<figure><img src="image_51.png" /><figcaption>**Figure 49.** (a) Comparison between the expected calorimetrically measured <sup>163</sup>Ho spectrum in the case of no sterile neutrino (black dashed line) and in the case of a heavy neutrino mass $m_4 = 2$ keV with a mixing of $U_{e4}^2 = 0.5$. (b) A magnification of (a) in the region of the kink.</figcaption></figure>

line) and in the case of a heavy neutrino mass $m_4 = 2$ keV with an unrealistic mixing of $U_{e4}^2 = 0.5$. The two spectra have been normalized to both have an integral equal to 1. The magnification in figure 49 shows, in more details, the region of the kink.

### 9.3.1 The electron capture in <sup>163</sup>Ho experiment ECHO (authors: L. Gastaldo, T. Lasserre, A. Faessler)

The Electron Capture in <sup>163</sup>Ho Experiment, ECHO, has been designed to investigate the electron neutrino mass in the energy range below 1 eV by a high precision and high statistics calorimetric measurement of the <sup>163</sup>Ho electron capture spectrum [922].

Presently the detectors that can detect with the highest precision energy input below 3 keV, as is needed for the calorimetric measurement of the <sup>163</sup>Ho, are low temperature micro-calorimeters [937]. They are energy dispersive detectors typically operated at temperatures below 50 mK. These detectors can be classified on the basis of the temperature sensor. Within the ECHO experiment, low temperature metallic magnetic calorimeters (MMCs) will be used [938]. The spectral resolving power of a state of the art MMCs for soft X-rays is above 3000. For completely micro-structured detectors, an energy resolution of $\Delta E_{FWHM} = 1.6$ eV at 6 keV has been achieved [939]. Sub-eV energy resolution is expected to be reached in future design with SQUID readout integrated on the detector chip. Such an energy resolution will allow to have a precise characterization of the endpoint region of the spectrum with a minimal spread of the events. The typical signal rise-time is $\tau_r = 90$ ns [940]. Among the different temperature sensors presently used to read-out the temperature of micro-calorimeters, MMCs show the fastest risetime. This feature is extremely important to reduce a source of background which is intrinsic to the calorimetric measurements: un-resolved pile-up events. The spectral shape of this background is given by the autoconvolution of the <sup>163</sup>Ho spectrum with the integral given by the so-called unresolved pileup fraction which can be written in first approximation as the activity in the detector A times the risetime of the signal $\tau_r$. For the ECHO experiment an unresolved pile-up fraction below $10^{-5}$ is required. This unresolved pile up fraction, combined with the typical risetime of MMCs, implies a limit in the maximal
activity per pixel to a few tens of Bequerel. Figure 50 compares the ¹⁶³Ho spectrum without unresolved pile up (blue dashed line) with the ¹⁶³Ho spectrum in the case of an unresolved pileup fraction of 10⁻⁶ (red solid line).

In the ECHo experiment, the required activity of ¹⁶³Ho to reach a sub-eV sensitivity is a few MBq. The reduced activity per pixel, in order to limit the unresolved pile-up events, implies that in the order of 10⁵ single detectors have to be simultaneously measured. A convenient approach to read out so many detectors is the use of a multiplexing scheme. The choice within the ECHo collaboration is to use the microwave SQUID multiplexing scheme [941] which allows to have a large bandwidth for each pixel and a reduced degradation of the detectors performance respect to the single pixel readout [942].

The ECHo collaboration has already demonstrated the possibility to perform a calorimetric measurement of the ¹⁶³Ho with high energy resolution using MMC detectors with ion implanted ¹⁶³Ho [929]. The ¹⁶³Ho activity per pixel was about 10⁻² Bq. The implantation process did not degrade the performance of the MMC [943]. An energy resolution of ΔE<sub>FWHM</sub> ≃ 7.6 eV, at a working temperature of about 30 mK, and the rise-time τ<sub>r</sub> ≃ 130 ns have been measured. One of the next important goals within ECHo is to demonstrate that very good energy resolutions, ΔE<sub>FWHM</sub> < 2 eV can be achieved for MMCs having ¹⁶³Ho ions embedded in the absorber and read out using the microwave multiplexing technique.

The information on the neutrino mass is obtained by the analysis of the events in a very small energy range around the endpoint of the spectrum. Therefore to have an independent measurement of the $Q_{EC}$ for the ¹⁶³Ho decay to be compared to the value that can be extracted by fitting the spectrum is of outmost importance for the reduction of systematic errors. By the analysis of calorimetrically measured spectra the best values for $Q_{EC}$ are approximately 2.8 keV [929, 944]. These results do not agree with the recommended value $Q_{EC} = (2.55 \pm 0.016)$ keV published by the Atomic Mass Evaluation edited in 2012 [945].

One of the priority of the ECHo collaboration was therefore to perform and independent measurement of the $Q_{EC}$ by precisely measuring the mass of the parent atom, ¹⁶³Ho, and daughter atom ¹⁶³Dy. This has been performed by high precision Penning traps mass spectrometry [946]. The measurement has been performed at the Penning-trap mass spectrometer SHIPTRAP [947] applying the novel phase-imaging ion-cyclotron-resonance technique [948] and the laser ionization of the source developed at the TRIGA-TRAP [949, 950]. This measurement has been able to strongly reduce the uncertainties on $Q_{EC}$. The value that has been obtained, $Q_{EC} = (2.833 \pm 0.030^{\text{stat}} \pm 0.015^{\text{syst}})$ keV [925] is in very good agreement with the $Q_{EC}$-value obtained by the analysis of calorimetrically measured ¹⁶³Ho spectra.

In order to remove systematic uncertainties, at a few eV level, on the $Q_{EC}$-value as determined by the analysis of the calorimetrically measured spectra, which could derive from solid state effects, an independent measurement at 1 eV precision level is of outmost importance. This precision will be achieved by measuring the masses of ¹⁶³Ho and ¹⁶³Dy with the newly developed PENTATRAP [951, 952] at the Max Planck Institute for Nuclear Physics in Heidelberg.

The spectral shape as described in equation (9.5) considers only first order transitions where the excited states of the daughter atom ¹⁶³Dy can be characterized by a hole at the level of the captured electron and an additional electron in the 4f-shell. In order to describe small structures in the spectrum above the NI-line, second and third order excitations have been theoretically investigated [953–955]. Presently there is no good agreement between the experimentally observed structures and the ones expected by the theoretical models. Though, some of the theoretically calculated structures coincide in energy with observed ones. New models
for the description of atomic de-excitation are under investigation [956] as well as dedicated experiments will be performed to better characterize the electron capture decay in $^{163}$Ho.

The aim of the ECHo collaboration is to gain a precise understanding of background sources which could affect the $^{163}$Ho spectrum and to develop methods to reduce them to a level where their contribution will be smaller compared to the unresolved pile-up events in the endpoint region of the spectrum. To reach this limit the background level should be smaller than $10^{-5}$ events/eV/day/det. The next step of the ECHo collaboration is to perform a medium scale experiment, ECHo-1k, which will run during the years 2015-2018. In ECHo-1k first prototypes of MMC array with implanted $^{163}$Ho will be fabricated. The $^{163}$Ho source will be produced through neutron irradiation of a $^{162}$Er-enriched target and dedicated chemical purifications step along with mass separation will be used to remove radioactive contamination to a not detectable level. The sum of the activity of all the pixels will be approximately 1 kBq. With this first medium scale experiment the ECHo collaboration aims to reduce the present limit on the electron neutrino mass by more than one order of magnitude, from a present upper limit of $m(\nu_e) = 225$ eV [957] to below $m(\nu_e) = 20$ eV and show the scalability of the developed techniques for the construction of the next generation experiment, ECHo-1M. The goal of ECHo-1M is to measure a $^{163}$Ho EC spectrum with a statistics of more than $10^{14}$ events using a $^{163}$Ho source of the order of 1 MBq distributed over a very large number of single pixels. With such an experiment it will be possible to reach the sub-eV sensitivity on the electron neutrino mass.

**keV sterile neutrino program in ECHo.** The calorimetric technique to measure the $^{163}$Ho spectrum has the intrinsic property that all the events generated in the detectors produce a signal. Therefore, in respect to an experiment as KATRIN, where a MAC-E filter selects only electrons close to the endpoint of the Tritium spectrum, in ECHo there is the possibility to acquire all the events occurring in the detector, even if for the determination of the electron neutrino mass mainly the events at the end point are important. The ECHo program to investigate the effect of keV sterile neutrino on the $^{163}$Ho EC spectrum can be divided into two parts:

* assess systematic effects and analysis of high statistics $^{163}$Ho EC spectra searching for a kink at $Q_{EC} - m_4$

* develop efficient methods to acquire and store large number of events

The first part of this investigation will be carried on during the first stage of the ECHo experiment, ECHo-1k. The assess of systematic effects due to the not precise knowledge of the calorimetrically measured spectrum of $^{163}$Ho is a fundamental milestone to reach the sub-eV sensitivity. The precise knowledge of the $Q_{EC}$ is of utmost importance not only for the investigation of the “standard” effective electron neutrino mass, but also to define with high precision the value of the heavy neutrino mass $m_4$ through the difference between the position of the possible kink and the endpoint of the spectrum. The uncertainties on the $Q_{EC}$ have already been strongly reduced by the measurements performed using Penning traps [925] and this achievement paved the way for future experiments aiming to the 1 eV precision.

The effects due to higher order excitation states in the $^{163}$Dy atom after the electron capture in $^{163}$Ho is presently a topic of high interest. In the high resolution spectrum measured within the ECHo experiment, additional structures above the NI-line, which can hardly be explained as being due to background sources, have been detected [958]. This experimental evidence has already triggered the work of different groups [953–956]. In these works,
<figure><img src="image_52.png" /><figcaption>**Figure 50.** The $^{163}$Ho spectrum with no unresolved pile up (blue dashed line) is compared with the $^{163}$Ho spectrum in the case of an unresolved pileup fraction of $10^{-6}$ (red solid line) for a total statistics of $10^{14}$ events.</figcaption></figure>

some of them performed within the ECHo experiment, the modifications to the calorimetrically measured spectrum due to excitations in the $^{163}$Dy atoms including two and three holes have been calculated. Presently the agreement between theoretical calculations and the ECHo data is still not satisfactory, but there is already evidence that this approach can be used to refine the description of the spectrum. Within ECHo-1k several experiments will be performed to better understand the shape of the $^{163}$Ho spectrum. In particular spectra with higher statistics and with a reduced background level, in a way that the shape of the additional structures will be better characterized, will be available to the theorists.

As already mentioned, one of the milestones of ECHo-1k is the identification and reduction of the background in the $^{163}$Ho spectrum deriving from contaminations in the $^{163}$Ho source, from natural radioactivity and from cosmic rays. The goal is to reduce all these contributions to a negligible level with respect to the intrinsic background due to unresolved pile-up events. This requirement, in the case of an unresolved pileup fraction of $10^{-6}$, leads to an allowed background activity per pixel of less than $10^{-5}$ events eV/det/day in the energy region below the endpoint of the $^{163}$Ho spectrum.

A good theoretical description of the $^{163}$Ho spectrum as well as of the background spectrum will allow also for a precise description of the unresolved pile up spectrum. The presence of additional small structures in the spectrum due to unresolved pileup could complicate the identification of a kink due to the existence of sterile neutrinos. Even if the choice made by the ECHo collaboration to keep the level of the unresolved pileup fraction below $10^{-5}$ implies that over a large part of the spectrum, the number of the expected unresolved pile up events is smaller than the statistical error for the counts in the $^{163}$Ho spectrum, a precise knowledge of this background spectrum is very important to push the sensitivity to detect a kink to heavy neutrinos having a very small mixing element. One of the aims of ECHo-1k is therefore to define a precise paremeterization for the calorimetrically measured $^{163}$Ho spectrum.

With the planned activity of 1 kBq and a measuring time of about one year a total statistics in the spectrum of about $10^{10}$ events will be acquired at the end of the first phase of
<figure><img src="image_53.png" /><figcaption>**Figure 51.** Achievable sensitivity 90% C.L. for the detection of a kink in the calorimetrically measured spectrum in the case of a perfect knowledge of the expected shape and for a total statistics of (a) 10¹⁰ and (b) 10¹⁴ events.</figcaption></figure>

the ECHo experiment. Figure 51a shows the achievable sensitivity for the detection of a kink in the calorimetrically measured spectrum in the case of a perfect knowledge of the expected shape of the spectrum and for the total statistics foreseen for the ECHo-1k experiment. For these calculations, $Q_{EC} = 2.8$ keV has been used. The best sensitivity to detect a kink in the spectrum is achieved for a heavy neutrino mass $1 \text{ keV} < m_4 < 2 \text{ keV}$, which corresponds to the part of the spectrum between the M- and N-lines. In this energy range it will be possible to test the mixing element down to about $|U_{e4}|^2 = 4 \cdot 10^{-5}$. For the second phase of the ECHo experiment, ECHo-1M, an activity of 1 MBq to a few MBq is foreseen. With such an activity it will be possible to acquire, within one year of measuring time, about 10¹⁴ events in the ¹⁶³Ho spectrum. With this statistics it will be possible to improve the sensitivity to find evidence of sterile neutrinos. Figure 51b shows the achievable sensitivity with a total statistics of 10¹⁴ events and a perfect knowledge of the spectral shape. In this case, for $1 \text{ keV} < m_4 < 2 \text{ keV}$, the mixing element could be tested down to about $|U_{e4}|^2 = 4 \cdot 10^{-7}$.

The sensitivity to detect a kink due to sterile neutrinos achieved considering only statistical errors on the counts per bin is very promising. More investigations are going on to define the influence on the reachable sensitivity of the finite energy resolution of the detectors and of the presence of background, in particular of the unresolved pile-up events.

From the experimental point of view it is important to point out that the acquisition and the storage of the ¹⁶³Ho events over the full spectrum is not a negligible aspect of the investigation. During ECHo-1k about 1000 ¹⁶³Ho events per second will occur. For this moderate rate, the acquisition of the full signal shape for all the events will still be possible. With the corresponding data it will be possible to develop routines to be applied for the on-line analysis of the data in the next stage of ECHo, ECHo-1M. In this experiment only a few characteristic parameters of each signal will be stored for the building of the complete spectrum. Nevertheless the aim is to store information for the pulses all over the energy range. This is not only important to reduce systematics in the analysis of the end point region of the spectrum, but it will allow for the analysis, over the complete spectrum for the search of a kink related to the existence of sterile neutrinos.
<table><caption>**Table 17.** Nuclides with relevant energy balance and suitable half-life to be used in potential future experiments to investigate keV sterile neutrinos by the analysis of the calorimetrically measured electron capture spectrum.</caption><thead><tr><th>Nuclide</th><th><i>T</i><sub>1/2</sub><br>[960]</th><th><i>Q</i><sub>EC</sub> [keV]<br>[961]</th><th><i>E</i><sub>i</sub> [keV]<br>[962]</th><th><i>E</i><sub>j</sub> [keV]<br>[962]</th><th><i>φ</i><sub>i</sub><sup>2</sup>(0)/<i>φ</i><sub>j</sub><sup>2</sup>(0)<br>[963]</th></tr></thead><tbody><tr><td><sup>157</sup>Tb</td><td>71 a</td><td>60.04</td><td>K: 50.2391</td><td>LI: 8.3756</td><td>7.124</td></tr><tr><td><sup>163</sup>Ho</td><td>4570 a</td><td>2.833 [925]</td><td>MI: 2.0468</td><td>NI: 0.4163</td><td>4.151</td></tr><tr><td><sup>179</sup>Ta</td><td>1.82 a</td><td>105.6</td><td>K: 65.3508</td><td>LI: 11.2707</td><td>6.711</td></tr><tr><td><sup>193</sup>Pt</td><td>50 a</td><td>56.63</td><td>LI: 13.4185</td><td>MI: 3.1737</td><td>4.077</td></tr><tr><td><sup>205</sup>Pb</td><td>15 Ma</td><td>50.6</td><td>K: 15.3467</td><td>LI: 3.7041</td><td>4.036</td></tr></tbody></table>

### 9.3.2 Other nuclides from the electron capture sector (authors: L. Gastaldo, Y. Novikov)

Several models and observations allow the sterile neutrino mass $m_s$ to cover a large range. In the electron capture sector, the analysis of the <sup>163</sup>Ho electron capture spectrum allows only to investigate heavy neutrino masses up to the $Q_{EC}$ value which, even allowing for uncertainties due to solid state effects, will hardly exceed 3 keV. On the other hand, the same methods applied within the ECHo experiment [922] could be adapted to other nuclides showing higher $Q_{EC}$ therefore allowing for investigating massive neutrinos in a larger mass region. The idea is to perform a calorimetric measurement of the electron capture spectrum of the interesting isotopes and search for the signature of a heavy neutrino mass. The method consists in embedding the source in the absorber of low temperature micro-calorimeters in a way that all the energy released in the electron capture process is measured by the detector. In low temperature micro-calorimeters the relatively small energy release in electron capture processes leads to an increase of temperature, which is measured by very sensitive thermometers. For the ECHo experiment, low temperature metallic magnetic calorimeters [938] will be used. These detectors are also suitable to be used for the calorimetric measurement of the electron capture spectrum of a large variety of other nuclides. The possibility to use metallic magnetic calorimeters for the search of the signature of sterile neutrinos in calorimetrically measured electron capture spectra was first investigated by Filianin et al. [959]. In that work, the achievable sensitivity to detect the effect of massive neutrinos of different masses and mixing was discussed for several nuclides in the electron capture sector. The proposed isotopes were selected on the base of their $Q_{EC}$ value and/or half-life. Table 17 shows a list of nuclides which have been selected from the list proposed in [959]. With respect to the other nuclides presented in [959] the ones listed in table 17 are more suitable, due to their decay schemes, to be investigated with micro-calorimetric techniques in future experiments, as discussed in the same paper. The sensitivity to investigate the mass and mixing of sterile neutrinos can be determined by considering the fact that the presence of a massive neutrino will reduce the phase space for energy above ($Q_{EC} - m_s$). If the value ($Q_{EC} - m_s$) were between the binding energies of two electronic states from which electrons can be captured, then the ratio between the amplitude of the two corresponding lines in the calorimetrically measured spectrum would be affected. From eq. (9.5), where the expected shape of the calorimetrically measured EC spectrum was
given considering only first order transitions, the amplitude for each line can be calculated:

$$ \lambda_H = A(Q_{EC} - E_H)^2 \sqrt{1 - \frac{m_\nu^2}{(Q_{EC} - E_H)^2}} C_H n_H B_H \phi_H^2(0) \quad (9.9) $$

with a scaling constant A, the peak energy $E_H$, the nuclear shape factors $C_H$, the fraction of occupancy of the H-atomic shell $n_H$, the squared wave-function of the captured electron calculated at the nucleus $\phi_H^2(0)$ and the exchange and overlap correction, $B_H$. The Breit-Wigner resonances are then modulated by the phase space factor which depends on the square of the electron neutrino mass $m(\nu_e)^2$ and the energy available to the decay $Q_{EC}$. Second order transitions which require the formation of two or more hole states in the final atom are here neglected since at the present level of investigation their effect would be marginal.

