Direct<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violation and isospin triangles of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>decays

邢志忠,; Xing, Z.

doi:10.1103/physrevd.68.071301

Cited by 18 publications

(31 citation statements)

References 20 publications

(13 reference statements)

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“…In such a so-called Vissani graph, a two-dimensional "well" can appear in the NMO situation due to a significant cancellation among the three components of m ee . The bottom of the well signifies the case of | m ee | → 0 [17][18][19][20], a disappointing possibility which is definitely consistent with the present experimental data. Two immediate questions are in order: (1) how possible for the three neutrinos to have a NMO; (2) how possible for the actual value of | m ee | to fall into the well and become unobservable in any realistic 0ν2β experiments.…”

supporting

confidence: 88%

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

Zhang

Zhao

2017

Eur. Phys. J. C

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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 a Majorana nature and have a normal mass ordering, the effective neutrino mass term m ee of a 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 | m 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 identify a novel threshold of | m ee | in terms of the neutrino masses and flavor mixing angles: | m ee | * = m 3 sin 2 θ 13 in connection with tan θ 12 = m 1 /m 2 and ρ = π . This threshold point, which links the local minimum and maximum of | m ee |, can be used to signify observability or sensitivity of the future 0ν2β-decay experiments. Given current neutrino oscillation data, the possibility of | m ee | < | m ee | * is found to be very small.Since Majorana first formulated a fermionic particle that should be its own antiparticle in 1937 [1], a huge amount of attention has been paid to the Majorana fermions in particle and nuclear physics and the Majorana zero modes in solid-state physics [2]. In particular after the experimental discoveries of solar, atmospheric, reactor and accelerator neutrino oscillations [3], whether massive neutrinos are Majorana fermions becomes an especially burning question among a number of fundamentally important questions in neutrino physics and cosmology. If this is the case, then the neutrinoless double-beta (0ν2β) decays of some even-even nuclei are expected to take place [4]. Namely, N (A, Z ) → N (A, Z + 2) + 2e − , where the lepton number is violated by two units. Given the fact that the neutrino masses are so small that all the lepton-number-violating processes must be desa e-mail: zhaozhenhua@ihep.ac.cn perately suppressed, currently the unique and only feasible way to demonstrate the Majorana nature of massive neutrinos is to observe the 0ν2β decays. In this respect a number of ambitious experiments are either under way or in preparation [5][6][7].In the standard scheme of three neutrino flavors the rate of a 0ν2β decay is proportional to the squared modulus of the effective Majorana neutrino mass term [8][9][10] where m i denotes the ith neutrino mass (for i = 1, 2, 3), U ei is the corresponding element of the 3 × 3 neutrino mixing matrix U [14,15], and ρ and σ stand for the Majorana phases. One often chooses to parametrize |U ei | as follows [3]: |U e1 | = cos θ 12 cos θ 13 , |U e2 | = sin θ 12 cos θ 13 , and |U e3 | = sin θ 13 . The three mixing angles θ 12 , θ 13 and θ 23 have been determined to a good degree of accuracy from current neutrino oscillation data, so have been the value of m 2 21 ≡ m 2 2 − m 2 1 and the modulus of m 2 31 ≡ m 2 3 − m 2 1 [3]. But the sign of m 2 31 and the two phase parameters in Eq. (1) remain unknown, nor does the ...

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supporting

confidence: 88%

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

Zhang

Zhao

2017

Eur. Phys. J. C

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“…Note that the current experimental errors on these parameters have been reduced to the percent level [29], and hence σ th is secondary to the significant σ ee in Eq. (9). In addition, the uncertainty factor ξ , which originates from the NME calculation and thus takes a value in the range …”

Section: Limits Of M 1and ρ From a Signal Of The 0ν2β Decaymentioning

confidence: 99%

“…While an observation of the 0ν2β decay must point to an appreciable value of | m ee |, a null experimental result does not necessarily mean that massive neutrinos are the Dirac fermions because m ee ∼ 0 is not impossible even though the neutrinos themselves are the Majorana particles [9,10]. Hence how to interpret a discovery or null result of the 0ν2β decay in the foreseeable future is highly nontrivial and deserves special attention (for instance, some particular attention has been paid to the role of the Majorana phases in the 0ν2β decay in [11][12][13][14][15][16][17][18][19][20][21][22][23][24]).…”

Section: Introductionmentioning

confidence: 99%

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

2015

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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.

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“…where the Greek and Latin subscripts run over (e, µ, τ ) and (1,2,3), respectively. The six orthogonality relations geometrically define six leptonic unitarity triangles (UTs) in the complex plane [10], as illustrated in Fig.…”

Section: Cp Violation In the Lepton Sector Is Another Open Question mentioning

confidence: 99%

“…where the Greek and Latin subscripts run over (e, µ, τ ) and (1,2,3), respectively. αi βj are not automatically real if α = β and i = j.…”

Section: Dirac Angle Matrix Vs Majorana Angle Matrixmentioning

confidence: 99%

Dirac leptonic angle matrix versus Majorana leptonic angle matrix and their renormalization group running behaviors

Luo

2012

Phys. Rev. D

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Enlightened by the idea of the 3 × 3 CKM angle matrix proposed recently by Harrison et al.,we introduce the Dirac angle matrix Φ and the Majorana angle matrix Ψ in the lepton sector for Dirac and Majorana neutrinos respectively. We show that in the presence of CP violation, the angle matrix Φ or Ψ is entirely equivalent to the complex MNS matrix V itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles (UTs) and do not depend on any particular parametrization of V . In this paper, we further analyzed how the angle matrices evolve with the energy scale. The one-loop Renormalization Group Equations (RGEs) of Φ, Ψ and some other rephasing invariant parameters are derived and the numerical analysis is performed to compare between the case of Dirac and Majorana neutrinos. Different neutrino mass spectra are taken into account in our calculation. We find that apparently different from the case of Dirac neutrinos, for Majorana neutrinos the RG-evolutions of Φ, Ψ and J strongly depend on the Majorana-type CP-violating parameters and are more sensitive to the sign of ∆m 2 31 .They may receive significant radiative corrections in the MSSM with large tan β if three neutrino masses are nearly degenerate.

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DirectCPviolation and isospin triangles ofB→ππdecays

Cited by 18 publications

References 20 publications

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

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

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

Dirac leptonic angle matrix versus Majorana leptonic angle matrix and their renormalization group running behaviors

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