arXiv subjects

Zhi-zhong Xing

Publications and source records attributed to Zhi-zhong Xing.

At least 55 records · Page 3Linked to original sources

arXiv2020

Distinguishing between the twin $b$-flavored unitarity triangles on a circular arc

With the help of the generalized Wolfenstein parametrization of quark flavor mixing and CP violation, we calculate fine differences between the twin $b$-flavored unitarity triangles defined by $V^{*}_{ub} V^{}_{ud} + V^{*}_{cb} V^{}_{cd} + V^{*}_{tb} V^{}_{td} = 0$ and $V^{*}_{ud} V^{}_{td} + V^{*}_{us} V^{}_{ts} + V^{*}_{ub} V^{}_{tb} = 0$ in the complex plane. We find that vertices of the rescaled versions of these two triangles, described respectively by $\barρ + {\rm i} \barη = -\left(V^{*}_{ub} V^{}_{ud}\right)/\left(V^{*}_{cb} V^{}_{cd}\right)$ and $\widetildeρ + {\rm i} \widetildeη = -\left(V^{*}_{ub} V^{}_{tb}\right)/\left(V^{*}_{us} V^{}_{ts}\right)$, are located on a circular arc whose center and radius are given by $O = \left(0.5, 0.5 \cotα\right)$ and $R = 0.5 \cscα$ with $α$ being their common inner angle. The small difference between $(\barρ, \barη)$ and $(\widetildeρ, \widetildeη)$ is characterized by $\widetildeρ - \barρ \sim \widetildeη - \barη \sim {\cal O}(λ^2)$ with $λ\simeq 0.22$ being the Wolfenstein expansion parameter, and these two vertices are insensitive to the two-loop renormalization-group running effects up to the accuracy of ${\cal O}(λ^4)$. Some comments are also made on similar features of three pairs of the rescaled unitarity triangles of lepton flavor mixing and CP violation.

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arXiv2019

Sum rules and asymptotic behaviors of neutrino mixing in dense matter

It has proved convenient to define the effective lepton flavor mixing matrix $\widetilde{U}$ and neutrino mass-squared differences $\widetildeΔ^{}_{ji} \equiv \widetilde{m}^2_j - \widetilde{m}^2_i$ (for $i,j =1,2,3$) to describe the phenomena of neutrino mixing and flavor oscillations in a medium, but the prerequisite is to establish direct and transparent relations between these effective quantities and their fundamental counterparts in vacuum. With the help of two sets of sum rules for $\widetilde{U}$ and $\widetildeΔ^{}_{ji}$, we derive new and exact formulas for moduli of the nine elements of $\widetilde{U}$ and the sides of its three Dirac unitarity triangles in the complex plane. The asymptotic behaviors of $|\widetilde{U}^{}_{αi}|^2$ and $\widetildeΔ^{}_{ji}$ (for $α= e, μ, τ$ and $i,j =1,2,3$) in very dense matter (namely, allowing the matter parameter $A = 2\sqrt{2} ~ G^{}_{\rm F} N^{}_e E$ to mathematically approach infinity) are analytically unraveled for the first time, and in this connection the confusion associated with the parameter redundancy of $\widetildeθ^{}_{12}$, $\widetildeθ^{}_{13}$, $\widetildeθ^{}_{23}$ and $\widetildeδ$ in the standard parametrization of $\widetilde{U}$ is clarified.

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arXiv2019

Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays

In this paper, we emphasize why it is important for future neutrinoless double-beta ($0νββ$) decay experiments to reach the sensitivity to the effective neutrino mass $|m^{}_{ββ}| \approx 1~{\rm meV}$. Assuming such a sensitivity and the precisions on neutrino oscillation parameters after the JUNO experiment, we fully explore the constrained regions of the lightest neutrino mass $m^{}_1$ and two Majorana-type CP-violating phases $\{ρ, σ\}$. The implications for the neutrino mass spectrum, the effective neutrino mass $m^{}_β$ in beta decays and the sum of three neutrino masses $Σ\equiv m^{}_1 + m^{}_2 + m^{}_3$ relevant for cosmological observations are also discussed.

