Relic right-handed Dirac neutrinos and implications for detection of cosmic neutrino background

Abstract

It remains to be determined experimentally if massive neutrinos are Majorana or Dirac particles. In this connection, it has been recently suggested that the detection of cosmic neutrino background of left-handed neutrinos ν L and right-handed antineutrinos ν R in future experiments of neutrino capture on beta-decaying nuclei (e.g., ν e + 3 H → 3 He+e − for the PTOLEMY experiment) is likely to distinguish between Majorana and Dirac neutrinos, since the capture rate is twice larger in the former case. In this paper, we investigate the possible impact of right-handed neutrinos on the capture rate, assuming that massive neutrinos are Dirac particles and both right-handed neutrinos ν R and left-handed antineutrinos ν L can be efficiently produced in the early Universe. It turns out that the capture rate can be enhanced at most by 28% due to the presence of relic ν R and ν L with a total number density of 95 cm −3 , which should be compared to the number density 336 cm −3 of cosmic neutrino background. The enhancement has actually been limited by the latest cosmological and astrophysical bounds on the effective number of neutrino generations N eff = 3.14 +0.44 −0.43 at the 95% confidence level. For illustration, two possible scenarios have been proposed for thermal production of right-handed neutrinos in the early Universe.PACS number(s): 14.60. St, 95.35.+d, 98.70.Vc Although a number of elegant neutrino oscillation experiments in the past few decades have well established that neutrinos are massive particles, it is still unclear whether massive neutrinos are of Dirac or Majorana nature [1,2]. Thus far, tremendous efforts have been placed on the experimental searches for neutrinoless double-beta (0νββ) decays, which take place only if lepton number violation exists and massive neutrinos are Majorana particles [3,4,5,6]. The experimental discovery of 0νββ decays will provide us with a robust evidence for Majorana neutrinos. However, in case that 0νββ decays are not detected in all the future 0νββ experiments, it is still possible that neutrinos are Majorana particles, if neutrino mass ordering is normal (i.e., m 1 < m 2 < m 3 ) and an intricate cancellation occurs in the effective neutrino mass relevant for 0νββ decays (see, e.g., Ref. [7]). In this case, another independent approach should be utilized to probe the Dirac or Majorana nature of massive neutrinos.More than fifty years ago, Weinberg pointed out [8] that the cosmic neutrino background (CνB) predicted by the standard Big Bang theory of cosmology can be detected via neutrino capture on betadecaying nuclei, e.g., ν e + 3 H → 3 He + e − . This possibility has been extensively studied in many recent works [9,10,11,12,13,14]. In particular, for the future experiment PTOLEMY [15] with 100 grams of tritium, the capture rate Γ(ν e + 3 H → 3 He + e − ) has been found to be [14]

Relic Right-handed Dirac Neutrinos and Cosmic Neutrino Background

“…However, the huge hierarchy between neutrino masses m ν 0.1 eV and top-quark mass m t = 1.71×10 12 eV needs to be further explained. Since the Yukawa couplings of Dirac neutrinos are extremely small y ν 10 −12 , the direct production of right-handed neutrinos ν R and left-handed antineutrinos ν L in the early Universe is highly suppressed [8,9]. Therefore, we have n ν r = n ν l = 0 at T = T L and today as well.…”

“…[9], a working example has been given to thermally produce right-handed neutrinos ν R and left-handed antineutrinos ν L . In this scenario, primordial magnetic fields B 0 ≈ 10 24 G within a domain size L 0 > 10 −7 cm are assumed to be generated during the electroweak phase transition at T = 100 GeV.…”

“…The extra effective number of neutrinos ∆N eff is shown with respect to the decoupling temperature T R of right-handed neutrinos [9].…”

“…We should calculate the number densities of ν r and ν l at present by assuming that the upper bound ∆N eff < 0.53 is saturated. First, it is straightforward to find the number density at T L [9] …”

The μ-τ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections

“…refs. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. 6 For a recent review of this topic see ref.…”