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

Zhi-zhong Xing; Zhen-hua ZhaoSubjects: Physics >> General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

The neutrinoless double-beta (0ν2β) decay is currently the only feasible process in particle and nuclear physics to probe whether massive neutrinos are the Majorana fermions. If they are of the Majorana nature and have a normal mass ordering, the e?ective neutrino mass term mee of a 0ν2β decay may su?er signi?cant cancellations among its three components and thus sink into a decline,resulting in a “well” in the three-dimensional graph of |mee| against the smallest neutrino mass m1 and the relevant Majorana phase ρ. We present a new and complete analytical understanding of the ?ne issues inside such a well, and identify a novel threshold of |mee| in terms ofthe neutrino masses and ?avor mixing angles: |mee|? = m3 sin2 θ13 in connection with tan θ12 = m1/m2 and ρ = π. This threshold point, which links the local minimum and maximum of |mee|, can be used to signify observability or sensitivity of the future 0ν2β-decay experiments. Given current neutrino oscillation data, the possibility of |mee| < |mee|? is found to be very small. |

Quark Flavor Mixings from Hierarchical Mass Matrices

Rohit Verma; Shun ZhouSubjects: Physics >> Nuclear Physics

In this paper, we extend the Fritzsch ansatz of quark mass matrices while retaining their hierarchical structures and show that the main features of the Cabibbo-Kobayashi-Maskawa (CKM) matrix?V, including?|Vus|?|Vcd|,?|Vcb|?|Vts|?and?|Vub|/|Vcb|<|Vtd|/|Vts|, can be well understood. This agreement is observed especially when the mass matrices have non-vanishing?(1,3)?and?(3,1)?off-diagonal elements. The phenomenological consequences of these for the allowed texture content and gross structural features of `hierarchical' quark mass matrices are addressed from a model independent prospective under the assumption of factorizable phases in these. The approximate and analytical expressions of the CKM matrix elements are derived, and a detailed analysis reveals that such structures are in good agreement with the observed quark flavor mixing angles and the CP-violating phase at the?1σ?level and call upon a further investigation of the realization of these structures from a top-down prospective. |

Leptonic Unitarity Triangles and Effective Mass Triangles of the Majorana Neutrinos

Zhi-zhong Xing; Jing-yu ZhuSubjects: Physics >> Nuclear Physics

Given the best-fit results of six neutrino oscillation parameters, we plot the Dirac and Majorana unitarity triangles (UTs) of the 3\times 3 lepton flavor mixing matrix to show their real shapes for the first time. The connections of the Majorana UTs with neutrino-antineutrino oscillations and neutrino decays are explored, and the possibilities of right or isosceles UTs are discussed. In the neutrino mass limit of m_1 \to 0 or m_3 \to 0, which is allowed by current experimental data, we show how the six triangles formed by the effective Majorana neutrino masses \langle m\rangle_{\alpha\beta} (for \alpha, \beta = e, \mu, \tau) and their corresponding component vectors look like in the complex plane. The relations of such triangles to the Majorana phases and to the lepton-number-violating decays H^{++} \to \alpha^+ \beta^+ in the type-II seesaw mechanism are also illustrated. |

Subjects: Physics >> Nuclear Physics

The latest results from atmospheric and accelerator neutrino experiments indicate that the normal neutrino mass ordering?m1 |

Subjects: Physics >> Nuclear Physics

Motivated by recent intensive experimental efforts on searching for neutrinoless double-beta decays, we perform a detailed analysis of the physics potential of the experiments based on?76Ge. Assuming no signals, current and future experiments could place a?90%?lower limit on the half life?T0ν1/2?4×1026?yr?and?T0ν1/2?7×1027?yr, respectively. Then, how to report an evidence for neutrinoless double-beta decays is addressed by following the Bayesian statistical approach. For the first time, we present a quantitative description of experimental power to distinguish between normal and inverted neutrino mass orderings. Taking an exposure of?104?kg?yr?and a background rate of?10?4?counts/(keV?kg?yr), we find that a moderate evidence for normal neutrino mass ordering (i.e., with a Bayes factor?B?given by?ln(B)?2.5?or a probability about?92.3%?according to the Jeffreys scale) can be achieved if the true value of effective neutrino mass?mββ?turns out to be below?0.01?eV. |

How to interpret a discovery or null result of the $0\nu 2\beta$ decay

Zhi-zhong Xing; Zhen-hua Zhaoy; Ye-Ling ZhouSubjects: Physics >> Nuclear Physics

The Majorana nature of massive neutrinos will be crucially probed in the next-generation experiments of the neutrinoless double-beta (0ν2β) decay. The effective mass term of this process,??m?ee, may be contaminated by new physics. So how to interpret a discovery or null result of the?0ν2β?decay in the foreseeable future is highly nontrivial. In this paper we introduce a novel three-dimensional description of?|?m?ee|, which allows us to see its sensitivity to the lightest neutrino mass and two Majorana phases in a transparent way. We take a look at to what extent the free parameters of?|?m?ee|?can be well constrained provided a signal of the?0ν2β?decay is observed someday. To fully explore lepton number violation, all the six effective Majorana mass terms??m?αβ?(for?α,β=e,μ,τ) are calculated and their lower bounds are illustrated with the two-dimensional contour figures. The effect of possible new physics on the?0ν2β?decay is also discussed in a model-independent way. We find that the result of?|?m?ee|?in the normal (or inverted) neutrino mass ordering case modified by the new physics effect may somewhat mimic that in the inverted (or normal) mass ordering case in the standard three-flavor scheme. Hence a proper interpretation of a discovery or null result of the?0ν2β?decay may demand extra information from some other measurements. |

On the four-zero texture of quark mass matrices and its stability

Zhi-zhong Xing; Zhen-hua ZhaoSubjects: Physics >> Nuclear Physics

We carry out a new study of quark mass matricesMu(up-type) and Md(down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns ofMu and Md with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of Mu and Md are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations. |

Subjects: Physics >> Nuclear Physics

Given an accelerator-based neutrino experiment with the beam energy E \lesssim 1 GeV, we expand the probabilities of \nu_\mu \to \nu_e and \overline {\nu}_\mu \to \overline {\nu}_e oscillations in matter in terms of two small quantities \Delta_{21}/\Delta_{31} and A/\Delta_{31}, where \Delta_{21} \equiv m^2_2 - m^2_1 and \Delta_{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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