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arXiv2019

A U-spin prediction for the CP-forbidden transition $e^+ e^- \to D^0\bar{D}^0 \to (K^+ K^-)_D (π^+ π^-)_D$

The LHCb Collaboration has recently reported the discovery of direct CP violation in combined $D^0 \to K^+ K^-$ and $D^0 \to π^+ π^-$ decay modes at the $5.3 σ$ level. Assuming U-spin symmetry (i.e., $d \leftrightarrow s$ interchange symmetry) for the strong-interaction parts of these two channels, we find that their corresponding direct CP-violating asymmetries are ${\cal A}^{}_{\rm CP} (K^+ K^-) \simeq \left(-7.7 \pm 1.5\right) \times 10^{-4}$ and ${\cal A}^{}_{\rm CP} (π^+ π^-) \simeq \left(7.7 \pm 1.5\right) \times 10^{-4}$. The CP-forbidden transition $e^+ e^- \to D^0\bar{D}^0 \to \left(K^+ K^-\right)^{}_D \left(π^+ π^-\right)^{}_D$ on the $ψ(3770)$ resonance is therefore expected to have a rate of ${\cal O}(10^{-10})$ or smaller under U-spin symmetry, and it can be observed at a high-luminosity super-$τ$-charm factory if at least $10^{10}$ pairs of coherent $D^0$ and $\bar{D}^0$ events are accumulated.

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arXiv2019

Testing unitarity of the $3\times 3$ neutrino mixing matrix in an atomic system

Unitarity of the $3\times 3$ lepton flavor mixing matrix $V$ is unavoidably violated in a seesaw mechanism if its new heavy degrees of freedom are slightly mixed with the active neutrino flavors. We propose to use the atomic transition process ${\left| \rm e \right> \to\left|\rm g \right> + γ+ ν^{}_{i} + \overlineν^{}_{j}}$ (for $i, j = 1, 2, 3$), where $\left|\rm e \right>$ and $\left|\rm g \right>$ stand respectively for the excited and ground levels of an atomic system, to probe or constrain the unitarity-violating effects of $V$. We find that the photon spectrum of this transition will be distorted by the effects of $V V^\dagger \neq {\bf 1}$ and $V^\dagger V \neq {\bf 1}$ as compared with the $V V^\dagger = V^\dagger V = {\bf 1}$ case. We locate certain frequencies in the photon spectrum to minimize the degeneracy of effects of the unitarity violation and uncertainties of the flavor mixing parameters themselves. The requirements of a nominal experimental setup to test the unitarity of $V$ are briefly discussed.

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arXiv2019

Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S^{}_3$ reflection symmetry

In the canonical seesaw mechanism we require the relevant neutrino mass terms to be invariant under the $S^{}_3$ charge-conjugation transformations of left- and right-handed neutrino fields. Then both the Dirac mass matrix $M^{}_{\rm D}$ and the right-handed neutrino mass matrix $M^{}_{\rm R}$ are well constrained, so is the effective light Majorana neutrino mass matrix $M^{}_ν$ via the seesaw formula. We find that these mass matrices can be classified into 22 categories, among which some textures respect the well-known $μ$-$τ$ permutation or reflection symmetry and flavor democracy. It is also found that there exist remarkable structural equalities or similarities between $M^{}_ν$ and $M^{}_{\rm R}$, reflecting a seesaw mirroring relationship between light and heavy Majorana neutrinos. We calculate the corresponding light neutrino masses and flavor mixing parameters as well as the CP-violating asymmetries in decays of the lightest heavy Majorana neutrino, and show that only the flavored leptogenesis mechanism is possible to work for three categories of $M^{}_{\rm D}$ and $M^{}_{\rm R}$ in the $S^{}_3$ reflection symmetry limit.

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arXiv2018

Correlation of normal neutrino mass ordering with upper octant of $θ^{}_{23}$ and third quadrant of $δ$ via RGE-induced $μ$-$τ$ symmetry breaking

The recent global analysis of three-flavor neutrino oscillation data indicates that the {\it normal} neutrino mass ordering is favored over the inverted one at the $3σ$ level, and the best-fit values of the largest neutrino mixing angle $θ^{}_{23}$ and the Dirac CP-violating phase $δ$ are located in the higher octant and the third quadrant, respectively. We show that all these important issues can be naturally explained by the $μ$-$τ$ reflection symmetry breaking of massive neutrinos from a superhigh energy scale down to the electroweak scale due to the one-loop renormalization-group equations (RGEs) in the minimal supersymmetric standard model (MSSM). The complete parameter space is explored {\it for the first time} in both Majorana and Dirac cases, by allowing the smallest neutrino mass $m^{}_1$ and the MSSM parameter $\tanβ$ to vary in their reasonable regions.

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arXiv2018

Naumov- and Toshev-like relations in the renormalization-group evolution of quarks and Dirac neutrinos

In an analytical way of studying matter effects on neutrino oscillations, the Naumov and Toshev relations have been derived to respectively link the Jarlskog invariant of CP violation and the Dirac phase in the standard parametrization of the $3\times 3$ flavor mixing matrix to their matter-corrected counterparts. Here we show that there exist similar relations for Dirac neutrinos and charged leptons evolving with energy scales via the one-loop renormalization-group (RG) equations in the tau-dominance approximation, and for the running behaviors of up- and down-type quarks in the top-dominance approximation, provided a different parametrization is taken into account.

