Exploring asymmetries in three-body cLFV lepton decays: probing CP violation in HNL extensions of the SM

TL;DR

The paper investigates CP violation in SM extensions with heavy neutral leptons by developing and analyzing angular observables in polarised three-body cLFV decays. Using a minimal 3+2 HNL model, it derives P-, P'-, and T-odd asymmetries, including forward-backward variants, across all flavour configurations and thoroughly examines their dependence on heavy masses, mass splittings, and CP-violating phases. The study shows that the asymmetries can reach sizeable values (up to about 25% in some muon channels) and exhibit distinctive angular patterns, offering a powerful way to disentangle operator contributions beyond total rates. It also discusses experimental prospects at Mu3e, Belle II, STCF, and FCC-ee, highlighting synergies between muon and tau channels and emphasizing that joint measurements of rates and asymmetries can strongly constrain or falsify the CP-violating HNL scenario, potentially linking to leptogenesis in a broader framework.$

Abstract

In the context of Standard Model extensions via Majorana sterile fermions, the presence of additional CP violating phases (Dirac and Majorana) has been shown to be at source of important effects in charged lepton flavour violating (cLFV) transitions and decays. Here we will consider further angular observables that can be studied for polarised $τ$ and $μ$ cLFV decays. These include, among others, parity asymmetries and time-reversal asymmetries for generic cLFV 3-body decays, $\ell_α^+ \to \ell_β^+ \ell_γ^+ \ell_δ^-$. We address relevant correlations between the different classes of observables, and show that one can have sizeable asymmetries, which can be used to further probe this interesting class of SM extensions. Our study leads to the prediction of particular patterns of angular observables, which would allow to potentially falsify the model, should a cLFV signal be observed.

Figures (15)

• Figure 1: Rest frame of the decaying charged lepton $\ell_\alpha^+$, with $\vec{P}$ denoting its polarisation.
• Figure 2: Asymmetries for the $\tau^+ \to \mu^+ e^+ e^-$ decay as a function of the degenerate heavy sterile masses $m_{4,5}$ (in GeV). We have chosen $s_{14} = s_{1 5} = 0.006$, $s_{24} = -s_{2 5} = -0.02$, $s_{34} = s_{3 5} = 0.036$, with all phases set to 0. The coloured full lines denote the distinct asymmetries associated with the decay: $P$ (blue), $P^\prime$ (orange), $T$ (green), $FB$ (red), $FB, P$ (purple), $FB, P^\prime$ (brown) and $FB, T$ (pink).
• Figure 3: Form factors contributing to the $\tau^+ \to \mu^+ e^+ e^-$ decay as a function of the degenerate heavy sterile masses $m_{4,5}$ (in GeV): absolute values of the dipole, anapole and $Z$ penguins, as well as the box contributions, respectively associated with blue, orange, green and red lines.
• Figure 4: Asymmetries for the $\tau^+ \to \mu^+ e^+ e^-$ decay as function of the heavy sterile mass difference $\Delta m_{45} = m_5-m_4$ (in GeV), setting $m_4 = 1$ TeV. We have chosen $s_{14} = s_{1 5} = 0.006$, $s_{24} = -s_{2 5} = -0.02$, $s_{34} = s_{3 5} = 0.036$, with all phases set to 0. Line and colour code as in Fig. \ref{['fig:AsymMass3211:m4m5']}.
• Figure 5: Asymmetries for the $\tau^+ \to \mu^+ e^+ e^-$ decay vs. the Dirac phase, $\delta_{14}$. We choose $s_{14} = s_{1 5} = 0.006$, $s_{24} = -s_{2 5} = -0.02$, $s_{34} = s_{3 5} = 0.036$, with all other phases set to zero, and take $m_4 = m_5 = 1$ TeV. The top panel displays the distinct asymmetries (with the line and colour code as in Fig. \ref{['fig:AsymMass3211:m4m5']}); the lower panels respectively illustrate the dependency of the form factors - absolute value (on the left) and argument (on the right) - on $\delta_{24}$.