures of active and sterile Majorana neutrinos. The present article is intended to summarize the latest progress made in exploring the properties of this minimal flavor symmetry, its translational and rotational extensions, its soft breaking effects via radiative corrections from a superhigh energy scale to the electroweak scale, and its various phenomenological implications.

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arXiv2023

The formal seesaw mechanism of Majorana neutrinos with unbroken gauge symmetry

We reformulate the canonical seesaw mechanism in the case that the electroweak gauge symmetry is unbroken, and show that it can "formally" work and allow us to derive an exact seesaw formula for the light and heavy Majorana neutrinos. We elucidate the reason why there is a mismatch between the mass eigenstates of heavy Majorana neutrinos associated with thermal leptogenesis and those associated with the seesaw framework, and establish the exact and explicit relations between the "original" and "derivational" seesaw parameters by using an Euler-like parametrization of the $6\times 6$ active-sterile flavor mixing matrix.

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arXiv2022

The translational $μ$-$τ$ reflection symmetry of Majorana neutrinos

The present neutrino oscillation data allow $m^{}_1 = 0$ (or $m^{}_3 = 0$) for the neutrino mass spectrum and support $θ^{}_{23} \simeq π/4$ and $δ\simeq -π/2$ as two good approximations for the PMNS lepton flavor mixing matrix $U$. We show that these intriguing possibilities can be a very natural consequence of the {\it translational} $μ$-$τ$ reflection symmetry -- the effective Majorana neutrino mass term keeps invariant under the transformations $ν^{}_{e \rm L} \to (ν^{}_{e \rm L})^c + U^*_{e i} z^{c}_ν$, $ν^{}_{μ\rm L} \to (ν^{}_{τ\rm L})^c + U^*_{τi} z^{c}_ν$ and $ν^{}_{τ\rm L} \to (ν^{}_{μ\rm L})^c + U^*_{μi} z^{c}_ν$ (for $i = 1$ or $3$), where $z^{c}_ν$ is the charge conjugation of a constant spinor field $z^{}_ν$. Extending such a working flavor symmetry to the canonical seesaw mechanism at a superhigh-energy scale, we calculate its soft breaking effects at the electroweak scale by using the one-loop renormalization-group equations.

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arXiv2022

Towards identifying the minimal flavor symmetry behind neutrino oscillations

Current neutrino oscillation data indicate that the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata matrix $U$ exhibits a $μ$-$τ$ flavor interchange symmetry $|U^{}_{μi}| = |U^{}_{τi}|$ (for $i = 1, 2, 3$) as a good approximation. In particular, the T2K measurement implies that the maximal neutrino mixing angle $θ^{}_{23}$ and the CP-violating phase $δ$ should be close to $π/4$ and $-π/2$, respectively. Behind these observations lies a minimal flavor symmetry -- - the effective Majorana neutrino mass term keeps invariant under the transformations $ν^{}_{e \rm L} \to (ν^{}_{e \rm L})^c$, $ν^{}_{μ\rm L} \to (ν^{}_{τ\rm L})^c$ and $ν^{}_{τ\rm L} \to (ν^{}_{μ\rm L})^c$. Extending this flavor symmetry to the canonical seesaw mechanism, we find that the $R$-matrix describing the strength of weak charged-current interactions of heavy Majorana neutrinos satisfies $|R^{}_{μi}| = |R^{}_{τi}|$ as a consequence of $|U^{}_{μi}| = |U^{}_{τi}|$. This result can be used to set a new upper bound, which is about three orders of magnitude more stringent than before, on the flavor mixing factor associated with the charged-lepton-flavor-violating decay mode $τ^- \to e^- + γ$.

