arXiv subjects

Shun Zhou

Publications and source records attributed to Shun Zhou.

At least 55 records · Page 3Linked to original sources

arXiv2022

General Remarks on the One-loop Contributions to the Muon Anomalous Magnetic Moment

The latest measurement of the muon anomalous magnetic moment $a^{}_μ \equiv (g^{}_μ- 2)/2$ at the Fermi Laboratory has found a $4.2\,σ$ discrepancy with the theoretical prediction of the Standard Model (SM). Motivated by this exciting progress, we investigate in the present paper the general one-loop contributions to $a^{}_μ$ within the SM and beyond. First, different from previous works, the analytical formulae of relevant loop functions after integration are now derived and put into compact forms with the help of the Passarino-Veltman functions. Second, given the interactions of muon with new particles running in the loop, we clarify when the one-loop contribution to $a^{}_μ$ could take the correct positive sign as desired. Third, possible divergences in the zero- and infinite-mass limits are examined, and the absence of any divergences in the calculations leads to some consistency conditions for the construction of ultraviolet complete models. Applications of our general formulae to specific models, such as the SM, seesaw models, $Z^\prime$ and leptoquark models, are also discussed.

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arXiv2021

Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter

Three-flavor neutrino oscillations in matter can be described by three effective neutrino masses $\widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the effective mixing matrix $V^{}_{αi}$ (for $α= e, μ, τ$ and $i = 1, 2, 3$). When the matter parameter $a \equiv 2\sqrt{2} G^{}_{\rm F} N^{}_e E$ is taken as an independent variable, a complete set of first-order ordinary differential equations for $\widetilde{m}^2_i$ and $|V^{}_{αi}|^2$ have been derived in the previous works. In the present paper, we point out that such a system of differential equations possesses both the continuous symmetries characterized by one-parameter Lie groups and the discrete symmetry associated with the permutations of three neutrino mass eigenstates. The implications of these symmetries for solving the differential equations and looking for differential invariants are discussed.

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arXiv2021

Non-unitary Leptonic Flavor Mixing and CP Violation in Neutrino-antineutrino Oscillations

If massive neutrinos are Majorana particles, then the lepton number should be violated in nature and neutrino-antineutrino oscillations $ν^{}_α\leftrightarrow \overlineν^{}_β$ (for $α, β= e, μ, τ$) will definitely take place. In the present paper, we study the properties of CP violation in neutrino-antineutrino oscillations with the non-unitary leptonic flavor mixing matrix, which is actually a natural prediction in the canonical seesaw model due to the mixing between light and heavy Majorana neutrinos. The oscillation probabilities $P(ν^{}_α\to \overlineν^{}_β)$ and $P(\overlineν^{}_α\to ν^{}_β)$ are derived, and the CP asymmetries ${\cal A}^{}_{αβ} \equiv [P(ν^{}_α\to \overlineν^{}_β) - P(\overlineν^{}_α\to ν^{}_β)]/[P(ν^{}_α\to \overlineν^{}_β) + P(\overlineν^{}_α\to ν^{}_β)]$ are also calculated. Taking into account current experimental bounds on the leptonic unitarity violation, we show that the CP asymmetries induced by the non-unitary mixing parameters can significantly deviate from those in the limit of a unitary leptonic flavor mixing.

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arXiv2021

The Smallest Neutrino Mass Revisited

As is well known, the smallest neutrino mass turns out to be vanishing in the minimal seesaw model, since the effective neutrino mass matrix $M^{}_ν$ is of rank two due to the fact that only two heavy right-handed neutrinos are introduced. In this paper, we point out that the one-loop matching condition for the effective dimension-five neutrino mass operator can make an important contribution to the smallest neutrino mass. By using the available one-loop matching condition and two-loop renormalization group equations in the supersymmetric version of the minimal seesaw model, we explicitly calculate the smallest neutrino mass in the case of normal neutrino mass ordering and find $m^{}_1 \in [10^{-10}, 10^{-8}]~{\rm eV}$ at the Fermi scale $Λ^{}_{\rm F} = 91.2~{\rm GeV}$, where the range of $m^{}_1$ results from the uncertainties on the choice of the seesaw scale $Λ^{}_{\rm SS}$ and on the input values of relevant parameters at $Λ^{}_{\rm SS}$.