By explicitly introducing the dependency on the neutrino masses and reducing this to a 1+1 model, the electron neutrino state is given by the sum of a massless neutrino $|\nu_a\rangle$, to represent the three small mass active neutrino masses, and one massive neutrino $|\nu_4\rangle$:

$$ |\nu_e\rangle = \sum_{i=1}^{3} U_{ei}|\nu_i\rangle + U_{e4}|\nu_4\rangle = U_{ea}|\nu_a\rangle + U_{e4}|\nu_4\rangle \quad (9.10) $$

With this approximation the amplitude of the line H can be written as:

$$ \lambda_H = A \left( (Q_{EC} - E_H)^2 (1 - U_{e4}^2) + (Q_{EC} - E_H)^2 U_{e4}^2 \sqrt{1 - \frac{m_4^2}{(Q_{EC} - E_H)^2}} \right) C_H n_H B_H \phi_H^2(0) \quad (9.11) $$

If no keV sterile exists, then the amplitude of the line H in the approximation of vanishing active masses can be written as:

$$ \lambda_H = A(Q_{EC} - E_H)^2 C_H n_H B_H \phi_H^2(0) \quad (9.12) $$

Using Equation 9.11 and Equation 9.12 the ratio between the amplitude of two lines in the spectrum can be written as:

$$ \left(\frac{\lambda_i}{\lambda_j}\right) = \left(\frac{\lambda_i}{\lambda_j}\right)_{\text{act}} \frac{U_{e4}^2 \left(H \left[ (Q_{EC} - E_i) - m_4 \right] \sqrt{1 - m_4^2/(Q_{EC} - E_i)} - 1 \right) + 1}{U_{e4}^2 \left(H \left[ (Q_{EC} - E_j) - m_4 \right] \sqrt{1 - m_4^2/(Q_{EC} - E_j)} - 1 \right) + 1} \quad (9.13) $$

with $H [(Q_{EC} - E_i) - m_4]$ the Heaviside step function and

$$ \left(\frac{\lambda_i}{\lambda_j}\right)_{\text{act}} = \frac{(Q_{EC} - E_i)^2 C_i n_i B_i \phi_i^2(0)}{(Q_{EC} - E_j)^2 C_j n_j B_j \phi_j^2(0)} \quad (9.14) $$

From eq. (9.13) it appears evident that the signature of the existence of a sterile neutrino is a deviation of the ratio between the amplitudes of two lines of the electron capture spectrum with respect to the value expected in the case of only three active neutrinos. The magnitude of this deviation depends on the position of $(Q_{EC} - m_s)$ with respect to the energy of the two lines and of course on the mixing of the sterile neutrino $U_{e4}^2$.

In order to be able to identify the effect of the existence of a sterile neutrino by the analysis of the ratio between two lines of the electron capture spectrum, it is important to minimize all systematic effects which could mimic a deviation from the expected amplitude ratio for only active neutrinos. The most relevant aspects that need to be considered are:
* a precise knowledge of the $Q_{EC}$-value

* a precise knowledge of the de-excitation processes after the electron capture

* a reduced unresolved pile-up fraction

* a reduced unknown background

A precise knowledge of the $Q_{EC}$-value is very important since the amplitude of the lines in the electron capture spectrum is modulated by the phase space factor. The more a line in the spectrum is close to the end-point, the more the amplitude of this line is reduced with respect to the factor $C_H n_i B_H \phi_H^2(0)$. A large uncertainty in this value leads to a large uncertainty in the expected ratio between the amplitude of two lines of the spectrum. The most promising method to determine the $Q_{EC}$-value of radioactive nuclide is by the precise measurement of the mass of parent and daughter atoms whose difference provides the energy available to the decay. Penning trap mass spectrometry [946] is presently the best technique to precisely measure the mass of atoms. In these measurements, the cyclotron frequencies $\nu_C$ of the initial and final ionic states of the transition are measured in the crossing electrostatic and strong homogeneous magnetic field $B$. The mass $M$ of an ion having charge $q$ can be determined using the following relation:

$$ \nu_C = \frac{qB}{2\pi M} \qquad (9.15) $$

In order to reach eV precision for the $Q_{EC}$-value of heavy nuclides, a novel cryogenic Penning-trap mass spectrometer, PENTATRAP, is currently under construction at the Max-Planck Institute for Nuclear Physics in Heidelberg [951, 952]. With this mass spectrometer a relative mass accuracy of $10^{-11}$ will be reached allowing for a few eV precision on the $Q_{EC}$-value of the discussed nuclides. Figure 52 shows, at the 90% confidence level, the sensitivity for the sterile neutrino mass and mixing that can be reached by the analysis of the calorimetrically measured spectrum of the nuclides listed in table 17, under the assumptions that the uncertainties of the absolute atomic mass difference are 1 eV and that the capture probability for each line is perfectly known while the position of the lines is known with an uncertainty of 0.1 eV. In this approach, the limiting factor for the achievable minimal sterile neutrino mixing is the relative error for the $Q_{EC}$-value.

The curves in figure 52 have been calculated by considering that the de-excitation processes after the electron capture, which define the intrinsic amplitude of the lines, are perfectly known. Recently the case of the electron capture in $^{163}$Ho received attention due to the identification of additional small lines above the line corresponding to the capture of 4s electrons, the NI-line, in calorimetrically measured spectra [929]. A possible explanation of these lines seems to be related to higher order transitions which include the creation of two holes in the atom after the capture process [953, 954]. Presently there is still not satisfactory match between models and data. More theoretical investigations are presently on going to determine the mechanism which leads to the satellite lines observed in the $^{163}$Ho spectra.

A possible way to remove the uncertainty given by the limited knowledge of the intrinsic amplitude of the lines is to compare the same ratios for the intensities in different isotopes of the same chemical element. As the authors of [959] discussed, the influence of the uncertainties on the intrinsic amplitudes cancel to a large extent. The capture intensity ratios for
<figure><img src="image_54.png" /><figcaption>**Figure 52.** Minimal sterile neutrino mixing matrix element to the square that can be deduced at 90 % confidence level versus the mass $m_4$. The curves are calculated for a total statistics in the spectrum of 10¹³ events under the assumptions that the uncertainties on the absolute atomic mass difference are 1 eV and that the capture probability for each line is perfectly known while the position of the lines is given with an uncertainty of 0.1 eV.</figcaption></figure>

the isotopes 1 and 2 can be written as:

$$ \Theta = \frac{(\lambda_i/\lambda_j)_1}{(\lambda_i/\lambda_j)_2} \qquad (9.16) $$

$$ \Theta = \Theta_{\text{act}} \frac{U_{\text{e4}}^2 \left( H_{1i} \sqrt{1 - \frac{m_4^2}{(Q_{\text{EC1}} - E_i)^2}} - 1 \right) + 1}{U_{\text{e4}}^2 \left( H_{1j} \sqrt{1 - \frac{m_4^2}{(Q_{\text{EC1}} - E_j)^2}} - 1 \right) + 1} \frac{U_{\text{e4}}^2 \left( H_{2j} \sqrt{1 - \frac{m_4^2}{(Q_{\text{EC2}} - E_j)^2}} - 1 \right) + 1}{U_{\text{e4}}^2 \left( H_{2i} \sqrt{1 - \frac{m_4^2}{(Q_{\text{EC2}} - E_i)^2}} - 1 \right) + 1} \qquad (9.17) $$

with

$$ \Theta_{\text{act}} = \left[ \frac{(Q_{\text{EC1}} - E_i)(Q_{\text{EC2}} - E_j)}{(Q_{\text{EC1}} - E_j)(Q_{\text{EC2}} - E_i)} \right] \qquad (9.18) $$

and

$$ H_{ki} = H [(Q_{ECk} - E_i) - m_4] \qquad (9.19) $$

the Heaviside functions to ensure real solutions for the square roots. In [959] two interesting cases have been discussed: the pair $^{157}$Tb-$^{158}$Tb and the pair $^{202}$Pb-$^{205}$Pb. While the calorimetric measurements of $^{157}$Tb and $^{205}$Pb do not present particular difficulties, the analysis of the $^{158}$Tb and $^{202}$Pb spectra is complicated by their decay modes.

In the case of $^{158}$Tb there are two aspects which could complicate the analysis. First of all, a completely calorimetric measurement on the full spectrum can not be performed due to the high $Q_{EC}$-value of about 1.2 MeV. On the other hand, for the important energy range, up to the KI-line, the total energy released in the decay minus the one of the neutrino can be measured, and therefore the study of the effects due to the existence of heavy neutrinos will still be possible after estimating the effects on the spectrum of EC processes of higher energy. A more
important aspect to consider is the fact that $^{158}$Tb undergoes in 16.6 % of the cases a beta decay to $^{158}$Dy. The energy released by the electrons in the microcalorimeters should then be precisely modeled in order to extract the features of the spectrum due to the EC processes.

In the case of the $^{202}$Pb it is important to understand the background in the spectrum due to the partial $\alpha$-decay to $^{198}$Hg and due to fact that the daughter atom following the EC in $^{202}$Pb, $^{202}$Tl, is not stable and decays via $\text{EC}/\beta^+$ to stable $^{202}$Hg.

The cases of $^{158}$Tb and $^{202}$Pb show that decay schemes which are different from the one branch mode, where the daughter atom is a stable nuclide, lead to the presence of additional events in the measured spectra, which do not belong to the interesting EC branch. Therefore, before planning experiments with such nuclides, it is important to characterize the calorimetrically measured spectra related to the different decay modes. In this way the contribution to the background related to these events can be reduced.

On the other hand the calorimetric measurements of the electron capture spectra have an intrinsic background which consists in the un-resolved pile-up events. Such events are generated when two or more EC decays occur within a time interval which is shorter than the rise-time of the detector signal. The fraction of these events is given by the product of the activity in the detector and the rise-time. As was discussed in the case of $^{163}$Ho the reduction of this background leads to a reduced allowed activity in the detectors which in turn leads to a large number of single detectors to host the required activity. The shape of the unresolved pile-up spectrum can be calculated with confidence if all the parameters describing the EC spectrum of the decay under study are also known with confidence. Other sources of background due to natural radioactivity and cosmic rays should also be characterized with high precision and reduced to minimum to avoid that possible structures of the background spectrum could mimic additional counts in one of the interesting lines of the EC spectrum.

The nuclides discussed here, besides the case of $^{163}$Ho, are presently not considered to be employed in large experiments for the search of sterile neutrino signatures. Figure 52 shows, for the different nuclides, the mass region for the heavy sterile neutrino state where the highest sensitivity to the mixing element can be reached. The minimum mixing factors showed in figure 52 are mainly limited by the uncertainties on the $Q_{\text{EC}}$-values. If future observations would indicate that an interesting mass region for the heavy neutrino state would be one of those where the discussed nuclides have higher sensitivity, a different method of analysis should be considered which reduces the effects of the uncertainties on the spectrum parameters. As already demonstrated by the KATRIN collaboration [129] as well as by the ECHo collaboration (see section 9.3.1) the fitting of the kind at $Q_{\text{EC}} - m_4$ leads to higher sensitivity. In this case the uncertainties on the $Q_{\text{EC}}$-value will lead to an uncertainty on the value of $m_4$ while the uncertainty on the mixing element will be related to the precise knowledge of the spectral shape and of the background.

## 9.4 Direct detection

A measurement of *relic sterile neutrinos in the laboratory* will ultimately provide the strongest evidence for this interpretation of the dark matter. Whereas other experiments, e.g. the search for kinks in beta decay spectra, may establish sterile neutrinos as a part of the fundamental theory of Nature, such measurements do not directly assess the role of sterile neutrinos as the dark matter. Similarly astrophysical observations such as X-ray spectroscopy may reveal the dark matter to be an unstable particle, but they leave open the possibility that the dark matter is not a neutrino. Thus it is necessary to explore strategies for the direct detection of relic sterile neutrinos in the laboratory.
### 9.4.1 Direct detection via inverse β decay (authors: Y. Li, W. Liao, and Z. Xing)

One of the most promising methods for direct detection of keV sterile neutrino DM in the laboratory is the captures of cosmic electron neutrinos on radioactive β-decaying nuclei [964, 965]. Through the mixing with the active electron (anti)neutrino $\nu_e(\bar{\nu}_e)$, the DM candidate $N_1$ at the keV mass scale can undergo the capture reactions

$$N_1 + \mathcal{N}(A, Z) \rightarrow \mathcal{N}'(A, Z \mp 1) + e^{\pm}, \qquad (9.20)$$

where A and Z are the mass and atomic numbers of the parent nucleus respectively. The signatures of the capture reactions are measured by the outgoing mono-energetic electrons (positrons), which are located beyond the corresponding β-decay endpoint $Q_β$. A measurement of the distance between the decay and capture processes will directly probe keV sterile neutrino DM and determine or constrain the corresponding mass and mixing parameters. It should be noted that similar capture methods have been considered for detection of the cosmic neutrino background [966–970].

The differential capture rate of keV sterile neutrino DM is the product of the capture cross-section times neutrino velocity (i.e., $\sigma_\nu \times v_\nu$), the neutrino number density (i.e., $n_\nu$), and the squared norm of the active-sterile mixing (i.e., $|U_{e4}|^2$). Among the above mentioned factors, the cross-section times neutrino velocity can be derived as [966]

$$\sigma_{\nu} \times v_{\nu} = \frac{2\pi^2}{\mathcal{A}} \cdot \frac{\ln 2}{T_{1/2}}, \qquad (9.21)$$

where $\mathcal{A}$ is the nuclear factor and $T_{1/2}$ the half-life of the decaying nuclei, respectively. $\mathcal{A}$ is the function of the neutrino energy and characterized by $Q_β$ and Z. Here the half-life $T_{1/2}$ is introduced to express the nuclear matrix element of this process using the experimental data of the associated beta decay, which is of the same energy scale as the process under discussion.

Assuming the mass density of DM around the Earth is 0.3 GeV cm⁻³ [171], we can calculate the DM number density as $n_\nu \simeq 10^5$ (3 keV/m₄) cm⁻³, where m₄ is the mass of the sterile neutrino DM candidate. The estimation of the mixing parameter $|U_{e4}|^2$ depends on the production mechanisms at the early Universe. A search for the X-ray flux from the radiative decay of $N_1$ can set a model-independent bound as follows:

$$|U_{e4}|^2 \lesssim 1.8 \times 10^{-5} \left( \frac{1 \text{ keV}}{m_4} \right)^5 . \qquad (9.22)$$

Finally another important factor for the nuclei candidate selection is the average target number during the detecting time interval t,

$$\bar{N}_{\text{T}} = N(0) \cdot \frac{1}{\lambda t} \cdot (1 - e^{-\lambda t}), \qquad (9.23)$$

where $N(0)$ is the initial target number at $t = 0$ and $\lambda = \ln 2/T_{1/2}$.

To maximize the observability of the neutrino capture process, one should find the nucleus candidate with a larger cross-section times neutrino velocity, and require the half-life to be at least compatible with the exposure time. Therefore, we consider the ruthenium (¹⁰⁶Ru) and tritium (³H) nuclei as the candidate targets to capture keV sterile neutrino DM. The typical values of $Q_β$, $T_{1/2}$ and $\sigma_\nu \times v_\nu$ for these two kinds of nuclei are quoted as follows [966]: $Q_β = 39.4$ keV, $T_{1/2} = 3.2278 \times 10^7$ s and $\sigma_\nu \times v_\nu = 5.88 \times 10^{-45}$ cm² for ¹⁰⁶Ru
<figure><img src="image_55.png" /><figcaption>**Figure 53.** The keV sterile neutrino capture rate as a function of the kinetic energy of electrons with $^{106}$Ru (left panel) and $^{3}$H (right panel) as the capture targets [965]. The solid (or dotted) curves denote the signals with (or without) the half-life effect.</figcaption></figure>

or $Q_β = 18.59$ keV, $T_{1/2} = 3.8878 \times 10^8$ s and $\sigma_ν \times v_ν = 7.84 \times 10^{-45}$ cm$^2$ for $^{3}$H. Taking 10 kg $^{3}$H and 1 ton $^{106}$Ru as the target masses, and assuming $m_4 = 2$ keV and $|U_{e4}|^2 \simeq 5 \times 10^{-7}$, we calculate the event rates of $^{106}$Ru and $^{3}$H respectively as

$$R^{\text{keV}}(1 \text{ ton } ^{106}\text{Ru}) \simeq 1.8 \text{ year}^{-1}, \quad R^{\text{keV}}(10 \text{ kg } ^{3}\text{H}) \simeq 1.3 \text{ year}^{-1}. \qquad (9.24)$$

Next we shall discuss the relevant backgrounds for neutrino capture signals. The corresponding $\beta$-decay events can extend to higher energy regions due to the finite energy resolution, and therefore mimic the desired neutrino capture signals. To suppress the $\beta$-decay background, the energy resolution $\Delta$ (i.e., full width at half maximum) should be smaller than $m_4/4$, which is $\Delta \lesssim 0.5$ keV for the above assumption of $m_4 = 2$ keV. In the numerical illustration of figure 53, we take $\Delta = 0.4$ keV as an example, and present the keV sterile neutrino DM capture rate as a function of the kinetic energy of electrons with $^{106}$Ru (left panel) and $^{3}$H (right panel) as the capture targets [965]. The solid (or dotted) curves denote the signals with (or without) the half-life effect. The lifetime effect is negligible for $^{3}$H, but important for $^{106}$Ru. It can reduce around 30% of the capture rate on $^{106}$Ru.

