$N_{\textrm{eff}}$ Constraint on Pseudo-Dirac Neutrinos

TL;DR

This paper investigates the constraints on pseudo-Dirac neutrinos, especially the third mass splitting, using cosmological data, and proposes that future CMB observations could significantly tighten these bounds.

Contribution

It introduces an effective 3+1 model for pseudo-Dirac neutrinos and derives new constraints on the third mass splitting from CMB $N_{eff}$ measurements.

Findings

Current $|\delta m_3^2|$ constraint is $< 2 imes 10^{-6} ext{ eV}^2$

Future CMB experiments can improve the bound by an order of magnitude

Solar neutrino data strongly constrain the first two mass splittings

Abstract

After the electroweak symmetry breaking, we can write down two types of mass for the Standard Model neutrinos, Dirac or Majorana. It is often said that both types of mass cannot be distinguished in neutrino oscillation phenomena. This is in fact not true if neutrinos are pseudo-Dirac (strictly speaking still Majorana) where they mix almost maximally with sterile neutrinos to form pseudo-Dirac pairs. If this is indeed realized in Nature, what we observe experimentally as three mass eigenstates are actually three pairs of mass eigenstates with yet-to-be-measured new mass splitting among each pair. While the new mass squared splitting of the first and second mass eigenstates have stringent constraints from solar neutrino to be $|\delta m_{1,2}^2| \lesssim10^{-11}\,\textrm{eV}^{2}$, the one regarding the third mass eigenstate has a weaker constraint $|\delta m_3^2| \lesssim10^{-5}\,\textrm{eV}^{2}$. By keeping only one nonzero pseudo-Dirac mass squared splitting at a time, we derive an effective 3+1 description for the pseudo-Dirac scenario. Then we use the Cosmic Microwave Background (CMB) constraint on neutrino relativistic degrees of freedom $N_{\textrm{eff}}$ to derive a new constraint $|\delta m_3^2| < 2 \times 10^{-6}\,{\rm eV}^2$ and show that the future CMB-S4 and CMB-HD can improve this bound by an order of magnitude.