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arXiv2018

Interference effects in reactor antineutrino oscillations

We reformulate the probabilities of disappearance neutrino or antineutrino oscillations so as to single out the interference term proportional to the product of \sin[Δm^2_{21} L/(4 E)] and \sin[(Δm^2_{31} + Δm^2_{32}) L/(4 E)], which is transparently sensitive to the neutrino mass ordering. We elaborate this issue for a reactor-based antineutrino oscillation experiment like JUNO, and take account of terrestrial matter effects. If a light sterile neutrino species contributes to P(\overlineν_e \to \overlineν_e), we find that there will be a new interference term proportional to the product of \sin^2 2θ_{14}, \sin[Δm^2_{21} L/(4 E)] and \sin[(Δm^2_{41} + Δm^2_{42}) L/ (4 E)] in the standard parametrization of the (3+1) X (3+1) active-sterile neutrino mixing matrix.

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arXiv2018

Indirect unitarity violation entangled with matter effects in reactor antineutrino oscillations

If finite but tiny masses of the three active neutrinos are generated via the canonical seesaw mechanism with three heavy sterile neutrinos, the 3\times 3 Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix V will not be exactly unitary. This kind of indirect unitarity violation can be probed in a precision reactor antineutrino oscillation experiment, but it may be entangled with terrestrial matter effects as both of them are very small. We calculate the probability of \overlineν_e \to \overlineν_e oscillations in a good analytical approximation, and find that, besides the zero-distance effect, the effect of unitarity violation is always smaller than matter effects, and their entanglement does not appear until the next-to-leading-order oscillating terms are taken into account. Given a 20-kiloton JUNO-like liquid scintillator detector, we reaffirm that terrestrial matter effects should not be neglected but indirect unitarity violation makes no difference, and demonstrate that the experimental sensitivities to the neutrino mass ordering and a precision measurement of θ_{12} and Δ_{21} \equiv m^2_2 - m^2_1 are robust.

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arXiv2018

Renormalization-Group Equations of Neutrino Masses and Flavor Mixing Parameters in Matter

We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter $a \equiv 2\sqrt{2} \ G^{}_{\rm F} N^{}_e E$ to be an arbitrary scale-like variable with $N^{}_e$ being the net electron number density and $E$ being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix $V$ and the effective neutrino masses $\widetilde{m}^{}_i$ (for $i = 1, 2, 3$). Given the standard parametrization of $V$, the RGEs for $\{\widetildeθ^{}_{12}, \widetildeθ^{}_{13}, \widetildeθ^{}_{23}, \widetildeδ\}$ in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial $μ$-$τ$ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of $V$ are also obtained as a by-product.

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arXiv2018

$ μ-τ$ Reflection Symmetry Embedded in Minimal Seesaw

We embed $μ-τ$ reflection symmetry into the minimal seesaw formalism, where two right-handed neutrinos are added to the Standard Model of particle physics. Assuming that both the left- and right-handed neutrino fields transform under $μ-τ$ reflection symmetry, we obtain the required forms of the neutrino Dirac mass matrix and the Majorana mass matrix for the right-handed neutrinos. To investigate the neutrino phenomenology at low energies, we first consider the breaking of $μ-τ$ reflection symmetry due to the renormalization group running, and then systematically study various breaking schemes by introducing explicit breaking terms at high energies.

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arXiv2017

The $μ-τ$ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections

Given the Dirac neutrino mass term, we explore the constraint conditions which allow the corresponding mass matrix to be invariant under the μ-τreflection transformation, leading us to the phenomenologically favored predictions θ_{23} = π/4 and δ= 3π/2 in the standard parametrization of the 3\times 3 lepton flavor mixing matrix. If such a flavor symmetry is realized at a superhigh energy scale Λ_{μτ}, we investigate how it is spontaneously broken via the one-loop renormalization-group equations (RGEs) running from Λ_{μτ} down to the Fermi scale Λ_{\rm F}. Such quantum corrections to the neutrino masses and flavor mixing parameters are derived, and an analytical link is established between the Jarlskog invariants of CP violation at Λ_{μτ} and Λ_{\rm F}. Some numerical examples are also presented in both the minimal supersymmetric standard model and the type-II two-Higgs-doublet model, to illustrate how the octant of θ_{23}, the quadrant of δand the neutrino mass ordering are correlated with one another as a result of the RGE-induced μ-τreflection symmetry breaking effects.