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arXiv2022

One-loop radiative correction to the Toshev relation for neutrino oscillations in matter

The one-loop electroweak radiative corrections to coherent forward neutrino scattering in a medium slightly violates the tree-level universality of neutral-current contributions of three neutrino flavors to the matter potential that is relevant to neutrino oscillations in matter. We examine this small but nontrivial quantum effect by deriving the differential equations of those effective neutrino oscillation quantities with respect to the electron number density of matter. The tree-level Toshev relation $\sin 2\tildeθ_{23} \sin\tildeδ = \sin 2θ_{23} \sinδ$, which links the fundamental flavor-mixing and CP-violating parameters

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arXiv2022

Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations

In the canonical seesaw framework flavor mixing and CP violation in weak charged-current interactions of light and heavy Majorana neutrinos are correlated with each other and described respectively by the $3\times 3$ matrices $U$ and $R$. We show that the very possibility of $\big|U^{}_{μi}\big| = \big|U^{}_{τi}\big|$ (for $i = 1, 2, 3$), which is strongly indicated by current neutrino oscillation data, automatically leads to a novel prediction $\big|R^{}_{μi}\big| = \big|R^{}_{τi}\big|$ (for $i = 1, 2, 3$). We prove that behind these two sets of equalities and the experimental evidence for leptonic CP violation lies a minimal flavor symmetry -- the overall neutrino mass term keeps invariant when the left-handed neutrino fields transform as $ν^{}_{e \rm L} \to (ν^{}_{e \rm L})^c$, $ν^{}_{μ\rm L} \to (ν^{}_{τ\rm L})^c$, $ν^{}_{τ\rm L} \to (ν^{}_{μ\rm L})^c$ and the right-handed neutrino fields undergo an arbitrary unitary CP transformation. Such a generalized $μ$-$τ$ reflection symmetry may help constrain the flavor textures of active and sterile neutrinos to some extent in the seesaw mechanism.

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arXiv2021

A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations $ψ^{}_{α\rm L (R)} \to ψ^{}_{α\rm L (R)} + n^{}_α z^{}_{ψ\rm L(R)}$ in the flavor space, where $n^{}_α$ and $z^{}_{ψ\rm L(R)}$ stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that $n^{}_α$ can be identified as the elements $U^{}_{αi}$ in the $i$-th column of the unitary matrix $U$ used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix $M^{}_ψ$, and $m^{}_i = 0$ holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

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arXiv2021

Correlations between quark mass and flavor mixing hierarchies

We calculate the quark flavor mixing matrix $V$ based on the Hermitian quark mass matrices $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with vanishing $(1,1)$, $(1,3)$ and $(3,1)$ entries. The popular leading-order prediction $|V^{}_{ub}/V^{}_{cb}| \simeq \sqrt{m^{}_u/m^{}_c}$ is significantly modified, and the result agrees with the current experimental value. We find that behind the strong {\it mass} hierarchy of up- or down-type quarks is the weak {\it texture} hierarchy of $M^{}_{\rm u}$ or $M^{}_{\rm d}$ characterized by an approximate seesaw-like relation among its $(2,2)$, $(2,3)$ and $(3,3)$ elements.

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arXiv2021

A full parametrization of the $9\times 9$ active-sterile flavor mixing matrix in the inverse or linear seesaw scenario of massive neutrinos

The inverse and linear seesaw scenarios are two typical extensions of the canonical seesaw mechanism, which contain much more sterile degrees of freedom but can naturally explain the smallness of three active neutrino masses at a sufficiently low energy scale (e.g., the TeV scale). To fully describe the mixing among three active neutrinos, three sterile neutrinos and three extra gauge-singlet neutral fermions in either of these two seesaw paradigms, we present the {\it first} full parametrization of the $9\times 9$ flavor mixing matrix in terms of 36 rotation angles and 36 CP-violating phases. The exact inverse and linear seesaw formulas are derived, respectively; and possible deviations of the $3\times 3$ active neutrino mixing matrix from its unitary limit are discussed by calculating the effective Jarlskog invariants and unitarity nonagons.

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arXiv2021

3D mapping of the effective Majorana neutrino masses with neutrino oscillation data

With the help of current neutrino oscillation data, we illustrate the three-dimensional (3D) profiles of all the six distinct effective Majorana neutrino masses $|\langle m\rangle^{}_{αβ}|$ (for $α, β= e, μ, τ$) with respect to the unknown neutrino mass scale and effective Majorana CP phases. Some salient features of $|\langle m\rangle^{}_{αβ}|$ and their phenomenological implications are discussed in both the normal and inverted neutrino mass ordering cases.

