We study the CP violation in lepton number violating meson decays M ± → ±can become appreciable when two intermediate on-shell Majorana neutrinos Nj (j = 1, 2) participate in these decays. Our calculations show that the asymmetry becomes largest when the masses of N1 and N2 are almost degenerate, i.e., when the mass difference ∆MN becomes comparable with the (small) decay widths ΓN of these neutrinos: ∆MN ΓN . We show that in such a case, the CP ratio] becomes a quantity ∼ 1. The observation of CP violation in these decays would be consistent with the existence of the well-motivated νMSM model with two almost degenerate heavy neutrinos in the mass range between MN ∼ 0.1-10 1 GeV.
We study the pion decays with intermediate on-shell neutrinos N into two electrons and a muon, π ± → e ± N → e ± e ± µ ∓ ν. We investigate the branching ratios Br± = [Γ(π − → e − e − µ + ν) ± Γ(π + → e + e + µ − ν)]/Γ(π − → all) and the CP asymmetry ratio ACP = Br−/Br+ for such decays, in the scenario with two different on-shell neutrinos. If N is Dirac, only the lepton number conserving (LC) decays contribute (LC: ν = νe orνe); if N is Majorana, both LC and lepton number violating (LV) decays contribute (LV: ν =νµ or ν = νµ). The results show that the CP asymmetry ACP is in general very small, but increases and becomes ∼ 1 when the masses of the two intermediate neutrinos get closer to each other, i.e., when their mass difference becomes comparable with their decay width, ∆MN ΓN . The observation of CP violation in pion decays would be consistent with the existence of the well-motivated νMSM model with two almost degenerate heavy neutrinos.
Some of the outstanding questions of particle physics today concern the neutrino sector, in particular whether there are more neutrinos than those already known and whether they are Dirac or Majorana particles. There are different ways to explore these issues. In this article we describe neutrino-mediated decays of charged pseudoscalar mesons such as π ± , K ± and B ± , in scenarios where extra neutrinos are heavy and can be on their mass shell.We discuss semileptonic and leptonic decays of such kinds. We investigate possible ways of using these decays in order to distinguish between the Dirac and Majorana character of neutrinos. Further, we argue that there are significant possibilities of detecting CP violation in such decays when there are at least two almost degenerate Majorana neutrinos involved. This latter type of scenario fits well into the known neutrino minimal standard model (νMSM) which could simultaneously explain the Dark Matter and Baryon Asymmetry of the Universe.
In a scenario with two almost mass degenerate heavy sterile Majorana neutrinos with a mass ∼ 1 GeV, we present the semileptonic decay widths of heavy charged pseudoscalars such as B mesons, either lepton-number-violating (B ± → µ ± e ± π ∓ ), or lepton-number-conserving (B ± → µ ± e ∓ π ± ), mediated by such on-shell neutrinos. It had been explained in the literature that such decays may be eventually detected, and that they can present even detectable CP violation effects. In this work we point out that, in addition, such decays may present detectable effects of heavy neutrino oscillation, allowing us to extract the oscillation length and thus the heavy neutrino mass difference ∆MN , as well as a CP-violating Majorana phase.
In this work, we study the lepton number violating W boson and top quark decays via intermediate on-shell Majorana neutrinos Nj into three charged leptons and a light neutrino. We discuss the neutrino oscillation effects present in the decay due to the small mass gap between the heavy neutrino states (∆MN ∼ ΓN ). We focus on a scenario that contains at least two heavy Majorana neutrinos in the mass range ∼ 2−80 GeV. The results indicate that the modulation of the branching ratios as a function of the distance between the vertices may be detected in a future experiment such as High-Luminosity Large Hadron Collider. As a secondary result, the CP-violating phases could be explored. Experiment type Decays Comments π → eN [83-87] The 90% C. L. limits Meson decay K → eN [88] for e (µ) on |BeN | 2 (|BµN | 2 ) K → µN [ [88][89][90][91][92] shown in Fig. 1 (Fig. 2) as 'Belle'. Heavier meson/ B → X N, N → π [93] BB pair coming from baryon decay[94-96] Υ(4s) resonance which can put 90% C. L. limits on |BeN | 2 and |BµN | 2 for the RHN between 500 MeV≤ MN ≤ 5 GeV are shown as 'Belle'.TABLE I: Peak search experiments to study the constraints on |B N | 2 .π → µN [97-101] limit is derived between 1 MeV ≤ MN ≤ 30 MeV and has been omitted from Fig. 2 due to the choice of MN .
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