Another potential background is the electron events produced by the scattering of low energy solar pp neutrinos with electrons in the target matter [971]. Taking account of the bound state features of orbital electrons in the $^{106}$Ru atom, one can estimate the background rate of $^{106}$Ru as [971]

$$R^{pp}(1 \text{ ton } ^{106}\text{Ru}) \simeq 0.02 \times \frac{\Delta}{10 \text{ eV}} \text{ year}^{-1}. \qquad (9.25)$$

In comparison, the background rate of $^{3}$H is two orders of magnitude smaller because of the much smaller target mass of $^{3}$H. From eq. (6), one find a better energy resolution is desirable to suppress the scattering background of solar pp neutrinos. The background generated by captures of low energy solar pp neutrinos on $^{106}$Ru or $^{3}$H is $10^{-3}$ per year [964] for the target masses of eq. (5), and is negligible in our studies.

As can be seen in the nuclear factor $\mathcal{A}$ of eq. (2), a great virtue of the neutrino capture reaction is that the energy scale of this process is determined by the energy release of the corresponding $\beta$-decay, not by the mass of keV sterile neutrino DM, i.e., $\sigma_ν \propto p_e E_e$, where
$p_e$ and $E_e$ are the momentum and energy of the outgoing electron respectively, with $E_e = m_e + Q_\beta + m_4 \approx m_e + Q_\beta$. As a consequence, the cross section of this process can be several orders of magnitude larger than the neutrino scattering process $N_1 + e^- \to \nu_i + e^-$ ($i = 1, 2, 3$), in which the energy scale is characterized by the mass of keV sterile neutrino DM [972, 973]. $\beta$-decaying nuclei can only be used to capture the neutrino component of DM. One need consider the electron-capture decaying nuclei as possible capture targets of keV sterile antineutrino DM. In this regard the isotope $^{163}$Ho is an interesting candidate [974]. A signal rate of one per year requires a target mass of 600 ton $^{163}$Ho in assumption of $m_4 = 2$ keV and $|U_{e4}|^2 \simeq 5 \times 10^{-7}$. One should stress that captures of both the neutrino and antineutrino components are important to test the symmetric or asymmetric nature of the warm DM candidate, which is otherwise impossible with only the $\beta$-decaying nuclei.

In summary, we have discussed direct detection of keV sterile neutrino DM using $\beta$-decaying or electron-capture decaying nuclei. We calculated the capture signal rates for the $^{106}$Ru and $^{3}$H nuclei and identified the main sources of backgrounds. We stress that although the current experimental approach meets several technical challenges, but it should not be hopeless in the long run.

## 9.4.2 Prospects for sterile neutrino dark matter direct detection (author: A.J. Long)

Two strategies for direct detection will be discussed: neutrino conversion on atomic electrons and neutrino capture on beta decaying nuclei. Conversion refers to the scattering $\nu_4 + e^- \to \nu_i + e^-$ in which a sterile neutrino (heavy mass eigenstate) $\nu_4$ becomes an active neutrino (light mass eigenstate) $\nu_i$, and the signal is an electron that recoils with momentum of order the sterile's mass $p_e \approx m_4$. Capture may occur when a neutrino is incident on a beta decaying nucleus, $\nu_4 + N(A, Z) \to e^- + N'(A, Z+1)$, and the signal is a peak in the beta decay spectrum at $\Delta E_e \approx m_4$ above the endpoint. The leading-order Feynman graphs are shown in figure 54.

The prospects for relic sterile neutrino detection through the neutrino conversion process was studied by Ando & Kusenko (2010) [972]. In the laboratory frame, the spin-averaged scattering cross section is given by [972]

$$ \sigma_{\text{conv}} = Z^2 \frac{G_F^2 |U_{e4}|^2}{2\pi v} m_4^2 (c_V^2 + 3c_A^2), \qquad (9.26) $$

where $v \sim 10^{-3}c$ is the sterile neutrino velocity, and the active-sterile mixing is assumed to be dominated by the matrix element $U_{e4}$. Averaging the spin of the non-relativistic neutrino $\nu_4$ brings a factor of 1/2 that had not been included in ref. [972]. The momentum transfer is $p_e \approx m_4$, and if the corresponding de Broglie wavelength exceeds the atomic radius, $h/(p_e) \gtrsim 10^{-8}$ cm or $m_4 \lesssim O(10 \text{ keV})$, then the neutrino interacts coherently with all the electrons in the atom, which enhances the cross section by a factor of the squared atomic number, $Z^2$.

Consider an experiment consisting of $N$ target atoms that each have atomic number $A$, and thus the total mass of the target is $M \approx NAu$ with $u$ the atomic mass unit. The rate of sterile neutrino conversions is given by $\Gamma_{\text{conv}} \approx \sigma_{\text{conv}}vn_4N$ where $n_4$ is the density of $\nu_4$ at the Earth. If sterile neutrinos make up all of the dark matter, then $n_4 \approx \rho_{\text{DM}}/m_4$ where $\rho_{\text{DM}} \simeq 0.3 \text{ GeV cm}^{-3}$ is the local dark matter energy density inferred from stellar motions [975]. The expected signal rate at a Xenon-based detector ($Z_{\text{Xe}} = 54$ and $A_{\text{Xe}} = 131$) using $M \approx 1000$ kg of target material is approximately

$$ \Gamma_{\text{conv}} \approx (0.5 \text{ yr}^{-1}) \left( \frac{|U_{e4}|^2}{10^{-6}} \right) \left( \frac{m_4}{10 \text{ keV}} \right) \left( \frac{Z}{54} \right)^2 \left( \frac{A}{131} \right)^{-1} \left( \frac{M}{10^3 \text{ kg}} \right). \qquad (9.27) $$
<figure><img src="image_56.png" /><figcaption>**Figure 54.** The leading order Feynman graphs contributing to the neutrino conversion (1a and 1b) and neutrino capture (2) processes.</figcaption></figure>

The recoiling electron carries a kinetic energy $T_e \approx m_4^2/(2m_e) \approx (98 \text{ eV})(m_4/10 \text{ keV})^2$. With sufficient energy, the electron can ionize nearby atoms producing a detectable signal. It has recently been suggested that a WIMP direct detection experiment could have sensitivity to sterile neutrino dark matter in this channel [885].

The capture of neutrinos on beta decaying nuclei was originally proposed as a strategy to measure the cosmic neutrino background [976, 977]. The same channel may be used to detect the heavier sterile neutrinos, and this possibility has been explored recently by refs. [964, 965, 968]. In the laboratory frame, the spin-averaged cross section for neutrino capture is given by [978]

$$ \sigma_{\text{cap}} = |V_{ud}|^2 F(Z, E_e) \frac{G_F^2 |U_{e4}|^2}{2\pi v} E_e p_e \left( \langle f_F \rangle^2 + (g_A/g_V)^2 \langle g_{GT} \rangle^2 \right). \quad (9.28) $$

Here $V_{ud} \approx 0.974$ is the first element of the CKM matrix, $F(Z, E_e) \approx 1$ is the Fermi function, and the parenthetical factor contains combinations of nuclear matrix elements that evaluate to $\approx 5.5$. The cross section in eq. (9.28) differs by a factor of two from earlier calculations [966, 967], and it can be understood to arise from the non-relativistic nature of the neutrinos [978]. Reference [966] surveyed various beta-decaying nuclei and found that tritium is favorable for a neutrino capture experiment because of its relatively large cross section ($\sigma_{\text{cap}} \approx (4 \times 10^{-45} \text{ cm}^2)|U_{e4}|^2(c/v)$ for $m_4 \lesssim Q_\beta \approx 18.6 \text{ keV}$) and long lifetime ($\tau \approx 12 \text{ yr}$). We will focus on this case for the following discussion. In an experiment using $M_T \approx 10 \text{ kg}$ of tritium for target material, the expected capture rate is

$$ \Gamma_{\text{cap}} \approx (0.3 \text{ yr}^{-1}) \left( \frac{|U_{e4}|^2}{10^{-6}} \right) \left( \frac{m_4}{10 \text{ keV}} \right)^{-1} \left( \frac{M_T}{10 \text{ kg}} \right). \quad (9.29) $$

In comparing neutrino conversion and neutrino capture, eq. (9.27) and (9.29), the former is better suited to the detection of heavy neutrinos and the latter to lighter ones. It should be noted that the fiducial detector size, $M_T \approx 10 \text{ kg}$, represents a significant fraction of the global tritium supply, but since most tritium is manmade the amount can increase in the future.

In a neutrino capture experiment, one would seek to measure the beta decay spectrum, and the signal of the relic sterile neutrinos would be a peak in the spectrum at an energy $\Delta E_e \approx m_4$ above the beta decay endpoint. Such a measurement poses a number of experimental challenges. First, the electron energy must be measured sufficiently precisely so as to distinguish the signal electrons from the background of beta decay electrons. The energy resolution of the detector should satisfy $\delta E_e \lesssim m_4$ [966, 967, 978]. Second, efforts should be made
to detect every capture event since the signal rate is expected to be low. This concern favors an experimental design with large angular coverage. Additionally it disfavors a cut-and-count strategy, such as measuring the spectrum with a MAC-E filter, which might eliminate potential signal. Third, solar pp neutrinos will scatter from atomic electrons producing a smooth component to the beta decay spectrum that extends above the endpoint. Generalizing the result of ref. [971] for tritium, the rate of pp background events in an energy bin of width $\Delta E_e$ is estimated as $\Gamma_{pp} \sim (10^{-4} \text{yr}^{-1})(\Delta E_e/10 \text{eV})(M_{\text{T}}/10 \text{kg})$. This background is smaller than the signal rate in eq. (9.29) provided that $|U_{e4}|^2 \gtrsim 10^{-10}(m_4/10 \text{keV})$.

Perhaps the most confounding experimental challenge is the issue of backscatter. While backscatter is already a problem for beta decay experiments aiming to measure the endpoint with high precision, the problem is only exacerbated for a neutrino capture experiment, which requires many more nuclei to act as target material. After the capture event has occurred, the recoiling electron might scatter on one (or many) of the tritium atoms before reaching the detector where its energy is measured. The cross section for inelastic electron-tritium scattering is $\sigma_{eT} \sim 10^{-18} \text{cm}^2$ [902] and assuming a homogenous gas of tritium in cubical volume $L^3$, the mean free path is given by $\lambda = 1/(\sigma_{eT}n_{\text{T}}) \sim (10^{-4}\text{cm})(L/100\text{cm})^3(M_{\text{T}}/10\text{kg})^{-1}$. If $\lambda \gg L$ a large number of scatterings can occur, and their collective effect is to broaden the electron spectrum. Determining an acceptable degree of broadening depends on a number of factors, such as the anticipated signal rate, background rate, and energy resolution. Even if the electron-tritium scattering is avoided, one may worry about the scattering of signal electrons on the beta decay electrons, which are produced at a rate $\sim 10^{18} \text{s}^{-1}(M_{\text{T}}/10 \text{kg})$.

For both the conversion and capture processes discussed here, the scattering cross section is inversely proportional to the relative neutrino-detector velocity, i.e. $\sigma \propto 1/v$ in eqs. (9.26) and (9.28). This should be contrasted with the elastic scattering of a weakly interacting massive particle (WIMP) on a nucleus for which the cross section is independent of $v$. Unlike WIMP scattering, the predicted neutrino signal rates in eqs. (9.27) and (9.29) are insensitive to the velocity distribution of sterile neutrinos in the galaxy (halo model). For the same reason, the capture rate is not expected to display an annular modulation due to the relative motions of the Earth and the solar system [967].

In closing, it should be noted that the fiducial neutrino mass and mixing used here, $m_4 \simeq 10 \text{ keV}$ and $|U_{e4}|^2 \simeq 10^{-6}$, are already excluded by X-ray observations, which impose $|U_{e4}|^2 \lesssim 10^{-10}$ at $m_4 \simeq 10 \text{ keV}$. The X-ray bound weakens for lighter neutrinos, $|U_{e4}|^2 \lesssim 10^{-5}$ at $m_4 \simeq 1 \text{ keV}$, where the allowed region of parameter space may be probed using the neutrino capture strategy. Nevertheless, a direct detection even in the excluded parameter regime would be an interesting possibility: not only would it provide evidence for the sterile neutrino interpretation of dark matter, but it would also hint at new physics, which is required to bring the measurement in agreement with the X-ray bounds.

## 9.5 Search for heavy sterile neutrinos with SHiP (author: R. Jacobsson on behalf of SHiP)

The keV range sterile neutrino is a cornerstone in the νMSM [186, 188, 189] which is one of the models that will be explored by the Search for Hidden Particles (SHiP) experiment. The νMSM is a low-scale seesaw model which is based on introducing three right-handed sterile neutrinos, also referred to as Heavy Neutral Leptons. It assumes masses for the sterile neutrinos which are similar to those in the quark and charged lepton sector. The keV range sterile neutrino provides a decaying form of dark matter. The other two sterile neutrino are in the GeV range allowing them to produce the expected pattern of neutrino flavor
oscillations and masses, and allowing them to generate baryon asymmetry of the Universe via leptogenesis. In order to guarantee sufficient production of keV sterile neutrinos at around temperatures of 100 MeV in the Universe, the heavier sterile neutrinos are required to produce a large lepton asymmetry which survives down to these temperatures. This allows making a natural connection in the $\nu$MSM between the GeV masses for the two heavier sterile neutrinos and the constraints on the keV DM sterile neutrino. In these respects the $\nu$MSM is one of the most economical extensions of the Standard Model which simultaneously allows accounting for neutrino masses and oscillations, baryogenesis, and dark matter.

In the $\nu$MSM the sterile-active neutrino mixing leads to production of the heavier sterile neutrinos in weak decays of hadrons, making them accessible in an accelerator based experiment. The same mixing gives rise to decays to SM particles. As a consequence of the small mixing angles allowed in the $\nu$MSM and the interesting mass range, the lifetimes are in the order microseconds to milliseconds. For the keV sterile neutrinos, the upper limit on the Yukawa coupling means that its production is completely negligible in an accelerator based experiment.

More generally, the $\nu$MSM is part of a large class of models [402] with portals to a Hidden Sector which addresses the shortcomings of the Standard Model including inflation, the hierarchy problem etc, without involving a new scale. Instead they are based on introducing very weakly interacting particles such as Majorana leptons, dark photons, dark scalars or axion-like particles (ALPs) with masses below the electroweak scale. Even in the scenarios in which BSM physics is related to high mass scales such as SUSY, many models contain degrees of freedom with suppressed couplings that stay relevant at much lower energies. For example, in the extensively studied MSSM, the existence of light neutralinos and some other light SUSY particles has not been excluded. Motivated by dark matter phenomenology, hidden sectors have also been introduced in weak-scale supersymmetric models with gauge mediated or gravity mediated SUSY breaking. If the SUSY breaking feeds into the hidden sector only via some suppressed mechanism such as gauge kinetic mixing, a GeV scale mass spectrum for the hidden sector may be dynamically generated [979, 980].

Given the small couplings and mixings, and hence typically long lifetimes, the hidden particles have not been significantly constrained by previous experiments, and the reach at current experiments is limited by both luminosity and acceptance. The strongest bounds on the interaction strength of new light particles exist up to the mass of the kaon. Above this scale the bounds weaken significantly. SHiP is a new type of intensity frontier experiment motivated by the possibility of searching for any type of hidden particles with masses from sub-GeV up to $\mathcal{O}(10)$ GeV with super weak couplings down to $10^{-10}$. Consequently, SHiP has also a complementary sensitive to a part of the SUSY low-energy parameter space.

As with the GeV range sterile neutrino, many of the hidden particles in the same mass range are produced in the decays of heavy hadrons. In addition, the coupling of the dark photons and the ALPs to gauge bosons means that they may also be produced through photons: dark photons from proton bremsstrahlung, electromagnetic decays of mesons, as well as through direct QCD production, and ALPs through Primakoff production.

The key experimental parameters in the phenomenology of the Hidden Sector models are relatively similar. This allows a common optimization of the design of the experimental facility and of the SHiP detector (figure 55) [981]. Since the hidden particles are expected to be predominantly accessible through the decays of heavy hadrons and photon interactions, the facility is designed to maximize their production and the detector acceptance while providing the cleanest possible environment. The proposal locates the SHiP experiment on a new beam
<figure><img src="image_57.png" /><figcaption>**Figure 55.** Overview of the SHiP experimental facility.</figcaption></figure>

extraction line which branches off from the CERN SPS transfer line to the North Area. The high intensity of the 400 GeV beam and the unique operational mode of the SPS provide ideal conditions. The current design of the experimental facility and the estimates of the physics sensitivities assume the SPS accelerator in its present state. Sharing the SPS beam time with the other SPS fixed target experiments and the LHC allows producing $2 \times 10^{20}$ protons on target in five years of nominal operation. In order to maximize charm and beauty production, and the production and interactions of photons, while minimizing the neutrino background from pions and kaons, the choice of the target material is driven by the requirement of high atomic mass number, high atomic number, and short interaction length. Currently the target is a hybrid design of a molybdenum alloy and pure tungsten. As a result, with $2 \times 10^{20}$ protons on target, the expected yields of different hidden particles greatly exceed those of any other existing or planned facility in decays of both charm and beauty hadrons.

