Distinguishing Dirac vs. Majorana neutrinos: a cosmological probe

Abstract

Cosmic background neutrinos (CνB) helicity composition is different for Dirac or Majorana neutrinos making detectors based on CνB capture sensitive to the nature of neutrinos. We calculate, for the first time, the helicity changes of neutrinos crossing dark matter fields, to quantitatively calculate this effect on the capture rate. We show that a fraction of neutrinos change their helicity, regardless of them being deflected by a void or a dark matter halo. The average signal from the 100 most massive voids or halos in a Gpc3 gives a prediction that if neutrinos are Dirac, the density of the CνB background measured on Earth should be 48 cm-3 for left-helical neutrinos, a decrease of 15% (53.6 cm-3; 5%) for a halo (void) with respect to the standard calculation without including gravitational effects due to large scale structures. In terms of the total capture rate in a 100 g tritium detector, this translates in 4.9+1.1 -0.8 neutrinos per year for the Dirac case, as a function of the unknown neutrino mass scale, or 8.1 per year if neutrinos are Majorana. Thus although smaller than the factor two for the non-relativistic case, it is still large enough to be detected and it highlights the power of future CνB detectors, as an alternative to neutrinoless double beta decay experiments, to discover the neutrino nature.

Cosmic Background Neutrinos Deflected by Gravity: DEMNUni Simulation Analysis

“…In our previous work [9], we demonstrated that the neutrino velocity field is locally deflected over time and, indeed, the helicity content of Dirac neutrinos is modified. In that work, we assumed that different neutrinos mass eigenstates were equally populated, but, in reality, this is not the case: different neutrinos masses have different velocity fields so will suffer different deflection when falling into the same gravitational potential.…”

“…As the Universe is clustered and non-linear gravitational structures exist, neutrinos will suffer a deflection angle when falling into a gravitational potential. This means that the helicity content of the C ν B is modified by gravity in the case that neutrinos are Dirac particles, which results in a decrease of the Dirac capture rates for experiments based on cosmic background neutrinos capture as Ptolemy [9,11]. Capture rates depend on neutrino mass and neutrinos helicity states densities.…”

“…The deflection angle is calculated between neutrinos velocities at z = 3, which is enough, and at z = 0 as done in [9].…”

“…To get the total deflection angle distribution for a specific neutrino mass, we sum up normalised partial angle distributions weighted by the number of neutrinos in each beta range obtained from the Fermi-Dirac distribution for that specific neutrino mass (Eq. 2.2) We continue to use our reference case from previous work [9], namely, (2.4a)…”

“…We update the calculations in [9] computing the helicity states density for a general mass eigenstate. Coming up with a general formula is needed because the actual mass of neutrinos remains unknown.…”