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arXiv2021

Reply to "Comment on 'Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos'"

In the preprint arXiv:2110.08210, some comments on our paper recently published in JHEP \textbf{09} (2021) 053 have been made. Since some of the comments are completely wrong and others are quite misleading, we decide to clarify the relevant issues in a formal reply. First of all, nothing is wrong about our calculations and physical results in the original paper. Second, there is no logical gap to fill at all. The fact that the $N$-dimensional unitary group over the field of complex numbers ${\rm U}(N,\mathbb{C})$ is not a linear algebraic group is actually irrelevant for the validity of the Molien-Weyl formula. As we shall explain in this reply, all the comments in arXiv:2110.08210 arise from the misunderstanding and misinterpretation of our discussions and results.

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arXiv2021

The number of sufficient and necessary conditions for CP conservation with Majorana neutrinos: three or four?

As is well-known, there exist totally three CP-violating phases in the leptonic sector if three ordinary neutrinos are massive Majorana particles. In this short note, we raise the question whether the number of sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos is three or four. An intuitive answer to this question would be three, which is also the total number of independent CP-violating phases. However, we give a counter example, in which three conditions are in general not sufficient for CP conservation. Only for all the lepton masses and mixing angles within their experimentally allowed ranges can we demonstrate that it is possible to find out three weak-basis invariants, which should be vanishing to guarantee leptonic CP conservation.

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arXiv2021

Inverse Seesaw Model with a Modular $S^{}_4$ Symmetry: Lepton Flavor Mixing and Warm Dark Matter

In this paper, we present a systematic investigation on simple inverse seesaw models for neutrino masses and flavor mixing based on the modular $S^{}_4$ symmetry. Two right-handed neutrinos and three extra fermion singlets are introduced to account for light neutrino masses through the inverse seesaw mechanism, and to provide a keV-mass sterile neutrino as the candidate for warm dark matter in our Universe. Considering all possible modular forms with weights no larger than four, we obtain twelve models, among which we find one is in excellent agreement with the observed lepton mass spectra and flavor mixing. Moreover, we explore the allowed range of the sterile neutrino mass and mixing angles, by taking into account the direct search of $X$-ray line and the Lyman-$α$ observations. The model predictions for neutrino mixing parameters and the dark matter abundance will be readily testable in future neutrino oscillation experiments and cosmological observations.

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arXiv2021

Neutrino Masses, Leptonic Flavor Mixing and Muon $(g-2)$ in the Seesaw Model with the $U(1)^{}_{L^{}_μ-L^{}_τ}$ Gauge Symmetry

The latest measurements of the anomalous muon magnetic moment $a^{}_μ\equiv (g^{}_μ- 2)/2$ show a $4.2σ$ discrepancy between the theoretical prediction of the Standard Model and the experimental observations. In order to account for such a discrepancy, we consider a possible extension of the type-(I+II) seesaw model for neutrino mass generation with a gauged $L^{}_μ- L^{}_τ$ symmetry. By explicitly constructing an economical model with only one extra scalar singlet, we demonstrate that the gauge symmetry $U(1)^{}_{L^{}_μ- L^{}_τ}$ and its spontaneous breaking are crucially important not only for explaining the muon $(g - 2)$ result but also for generating neutrino masses and leptonic flavor mixing. Various phenomenological implications and experimental constraints on the model parameters are also discussed.

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arXiv2021

Hilbert Series for Leptonic Flavor Invariants in the Minimal Seesaw Model

In this paper, we examine the leptonic flavor invariants in the minimal seesaw model (MSM), in which only two right-handed neutrino singlets are added into the Standard Model in order to accommodate tiny neutrino masses and explain cosmological matter-antimatter asymmetry via leptogenesis mechanism. For the first time, we calculate the Hilbert series (HS) for the leptonic flavor invariants in the MSM. With the HS we demonstrate that there are totally 38 basic flavor invariants, among which 18 invariants are CP-odd and the others are CP-even. Moreover, we explicitly construct these basic invariants, and any other flavor invariants in the MSM can be decomposed into the polynomials of them. Interestingly, we find that any flavor invariants in the effective theory at the low-energy scale can be expressed as rational functions of those in the full MSM at the high-energy scale. Practical applications to the phenomenological studies of the MSM, such as the sufficient and necessary conditions for CP conservation and CP asymmetries in leptogenesis, are also briefly discussed.

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arXiv2021

Flavor Invariants and Renormalization-group Equations in the Leptonic Sector with Massive Majorana Neutrinos

In the present paper, we carry out a systematic study of the flavor invariants and their renormalization-group equations (RGEs) in the leptonic sector with three generations of charged leptons and massive Majorana neutrinos. First, following the approach of the Hilbert series from the invariant theory, we show that there are 34 basic flavor invariants in the generating set, among which 19 invariants are CP-even and the others are CP-odd. Any flavor invariants can be expressed as the polynomials of those 34 basic invariants in the generating set. Second, we explicitly construct all the basic invariants and derive their RGEs, which form a closed system of differential equations as they should. The numerical solutions to the RGEs of the basic flavor invariants have also been found. Furthermore, we demonstrate how to extract physical observables from the basic invariants. Our study is helpful for understanding the algebraic structure of flavor invariants in the leptonic sector, and also provides a novel way to explore leptonic flavor structures.