The target is followed by a hadron stopper and an active muon shield which deflects the high flux of muon background away from the detector. The detector for the hidden particles is designed to fully reconstruct their exclusive decays and to reject the background down to below 0.1 events in $2 \times 10^{20}$ protons on target. The detector consists of a large magnetic spectrometer located downstream of a 50m long and 5m × 10m wide decay volume. In order to suppress the background from neutrinos interacting in the fiducial volume, it is maintained under vacuum. The spectrometer is designed to accurately reconstruct the decay vertex, the mass, and the impact parameter of the decaying particle at the target. A set of calorimeters and muon chambers provide identification of electrons, photons and muons, and pions. A dedicated high resolution timing detector measures the coincidence of the decay products which allows rejecting combinatorial backgrounds. The decay volume is surrounded by background taggers to veto neutrino and muon inelastic scattering in the surrounding structures which may produce long-lived SM $V^0$ particles, such as $K_L$ etc.
<figure><img src="image_58.png" /><figcaption>**Figure 56.** Sensitivity to the heavier sterile neutrino (HNL) as function of the mass in the scenario with inverted mass hierarchy for the active neutrinos and Yukawa couplings with electron flavour dominance [981]. The region left of the “BBN” line is excluded by constraints from primordial nucleosynthesis, the region below the “seesaw” line is inconsistent with neutrino oscillation data. The baryon asymmetry of the universe can be explained in the region between the “BAU” lines, The green lines indicate upper bounds from past experiments. An updated global analysis of these constraints can be found in ref. [982].</figcaption></figure>

With $2 \times 10^{20}$ protons on target, the experiment is able to achieve sensitivities which are up to four orders of magnitude better than previous searches. As shown in figure 56, for sterile neutrinos below the mass of the D-meson, SHiP can probe the cosmologically interesting region of parameters and approach the lower limit in couplings, determined by the neutrino oscillations. Such an experiment would clearly be an essential complement to the searches for Dark Matter in astroparticle physics experiments and for new physics in accelerator based experiments.
10 Discussion — pro and cons for keV neutrino as Dark Matter and perspectives

Section Editors:

Marco Drewes, Thierry Lasserre, Alexander Merle, Susanne Mertens

Although well established by many astrophysical observations the nature of Dark Matter (DM) still remains a mystery. Only a modest fraction of (hot) DM is made of neutrinos and the Standard Model (SM) of elementary particle physics does not provide any relevant non-baryonic candidate. Hence theories beyond the SM have to be explored.

The most popular candidates are Weakly Interacting Massive Particles (WIMPs), often associated with 100 MeV–10 TeV neutralinos in supersymmetric extensions of the SM. So far, no direct DM search experiment has conclusively reported any WIMP detection but the experimental methods are progressing fast. Indeed, direct detection experiments may exclude WIMPs as a relevant DM candidate in the coming years. This hypothetical but plausible scenario is adding a further motivation for in-depth investigation of alternative DM candidates.

In this White Paper we have attempted to provide an up-to-date comprehensive document reviewing the case of keV-scale sterile neutrinos as DM candidates. In particular we cross-linked the expertise from astrophysicists, cosmologists, nuclear and particle physicists, reviewing particle physics theories as well as cosmological models, and confronting them with astrophysical observations.

What is the current situation?

Sterile neutrinos could indeed account for the DM. Section 2 shows that their existence is well motivated in several extensions of the SM. These new elementary particles act as right-handed neutral fermions only interacting through their mixing with active neutrinos (expected to be tiny, however) or if further new particles exist to which they could couple. Although right-handed neutrinos are well-motivated, no theory can predict their exact mass scale. It is an important point to underline that the DM relevant keV-scale only arises when taking into account astrophysical and cosmological considerations.

Over the past 15 years a robust cosmological model has been established, combining the theory of the General Relativity and the SM of elementary particles. This model includes a DM component which is still unknown but characterized by its lack of electromagnetic interaction. Its velocity dispersion is not too large, which is why it is typically assumed to be cold DM (CDM) — although in fact we have not sufficient observational evidence to conclude anything beyond DM not being hot. Finally, to reproduce all large-scales observations, a non-vanishing vacuum energy is mandatory, leading to the so-called ΛCDM cosmological model. Section 3 first reviews the role of the three standard model neutrino flavors in this cosmological framework and then discusses the consequences of incorporating sterile neutrinos. Indeed cosmology could accommodate for their existence, especially at the keV-scale and beyond.

In relation to keV-scale sterile neutrino motivations, the entanglement between the type of DM (particularly its velocity) and the formation of structures in the Universe, at all-scales, is of upmost importance. While the current cosmological model perfectly fits the data for galaxy clusters and scales beyond, section 4 discusses observational at galactic scales and their comparison with the ΛCDM predictions. In CDM models every DM halo contains ever increasing number of smaller and smaller mass substructures. However, when compared to observations some discrepancies arise at scales smaller than 10 kpc. Too few
dwarf satellite galaxies are yet observed compared to what CDM settings predict, leading to the so-called missing satellite problem. Furthermore, the number of the largest dwarf satellite galaxies is less than expected from CDM-based simulations, making the astrophysical feedback explanation problematic and leading to the too-big-to-fail issue. Finally, some observations seem to favor a galactic center with a cored profile, while CDM simulations predict a cuspy matter distribution with a large rise in matter density at the innermost regions. Although astrophysical feedback effects or refinement of the simulations to fully include baryonic feedback could perhaps solve these CDM issues, as-of-yet no consensus has been reached in the community. Interestingly, the apparent discrepancy could also arise from alternative DM physics if the candidate particle velocity distribution is not cold but rather warm or even non-thermal. This fact motivates the keV mass scale for sterile neutrinos, as it marks a departure from the standard CDM scenario.

Astrophysical observations strongly constrain sterile neutrino DM, as shown in section 5. The solid Tremaine-Gunn bound indicates that sterile neutrinos need to have masses greater than ~0.5 keV. Putting aside the tentative signal for now, another strong astrophysical bound comes from the non-observation of the monoenergetic X-rays induced by the decay of sterile neutrinos. This limit generically forces the relevant mass range to be within a few tens of keV. Nevertheless, as just hinted, two groups have independently reported a hint for a 3.5 keV X-ray emission line that could be related to a 7 keV relic sterile neutrino with an active-sterile mixing angle of $sin^2(2\theta) \sim 10^{-10}$, a tiny value that has important consequences when it comes to experimental considerations. This observation, at the cutting edge of the best X-ray telescope sensitivities, is being discussed and debated meticulously in section 5.3.2. Further interesting constraints arise from the analysis of Lyman-$\alpha$ forest data. These bounds however rely heavily on the actual DM velocity spectrum, as they ultimately track the structures grown in space. The reader should be aware that, in some of models, the DM velocity spectrum significantly deviates from a thermal spectrum. Consequently, keV-sterile neutrinos could act as warm, cool, or even cold DM, thus possibly circumventing current Lyman-$\alpha$ constraints and/or X-ray bounds, as published.

Section 6 reviews how sterile neutrinos could have been produced in the early Universe, within the framework of extensions of the Standard Models of particle physics and cosmology. The so-called Dodelson-Widrow (DW) mechanism is the simplest way to produce sterile neutrinos, but in contradiction to astrophysical observations. However, resonantly enhanced oscillations in the early Universe driven by a net lepton number asymmetry in the early Universe (Shi-Fuller mechanism) are easier to bring into accordance with observations, and they could also explain the 3.5 keV X-ray signal. Another alternative relies in the decay of a new particle at early times. This could be the inflaton or also a more general electrically neutral or charged particle that may be produced from the primordial plasma. Again, current X-ray and Lyman-$\alpha$ bounds could be evaded for some of these alternative production mechanisms. Finally, beyond the SM of elementary particle physics, thermal production of sterile neutrinos could have happened if accompanied with a strong subsequent entropy dilution. The important message of this section is that several possibilities beyond ordinary thermal freeze-out do exist to produce sterile neutrino DM. They may partially lead to rich non-thermal spectra beyond the simple cold, warm, or hot scenarios. While this complicates the conversion of the astrophysical observables into sterile neutrino mass and mixing parameters, it may also help to distinguish between the various models.

Section 7 turns to particle physics, discussing mechanisms generating keV-scale sterile neutrinos. Typically this scale it not only regarded as “unnatural”, but it is also not desired
for all the sterile neutrinos in order to match the phenomenology of active neutrino masses and mixings. This is achieved by forcing the mass of only one sterile neutrino to be smaller than those of the others, either by perturbing a framework in which this mass is naturally zero or by suppressing one mass compared to the others. Different models achieving a suitable mass spectrum exist in the literature. The most interesting ones link the properties of the sterile neutrinos to those of the active neutrinos, e.g. by predicting correlations between light neutrino observables, such that a more precise determination of the neutrino oscillation parameters could be used to indirectly test sterile neutrino scenarios.

The final sections look at the current and future searches for keV-scale sterile neutrinos, both with astrophysical (section 8) and with laboratory (section 9) experiments. On the astrophysical side, two direct observations are extremely promising: X-ray searches and the Lyman-α forest data. Both are going to be improved significantly in the near future, with the delivery of new data awaited from more sensitive instruments. But the interpretation of these results could still remain somewhat ambiguous, since it ultimately relies on the DM model being considered. Other indirect observations may further constrain the current panorama, like pulsar kicks or supernova explosions, but they unfortunately lack a smoking gun signature to corroborate any positive detection. While many experiments are currently searching for WIMPs, there is no ground-based laboratory to test the existence of keV sterile neutrinos of cosmological interest. However, several studies or R&D have been initiated in this direction. In particular experiments based on single beta decays, electron capture, or neutrino capture processes could probably reach reasonable sensitivities, although only at the upper bound of the cosmologically relevant region in terms of mixing. Nevertheless future experimental advances may lead to serious new insights into the field in the future, but the question remains open whether a laboratory searches could eventually explore sterile neutrino mixings of less than 1 part per million.

In this White Paper we have presented state-of-the-art insights and we have summarized different viewpoints, sometimes conflicting within the community. A summary of all generic constraints on keV sterile neutrino DM is presented in figure 57. The figure shows the $sin^2(2\theta)-M_1$ plane, where the sterile neutrino mass $M_1$ is displayed in units of keV and the total mixing angle is defined by $\theta^2 = \sum_{\alpha=e,\mu,\tau} |\theta_{\alpha 1}|^2$. The strongest bound on $sin^2(2\theta)$ is derived from the non-observation of X-ray photons from sterile neutrino decay (e.g. [345-347, 485, 572, 602, 616, 617]), see sections 5.3, 8.1, and 8.2 for a complete list of references). This excludes the region above the green line. For very small sterile neutrino masses, the main upper bound on the mixing angle arises from not producing too much DM by non-resonant production [177, 320], cf. sections 6.1 and 6.2. The correct DM density is produced for any combination of $M_1$ and $sin^2(2\theta)$ along the yellow-gold line, above this line DM is overproduced. Weaker bounds arise from constraints on the effective number of relativistic species $N_{\text{eff}}$ at the time of CMB decoupling (“dark radiation”, red dashed line) [1]. A deviation of $N_{\text{eff}}$ from its SM prediction $N_{\text{eff}} = 3.046$ [262] appears in case the keV sterile neutrino is not actually DM, but instead decays into some type of invisible radiation (e.g., lighter sterile neutrinos) [983]. This region is in fact contained in the parameter space, as for large enough active-sterile mixing, already the decay modes $N_1 \to 3\nu$ and $N_1 \to \nu\gamma$ induced by active-sterile mixing enforce a sterile neutrino lifetime smaller than the age of the Universe (black dashed line). The most optimistic regions for the KATRIN/TRISTAN [908, 909] (purple line, cf. section 9.2) and ECHo [959] (brown line, statistical sensitivity for 3 years, cf. section 9.3) are displayed, this time assuming that the full mixing is contained in the electron sector ($\theta = \theta_{e1}$). The newest idea for a possible lab detection is based on relic keV
<figure><img src="image_59.png" /><figcaption>**Figure 57.** Summary of experimental and observational constraints on keV sterile neutrino Dark Matter.</figcaption></figure>

sterile neutrinos enabling sterile neutrino capture transitions of the otherwise *stable* isotope Dy-163 [984], which may be the most promising given that it is scalable without the use of radioactive material. Example sensitivities are indicated by the blue lines in the plot.

The most model-independent constraint on $M_1$ comes from the phase space constraint on fermionic DM [311, 312], i.e., from the Tremaine-Gunn bound [75], see the gray-shaded area on the left of the plot (this bound becomes stronger when a particular production mechanism is assumed, see [311]). Taking into account the Lyman-$\alpha$ forest data (see section 8.3), the lower bound can be considerably strengthened. These tighter bounds, however, have theoretical and observational uncertainties [59, 331, 538]. In particular, at small scales the neutral hydrogen stops following the underlying DM distribution due to its pressure and temperature. The limits on non-cold DM settings thus become strongly degenerate with the temperature of the intergalactic medium that has not been independently constrained at high redshifts [538]. By the orange dashed lines, we indicated bounds based on the Lyman-$\alpha$ constraints based on [538], with primordial distribution functions from scalar decay production, see section 6.3 [663, 664, 670, 686, 730, 747] and resonant production [314, 316, 317, 691], see sections 6.1 and 6.2. If in the future the temperature of the intergalactic medium will be measured (e.g. via the broadening of individual lines, [867]) and found sufficiently high, the considerably stronger bounds from [331] would be applicable (found e.g. in [740]). The bounds from halo counting (comparison between the observed number of dwarf satellite galaxies around the Milky Way and theoretical predictions) provide restrictions on sterile neutrino parameters, similar to those from the Lyman-$\alpha$ bounds shown in figure 57. However, such bounds have intrinsic systematic uncertainty, due to the strong scatter in galactic halo realizations in numerical simulations (see e.g. the discussion in [534, 535]) and the fact that we do not know observationally how typical the Milky Way (or the Local Group) and its satellite distribution is.
We note in passing that the statement in the recent paper from NuSTAR [621] of these bounds practically closing the parameter space for sterile neutrino Dark Matter is clearly too strong, as such a bound depends on the production mechanism. Since resonant production is driven by the presence of a lepton asymmetry in the primordial plasma that is much larger than the baryon asymmetry, a lower bound on $sin^2(2\theta)$ can in principle be derived by estimating the asymmetry that can realistically be generated [398] and is consistent with known constraints from BBN [261, 985]. We do not display such a bound because the lepton asymmetry is strongly model-dependent. Based on the results displayed here, scalar production leads to slightly cooler spectra — hence the less restrictive lower bounds on $M_1$ for that production mechanism. This means that, if the 3.5 keV line signal survives after all, or if a new signal shows up, one could possibly distinguish the different production mechanisms by constraints from cosmic structure formation [688].

We would like to end this journey by emphasizing that the field of keV-scale sterile neutrino DM is still in development. Many observations, simulations, or theoretical results have to be clarified and it remains an open question whether keV-scale sterile neutrinos exist and if they account for a significant part of the DM in the Universe. Our common goal for the future shall thus be to continue improving the current picture by corroborating theoretical and observational information from all sides: nuclear and particle physics, astrophysics, and cosmology.
Acknowledgments

The work of C. Giunti was partially supported by the research grant Theoretical Astroparticle Physics number 2012CPPYP7 under the program PRIN 2012 funded by the Ministero dell'Istruzione, Università e della Ricerca (MIUR). The authors of section 2 would like to thank A. Vincent for discussion and comments. The work of A. Mirizzi is supported by the Italian Ministero dell'Istruzione, Università e Ricerca (MIUR) and Istituto Nazionale di Fisica Nucleare (INFN) through the "Theoretical Astroparticle Physics" projects. The work of A. Ibarra was supported in part by the DFG cluster of excellence "Origin and Structure of the Universe" and by the ERC Advanced Grant project "FLAVOUR" (267104). M. Viel is supported by the ERC StG "cosmoIGM". The work of O. Dragoun was supported by the GACR (contract P203/12/1896) and the ASCR (contract IRP AV02 10480585). This work was supported in part by the Gottfried Wilhelm Leibniz Programme of the Deutsche Forschungsgemeinschaft (DFG) and the NSF grant PHY-1307372 at UCSD. M. Laine was supported in part by the Swiss National Science Foundation (SNF) under grant 200020-155935. A. Merle acknowledges partial support by the Micron Technology Foundation, Inc. V. Niro acknowledges support by Spanish MINECO through project FPA2012-31880, by Spanish MINECO (Centro de excelencia Severo Ochoa Program) under grant SEV-2012-0249 as well as the Spanish grants FPA2014-58183-P, Multidark CSD2009-00064 and SEV-2014-0398 (MINECO) and by the PROMETEOII/2014/084 grant from Generalitat Valenciana; the work of V. Niro was also supported by the Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Centre SFB 676 "Particles, Strings and the Early Universe" (through an SFB fellowship). M. Drewes acknowledges support by the Gottfried Wilhelm Leibniz program of the Deutsche Forschungsgemeinschaft (DFG) and the DFG cluster of excellence Origin and Structure of the Universe. D. Robinson is supported by the NSF under grant No. PHY-1002399. Y. Tsai acknowledges support by the NSF under grant No. PHY-1315155 and the Maryland Center for Fundamental Physics. This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), (A. Gomes Dias, C.A. de S. Pires, and P.S. Rodrigues da Silva), by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), (A. Gomes Dias), and by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under grant 103.03-2012.49 (N. Anh Ky and N. T. Hong Van). The work of J. Heeck is funded in part by IISN and by Belgian Science Policy (IAP VII/37). The work of N.E. Mavromatos is supported in part by the London Centre for Terauniverse Studies (LCTS), using funding from the European Research Council via the Advanced Investigator Grant 267352, and by the U.K. Science and Technology Facilities Council (STFC) under the research grants ST/J002798/1 and ST/L000326/1. The work of A. Pilaftsis is supported in part by the Lancaster-Manchester-Sheffield Consortium for Fundamental Physics, under STFC (U.K.) research grant: ST/J000418/1. L. Gastaldo would like to acknowledge the support by the DFG Research Unit FOR 2202 "Neutrino Mass Determination by Electron Capture in $^{163}$Ho, ECH" (funding under GA 2219/2-1). T. Lasserre would like to acknowledge the support of the Technische Universität München Institute for Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under grant agreement No. 291763, as well as the European Union Marie Curie COFUND program. S. Mertens gratefully acknowledges support of a Feodor Lynen fellowship by the Alexander von Humboldt Foundation and support by the Helmholtz Association. R. Shrock acknowledges support from the U.S. NSF grants NSF-PHY-13-16617 and NSF-PHY-16-1620628. The
work of Y. F. Li, W. Liao, and Z. Xing is supported in part by the National Natural Science Foundation of China under Grant No. 11135009. Several authors acknowledge (partial) support by the European Union through the FP7 Marie Curie Actions ITN INVISIBLES (PITN-GA-2011-289442). Furthermore, his project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreements No. 690575 (InvisiblesPlus RISE) and No. 674896 (Elusives ITN).