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arXiv2021

The minimal seesaw and leptogenesis models

Given its briefness and predictability, the minimal seesaw -- a simplified version of the canonical seesaw mechanism with only two right-handed neutrino fields -- has been studied in depth and from many perspectives, and now it is being pushed close to a position of directly facing experimental tests. This article is intended to provide an up-to-date review of various phenomenological aspects of the minimal seesaw and its associated leptogenesis mechanism in neutrino physics and cosmology. Our focus is on possible flavor structures of such benchmark seesaw and leptogenesis scenarios and confronting their predictions with current neutrino oscillation data and cosmological observations. In this connection particular attention will be paid to the topics of lepton number violation, lepton flavor violation, discrete flavor symmetries, CP violation and antimatter of the Universe.

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arXiv2020

Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation

We calculate the rates of radiative $β^- \to α^- + γ$ decays for $(α, β) = (e, μ)$, $(e, τ)$ and $(μ, τ)$ by taking the {\it unitary} gauge in the $(3+n)$ active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix $U$ extracted from $β^- \to α^- + γ$ decays in the {\it minimal unitarity violation} scheme differ from those obtained in the canonical seesaw mechanism with $n$ heavy Majorana neutrinos by a factor $5/3$. In such a natural seesaw case we show that the rates of $β^- \to α^- + γ$ can be used to cleanly and strongly constrain the effective apex of a unitarity polygon, and compare its geometry with the geometry of its three sub-triangles formed by two vectors $U^{}_{αi} U^*_{βi}$ and $U^{}_{αj} U^*_{βj}$ (for $i \neq j$) in the complex plane. We find that the areas of such sub-triangles can be described in terms of the Jarlskog-like invariants of CP violation ${\cal J}^{ij}_{αβ}$, and their small differences signify slight unitarity violation of the PMNS matrix $U$.

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arXiv2020

Towards establishing the second $b$-flavored CKM unitarity triangle

Some fine differences between the twin $b$-flavored unitarity triangles are calculated by means of a generalized Wolfenstein parametrization of the CKM matrix, and a possibility of experimentally establishing the second triangle is briefly discussed. We find that the apexes of these two triangles, characterized respectively by $(\overlineρ, \overlineη)$ and $(\widetildeρ, \widetildeη)$, are located on the same circular arc in the complex plane. This observation provides us with a new way to test consistency of the CKM picture of CP violation in the quark sector and probe possible new physics. The differences between the apexes (i.e., $\widetildeρ - \overlineρ$ and $\widetildeη - \overlineη$) are found to be of ${\cal O}(λ^2)$ with $λ\simeq 0.22$ being the Wolfenstein expansion parameter, and the shapes of these two triangles are found to be insensitive to the two-loop renormalization-group-equation running effects up to the accuracy of ${\cal O}\left(λ^4\right)$.

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arXiv2020

On the two-loop radiative origin of the smallest neutrino mass and the associated Majorana CP phase

Given a massless neutrino at a superhigh energy scale $Λ$ (e.g., in the minimal seesaw model with only two heavy Majorana neutrinos), we calculate quantum corrections to its initially vanishing mass $m^{}_1$ (or $m^{}_3$) and the associated Majorana CP phase $ρ$ (or $\varrho$) at the Fermi scale $Λ^{}_{\rm F}$ by means of the two-loop renormalization-group equations (RGEs) in the standard model and with the help of the latest neutrino oscillation data. The numerical results obtained from our analytical approximations are in good agreement with those achieved by numerically solving the two-loop RGEs. In particular, we confirm that a nonzero value of $m^{}_1$ (or $m^{}_3$) of ${\cal O}(10^{-13})$ eV at $Λ^{}_{\rm F}$ can be radiatively generated from $m^{}_1 =0$ (or $m^{}_3 =0$) at $Λ\simeq 10^{14}$ GeV in the SM, and find that $ρ$ (or $\varrho$) may accordingly acquire an appreciable physical value. As a nontrivial by-product, the evolution of all the other (initially nonzero) flavor parameters of massive neutrinos is studied both analytically and numerically, by just keeping their leading (i.e., one-loop) RGE-induced effects.