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arXiv2017

Neutrino mass ordering and μ-τreflection symmetry breaking

If the neutrino mass spectrum turns out to be m^{}_3 < m^{}_1 < m^{}_2, one may choose to relabel it as m^{\prime}_1 < m^{\prime}_2 < m^{\prime}_3 such that all the masses of fundamental fermions with the same electrical charges are in order. In this case the columns of the 3\times 3 lepton flavor mixing matrix U should be reordered accordingly, and the resulting pattern U^\prime may involve one or two large mixing angles in the standard parametrization or its variations. Since the Majorana neutrino mass matrix keeps unchanged in such a mass relabeling, a possible μ-τreflection symmetry is respected in this connection and its breaking effects are model-independently constrained at the 3σlevel by using current experimental data.

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arXiv2017

The breaking of flavor democracy in the quark sector

The democracy of quark flavors is a well-motivated flavor symmetry, but it must be properly broken in order to explain the observed quark mass spectrum and flavor mixing pattern. We reconstruct the texture of flavor democracy breaking and evaluate its strength in a novel way, by assuming a parallelism between the Q=+2/3 and Q=-1/3 quark sectors and using a nontrivial parametrization of the flavor mixing matrix. Some phenomenological implications of such democratic quark mass matrices, including their variations in the hierarchy basis and their evolution from the electroweak scale to a superhigh-energy scale, are also discussed.

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arXiv2017

The effective neutrino mass of neutrinoless double-beta decays: how possible to fall into a well

If massive neutrinos are the Majorana particles and have a normal mass ordering, the effective mass term $\langle m\rangle^{}_{ee}$ of a neutrinoless double-beta ($0ν2β$) decay may suffer significant cancellations among its three components and thus sink into a decline, resulting in a "well" in the three-dimensional graph of $|\langle m\rangle^{}_{ee}|$ against the smallest neutrino mass $m^{}_1$ and the relevant Majorana phase $ρ$. We present a new and complete analytical understanding of the fine issues inside such a well, and discover a novel threshold of $|\langle m\rangle^{}_{ee}|$ in terms of the neutrino masses and flavor mixing angles: $|\langle m\rangle^{}_{ee}|^{}_* = m^{}_3 \sin^2θ^{}_{13}$ in connection with $\tanθ^{}_{12} = \sqrt{m^{}_1/m^{}_2}$ and $ρ=π$. This threshold point, which links the {\it local} minimum and maximum of $|\langle m\rangle^{}_{ee}|$, can be used to signify observability or sensitivity of the future $0ν2β$-decay experiments. Given current neutrino oscillation data, the possibility of $|\langle m\rangle^{}_{ee}| < |\langle m\rangle^{}_{ee}|^{}_*$ is found to be very small.

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arXiv2016

Analytical approximations for matter effects on CP violation in the accelerator-based neutrino oscillations with E \lesssim 1 GeV

Given an accelerator-based neutrino experiment with the beam energy E \lesssim 1 GeV, we expand the probabilities of ν_μ\to ν_e and \overline ν_μ\to \overline ν_e oscillations in matter in terms of two small quantities Δ_{21}/Δ_{31} and A/Δ_{31}, where Δ_{21} \equiv m^2_2 - m^2_1 and Δ_{31} \equiv m^2_3 - m^2_1 are the neutrino mass-squared differences, and A measures the strength of terrestrial matter effects. Our analytical approximations are numerically more accurate than those made by Freund in this energy region, and thus they are particularly applicable for the study of leptonic CP violation in the low-energy MOMENT, ESS\nuSM and T2K oscillation experiments. As a by-product, the new analytical approximations help us to easily understand why the matter-corrected Jarlskog parameter \widetilde{\cal J} peaks at the resonance energy E_* \simeq 0.14 GeV (or 0.12 GeV) for the normal (or inverted) neutrino mass hierarchy, and how the three Dirac unitarity triangles are deformed due to the terrestrial matter contamination. We also affirm that a medium-baseline neutrino oscillation experiment with the beam energy E lying in the E_* \lesssim E \lesssim 2 E_* range is capable of exploring leptonic CP violation with little matter-induced suppression.

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arXiv2016

Terrestrial matter effects on reactor antineutrino oscillations at JUNO or RENO-50: how small is small?

We have carefully examined, in both analytical and numerical ways, how small the terrestrial matter effects can be in a given medium-baseline reactor antineutrino oscillation experiment like JUNO or RENO-50. Taking the ongoing JUNO experiment for example, we show that the inclusion of terrestrial matter effects may reduce the sensitivity of the neutrino mass ordering measurement by Δχ^2_{\rm MO} \simeq 0.6, and a neglect of such effects may shift the best-fit values of the flavor mixing angle θ_{12} and the neutrino mass-squared difference Δ_{21} by about 1σto 2σin the future data analysis. In addition, a preliminary estimate indicates that a 2σsensitivity of establishing the terrestrial matter effects can be achieved for about 10 years of data taking at JUNO with the help of a proper near detector implementation.

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