**History of the White Paper.** This White Paper was born at the NIAPP (Neutrinos in Astro- and Particle Physics) Workshop of the MIAPP (Munich Institute for Astro- and Particle Physics), organized by S. Schönert, G. G. Raffelt, A. Smirnov, and T. Lasserre and held at MIAPP in Garching, Germany, from 30 June – 25 July 2014. The lively discussions at this workshop and the interest of so many participants ultimately motivated us to undergo this enterprise of writing a White Paper on keV sterile neutrinos as Dark Matter, as we could see that many scientific communities are deeply interested in the topic and there is a strong need for a document including information on all aspects involved. This we have also experienced at the ν-Dark 2015 Workshop held at the Institute for Advanced Study of TUM, Garching, Germany from 7–9 December 2015, where we for the first time gathered representatives from all the relevant communities, many of which are co-authors of this document, for a critical discussion of the topic. At this stage we would like to acknowledge the efforts of the Chalonge School, Colloquiums, and Workshops that have been held in the same spirit. The discussions, focused on sterile neutrino WDM greatly advanced the collaboration and exchange between theory, observations, numerical simulations, particle physics, and experimental detection plans [986–991].

**Note on the figures.** All authors of the different texts have been explicitly informed that figures used within the White Paper must not be protected under copyright of any third party. The editors have made their best effort to ensure that no figure has been used in the same way anywhere else. However, should any dispute about copyright arise, the responsibility lies within the author(s) of the respective section where the decisive figure has been used. The editors take no responsibility for any of these cases, unless in cases where one of the editors is simultaneously an author of the respective section.
References

[1] PLANCK collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].

[2] M. Persic, P. Salucci and F. Stel, The universal rotation curve of spiral galaxies: 1. The dark matter connection, Mon. Not. Roy. Astron. Soc. 281 (1996) 27 [astro-ph/9506004] [INSPIRE].

[3] S.M. Faber and R.E. Jackson, Velocity dispersions and mass to light ratios for elliptical galaxies, Astrophys. J. 204 (1976) 668 [INSPIRE].

[4] N. Kaiser and G. Squires, Mapping the dark matter with weak gravitational lensing, Astrophys. J. 404 (1993) 441 [INSPIRE].

[5] D. Clowe, A. Gonzalez and M. Markevitch, Weak lensing mass reconstruction of the interacting cluster 1E0657-558: direct evidence for the existence of dark matter, Astrophys. J. 604 (2004) 596 [astro-ph/0312273] [INSPIRE].

[6] W.J. Percival et al., Measuring the baryon acoustic oscillation scale using the SDSS and 2dFGRS, Mon. Not. Roy. Astron. Soc. 381 (2007) 1053 [arXiv:0705.3323] [INSPIRE].

[7] R. Dave, L. Hernquist, N. Katz and D.H. Weinberg, The low redshift Lyman-α forest in cold dark matter cosmologies, Astrophys. J. 511 (1999) 521 [astro-ph/9807177] [INSPIRE].

[8] B. Paczynski, Gravitational microlensing by the galactic halo, Astrophys. J. 304 (1986) 1 [INSPIRE].

[9] K. Griest, Galactic microlensing as a method of detecting massive compact halo objects, Astrophys. J. 366 (1991) 412 [INSPIRE].

[10] EROS collaboration, T. Lasserre, Not enough stellar mass machos in the galactic halo, Astron. Astrophys. 355 (2000) L39 [astro-ph/0002253] [INSPIRE].

[11] D.P. Bennett, Large Magellanic cloud microlensing optical depth with imperfect event selection, Astrophys. J. 633 (2005) 906 [astro-ph/0502354] [INSPIRE].

[12] D. Clowe et al., A direct empirical proof of the existence of dark matter, Astrophys. J. 648 (2006) L109 [astro-ph/0608407] [INSPIRE].

[13] J. Yoo, J. Chaname and A. Gould, The end of the MACHO era: limits on halo dark matter from stellar halo wide binaries, Astrophys. J. 601 (2004) 311 [astro-ph/0307437] [INSPIRE].

[14] K. Griest, A.M. Cieplak and M.J. Lehner, New limits on primordial black hole dark matter from an analysis of Kepler source microlensing data, Phys. Rev. Lett. 111 (2013) 181302 [INSPIRE].

[15] P. Pani and A. Loeb, Tidal capture of a primordial black hole by a neutron star: implications for constraints on dark matter, JCAP 06 (2014) 026 [arXiv:1401.3025] [INSPIRE].

[16] M. Milgrom, A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis, Astrophys. J. 270 (1983) 365 [INSPIRE].

[17] C. Kraus et al., Final results from phase II of the Mainz neutrino mass search in tritium beta decay, Eur. Phys. J. C 40 (2005) 447 [hep-ex/0412056] [INSPIRE].

[18] V.M. Lobashev et al., Direct search for mass of neutrino and anomaly in the tritium beta spectrum, Phys. Lett. B 460 (1999) 227 [INSPIRE].

[19] E.W. Kolb and M.S. Turner, The early universe, Front. Phys. 69 (1990) 1 [INSPIRE].

[20] S.D.M. White, C.S. Frenk and M. Davis, Clustering in a neutrino dominated universe, Astrophys. J. 274 (1983) L1 [INSPIRE].

[21] P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: improved analysis, Nucl. Phys. B 360 (1991) 145 [INSPIRE].
[22] G. Jungman, M. Kamionkowski and K. Griest, *Supersymmetric dark matter*, Phys. Rept. **267** (1996) 195 [hep-ph/9506380] [INSPIRE].

[23] G.B. Gelmini and P. Gondolo, *Neutralino with the right cold dark matter abundance in (almost) any supersymmetric model*, Phys. Rev. D **74** (2006) 023510 [hep-ph/0602230] [INSPIRE].

[24] G. Bélanger, F. Boudjema, C. Hugonie, A. Pukhov and A. Semenov, *Relic density of dark matter in the NMSSM*, JCAP **09** (2005) 001 [hep-ph/0505142] [INSPIRE].

[25] J.F. Gunion, D. Hooper and B. McElrath, *Light neutralino dark matter in the NMSSM*, Phys. Rev. D **73** (2006) 015011 [hep-ph/0509024] [INSPIRE].

[26] G. Servant and T.M.P. Tait, *Is the lightest Kaluza-Klein particle a viable dark matter candidate?*, Nucl. Phys. B **650** (2003) 391 [hep-ph/0206071] [INSPIRE].

[27] K. Kong and K.T. Matchev, *Precise calculation of the relic density of Kaluza-Klein dark matter in universal extra dimensions*, JHEP **01** (2006) 038 [hep-ph/0509119] [INSPIRE].

[28] J. Bonnevier, H. Melbeus, A. Merle and T. Ohlsson, *Monoenergetic gamma-rays from non-minimal Kaluza-Klein dark matter annihilations*, Phys. Rev. D **85** (2012) 043524 [Erratum ibid. D **85** (2012) 109902] [arXiv:1104.1430] [INSPIRE].

[29] H. Melbeus, A. Merle and T. Ohlsson, *Higgs dark matter in UEDs: a good WIMP with bad detection prospects*, Phys. Lett. B **715** (2012) 164 [arXiv:1204.5186] [INSPIRE].

[30] L. Lopez Honorez, E. Nezri, J.F. Oliver and M.H.G. Tytgat, *The inert doublet model: an archetype for dark matter*, JCAP **02** (2007) 028 [hep-ph/0612275] [INSPIRE].

[31] E.M. Dolle and S. Su, *The inert dark matter*, Phys. Rev. D **80** (2009) 055012 [arXiv:0906.1609] [INSPIRE].

[32] M. Cirelli, *Indirect searches for dark matter: a status review*, Pramana **79** (2012) 1021 [arXiv:1202.1454] [INSPIRE].

[33] J. Goodman, M. Ibe, A. Rajaraman, W. Shepherd, T.M.P. Tait and H.-B. Yu, *Constraints on dark matter from colliders*, Phys. Rev. D **82** (2010) 116010 [arXiv:1008.1783] [INSPIRE].

[34] L. Baudis, *Direct dark matter detection: the next decade*, Phys. Dark Univ. **1** (2012) 94 [arXiv:1211.7222] [INSPIRE].

[35] CRESST-II collaboration, G. Angloher et al., *Results on low mass WIMPs using an upgraded CRESST-II detector*, Eur. Phys. J. C **74** (2014) 3184 [arXiv:1407.3146] [INSPIRE].

[36] XENON100 collaboration, E. Aprile et al., *Dark matter results from 225 live days of XENON100 data*, Phys. Rev. Lett. **109** (2012) 181301 [arXiv:1207.5988] [INSPIRE].

[37] LUX collaboration, D.S. Akerib et al., *First results from the LUX dark matter experiment at the Sanford Underground Research Facility*, Phys. Rev. Lett. **112** (2014) 091303 [arXiv:1310.8214] [INSPIRE].

[38] AMS collaboration, L. Accardo et al., *High statistics measurement of the positron fraction in primary cosmic rays of 0.5-500 GeV with the Alpha Magnetic Spectrometer on the International Space Station*, Phys. Rev. Lett. **113** (2014) 121101 [INSPIRE].

[39] FERMI-LAT collaboration, M. Ackermann et al., *Search for gamma-ray spectral lines with the Fermi Large Area Telescope and dark matter implications*, Phys. Rev. D **88** (2013) 082002 [arXiv:1305.5597] [INSPIRE].

[40] PAMELA collaboration, O. Adriani et al., *Cosmic-ray positron energy spectrum measured by PAMELA*, Phys. Rev. Lett. **111** (2013) 081102 [arXiv:1308.0133] [INSPIRE].

[41] ATLAS collaboration, *Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the ATLAS detector*, JHEP **04** (2013) 075 [arXiv:1210.4491] [INSPIRE].
[42] CMS collaboration, Search for dark matter and large extra dimensions in monojet events in pp collisions at $\sqrt{s} = 7$ TeV, JHEP 09 (2012) 094 [arXiv:1206.5663] [INSPIRE].

[43] CMS collaboration, Searches for electroweak production of charginos, neutralinos and sleptons decaying to leptons and W, Z and Higgs bosons in pp collisions at 8 TeV, Eur. Phys. J. C 74 (2014) 3036 [arXiv:1405.7570] [INSPIRE].

[44] ATLAS collaboration, Search for direct production of charginos, neutralinos and sleptons in final states with two leptons and missing transverse momentum in pp collisions at $\sqrt{s} = 8$ TeV with the ATLAS detector, JHEP 05 (2014) 071 [arXiv:1403.5294] [INSPIRE].

[45] V. Springel et al., Simulating the joint evolution of quasars, galaxies and their large-scale distribution, Nature 435 (2005) 629 [astro-ph/0504097] [INSPIRE].

[46] A.A. Klypin, A.V. Kravtsov, O. Valenzuela and F. Prada, Where are the missing galactic satellites?, Astrophys. J. 522 (1999) 82 [astro-ph/9901240] [INSPIRE].

[47] B. Moore et al., Dark matter substructure within galactic halos, Astrophys. J. 524 (1999) L19 [astro-ph/9907411] [INSPIRE].

[48] J. Dubinski and R.G. Carlberg, The structure of cold dark matter halos, Astrophys. J. 378 (1991) 496 [INSPIRE].

[49] J.F. Navarro, C.S. Frenk and S.D.M. White, The structure of cold dark matter halos, Astrophys. J. 462 (1996) 563 [astro-ph/9508025] [INSPIRE].

[50] A.V. Macciò, X. Kang, F. Fontanot, R.S. Somerville, S.E. Koposov and P. Monaco, On the origin and properties of ultrafaint milky way satellites in a $\Lambda$CDM universe, Mon. Not. Roy. Astron. Soc. 402 (2010) 1995 [arXiv:0903.4681] [INSPIRE].

[51] S. Garrison-Kimmel, M. Rocha, M. Boylan-Kolchin, J. Bullock and J. Lally, Can feedback solve the too big to fail problem?, Mon. Not. Roy. Astron. Soc. 433 (2013) 3539 [arXiv:1301.3137] [INSPIRE].

[52] S. Geen, A. Slyz and J. Devriendt, How does feedback affect milky way satellite formation?, EAS Publ. Ser. 48 (2011) 441 [arXiv:1101.2232] [INSPIRE].

[53] M. Boylan-Kolchin, J.S. Bullock and M. Kaplinghat, Too big to fail? The puzzling darkness of massive milky way subhaloes, Mon. Not. Roy. Astron. Soc. 415 (2011) L40 [arXiv:1103.0007] [INSPIRE].

[54] M. Boylan-Kolchin, J.S. Bullock and M. Kaplinghat, The milky way's bright satellites as an apparent failure of $\Lambda$CDM, Mon. Not. Roy. Astron. Soc. 422 (2012) 1203 [arXiv:1111.2048] [INSPIRE].

[55] A.M. Brooks and A. Zolotov, Why baryons matter: the kinematics of dwarf spheroidal satellites, Astrophys. J. 786 (2014) 87 [arXiv:1207.2468] [INSPIRE].

[56] Q. Zhu, F. Marinacci, M. Maji, Y. Li, V. Springel and L. Hernquist, Baryonic impact on the dark matter distribution in milky way-sized galaxies and their satellites, Mon. Not. Roy. Astron. Soc. 458 (2016) 1559 [arXiv:1506.05537] [INSPIRE].

[57] J. Herpich et al., MaGICC-WDM: the effects of warm dark matter in hydrodynamical simulations of disc galaxy formation, Mon. Not. Roy. Astron. Soc. 437 (2014) 293 [arXiv:1308.1088] [INSPIRE].

[58] M.R. Lovell et al., The haloes of bright satellite galaxies in a warm dark matter universe, Mon. Not. Roy. Astron. Soc. 420 (2012) 2318 [arXiv:1104.2929] [INSPIRE].

[59] A. Boyarsky, J. Lesgourgues, O. Ruchayskiy and M. Viel, Lyman-$\alpha$ constraints on warm and on warm-plus-cold dark matter models, JCAP 05 (2009) 012 [arXiv:0812.0010] [INSPIRE].

[60] E. Majorana, Theory of the symmetry of electrons and positrons, Nuovo Cim. 14 (1937) 171 [INSPIRE].
[61] A. Ibarra, E. Molinaro and S.T. Petcov, *Low energy signatures of the TeV scale see-saw mechanism*, Phys. Rev. D **84** (2011) 013005 [arXiv:1103.6217] [INSPIRE].

[62] O. Ruchayskiy and A. Ivashko, *Restrictions on the lifetime of sterile neutrinos from primordial nucleosynthesis*, JCAP **10** (2012) 014 [arXiv:1202.2841] [INSPIRE].

[63] A. Abada, D. Das, A.M. Teixeira, A. Vicente and C. Weiland, *Tree-level lepton universality violation in the presence of sterile neutrinos: impact for $R_K$ and $R_\pi$, JHEP **02** (2013) 048* [arXiv:1211.3052] [INSPIRE].

[64] O. Ruchayskiy and A. Ivashko, *Experimental bounds on sterile neutrino mixing angles*, JHEP **06** (2012) 100 [arXiv:1112.3319] [INSPIRE].

[65] A. Abada, A.M. Teixeira, A. Vicente and C. Weiland, *Sterile neutrinos in leptonic and semileptonic decays*, JHEP **02** (2014) 091 [arXiv:1311.2830] [INSPIRE].

[66] A. Merle, *keV neutrino model building*, Int. J. Mod. Phys. D **22** (2013) 1330020 [arXiv:1302.2625] [INSPIRE].

[67] M. Drewes, *The phenomenology of right handed neutrinos*, Int. J. Mod. Phys. E **22** (2013) 1330019 [arXiv:1303.6912] [INSPIRE].

[68] P. Hernández, M. Kekic and J. Lopez-Pavon, $N_{eff}$ in low-scale seesaw models versus the lightest neutrino mass, Phys. Rev. D **90** (2014) 065033 [arXiv:1406.2961] [INSPIRE].

[69] E. Fernandez-Martinez, J. Hernandez-Garcia, J. Lopez-Pavon and M. Lucente, *Loop level constraints on seesaw neutrino mixing*, JHEP **10** (2015) 130 [arXiv:1508.03051] [INSPIRE].

[70] M. Drewes, *Theoretical status of neutrino physics*, PoS(NUFACT2014)001 [arXiv:1502.06891] [INSPIRE].

[71] M. Drewes and B. Garbrecht, *Experimental and cosmological constraints on heavy neutrinos*, arXiv:1502.00477 [INSPIRE].

[72] S. Antusch and O. Fischer, *Testing sterile neutrino extensions of the Standard Model at future lepton colliders*, JHEP **05** (2015) 053 [arXiv:1502.05915] [INSPIRE].

[73] A. de Gouvêa and A. Kobach, *Global constraints on a heavy neutrino*, Phys. Rev. D **93** (2016) 033005 [arXiv:1511.00683] [INSPIRE].

[74] F.F. Deppisch, P.S. Bhupal Dev and A. Pilaftsis, *Neutrinos and collider physics*, New J. Phys. **17** (2015) 075019 [arXiv:1502.06541] [INSPIRE].

[75] S. Tremaine and J.E. Gunn, *Dynamical role of light neutral leptons in cosmology*, Phys. Rev. Lett. **42** (1979) 407 [INSPIRE].

[76] G. Bellini, L. Ludhova, G. Ranucci and F.L. Villante, *Neutrino oscillations*, Adv. High Energy Phys. **2014** (2014) 191960 [arXiv:1310.7858] [INSPIRE].

[77] Y. Wang and Z.-Z. Xing, *Neutrino masses and flavor oscillations*, arXiv:1504.06155 [INSPIRE].

[78] B. Pontecorvo, *Neutrino experiments and the problem of conservation of leptonic charge*, Sov. Phys. JETP **26** (1968) 984 [Zh. Eksp. Teor. Fiz. **53** (1967) 1717] [INSPIRE].

[79] B. Pontecorvo, *Mesonium and anti-mesonium*, Sov. Phys. JETP **6** (1957) 429 [Zh. Eksp. Teor. Fiz. **33** (1957) 549] [INSPIRE].

[80] B. Pontecorvo, *Inverse beta processes and nonconservation of lepton charge*, Sov. Phys. JETP **7** (1958) 172 [Zh. Eksp. Teor. Fiz. **34** (1957) 247] [INSPIRE].

