[Paper Review] Neutrinoless double beta decay: Electron angular correlation as a probe of new physics

Ahmed Ali, Borisov, A. V.+1 more|ArXiv.org|Jun 7, 2006

Neutrino Physics Research3 citations

TL;DR

This paper proposes that electron angular correlation in neutrinoless double beta decay (0ν2β) can distinguish between new physics models, particularly the long-range mechanism involving light Majorana neutrinos versus right-handed W bosons in left-right symmetric models. By deriving the angular distribution from a general Lorentz-invariant effective Lagrangian, the study shows that the angular coefficient K depends on the right-handed W-boson mass and the effective Majorana neutrino mass, enabling model discrimination when combined with half-life measurements.

ABSTRACT

The angular distribution of the final electrons in the so-called long range mechanism of the neutrinoless double beta decay ($0 u2β$) is derived for the general Lorentz invariant effective Lagrangian. Possible theories beyond the SM are classified from their effects on the angular distribution, which could be used to discriminate among various particle physics models inducing $0 u2β$ decays. However, additional input on the effective couplings will be required to single out the light Majorana-neutrino mechanism. Alternatively, measurements of the effective neutrino mass and angular distribution in $0 u2β$ decays can be used to test the correlations among the parameters of the underlying physics models. This is illustrated for the left-right symmetric model, taking into account current phenomenological bounds.

Motivation & Objective

• To determine whether electron angular correlation in 0ν2β decay can discriminate among competing new physics models beyond the Standard Model.
• To derive the general angular distribution for the long-range mechanism using a Lorentz-invariant effective Lagrangian.
• To examine the correlation between the angular coefficient K, the right-handed W-boson mass m_WR, and the effective Majorana neutrino mass |⟨m⟩| in the left-right symmetric model.
• To assess the sensitivity of angular correlation to model parameters under current phenomenological bounds.
• To demonstrate that angular correlation measurements can help disentangle competing mechanisms in 0ν2β decay when combined with half-life data.

Proposed method

• Derives the differential decay width dΓ/dcosθ for the long-range 0ν2β decay mechanism using a general Lorentz-invariant effective Lagrangian with all possible tensor structures (V±A, S±P, T_L,R).
• Expresses the angular distribution as dΓ/dcosθ ∝ 1 - Kcosθ, where K is the angular coefficient dependent on hadronic and leptonic current matrix elements.
• Relies on the QRPA model with p-n pairing for ⁷⁶Ge to compute nuclear matrix elements (|M_GT| = 1.846, χ_F = 0.274, χ_{2-} = 0.551).
• Uses phase space factors G_01 = 7.928×10⁻¹⁵ yr⁻¹ and G_02 = 12.96×10⁻¹⁵ yr⁻¹ from the literature to compute the decay width.
• Derives the key relation K = (y - 1)/(y + 1), with y proportional to (|⟨m⟩|/m_e)² × (m_WR/m_WL)⁴ × (G_01/G_02), linking K to |⟨m⟩| and m_WR.
• Constructs numerical plots (Figs. 1–4) showing the correlation between K, m_WR, and |⟨m⟩| for ε = 10⁻⁶ and 5×10⁻⁷, assuming m_WR ≥ 1 TeV.

Experimental results

Research questions

• RQ1 Can the angular correlation coefficient K in 0ν2β decay distinguish between the light Majorana neutrino mechanism and the right-handed W-boson mechanism in left-right symmetric models?
• RQ2 How does the angular coefficient K depend on the effective Majorana neutrino mass |⟨m⟩| and the right-handed W-boson mass m_WR?
• RQ3 What is the sensitivity of the electron angular distribution to variations in |⟨m⟩| and m_WR, particularly in the sub-eV and meV regimes?
• RQ4 Can the combination of angular correlation and half-life measurements help constrain or identify the dominant mechanism in 0ν2β decay?
• RQ5 How do current phenomenological bounds on m_WR and |⟨m⟩| affect the allowed range of the angular coefficient K?

Key findings

• The angular coefficient K in the 0ν2β decay distribution dΓ/dcosθ ∝ 1 - Kcosθ is sensitive to the interplay between the effective Majorana neutrino mass |⟨m⟩| and the right-handed W-boson mass m_WR.
• For |⟨m⟩| ≤ 10 meV, the angular correlation coefficient K can distinguish left-right symmetric models from the SM plus light Majorana neutrino mechanism.
• Numerical results show that K can vary from -1 to +1 depending on m_WR and |⟨m⟩|, with K ≈ -1 achievable for m_WR ≈ 1 TeV and |⟨m⟩| ≈ 1 meV.
• The sensitivity of the angular distribution to m_WR increases significantly at lower values of |⟨m⟩|, as shown in Fig. 5 (right), where K varies more strongly with m_WR for |⟨m⟩| = 1 meV than for 5 meV.
• The relation K = 1 - 2G_02(|M_GT|χ_{2-}ε)²(m_WL/m_WR)⁴T_{1/2} links the measurable half-life T_{1/2} and angular coefficient K to m_WR and ε, enabling model discrimination.
• For ε = 10⁻⁶ and m_WR ≥ 1 TeV, the angular coefficient K can be as low as -0.9 for |⟨m⟩| ≈ 1 meV, indicating a strong angular correlation that deviates significantly from the K = 1 of the light Majorana neutrino case.