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arXiv2021

Explicit Perturbations to the Stabilizer $τ= {\rm i}$ of Modular $A^\prime_5$ Symmetry and Leptonic CP Violation

In a class of neutrino mass models with modular flavor symmetries, it has been observed that CP symmetry is preserved at the fixed point (or stabilizer) of the modulus parameter $τ= {\rm i}$, whereas significant CP violation emerges within the neighbourhood of this stabilizer. In this paper, we first construct a viable model with the modular $A^\prime_5$ symmetry, and explore the phenomenological implications for lepton masses and flavor mixing. Then, we introduce explicit perturbations to the stabilizer at $τ= {\rm i}$, and present both numerical and analytical results to understand why a small deviation from the stabilizer leads to large CP violation. As low-energy observables are very sensitive to the perturbations to model parameters, we further demonstrate that the renormalization-group running effects play an important role in confronting theoretical predictions at the high-energy scale with experimental measurements at the low-energy scale.

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arXiv2021

Radiative Decays of Charged Leptons in the Seesaw Effective Field Theory with One-loop Matching

The canonical type-I seesaw model with three heavy Majorana neutrinos is one of the most natural extensions of the standard model (SM) to accommodate tiny Majorana masses of three ordinary neutrinos. At low-energy scales, Majorana neutrino masses and unitarity violation of lepton flavor mixing have been extensively discussed in the literature, which are respectively generated by the unique dimension-five Weinberg operator and one dimension-six operator in the seesaw effective field theory (SEFT) with the tree-level matching. In this work, we clarify that a self-consistent calculation of radiative decays of charged leptons $β^- \to α^- + γ$ requires the SEFT with one-loop matching, where new six-dimensional operators emerge and make important contributions. For the first time, the Wilson coefficients of all the relevant six-dimensional operators are computed by carrying out the one-loop matching between the effective theory and full seesaw model, and applied to calculate the total rates of radiative decays of charged leptons.

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arXiv2021

Quantum Simulations of the Non-Unitary Time Evolution and Applications to Neutral-Kaon Oscillations

In light of recent exciting progress in building up quantum computing facilities based on both optical and cold-atom techniques, the algorithms for quantum simulations of particle-physics systems are in rapid progress. In this paper, we propose an efficient algorithm for simulating the non-unitary time evolution of neutral-kaon oscillations $K^0 \leftrightarrow \overline{K}^0$, with or without CP conservation, on the quantum computers provided by the IBM company. The essential strategy is to realize the time-evolution operator with basic quantum gates and an extra qubit corresponding to some external environment. The final results are well consistent with theoretical expectations, and the algorithm can also be applied to open systems beyond elementary particles.

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arXiv2021

Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase

We investigate the transition probabilities for the "flavor" eigenstates in the two-level quantum system, which is described by a non-Hermitian Hamiltonian with the parity and time-reversal (PT) symmetry. Particularly, we concentrate on the so-called PT-broken phase, where two eigenvalues of the non-Hermitian Hamiltonian turn out to be a complex conjugate pair. In this case, we find that the transition probabilities will be unbounded in the limit of infinite time $t \to +\infty$. However, after performing a connection between a non-Hermitian system, which exhibits passive PT-symmetry and global decay, and the neutral-meson system in particle physics, we observe that the diverging behavior of the transition probabilities is actually applicable to the gauge-transformed neutral-meson states, whereas the transition probabilities for physical states are exponentially suppressed by the global decay. We also present a brief review on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.

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arXiv2021

Tentative sensitivity of future $0νββ$-decay experiments to neutrino masses and Majorana CP phases