[81] Z. Maki, M. Nakagawa and S. Sakata, *Remarks on the unified model of elementary particles*, Prog. Theor. Phys. **28** (1962) 870 [INSPIRE].

[82] M. Nakagawa, H. Okonogi, S. Sakata and A. Toyoda, *Possible existence of a neutrino with mass and partial conservation of muon charge*, Prog. Theor. Phys. **30** (1963) 727 [INSPIRE].
[83] SNO collaboration, S.N. Ahmed et al., Measurement of the total active $^8$B solar neutrino flux at the Sudbury Neutrino Observatory with enhanced neutral current sensitivity, Phys. Rev. Lett. 92 (2004) 181301 [nucl-ex/0309004] [INSPIRE].

[84] M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Updated fit to three neutrino mixing: status of leptonic CP-violation, JHEP 11 (2014) 052 [arXiv:1409.5439] [INSPIRE].

[85] PARTICLE DATA GROUP collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].

[86] W. Rodejohann and J.W.F. Valle, Symmetrical parametrizations of the lepton mixing matrix, Phys. Rev. D 84 (2011) 073011 [arXiv:1108.3484] [INSPIRE].

[87] O. Mena and S.J. Parke, Unified graphical summary of neutrino mixing parameters, Phys. Rev. D 69 (2004) 117301 [hep-ph/0312131] [INSPIRE].

[88] V.N. Gribov and B. Pontecorvo, Neutrino astronomy and lepton charge, Phys. Lett. B 28 (1969) 493 [INSPIRE].

[89] M.C. Gonzalez-Garcia and M. Maltoni, Phenomenology with massive neutrinos, Phys. Rept. 460 (2008) 1 [arXiv:0704.1800] [INSPIRE].

[90] SUPER-KAMIOKANDE collaboration, R. Wendell, Atmospheric results from Super-Kamiokande, in XXVI International Conference on Neutrino Physics and Astrophysics, Boston U.S.A., 2-7 June 2014 [AIP Conf. Proc. 1666 (2015) 100001] [arXiv:1412.5234] [INSPIRE].

[91] B.T. Cleveland et al., Measurement of the solar electron neutrino flux with the Homestake chlorine detector, Astrophys. J. 496 (1998) 505 [INSPIRE].

[92] F. Kaether, W. Hampel, G. Heusser, J. Kiko and T. Kirsten, Reanalysis of the GALLEX solar neutrino flux and source experiments, Phys. Lett. B 685 (2010) 47 [arXiv:1001.2731] [INSPIRE].

[93] SAGE collaboration, J.N. Abdurashitov et al., Measurement of the solar neutrino capture rate with gallium metal. III: results for the 2002-2007 data-taking period, Phys. Rev. C 80 (2009) 015807 [arXiv:0901.2200] [INSPIRE].

[94] SUPER-KAMIOKANDE collaboration, J. Hosaka et al., Solar neutrino measurements in Super-Kamiokande-I, Phys. Rev. D 73 (2006) 112001 [hep-ex/0508053] [INSPIRE].

[95] SUPER-KAMIOKANDE collaboration, J.P. Cravens et al., Solar neutrino measurements in Super-Kamiokande-II, Phys. Rev. D 78 (2008) 032002 [arXiv:0803.4312] [INSPIRE].

[96] SUPER-KAMIOKANDE collaboration, K. Abe et al., Solar neutrino results in Super-Kamiokande-III, Phys. Rev. D 83 (2011) 052010 [arXiv:1010.0118] [INSPIRE].

[97] Y. Koshio, Solar results from Super-Kamiokande, in XXVI International Conference on Neutrino Physics and Astrophysics, Boston U.S.A., 2-7 June 2014 [AIP Conf. Proc. 1666 (2015) 090001] [INSPIRE].

[98] SNO collaboration, B. Aharmim et al., Combined analysis of all three phases of solar neutrino data from the Sudbury Neutrino Observatory, Phys. Rev. C 88 (2013) 025501 [arXiv:1109.0763] [INSPIRE].

[99] G. Bellini et al., Precision measurement of the $^7$Be solar neutrino interaction rate in Borexino, Phys. Rev. Lett. 107 (2011) 141302 [arXiv:1104.1816] [INSPIRE].

[100] BOREXINO collaboration, G. Bellini et al., Measurement of the solar $^8$B neutrino rate with a liquid scintillator target and 3 MeV energy threshold in the Borexino detector, Phys. Rev. D 82 (2010) 033006 [arXiv:0808.2868] [INSPIRE].

[101] MINOS collaboration, P. Adamson et al., Measurement of neutrino and antineutrino oscillations using beam and atmospheric data in MINOS, Phys. Rev. Lett. 110 (2013) 251801 [arXiv:1304.6335] [INSPIRE].
[102] T2K collaboration, K. Abe et al., *Precise measurement of the neutrino mixing parameter $\theta_{23}$ from muon neutrino disappearance in an off-axis beam*, Phys. Rev. Lett. **112** (2014) 181801 [arXiv:1403.1532] [INSPIRE].

[103] MINOS collaboration, P. Adamson et al., *Electron neutrino and antineutrino appearance in the full MINOS data sample*, Phys. Rev. Lett. **110** (2013) 171801 [arXiv:1301.4581] [INSPIRE].

[104] T2K collaboration, K. Abe et al., *Observation of electron neutrino appearance in a muon neutrino beam*, Phys. Rev. Lett. **112** (2014) 061802 [arXiv:1311.4750] [INSPIRE].

[105] DAYA BAY collaboration, F.P. An et al., *Observation of electron-antineutrino disappearance at Daya Bay*, Phys. Rev. Lett. **108** (2012) 171803 [arXiv:1203.1669] [INSPIRE].

[106] RENO collaboration, J.K. Ahn et al., *Observation of reactor electron antineutrino disappearance in the RENO experiment*, Phys. Rev. Lett. **108** (2012) 191802 [arXiv:1204.0626] [INSPIRE].

[107] DAYA BAY collaboration, F.P. An et al., *New measurement of antineutrino oscillation with the full detector configuration at daya bay*, Phys. Rev. Lett. **115** (2015) 111802 [arXiv:1505.03456] [INSPIRE].

[108] RENO collaboration, S.-H. Seo, *New results from RENO and the 5 MeV excess*, in XXVI International Conference on Neutrino Physics and Astrophysics, Boston U.S.A., 2-7 June 2014 [AIP Conf. Proc. **1666** (2015) 080002] [arXiv:1410.7987] [INSPIRE].

[109] DOUBLE CHOOZ collaboration, Y. Abe et al., *Reactor electron antineutrino disappearance in the Double CHOOZ experiment*, Phys. Rev. D **86** (2012) 052008 [arXiv:1207.6632] [INSPIRE].

[110] DOUBLE CHOOZ collaboration, Y. Abe et al., *Improved measurements of the neutrino mixing angle $\theta_{13}$ with the Double CHOOZ detector*, JHEP **10** (2014) 086 [Erratum ibid. **02** (2015) 074] [arXiv:1406.7763] [INSPIRE].

[111] KAMLAND collaboration, A. Gando et al., *Constraints on $\theta_{13}$ from a three-flavor oscillation analysis of reactor antineutrinos at KamLAND*, Phys. Rev. D **83** (2011) 052002 [arXiv:1009.4771] [INSPIRE].

[112] F. Capozzi, G.L. Fogli, E. Lisi, A. Marrone, D. Montanino and A. Palazzo, *Status of three-neutrino oscillation parameters*, circa 2013, Phys. Rev. D **89** (2014) 093018 [arXiv:1312.2878] [INSPIRE].

[113] D.V. Forero, M. Tortola and J.W.F. Valle, *Neutrino oscillations refitted*, Phys. Rev. D **90** (2014) 093006 [arXiv:1405.7540] [INSPIRE].

[114] T.A. Mueller et al., *Improved predictions of reactor antineutrino spectra*, Phys. Rev. C **83** (2011) 054615 [arXiv:1101.2663] [INSPIRE].

[115] P. Huber, *On the determination of anti-neutrino spectra from nuclear reactors*, Phys. Rev. C **84** (2011) 024617 [Erratum ibid. C **85** (2012) 029901] [arXiv:1106.0687] [INSPIRE].

[116] G. Mention et al., *The reactor antineutrino anomaly*, Phys. Rev. D **83** (2011) 073006 [arXiv:1101.2755] [INSPIRE].

[117] Y. Declais et al., *Study of reactor anti-neutrino interaction with proton at Bugey nuclear power plant*, Phys. Lett. B **338** (1994) 383 [INSPIRE].

[118] A.A. Kuvshinnikov, L.A. Mikaelyan, S.V. Nikolaev, M.D. Skorokhvatov and A.V. Etenko, *Measuring the $\bar{\nu}_e + p \to n + e^+$ cross-section and beta decay axial constant in a new experiment at Rovno NPP reactor* (in Russian), JETP Lett. **54** (1991) 253 [Yad. Fiz. **52** (1990) 472] [Pisma Zh. Eksp. Teor. Fiz. **54** (1991) 259] [Sov. J. Nucl. Phys. **52** (1990) 300] [INSPIRE].

[119] Y. Declais et al., *Search for neutrino oscillations at 15-meters, 40-meters and 95-meters from a nuclear power reactor at Bugey*, Nucl. Phys. B **434** (1995) 503 [INSPIRE].
[120] G.S. Vidyakin et al., Detection of anti-neutrinos in the flux from two reactors, Sov. Phys. JETP 66 (1987) 243 [Zh. Eksp. Teor. Fiz. 93 (1987) 424] [INSPIRE].

[121] G.S. Vidyakin et al., Limitations on the characteristics of neutrino oscillations, JETP Lett. 59 (1994) 390 [Pisma Zh. Eksp. Teor. Fiz. 59 (1994) 364] [INSPIRE].

[122] H. Kwon et al., Search for neutrino oscillations at a fission reactor, Phys. Rev. D 24 (1981) 1097 [INSPIRE].

[123] CALTECH-SIN-TUM collaboration, G. Zacek et al., Neutrino oscillation experiments at the Gosgen nuclear power reactor, Phys. Rev. D 34 (1986) 2621 [INSPIRE].

[124] Z.D. Greenwood et al., Results of a two position reactor neutrino oscillation experiment, Phys. Rev. D 53 (1996) 6054 [INSPIRE].

[125] A.I. Afonin, S.N. Ketov, V.I. Kopeikin, L.A. Mikaelyan, M.D. Skorokhvatov and S.V. Tolokonnikov, A study of the reaction $\bar{\nu}_e + P \to e^+ + N$ on a nuclear reactor, Sov. Phys. JETP 67 (1988) 213 [Zh. Eksp. Teor. Fiz. 94N2 (1988) 1] [INSPIRE].

[126] C. Jarlskog, Commutator of the quark mass matrices in the standard electroweak model and a measure of maximal CP-violation, Phys. Rev. Lett. 55 (1985) 1039 [INSPIRE].

[127] R.E. Shrock, New tests for and bounds on, neutrino masses and lepton mixing, Phys. Lett. B 96 (1980) 159 [INSPIRE].

[128] TROITSK collaboration, V.N. Aseev et al., An upper limit on electron antineutrino mass from Troitsk experiment, Phys. Rev. D 84 (2011) 112003 [arXiv:1108.5034] [INSPIRE].

[129] KATRIN collaboration, J. Angrik et al., KATRIN design report 2004, FZKA-7090, (2005) [INSPIRE].

[130] J. Schechter and J.W.F. Valle, Neutrinoless double beta decay in SU(2) × U(1) theories, Phys. Rev. D 25 (1982) 2951 [INSPIRE].

[131] M. Duerr, M. Lindner and A. Merle, On the quantitative impact of the Schechter-Valle theorem, JHEP 06 (2011) 091 [arXiv:1105.0901] [INSPIRE].

[132] M. Lindner, A. Merle and W. Rodejohann, Improved limit on $\theta_{13}$ and implications for neutrino masses in neutrino-less double beta decay and cosmology, Phys. Rev. D 73 (2006) 053005 [hep-ph/0512143] [INSPIRE].

[133] A. Merle and W. Rodejohann, The elements of the neutrino mass matrix: allowed ranges and implications of texture zeros, Phys. Rev. D 73 (2006) 073012 [hep-ph/0603111] [INSPIRE].

[134] GERDA collaboration, M. Agostini et al., Results on neutrinoless double-$\beta$ decay of $^{76}$Ge from phase I of the GERDA experiment, Phys. Rev. Lett. 111 (2013) 122503 [arXiv:1307.4720] [INSPIRE].

[135] KAMLAND-ZEN collaboration, A. Gando et al., Limit on neutrinoless $\beta\beta$ decay of $^{136}$Xe from the first phase of KamLAND-Zen and comparison with the positive claim in $^{76}$Ge, Phys. Rev. Lett. 110 (2013) 062502 [arXiv:1211.3863] [INSPIRE].

[136] EXO-200 collaboration, J.B. Albert et al., Search for Majorana neutrinos with the first two years of EXO-200 data, Nature 510 (2014) 229 [arXiv:1402.6956] [INSPIRE].

[137] J.J. Gomez-Cadenas, J. Martin-Albo, M. Mezzetto, F. Monrabal and M. Sorel, The search for neutrinoless double beta decay, Riv. Nuovo Cim. 35 (2012) 29 [arXiv:1109.5515] [INSPIRE].

[138] W. Maneschg, A. Merle and W. Rodejohann, Statistical analysis of future neutrino mass experiments including neutrino-less double beta decay, Europhys. Lett. 85 (2009) 51002 [arXiv:0812.0479] [INSPIRE].

[139] NOvA collaboration, R.B. Patterson, The NOvA experiment: status and outlook, Nucl. Phys. Proc. Suppl. B 235-236 (2013) 151 [arXiv:1209.0716] [INSPIRE].
[140] T2K collaboration, K. Abe et al., The T2K experiment, Nucl. Instrum. Meth. A 659 (2011) 106 [arXiv:1106.1238] [INSPIRE].

[141] ICECUBE and PINGU collaborations, M.G. Aartsen et al., PINGU sensitivity to the neutrino mass hierarchy, arXiv:1306.5846 [INSPIRE].

[142] JUNO collaboration, M. He, Jiangmen Underground Neutrino Observatory, Nucl. Part. Phys. Proc. 265-266 (2015) 111 [arXiv:1412.4195] [INSPIRE].

[143] A. de Gouvêa, J. Jenkins and B. Kayser, Neutrino mass hierarchy, vacuum oscillations and vanishing $|U_{e3}|$, Phys. Rev. D 71 (2005) 113009 [hep-ph/0503079] [INSPIRE].

[144] H. Nunokawa, S.J. Parke and R. Zukanovich Funchal, Another possible way to determine the neutrino mass hierarchy, Phys. Rev. D 72 (2005) 013009 [hep-ph/0503283] [INSPIRE].

[145] F.T. Avignone, III, S.R. Elliott and J. Engel, Double beta decay, Majorana neutrinos and neutrino mass, Rev. Mod. Phys. 80 (2008) 481 [arXiv:0708.1033] [INSPIRE].

[146] A. de Gouvêa and P. Vogel, Lepton flavor and number conservation and physics beyond the Standard Model, Prog. Part. Nucl. Phys. 71 (2013) 75 [arXiv:1303.4097] [INSPIRE].

[147] LBNE collaboration, C. Adams et al., The Long-Baseline Neutrino Experiment: exploring fundamental symmetries of the universe, arXiv:1307.7335 [INSPIRE].

[148] HYPER-KAMIOKANDE WORKING GROUP collaboration, E. Kearns et al., Hyper-Kamiokande physics opportunities, arXiv:1309.0184 [INSPIRE].

[149] A.D. Sakharov, Violation of CP invariance, c asymmetry and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32 [JETP Lett. 5 (1967) 24] [Sov. Phys. Usp. 34 (1991) 392] [Usp. Fiz. Nauk 161 (1991) 61] [INSPIRE].

[150] L. Canetti, M. Drewes and M. Shaposhnikov, Matter and antimatter in the universe, New J. Phys. 14 (2012) 095012 [arXiv:1204.4186] [INSPIRE].

[151] P. Langacker, Neutrino masses from the top down, Ann. Rev. Nucl. Part. Sci. 62 (2012) 215 [arXiv:1112.5992] [INSPIRE].

[152] A. de Gouvêa, W.-C. Huang and J. Jenkins, Pseudo-Dirac neutrinos in the new Standard Model, Phys. Rev. D 80 (2009) 073007 [arXiv:0906.1611] [INSPIRE].

[153] P. Minkowski, $\mu \to e\gamma$ at a rate of one out of $10^9$ muon decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].

[154] T. Yanagida, Horizontal symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].

[155] M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].

[156] S.L. Glashow, The future of elementary particle physics, NATO Sci. Ser. B 61 (1980) 687 [INSPIRE].

[157] R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].

[158] J. Schechter and J.W.F. Valle, Neutrino masses in $SU(2) \times U(1)$ theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].

[159] K.N. Abazajian et al., Light sterile neutrinos: a white paper, arXiv:1204.5379 [INSPIRE].

[160] J.M. Conrad, W.C. Louis and M.H. Shaevitz, The LSND and MiniBooNE oscillation searches at high $\Delta m^2$, Ann. Rev. Nucl. Part. Sci. 63 (2013) 45 [arXiv:1306.6494] [INSPIRE].

[161] J. Kopp, P.A.N. Machado, M. Maltoni and T. Schwetz, Sterile neutrino oscillations: the global picture, JHEP 05 (2013) 050 [arXiv:1303.3011] [INSPIRE].

[162] C. Giunti, M. Laveder, Y.F. Li and H.W. Long, Pragmatic view of short-baseline neutrino oscillations, Phys. Rev. D 88 (2013) 073008 [arXiv:1308.5288] [INSPIRE].
[163] J.M. Conrad, C.M. Ignarra, G. Karagiorgi, M.H. Shaevitz and J. Spitz, *Sterile neutrino fits to short baseline neutrino oscillation measurements*, *Adv. High Energy Phys. 2013* (2013) 163897 [arXiv:1207.4765] [INSPIRE].

[164] PLANCK collaboration, P.A.R. Ade et al., *Planck 2013 results. XVI. Cosmological parameters*, *Astron. Astrophys. 571* (2014) A16 [arXiv:1303.5076] [INSPIRE].

