Sterile neutrino states

Neutrino masses are likely to be a manifestation of the right-handed, or sterile neutrinos. The number of sterile neutrinos and the scales of their Majorana masses are unknown. We explore theoretical arguments in favor of the high and low scale seesaw mechanisms, review the existing experimental results, and discuss the astrophysical hints regarding sterile neutrinos. 1. Sterile neutrinos in particle physics The term sterile neutrino was coined by Bruno Pontecorvo, who hypothesized the existence of the right-handed neutrinos in a seminal paper [1], in which he also considered vacuum neutrino oscillations in the laboratory and in astrophysics, the lepton number violation, the neutrinoless double beta decay, some rare processes, such as μ → eγ, and several other questions that have dominated the neutrino physics for the next four decades. Most models of the neutrino masses introduce sterile (or right-handed) neutrinos to generate the masses of the ordinary neutrinos via the seesaw mechanism [2]. The seesaw lagrangian L = LSM + N̄a (iγ ∂μ)Na − yαaH L̄αNa − Ma 2 N̄ c aNa + h.c. , (1) where LSM is the lagrangian of the Standard Model, includes some number n of singlet neutrinos Na with Yukawa couplings yαa. Here H is the Higgs doublet and Lα (α = e, μ, τ) are the lepton doublets. Theoretical considerations do not constrain the number n of sterile neutrinos. In particular, there is no constraint based on the anomaly cancellation because the sterile fermions do not couple to the gauge fields. The experimental limits exist only for the larger mixing angles [3]. To explain the neutrino masses inferred from the atmospheric and solar neutrino experiments, n = 2 singlets are sufficient [4], but a greater number is required if the lagrangian (1) is to explain the LSND [5], the r-process nucleosynthesis [6], the pulsar kicks [7, 8], dark matter [9, 10, 11, 12], and the formation of supermassive black holes [13]. The scale of the right-handed Majorana masses Ma is unknown; it can be much greater than the electroweak scale [2], or it may be as low as a few eV [5, 14]. The seesaw mechanism [2] can explain the smallness of the neutrino masses in the presence of the Yukawa couplings of order one if the Majorana masses Ma are much larger than the electroweak scale. Indeed, in this case the masses of the lightest neutrinos are suppressed by the ratios 〈H〉/Ma. However, the origin of the Yukawa couplings remains unknown, and there is no experimental evidence to suggest that these couplings must be of order 1. In fact, the Yukawa couplings of the charged leptons are much smaller than 1. For example, the Yukawa coupling of the electron is as small as 10. One can ask whether some theoretical models are more likely to produce the numbers of order one or much smaller than one. The two possibilities are, in fact, realized in two types of theoretical models. If the Yukawa couplings arise as some topological intersection numbers in string theory, they are generally expected to be of order one [15], although very small couplings are also possible [16]. If the Yukawa couplings arise from the overlap of the wavefunctions of fermions located on different branes in extra dimensions, they can be exponentially suppressed and are expected to be very small [17]. In the absence of the fundamental theory, one may hope to gain some insight about the size of the Yukawa couplings using ’t Hooft’s naturalness criterion [18], which states essentially that a number can be naturally small if setting it to zero increases the symmetry of the lagrangian. A small breaking of the symmetry is then associated with the small non-zero value of the parameter. This naturalness criterion has been applied to a variety of theories; it is, for example, one of the main arguments in favor of supersymmetry. (Setting the Higgs mass to zero does not increase the symmetry of the Standard Model. Supersymmetry relates the Higgs mass to the Higgsino mass, which is protected by the chiral symmetry. Therefore, the light Higgs boson, which is not natural in the Standard Model, becomes natural in theories with softly broken supersymmetry.) In view of ’t Hooft’s criterion, the small Majorana mass is natural because setting Ma to zero increases the symmetry of the lagrangian (1) [19, 5]. One can ask whether cosmology can provide any clues as to whether the mass scale of sterile neutrinos should be above or below the electroweak scale. It is desirable to have a theory that could generate the matter–antimatter asymmetry of the universe. In both limits of large and small Ma one can have a successful leptogenesis: in the case of the high-scale seesaw, the baryon asymmetry can be generated from the out-of-equilibrium decays of heavy neutrinos [20], while in the case of the low-energy seesaw, the matter-antimatter asymmetry can be produced by the neutrino oscillations [21]. The Big-Bang nucleosynthesis (BBN) can provide a constraint on the number of light relativistic species in equilibrium [22], but the sterile neutrinos with the small mixing angles may never be in equilibrium in the early universe, even at the highest temperatures [9]. Indeed, the effective mixing angle of neutrinos at high temperature is suppressed due to the interactions with plasma [23], and, therefore, the sterile neutrinos may never thermalize. High-precision measurements of the primordial abundances may probe the existence of sterile neutrinos and the lepton asymmetry of the universe in the future [24]. While many seesaw models assume that the sterile neutrinos have very large masses, which makes them unobservable, it is worthwhile to consider light sterile neutrinos in view of the above arguments, and also because they can explain several experimental results. In particular, sterile neutrinos can account for cosmological dark matter [9], they can explain the observed velocities of pulsars [7, 8], the x-ray photons from their decays can affect the star formation [25]. Finally, sterile neutrinos can explain the LSND result [5, 26, 27], which is currently being tested by the MiniBooNE experiment. 2. Experimental limits Laboratory experiments are able to set limits or discover sterile neutrinos with a large enough mixing angle. Depending on the mass, they can be searched in different experiments. The light sterile neutrinos, with masses below 10 eV, can be discovered in one of the neutrino oscillations experiments [28]. In fact, LSND has reported a result [29], which, in combination with the other experiments, implies the existence of at least one sterile neutrino, more likely, two sterile neutrinos [5, 26]. It is also possible that sterile neutrino decays, rather than oscillations, are the explanation of the LSND result [27]. In the eV to MeV mass range, the “kinks” in the spectra of beta-decay electrons can be used to set limits on sterile neutrinos mixed with the electron neutrinos [30]. Neutrinoless double beta decays can probe the Majorana neutrino masses [31]. For masses in the MeV–GeV range, peak searches in production of neutrinos provide the limits. The massive neutrinos νi, if they exist, can be produced in meson decays, e.g. π → μνi, with probabilities that depend on the mixing in the charged current. The energy spectrum of muons in such decays should contain monochromatic lines [30] at Ti = (m 2 π +m 2 μ − 2mπmμ −m 2 νi )/2mπ. Also, for the MeV–GeV masses one can set a number of constraints based on the decays of the heavy neutrinos into the “visible” particles, which would be observable by various detectors. These limits are discussed in Ref. [3]. 3. Sterile neutrinos in astrophysics and cosmology Sterile neutrinos can be produced in supernova explosions. The observations of neutrinos from SN1987A constrain the amount of energy that the sterile neutrinos can take out of the supernova, but they are still consistent with the sterile neutrinos that carry away as much as a half of the total energy of the supernova. A more detailed analysis shows that the emission of sterile neutrinos from a cooling newly born neutron star is anisotropic due to the star’s magnetic field [7]. The anisotropy of this emission can result in a recoil velocity of the neutron star as high as ∼ 10km/s. This mechanism can be the explanation of the observed pulsar velocities [8]. The range of masses and mixing angles required to explain the pulsar kicks is shown in Fig. 1. 10 -12 10 -11 10 -10 10 -9 10 -8 10 -7