In the near future, the neutrinoless double-beta ($0νββ$) decay experiments will hopefully reach the sensitivity of a few ${\rm meV}$ to the effective neutrino mass $|m^{}_{ββ}|$. In this paper, we tentatively examine the sensitivity of future $0νββ$-decay experiments to neutrino masses and Majorana CP phases by following the Bayesian statistical approach. Provided experimental setups corresponding to the sensitivity of $|m^{}_{ββ}| \simeq 1~{\rm meV}$, the null observation of $0νββ$ decays in the case of normal neutrino mass ordering leads to a very competitive bound on the lightest neutrino mass $m^{}_1$. Namely, the $95\%$ credible interval turns out to be $1.6~{\rm meV} \lesssim m^{}_1 \lesssim 7.3~{\rm meV}$ or $0.3~{\rm meV} \lesssim m^{}_1 \lesssim 5.6~{\rm meV}$ when the uniform prior on $m^{}_1/{\rm eV}$ or on $\log^{}_{10}(m^{}_1/{\rm eV})$ is adopted. Moreover, one of two Majorana CP phases is strictly constrained, i.e., $140^\circ \lesssim ρ\lesssim 220^\circ$ for both priors of $m^{}_1$. In contrast, if a relatively worse sensitivity of $|m^{}_{ββ}| \simeq 10~{\rm meV}$ is assumed, the constraint becomes accordingly $0.6~{\rm meV} \lesssim m^{}_1 \lesssim 26~{\rm meV}$ or $0 \lesssim m^{}_1 \lesssim 6.1~{\rm meV}$, while two Majorana CP phases will be essentially unconstrained. In the same statistical framework, the prospects for the determination of neutrino mass ordering and the discrimination between Majorana and Dirac nature of massive neutrinos in the $0νββ$-decay experiments are also discussed. Given the experimental sensitivity of $|m^{}_{ββ}| \simeq 10~{\rm meV}$ (or $1~{\rm meV}$), the strength of evidence to exclude the Majorana nature under the null observation of $0νββ$ decays is found to be inconclusive (or strong), no matter which of two priors on $m^{}_1$ is taken.

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arXiv2021

Double Covering of the Modular $A^{}_5$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model

In this paper, we investigate the double covering of modular $Γ^{}_5 \simeq A^{}_5$ group and derive all the modular forms of weight one for the first time. The modular forms of higher weights are also explicitly given by decomposing the direct products of weight-one forms. For the double covering group $Γ^\prime_5 \simeq A^\prime_5$, there exist two inequivalent two-dimensional irreducible representations, into which we can assign two right-handed neutrino singlets in the minimal seesaw model. Two concrete models with such a salient feature have been constructed to successfully explain lepton mass spectra and flavor mixing pattern. The allowed parameter space for these two minimal scenarios has been numerically explored, and analytically studied with some reasonable assumptions.

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arXiv2021

Constraining primordial black holes as dark matter at JUNO

As an attractive candidate for dark matter, the primordial black holes (PBHs) in the mass range ($10^{15} \sim 10^{16}$)$\mathrm{g}$ could be detected via their Hawking radiation, including neutrinos and antineutrinos of three flavors. In this paper, we investigate the possibility to constrain the PBH as dark matter by measuring (anti)neutrino signals at the large liquid-scintillator detector of Jiangmen Underground Neutrino Observatory (JUNO). Among six available detection channels, the inverse beta decay $\overlineν^{}_e + p \to e^+ + n$ is shown to be most sensitive to the fraction $f^{}_{\rm PBH}$ of PBHs contributing to the dark matter abundance. Given the PBH mass $M^{}_{\rm PBH} = 10^{15}~{\rm g}$, we find that JUNO will be able to place an upper bound $f^{}_{\rm PBH} \lesssim 3\times 10^{-5}$, which is 20 times better than the current best limit $f^{}_{\rm PBH} \lesssim 6\times 10^{-4}$ from Super-Kamiokande. For heavier PBHs with a lower Hawking temperature, the (anti)neutrinos become less energetic, leading to a relatively weaker bound.

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arXiv2021

Neutral-current background induced by atmospheric neutrinos at large liquid-scintillator detectors: I. model predictions

The experimental searches for diffuse supernova neutrino background and proton decay in next-generation large liquid-scintillator (LS) detectors are competitive with and complementary to those in the water-Cherenkov detectors. In this paper, we carry out a systematic study of the dominant background induced by atmospheric neutrinos via their neutral-current (NC) interactions with the $^{12}{\rm C}$ nuclei in the LS detectors. The atmospheric neutrino fluxes at the location of Jiangmen Underground Neutrino Observatory (JUNO) are used, as the JUNO detector is obviously a suitable representative for future LS detectors. Then, we implement the sophisticated generators \texttt{GENIE} and \texttt{NuWro} to simulate the neutrino interactions with the carbon nuclei, and the package \texttt{TALYS} to deal with the deexcitations of final-state nuclei. Finally, the event rates for the production of additional nucleons, $γ$'s, $α$'s, pions and kaons are obtained and categorized, and the systematic uncertainty of the NC background represented by a variety of data-driven nuclear models is estimated. The implications of the NC background from atmospheric neutrinos for the detection of diffuse supernova neutrino background and proton decay are also discussed.

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