[165] A. Mirizzi et al., *The strongest bounds on active-sterile neutrino mixing after Planck data*, *Phys. Lett. B* 726 (2013) 8 [arXiv:1303.5368] [INSPIRE].

[166] A. de Gouvêa and W.-C. Huang, *Constraining the (low-energy) type-I seesaw*, *Phys. Rev. D* 85 (2012) 053006 [arXiv:1110.6122] [INSPIRE].

[167] A. Donini, P. Hernández, J. Lopez-Pavon, M. Maltoni and T. Schwetz, *The minimal 3 + 2 neutrino model versus oscillation anomalies*, *JHEP 07* (2012) 161 [arXiv:1205.5230] [INSPIRE].

[168] P. Langacker, *A mechanism for ordinary sterile neutrino mixing*, *Phys. Rev. D* 58 (1998) 093017 [hep-ph/9805281] [INSPIRE].

[169] J. Sayre, S. Wiesenfeldt and S. Willenbrock, *Sterile neutrinos and global symmetries*, *Phys. Rev. D* 72 (2005) 015001 [hep-ph/0504198] [INSPIRE].

[170] A. Atre, T. Han, S. Pascoli and B. Zhang, *The search for heavy Majorana neutrinos*, *JHEP* 05 (2009) 030 [arXiv:0901.3589] [INSPIRE].

[171] A. Kusenko, *Sterile neutrinos: the dark side of the light fermions*, *Phys. Rept.* 481 (2009) 1 [arXiv:0906.2968] [INSPIRE].

[172] R.E. Shrock, *General theory of weak leptonic and semileptonic decays. 1. Leptonic pseudoscalar meson decays, with associated tests for and bounds on, neutrino masses and lepton mixing*, *Phys. Rev. D* 24 (1981) 1232 [INSPIRE].

[173] R.E. Shrock, *General theory of weak processes involving neutrinos. 2. Pure leptonic decays*, *Phys. Rev. D* 24 (1981) 1275 [INSPIRE].

[174] J. Barry, W. Rodejohann and H. Zhang, *Light sterile neutrinos: models and phenomenology*, *JHEP* 07 (2011) 091 [arXiv:1105.3911] [INSPIRE].

[175] A. Faessler, M. González, S. Kovalenko and F. Šimkovic, *Arbitrary mass Majorana neutrinos in neutrinoless double beta decay*, *Phys. Rev. D* 90 (2014) 096010 [arXiv:1408.6077] [INSPIRE].

[176] F.J. Escrihuela, D.V. Forero, O.G. Miranda, M. Tortola and J.W.F. Valle, *On the description of nonunitary neutrino mixing*, *Phys. Rev. D* 92 (2015) 053009 [arXiv:1503.08879] [INSPIRE].

[177] S. Dodelson and L.M. Widrow, *Sterile-neutrinos as dark matter*, *Phys. Rev. Lett.* 72 (1994) 17 [hep-ph/9303287] [INSPIRE].

[178] H.J. de Vega and N.G. Sanchez, *Model independent analysis of dark matter points to a particle mass at the keV scale*, *Mon. Not. Roy. Astron. Soc.* 404 (2010) 885 [arXiv:0901.0922] [INSPIRE].

[179] H.J. de Vega, P. Salucci and N.G. Sanchez, *The mass of the dark matter particle from theory and observations*, *New Astron.* 17 (2012) 653 [arXiv:1004.1908] [INSPIRE].

[180] H.J. de Vega and N.G. Sanchez, *Cosmological evolution of warm dark matter fluctuations I: efficient computational framework with Volterra integral equations*, *Phys. Rev. D* 85 (2012) 043516 [arXiv:1111.0290] [INSPIRE].

[181] H.J. de Vega and N.G. Sanchez, *Cosmological evolution of warm dark matter fluctuations II: solution from small to large scales and keV sterile neutrinos*, *Phys. Rev. D* 85 (2012) 043517 [arXiv:1111.0300] [INSPIRE].
[182] C. Destri, H.J. de Vega and N.G. Sanchez, *Fermionic warm dark matter produces galaxy cores in the observed scales because of quantum mechanics*, *New Astron.* **22** (2013) 39 [arXiv:1204.3090] [INSPIRE].

[183] C. Destri, H.J. de Vega and N.G. Sanchez, *Quantum WDM fermions and gravitation determine the observed galaxy structures*, *Astropart. Phys.* **46** (2013) 14 [arXiv:1301.1864] [INSPIRE].

[184] H.J. de Vega, P. Salucci and N.G. Sanchez, *Observational rotation curves and density profiles versus the Thomas-Fermi galaxy structure theory*, *Mon. Not. Roy. Astron. Soc.* **442** (2014) 2717 [arXiv:1309.2290] [INSPIRE].

[185] C. Destri, H.J. de Vega and N.G. Sanchez, *Warm dark matter primordial spectra and the onset of structure formation at redshift z*, *Phys. Rev. D* **88** (2013) 083512 [arXiv:1308.1109] [INSPIRE].

[186] A. Boyarsky, O. Ruchayskiy and M. Shaposhnikov, *The role of sterile neutrinos in cosmology and astrophysics*, *Ann. Rev. Nucl. Part. Sci.* **59** (2009) 191 [arXiv:0901.0011] [INSPIRE].

[187] A. Merle, *Constraining models for keV sterile neutrinos by quasi-degenerate active neutrinos*, *Phys. Rev. D* **86** (2012) 121701 [arXiv:1210.6036] [INSPIRE].

[188] T. Asaka and M. Shaposhnikov, *The νMSM, dark matter and baryon asymmetry of the universe*, *Phys. Lett. B* **620** (2005) 17 [hep-ph/0505013] [INSPIRE].

[189] T. Asaka, S. Blanchet and M. Shaposhnikov, *The νMSM, dark matter and neutrino masses*, *Phys. Lett. B* **631** (2005) 151 [hep-ph/0503065] [INSPIRE].

[190] E. Bulbul, M. Markevitch, A. Foster, R.K. Smith, M. Loewenstein and S.W. Randall, *Detection of an unidentified emission line in the stacked X-ray spectrum of galaxy clusters*, *Astrophys. J.* **789** (2014) 13 [arXiv:1402.2301] [INSPIRE].

[191] A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi and J. Franse, *Unidentified line in X-ray spectra of the Andromeda galaxy and Perseus galaxy cluster*, *Phys. Rev. Lett.* **113** (2014) 251301 [arXiv:1402.4119] [INSPIRE].

[192] F.L. Bezrukov, *νMSM-predictions for neutrinoless double beta decay*, *Phys. Rev. D* **72** (2005) 071303 [hep-ph/0505247] [INSPIRE].

[193] T. Asaka, S. Eijima and H. Ishida, *Mixing of active and sterile neutrinos*, *JHEP* **04** (2011) 011 [arXiv:1101.1382] [INSPIRE].

[194] A. Merle and V. Niro, *Influence of a keV sterile neutrino on neutrinoless double beta decay: how things changed in recent years*, *Phys. Rev. D* **88** (2013) 113004 [arXiv:1302.2032] [INSPIRE].

[195] T. Yanagida, *Horizontal symmetry and masses of neutrinos*, *Prog. Theor. Phys.* **64** (1980) 1103 [INSPIRE].

[196] E. Ma, *Pathways to naturally small neutrino masses*, *Phys. Rev. Lett.* **81** (1998) 1171 [hep-ph/9805219] [INSPIRE].

[197] M. Magg and C. Wetterich, *Neutrino mass problem and gauge hierarchy*, *Phys. Lett. B* **94** (1980) 61 [INSPIRE].

[198] T.P. Cheng and L.-F. Li, *Neutrino masses, mixings and oscillations in SU(2) × U(1) models of electroweak interactions*, *Phys. Rev. D* **22** (1980) 2860 [INSPIRE].

[199] G. Lazarides, Q. Shafi and C. Wetterich, *Proton lifetime and fermion masses in an SO(10) model*, *Nucl. Phys. B* **181** (1981) 287 [INSPIRE].

[200] R.N. Mohapatra and G. Senjanović, *Neutrino masses and mixings in gauge models with spontaneous parity violation*, *Phys. Rev. D* **23** (1981) 165 [INSPIRE].

[201] R. Foot, H. Lew, X.G. He and G.C. Joshi, *Seesaw neutrino masses induced by a triplet of leptons*, *Z. Phys. C* **44** (1989) 441 [INSPIRE].
[202] C.D. Froggatt and H.B. Nielsen, *Hierarchy of quark masses, Cabibbo angles and CP-violation*, Nucl. Phys. B **147** (1979) 277 [INSPIRE].

[203] Y. Chikashige, R.N. Mohapatra and R.D. Peccei, *Are there real Goldstone bosons associated with broken lepton number?*, Phys. Lett. B **98** (1981) 265 [INSPIRE].

[204] G.B. Gelmini and M. Roncadelli, *Left-handed neutrino mass scale and spontaneously broken lepton number*, Phys. Lett. B **99** (1981) 411 [INSPIRE].

[205] D. Wyler and L. Wolfenstein, *Massless neutrinos in left-right symmetric models*, Nucl. Phys. B **218** (1983) 205 [INSPIRE].

[206] M.C. Gonzalez-Garcia and J.W.F. Valle, *Fast decaying neutrinos and observable flavor violation in a new class of Majoron models*, Phys. Lett. B **216** (1989) 360 [INSPIRE].

[207] G.C. Branco, W. Grimus and L. Lavoura, *Relating the scalar flavor changing neutral couplings to the CKM matrix*, Phys. Lett. B **380** (1996) 119 [hep-ph/9601383] [INSPIRE].

[208] A. Abada, C. Biggio, F. Bonnet, M.B. Gavela and T. Hambye, *Low energy effects of neutrino masses*, JHEP **12** (2007) 061 [arXiv:0707.4058] [INSPIRE].

[209] M.B. Gavela, T. Hambye, D. Hernandez and P. Hernández, *Minimal flavour seesaw models*, JHEP **09** (2009) 038 [arXiv:0906.1461] [INSPIRE].

[210] A. Zee, *A theory of lepton number violation, neutrino Majorana mass and oscillation*, Phys. Lett. B **93** (1980) 389 [Erratum ibid. B **95** (1980) 461] [INSPIRE].

[211] E. Witten, *Neutrino masses in the minimal $O(10)$ theory*, Phys. Lett. B **91** (1980) 81 [INSPIRE].

[212] A. Zee, *Quantum numbers of Majorana neutrino masses*, Nucl. Phys. B **264** (1986) 99 [INSPIRE].

[213] K.S. Babu, *Model of 'calculable' Majorana neutrino masses*, Phys. Lett. B **203** (1988) 132 [INSPIRE].

[214] E. Ma, *Verifiable radiative seesaw mechanism of neutrino mass and dark matter*, Phys. Rev. D **73** (2006) 077301 [hep-ph/0601225] [INSPIRE].

[215] P. Fileviez Perez and M.B. Wise, *On the origin of neutrino masses*, Phys. Rev. D **80** (2009) 053006 [arXiv:0906.2950] [INSPIRE].

[216] V.V. Khoze and G. Ro, *Leptogenesis and neutrino oscillations in the classically conformal Standard Model with the Higgs portal*, JHEP **10** (2013) 075 [arXiv:1307.3764] [INSPIRE].

[217] S.F. King, A. Merle and L. Panizzi, *Effective theory of a doubly charged singlet scalar: complementarity of neutrino physics and the LHC*, JHEP **11** (2014) 124 [arXiv:1406.4137] [INSPIRE].

[218] T. Geib, S.F. King, A. Merle, J.M. No and L. Panizzi, *Probing the origin of neutrino masses and mixings via doubly charged scalars: complementarity of the intensity and the energy frontiers*, Phys. Rev. D **93** (2016) 073007 [arXiv:1512.04391] [INSPIRE].

[219] S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, *Neutrino mass and mixing: from theory to experiment*, New J. Phys. **16** (2014) 045018 [arXiv:1402.4271] [INSPIRE].

[220] T. Appelquist and R. Shrock, *Neutrino masses in theories with dynamical electroweak symmetry breaking*, Phys. Lett. B **58** (2002) 204 [hep-ph/0204141] [INSPIRE].

[221] T. Appelquist and R. Shrock, *Dynamical symmetry breaking of extended gauge symmetries*, Phys. Rev. Lett. **90** (2003) 201801 [hep-ph/0301108] [INSPIRE].

[222] T. Appelquist, M. Piai and R. Shrock, *Fermion masses and mixing in extended technicolor models*, Phys. Rev. D **69** (2004) 015002 [hep-ph/0308061] [INSPIRE].

[223] J. Barry and W. Rodejohann, *Neutrino mass sum-rules in flavor symmetry models*, Nucl. Phys. B **842** (2011) 33 [arXiv:1007.5217] [INSPIRE].
[224] L. Dorame, D. Meloni, S. Morisi, E. Peinado and J.W.F. Valle, Constraining neutrinoless double beta decay, Nucl. Phys. B 861 (2012) 259 [arXiv:1111.5614] [INSPIRE].

[225] S.F. King, A. Merle and A.J. Stuart, The power of neutrino mass sum rules for neutrinoless double beta decay experiments, JHEP 12 (2013) 005 [arXiv:1307.2901] [INSPIRE].

[226] M. Agostini, A. Merle and K. Zuber, Probing flavor models with $^{76}$Ge-based experiments on neutrinoless double-$\beta$ decay, Eur. Phys. J. C 76 (2016) 176 [arXiv:1506.06133] [INSPIRE].

[227] S.T. Petcov and W. Rodejohann, Flavor symmetry $L_e-L_\mu-L_\tau$, atmospheric neutrino mixing and CP-violation in the lepton sector, Phys. Rev. D 71 (2005) 073002 [hep-ph/0409135] [INSPIRE].

[228] D. Marzocca, S.T. Petcov, A. Romanino and M.C. Sevilla, Nonzero $|U_{e3}|$ from charged lepton corrections and the atmospheric neutrino mixing angle, JHEP 05 (2013) 073 [arXiv:1302.0423] [INSPIRE].

[229] P. Ballett, S.F. King, C. Luhn, S. Pascoli and M.A. Schmidt, Testing atmospheric mixing sum rules at precision neutrino facilities, Phys. Rev. D 89 (2014) 016016 [arXiv:1308.4314] [INSPIRE].

[230] P.F. Harrison, D.H. Perkins and W.G. Scott, A redetermination of the neutrino mass squared difference in tri-maximal mixing with terrestrial matter effects, Phys. Lett. B 458 (1999) 79 [hep-ph/9904297] [INSPIRE].

[231] P.F. Harrison, D.H. Perkins and W.G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].

[232] E. Ma, $A_4$ symmetry and neutrinos with very different masses, Phys. Rev. D 70 (2004) 031901 [hep-ph/0404199] [INSPIRE].

[233] G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, $A_4$ and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [INSPIRE].

[234] Z.-Z. Xing, Nearly tri bimaximal neutrino mixing and CP-violation, Phys. Lett. B 533 (2002) 85 [hep-ph/0204049] [INSPIRE].

[235] L.J. Hall, H. Murayama and N. Weiner, Neutrino mass anarchy, Phys. Rev. Lett. 84 (2000) 2572 [hep-ph/9911341] [INSPIRE].

[236] S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].

[237] R.N. Mohapatra and J.W.F. Valle, Neutrino mass and baryon number nonconservation in superstring models, Phys. Rev. D 34 (1986) 1642 [INSPIRE].

[238] M. Malinsky, J.C. Romao and J.W.F. Valle, Novel supersymmetric SO(10) seesaw mechanism, Phys. Rev. Lett. 95 (2005) 161801 [hep-ph/0506296] [INSPIRE].

[239] M. Shaposhnikov, A possible symmetry of the $\nu$MSM, Nucl. Phys. B 763 (2007) 49 [hep-ph/0605047] [INSPIRE].

[240] T. Araki and Y.F. Li, $Q_6$ flavor symmetry model for the extension of the minimal Standard Model by three right-handed sterile neutrinos, Phys. Rev. D 85 (2012) 065016 [arXiv:1112.5819] [INSPIRE].

[241] S. Antusch and O. Fischer, Non-unitarity of the leptonic mixing matrix: present bounds and future sensitivities, JHEP 10 (2014) 094 [arXiv:1407.6607] [INSPIRE].

[242] D.J. Fixsen, E.S. Cheng, J.M. Gales, J.C. Mather, R.A. Shafer and E.L. Wright, The cosmic microwave background spectrum from the full COBE FIRAS data set, Astrophys. J. 473 (1996) 576 [astro-ph/9605054] [INSPIRE].

[243] D.J. Fixsen, The temperature of the cosmic microwave background, Astrophys. J. 707 (2009) 916 [arXiv:0911.1955] [INSPIRE].
[244] PLANCK collaboration, R. Adam et al., Planck 2015 results. I. Overview of products and scientific results, Astron. Astrophys. 594 (2016) A1 [arXiv:1502.01582] [INSPIRE].

[245] PLANCK collaboration, P.A.R. Ade et al., Planck 2015 results. XVII. Constraints on primordial non-Gaussianity, arXiv:1502.01592 [INSPIRE].

[246] J.R. Bond, G. Efstathiou and M. Tegmark, Forecasting cosmic parameter errors from microwave background anisotropy experiments, Mon. Not. Roy. Astron. Soc. 291 (1997) L33 [astro-ph/9702100] [INSPIRE].

[247] BOSS collaboration, T. Delubac et al., Baryon acoustic oscillations in the Ly-α forest of BOSS DR11 quasars, Astron. Astrophys. 574 (2015) A59 [arXiv:1404.1801] [INSPIRE].

[248] A.G. Riess et al., A 3% solution: determination of the Hubble constant with the Hubble Space Telescope and Wide Field Camera 3, Astrophys. J. 730 (2011) 119 [Erratum ibid. 732 (2011) 129] [Erratum ibid. 752 (2012) 76] [arXiv:1103.2976] [INSPIRE].

[249] G. Efstathiou, $H_0$ revisited, Mon. Not. Roy. Astron. Soc. 440 (2014) 1138 [arXiv:1311.3461] [INSPIRE].

[250] A.G. Riess et al., A 2.4% determination of the local value of the Hubble constant, Astrophys. J. 826 (2016) 56 [arXiv:1604.01424] [INSPIRE].

