[Paper Review] Towards distinguishing Dirac from Majorana neutrino mass with gravitational waves

Stephen F. King, Danny Marfatia+1 more|arXiv (Cornell University)|Jun 8, 2023

Neutrino Physics Research11 citations

TL;DR

The paper proposes using gravitational-wave spectra to distinguish Dirac from Majorana neutrino mass generation: domain-wall–induced peaks for Dirac seesaws versus flat cosmic-string–induced spectra for Majorana seesaws, with NANOGrav implications.

ABSTRACT

We propose a new method towards distinguishing the Dirac versus Majorana nature of neutrino masses from the spectrum of gravitational waves (GWs) associated with neutrino mass genesis. Motivated by the principle of generating small neutrino masses without tiny Yukawa couplings, we assume generic seesaw mechanisms for both Majorana and Dirac neutrino masses. For Majorana neutrinos, we further assume a spontaneously broken gauged $U(1)_{B-L}$ symmetry, independently of the type of Majorana seesaw mechanism, which gives a cosmic string induced GW signal flat over a wide range of frequencies. For Dirac neutrinos, we assume the spontaneous breaking of a $Z_2$ symmetry, the minimal symmetry choice associated with all Dirac seesaw mechanisms, which is softly broken, generating a peaked GW spectrum from the annihilation of the resulting domain walls. In fact, the GW spectra for all types of Dirac seesaws with such a broken $Z_2$ symmetry are identical, subject to a mild caveat. As an illustrative example, we study the simplest respective type-I seesaw mechanisms, and show that the striking difference in the shapes of the GW spectra can help differentiate between these Dirac and Majorana seesaws, complementing results of neutrinoless double beta decay experiments. We also discuss detailed implications of the recent NANOGrav data for Majorana and Dirac seesaw models.

Motivation & Objective

• Motivate small neutrino masses without ultra-tiny Yukawa couplings via seesaw mechanisms.
• Show that symmetry breaking patterns (Z2 for Dirac, U(1)_{B−L} for Majorana) lead to distinct GW signatures.
• Demonstrate that Dirac seesaws yield peaked GW spectra from domain-wall annihilation, while Majorana seesaws yield flat spectra from cosmic strings.
• Assess current and future gravitational-wave observatories’ sensitivity to these signals and discuss NANOGrav data implications.

Proposed method

• Analyze Majorana mass generation via type-I seesaw with gauged U(1)_{B−L} leading to a cosmic-string GW background (Eq. 5–12).
• Analyze Dirac mass generation via Dirac seesaw with a broken Z2 symmetry leading to domain-wall-induced GWs (Eq. 24–27).
• Provide explicit Lagrangians and mass matrices for both setups (Eqs. 1–4).
• Derive domain-wall tension, bias potential, and annihilation timing to obtain the peak GW amplitude and frequency (Eqs. 16–27, 24–27, 29–34).
• Compute the GW spectra and compare the energy-density shapes (flat vs peaked) across frequency bands relevant to PTAs and other interferometers.
• Evaluate detectability via SNR metrics for current and future experiments (Eq. 35, Fig. 3–5).

Figure 2: Gravitational wave spectrum induced by cosmic strings generated via the spontaneous breaking of the gauged $U(1)_{B-L}$ symmetry responsible for Majorana mass of the neutrinos. $\Lambda$ denotes the scale of symmetry breaking.

Experimental results

Research questions

• RQ1 Can the spectral shapes of gravitational waves distinguish Dirac from Majorana neutrino mass generation mechanisms?
• RQ2 What are the characteristic GW signatures (peaked vs flat) associated with Dirac domain walls versus Majorana cosmic strings?
• RQ3 Are current PTA results (e.g., NANOGrav) compatible with Dirac or Majorana seesaw scenarios, and what future observations can test them?
• RQ4 What regions of the model parameter space (u, V_bias, λ, etc.) yield detectable GW signals without cosmological conflicts?

Key findings

• Majorana mass generation via U(1)_{B−L} cosmic strings yields a nearly flat GW spectrum over a wide frequency range.
• Dirac mass generation with Z2 breaking leads to domain-wall–induced GW signals that are peaked at a characteristic frequency.
• PTA data such as NANOGrav can be more naturally accommodated by the Dirac-domain-wall GW signal than by a Majorana-cosmic-string signal.
• There exist constrained regions of parameter space (u, V_bias, λ, etc.) where domain-wall GWs are detectable by SKA, μAres, LISA, AEDGE, DECIGO, BBO, AION, AEDGE, and by Advanced LIGO/Virgo, ET, CE in other bands.
• Benchmark points show peak frequencies and amplitudes compatible with current or near-future GW observatories (Fig. 3–5, Table 1).

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