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arXiv2020

Flavor structures of charged fermions and massive neutrinos

Most of the free parameters in the Standard Model (SM) -- a quantum field theory which has successfully elucidated the behaviors of strong, weak and electromagnetic interactions of all the known fundamental particles, come from the lepton and quark flavors. The discovery of neutrino oscillations has proved that the SM is incomplete, at least in its lepton sector; and thus the door of opportunity is opened to exploring new physics beyond the SM and solving a number of flavor puzzles. In this review article we give an overview of important progress made in understanding the mass spectra, flavor mixing patterns, CP-violating effects and underlying flavor structures of charged leptons, neutrinos and quarks in the past twenty years. After introducing the standard pictures of fermion mass generation, flavor mixing and CP violation in the SM extended with the presence of massive Dirac or Majorana neutrinos, we briefly summarize current experimental knowledge about the flavor parameters of quarks and leptons. Various ways of describing flavor mixing and CP violation are discussed, the renormalization-group evolution of flavor parameters is illuminated, and the matter effects on neutrino oscillations are interpreted. Taking account of possible extra neutrino species, we propose a standard parametrization of the $6\times 6$ flavor mixing matrix and comment on the phenomenological aspects of heavy, keV-scale and light sterile neutrinos. We pay particular attention to those novel and essentially model-independent ideas or approaches regarding how to determine the Yukawa textures of Dirac fermions and the effective mass matrix of Majorana neutrinos, including simple discrete and continuous flavor symmetries. An outlook to the future development in unravelling the mysteries of flavor structures is also given.

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arXiv2020

A direct link between unflavored leptogenesis and low-energy CP violation via the one-loop quantum corrections

In the type-I seesaw mechanism the Casas-Ibarra (CI) parametrization provides a convenient description of the Dirac neutrino mass matrix in terms of the light and heavy Majorana neutrino masses, the lepton flavor mixing matrix $U$ and an unknown complex orthogonal matrix $O$. If $O$ is assumed to be real, it will be impossible to generate {\it unflavored} thermal leptogenesis via the lepton-number-violating and CP-violating decays of the lightest heavy Majorana neutrino. We find that this observation can be invalidated after small but unavoidable quantum corrections to the CI parametrization are taken into account with the help of the one-loop renormalization-group equations (RGEs) between the seesaw and electroweak scales. We illustrate a novel and viable unflavored leptogenesis scenario of this kind based on the RGEs in the seesaw-extended standard model, and show its direct link to the CP-violating phases of $U$ at low energies.

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arXiv2020

Bridging resonant leptogenesis and low-energy CP violation with an RGE-modified seesaw relation

We propose a special type-I seesaw scenario in which the Yukawa coupling matrix $Y^{}_ν$ can be fully reconstructed by using the light Majorana neutrino masses $m^{}_i$, the heavy Majorana neutrino masses $M^{}_i$ and the PMNS lepton flavor mixing matrix $U$. It is the RGE-induced correction to the seesaw relation that helps interpret the observed baryon-antibaryon asymmetry of the Universe via flavored resonant thermal leptogenesis with $M^{}_1 \simeq M^{}_2 \ll M^{}_3$. We show that our idea works well in either the $τ$-flavored regime with equilibrium temperature $T \simeq M^{}_1 \in (10^9, 10^{12}]$ GeV or the $(μ+τ)$-flavored regime with $T \simeq M^{}_1 \in (10^5, 10^9]$ GeV, provided the light neutrinos have a normal mass ordering. We find that the same idea is also viable for a {\it minimal} type-I seesaw model with two nearly degenerate heavy Majorana neutrinos.

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