[251] C. Heymans et al., CFHTLenS tomographic weak lensing cosmological parameter constraints: mitigating the impact of intrinsic galaxy alignments, Mon. Not. Roy. Astron. Soc. 432 (2013) 2433 [arXiv:1303.1808] [INSPIRE].

[252] PLANCK collaboration, P.A.R. Ade et al., Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts, Astron. Astrophys. 594 (2016) A24 [arXiv:1502.01597] [INSPIRE].

[253] L. Samushia et al., The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measuring growth rate and geometry with anisotropic clustering, Mon. Not. Roy. Astron. Soc. 439 (2014) 3504 [arXiv:1312.4899] [INSPIRE].

[254] M. Wyman, D.H. Rudd, R.A. Vanderveld and W. Hu, Neutrinos help reconcile Planck measurements with the local universe, Phys. Rev. Lett. 112 (2014) 051302 [arXiv:1307.7715] [INSPIRE].

[255] J. Hamann and J. Hasenkamp, A new life for sterile neutrinos: resolving inconsistencies using hot dark matter, JCAP 10 (2013) 044 [arXiv:1308.3255] [INSPIRE].

[256] R.A. Battye and A. Moss, Evidence for massive neutrinos from cosmic microwave background and lensing observations, Phys. Rev. Lett. 112 (2014) 051303 [arXiv:1308.5870] [INSPIRE].

[257] B. Leistedt, H.V. Peiris and L. Verde, No new cosmological concordance with massive sterile neutrinos, Phys. Rev. Lett. 113 (2014) 041301 [arXiv:1404.5950] [INSPIRE].

[258] N. Palanque-Delabrouille et al., Constraint on neutrino masses from SDSS-III/BOSS Ly-α forest and other cosmological probes, JCAP 02 (2015) 045 [arXiv:1410.7244] [INSPIRE].

[259] BICEP2 collaboration, P.A.R. Ade et al., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett. 112 (2014) 241101 [arXiv:1403.3985] [INSPIRE].

[260] BICEP2 and PLANCK collaborations, P.A.R. Ade et al., Joint analysis of BICEP2/Keck Array and Planck data, Phys. Rev. Lett. 114 (2015) 101301 [arXiv:1502.00612] [INSPIRE].

[261] G. Mangano, G. Miele, S. Pastor, O. Pisanti and S. Sarikas, Updated BBN bounds on the cosmological lepton asymmetry for non-zero $\theta_{13}$, Phys. Lett. B 708 (2012) 1 [arXiv:1110.4335] [INSPIRE].

[262] G. Mangano, G. Miele, S. Pastor, T. Pinto, O. Pisanti and P.D. Serpico, Relic neutrino decoupling including flavor oscillations, Nucl. Phys. B 729 (2005) 221 [hep-ph/0506164] [INSPIRE].
[263] E. Grohs, G.M. Fuller, C.T. Kishimoto, M.W. Paris and A. Vlasenko, *Neutrino energy transport in weak decoupling and big bang nucleosynthesis*, Phys. Rev. D **93** (2016) 083522, [arXiv:1512.02205] [INSPIRE].

[264] J. Lesgourgues, G. Mangano, G. Miele and S. Pastor, *Neutrino cosmology*, Cambridge Univ. Press, Cambridge U.K. (2013).

[265] A.D. Dolgov, *Neutrinos in cosmology*, Phys. Rept. **370** (2002) 333 [hep-ph/0202122] [INSPIRE].

[266] S. Sarkar, *Big bang nucleosynthesis and physics beyond the Standard Model*, Rept. Prog. Phys. **59** (1996) 1493 [hep-ph/9602260] [INSPIRE].

[267] J.R. Primack, *Whatever happened to hot dark matter?, SLAC Beam Line 31N3* (2001) 50 [astro-ph/0112336] [INSPIRE].

[268] J. Lesgourgues and S. Pastor, *Massive neutrinos and cosmology*, Phys. Rept. **429** (2006) 307 [astro-ph/0603494] [INSPIRE].

[269] S. Bird, M. Viel and M.G. Haehnelt, *Massive neutrinos and the non-linear matter power spectrum*, Mon. Not. Roy. Astron. Soc. **420** (2012) 2551 [arXiv:1109.4416] [INSPIRE].

[270] R. Jimenez, T. Kitching, C. Pena-Garay and L. Verde, *Can we measure the neutrino mass hierarchy in the sky?, JCAP 05 (2010) 035* [arXiv:1003.5918] [INSPIRE].

[271] A.J. Cuesta, V. Niro and L. Verde, *Neutrino mass limits: robust information from the power spectrum of galaxy surveys*, Phys. Dark Univ. **13** (2016) 77 [arXiv:1511.05983] [INSPIRE].

[272] H. Gil-Marín et al., *The power spectrum and bispectrum of SDSS DR11 BOSS galaxies — II. Cosmological interpretation*, Mon. Not. Roy. Astron. Soc. **452** (2015) 1914 [arXiv:1408.0027] [INSPIRE].

[273] R.A. Battye, T. Charnock and A. Moss, *Tension between the power spectrum of density perturbations measured on large and small scales*, Phys. Rev. D **91** (2015) 103508 [arXiv:1409.2769] [INSPIRE].

[274] B. Audren, J. Lesgourgues, S. Bird, M.G. Haehnelt and M. Viel, *Neutrino masses and cosmological parameters from a Euclid-like survey: Markov chain Monte Carlo forecasts including theoretical errors*, JCAP **01** (2013) 026 [arXiv:1210.2194] [INSPIRE].

[275] A.C. Hall and A. Challinor, *Probing the neutrino mass hierarchy with CMB weak lensing*, Mon. Not. Roy. Astron. Soc. **425** (2012) 1170 [arXiv:1205.6172] [INSPIRE].

[276] J.R. Pritchard and E. Pierpaoli, *Constraining massive neutrinos using cosmological 21 cm observations*, Phys. Rev. D **78** (2008) 065009 [arXiv:0805.1920] [INSPIRE].

[277] W.L.K. Wu et al., *A guide to designing future ground-based cosmic microwave background experiments*, Astrophys. J. **788** (2014) 138 [arXiv:1402.4108] [INSPIRE].

[278] A. Font-Ribera, P. McDonald, N. Mostek, B.A. Reid, H.-J. Seo and A. Slosar, DESI and other dark energy experiments in the era of neutrino mass measurements, JCAP 05 (2014) 023 [arXiv:1308.4164] [INSPIRE].

[279] R.A. Alpher, H. Bethe and G. Gamow, *The origin of chemical elements*, Phys. Rev. **73** (1948) 803 [INSPIRE].

[280] R.V. Wagoner, W.A. Fowler and F. Hoyle, *On the synthesis of elements at very high temperatures*, Astrophys. J. **148** (1967) 3 [INSPIRE].

[281] L. Kawano, *Let's go: early universe. 2. Primordial nucleosynthesis: the computer way*, FERMILAB-PUB-92-004-A, Fermilab, Batavia U.S.A. (1992) [INSPIRE].

[282] O. Pisanti et al., *PArthENoPE: Public Algorithm Evaluating the Nucleosynthesis of Primordial Elements*, Comput. Phys. Commun. **178** (2008) 956 [arXiv:0705.0290] [INSPIRE].
[283] P.D. Serpico, S. Esposito, F. Iocco, G. Mangano, G. Miele and O. Pisanti, Nuclear reaction network for primordial nucleosynthesis: a detailed analysis of rates, uncertainties and light nuclei yields, JCAP 12 (2004) 010 [astro-ph/0408076] [INSPIRE].

[284] F. Iocco, G. Mangano, G. Miele, O. Pisanti and P.D. Serpico, *Primordial nucleosynthesis: from precision cosmology to fundamental physics*, Phys. Rept. **472** (2009) 1 [arXiv:0809.0631] [INSPIRE].

[285] E. Aver, K.A. Olive, R.L. Porter and E.D. Skillman, *The primordial helium abundance from updated emissivities*, JCAP **11** (2013) 017 [arXiv:1309.0047] [INSPIRE].

[286] R. Cooke, M. Pettini, R.A. Jorgenson, M.T. Murphy and C.C. Steidel, *Precision measures of the primordial abundance of deuterium*, Astrophys. J. **781** (2014) 31 [arXiv:1308.3240] [INSPIRE].

[287] G. Karagiorgi, *Toward solution of the MiniBooNE-LSND anomalies*, Nucl. Phys. Proc. Suppl. B **229-232** (2012) 50 [INSPIRE].

[288] K.N. Abazajian, *Telling three from four neutrinos with cosmology*, Astropart. Phys. **19** (2003) 303 [astro-ph/0205238] [INSPIRE].

[289] G. Mangano and P.D. Serpico, *A robust upper limit on $N_{\text{eff}}$ from BBN*, circa 2011, Phys. Lett. B **701** (2011) 296 [arXiv:1103.1261] [INSPIRE].

[290] Z. Hou, R. Keisler, L. Knox, M. Millea and C. Reichardt, *How massless neutrinos affect the cosmic microwave background damping tail*, Phys. Rev. D **87** (2013) 083008 [arXiv:1104.2333] [INSPIRE].

[291] M. Archidiacono, E. Giusarma, S. Hannestad and O. Mena, *Cosmic dark radiation and neutrinos*, Adv. High Energy Phys. **2013** (2013) 191047 [arXiv:1307.0637] [INSPIRE].

[292] M. Archidiacono, N. Fornengo, S. Gariazzo, C. Giunti, S. Hannestad and M. Laveder, *Light sterile neutrinos after BICEP-2*, JCAP **06** (2014) 031 [arXiv:1404.1794] [INSPIRE].

[293] J. Bergström, M.C. Gonzalez-Garcia, V. Niro and J. Salvado, *Statistical tests of sterile neutrinos using cosmology and short-baseline data*, JHEP **10** (2014) 104 [arXiv:1407.3806] [INSPIRE].

[294] M. Maltoni, T. Schwetz and J.W.F. Valle, *Status of four neutrino mass schemes: a global and unified approach to current neutrino oscillation data*, Phys. Rev. D **65** (2002) 093004 [hep-ph/0112103] [INSPIRE].

[295] G. Sigl and G. Raffelt, *General kinetic description of relativistic mixed neutrinos*, Nucl. Phys. B **406** (1993) 423 [INSPIRE].

[296] A.D. Dolgov, *Neutrinos in the early universe*, Sov. J. Nucl. Phys. **33** (1981) 700 [Yad. Fiz. **33** (1981) 1309] [INSPIRE].

[297] A.D. Dolgov, S.H. Hansen, S. Pastor, S.T. Petcov, G.G. Raffelt and D.V. Semikoz, *Cosmological bounds on neutrino degeneracy improved by flavor oscillations*, Nucl. Phys. B **632** (2002) 363 [hep-ph/0201287] [INSPIRE].

[298] A. Mirizzi, N. Saviano, G. Miele and P.D. Serpico, *Light sterile neutrino production in the early universe with dynamical neutrino asymmetries*, Phys. Rev. D **86** (2012) 053009 [arXiv:1206.1046] [INSPIRE].

[299] S. Hannestad, I. Tamborra and T. Tram, *Thermalisation of light sterile neutrinos in the early universe*, JCAP **07** (2012) 025 [arXiv:1204.5861] [INSPIRE].

[300] N. Saviano, A. Mirizzi, O. Pisanti, P.D. Serpico, G. Mangano and G. Miele, *Multi-momentum and multi-flavour active-sterile neutrino oscillations in the early universe: role of neutrino asymmetries and effects on nucleosynthesis*, Phys. Rev. D **87** (2013) 073006 [arXiv:1302.1200] [INSPIRE].

[301] S. Hannestad, R.S. Hansen and T. Tram, *How self-interactions can reconcile sterile neutrinos with cosmology*, Phys. Rev. Lett. **112** (2014) 031802 [arXiv:1310.5926] [INSPIRE].
[302] B. Dasgupta and J. Kopp, *Cosmologically safe eV-scale sterile neutrinos and improved dark matter structure*, Phys. Rev. Lett. **112** (2014) 031803 [arXiv:1310.6337] [INSPIRE].

[303] M. Archidiacono and S. Hannestad, *Updated constraints on non-standard neutrino interactions from Planck*, JCAP **07** (2014) 046 [arXiv:1311.3873] [INSPIRE].

[304] A. Mirizzi, G. Mangano, O. Pisanti and N. Saviano, *Collisional production of sterile neutrinos via secret interactions and cosmological implications*, Phys. Rev. D **91** (2015) 025019 [arXiv:1410.1385] [INSPIRE].

[305] N. Saviano, O. Pisanti, G. Mangano and A. Mirizzi, *Unveiling secret interactions among sterile neutrinos with big-bang nucleosynthesis*, Phys. Rev. D **90** (2014) 113009 [arXiv:1409.1680] [INSPIRE].

[306] T. Bringmann, J. Hasenkamp and J. Kersten, *Tight bonds between sterile neutrinos and dark matter*, JCAP **07** (2014) 042 [arXiv:1312.4947] [INSPIRE].

[307] X. Chu and B. Dasgupta, *Dark radiation alleviates problems with dark matter halos*, Phys. Rev. Lett. **113** (2014) 161301 [arXiv:1404.6127] [INSPIRE].

[308] C. Boehm, J.A. Schewtschenko, R.J. Wilkinson, C.M. Baugh and S. Pascoli, *Using the milky way satellites to study interactions between cold dark matter and radiation*, Mon. Not. Roy. Astron. Soc. **445** (2014) L31 [arXiv:1404.7012] [INSPIRE].

[309] M. Archidiacono, S. Hannestad, R.S. Hansen and T. Tram, *Cosmology with self-interacting sterile neutrinos and dark matter — a pseudoscalar model*, Phys. Rev. D **91** (2015) 065021 [arXiv:1404.5915] [INSPIRE].

[310] M.G. Walker, *Dark matter in the milky way’s dwarf spheroidal satellites*, arXiv:1205.0311 [INSPIRE].

[311] A. Boyarsky, O. Ruchayskiy and D. Iakubovskyi, *A lower bound on the mass of dark matter particles*, JCAP **03** (2009) 005 [arXiv:0808.3902] [INSPIRE].

[312] D. Gorbunov, A. Khmelnitsky and V. Rubakov, *Constraining sterile neutrino dark matter by phase-space density observations*, JCAP **10** (2008) 041 [arXiv:0808.3910] [INSPIRE].

[313] S. Horiuchi, P.J. Humphrey, J. Onorbe, K.N. Abazajian, M. Kaplinghat and S. Garrison-Kimmel, *Sterile neutrino dark matter bounds from galaxies of the local group*, Phys. Rev. D **89** (2014) 025017 [arXiv:1311.0282] [INSPIRE].

[314] X.-D. Shi and G.M. Fuller, *A new dark matter candidate: nonthermal sterile neutrinos*, Phys. Rev. Lett. **82** (1999) 2832 [astro-ph/9810076] [INSPIRE].

[315] K. Abazajian, G.M. Fuller and M. Patel, *Sterile neutrino hot, warm and cold dark matter*, Phys. Rev. D **64** (2001) 023501 [astro-ph/0101524] [INSPIRE].

[316] M. Laine and M. Shaposhnikov, *Sterile neutrino dark matter as a consequence of νMSM-induced lepton asymmetry*, JCAP **06** (2008) 031 [arXiv:0804.4543] [INSPIRE].

[317] T. Venumadhav, F.-Y. Cyr-Racine, K.N. Abazajian and C.M. Hirata, *Sterile neutrino dark matter: weak interactions in the strong coupling epoch*, Phys. Rev. D **94** (2016) 043515 [arXiv:1507.06655] [INSPIRE].

[318] S.P. Mikheev and A. Yu. Smirnov, *Resonance amplification of oscillations in matter and spectroscopy of solar neutrinos*, Sov. J. Nucl. Phys. **42** (1985) 913 [Yad. Fiz. **42** (1985) 1441] [INSPIRE].

[319] L. Wolfenstein, *Neutrino oscillations in matter*, Phys. Rev. D **17** (1978) 2369 [INSPIRE].

[320] T. Asaka, M. Laine and M. Shaposhnikov, *Lightest sterile neutrino abundance within the νMSM*, JHEP **01** (2007) 091 [Erratum ibid. **02** (2015) 028] [hep-ph/0612182] [INSPIRE].

[321] B.W. Lee and R.E. Shrock, *Natural suppression of symmetry violation in gauge theories: muon-lepton and electron lepton number nonconservation*, Phys. Rev. D **16** (1977) 1444 [INSPIRE].
[322] P.B. Pal and L. Wolfenstein, *Radiative decays of massive neutrinos*, Phys. Rev. D **25** (1982) 766 [INSPIRE].

[323] V.D. Barger, R.J.N. Phillips and S. Sarkar, *Remarks on the KARMEN anomaly*, Phys. Lett. B **352** (1995) 365 [Erratum ibid. B **356** (1995) 617] [hep-ph/9503295] [INSPIRE].

[324] A.D. Dolgov and S.H. Hansen, *Massive sterile neutrinos as warm dark matter*, Astropart. Phys. **16** (2002) 339 [hep-ph/0009083] [INSPIRE].

[325] A. Boyarsky, A. Neronov, O. Ruchayskiy and M. Shaposhnikov, *The masses of active neutrinos in the $ν$MSM from X-ray astronomy*, JETP Lett. **83** (2006) 133 [hep-ph/0601098] [INSPIRE].

[326] S.H. Hansen, J. Lesgourgues, S. Pastor and J. Silk, *Constraining the window on sterile neutrinos as warm dark matter*, Mon. Not. Roy. Astron. Soc. **333** (2002) 544 [astro-ph/0106108] [INSPIRE].

[327] M. Viel, J. Lesgourgues, M.G. Haehnelt, S. Matarrese and A. Riotto, *Can sterile neutrinos be ruled out as warm dark matter candidates?*, Phys. Rev. Lett. **97** (2006) 071301 [astro-ph/0605706] [INSPIRE].

[328] M. Viel, J. Lesgourgues, M.G. Haehnelt, S. Matarrese and A. Riotto, *Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-α forest*, Phys. Rev. D **71** (2005) 063534 [astro-ph/0501562] [INSPIRE].

[329] U. Seljak, A. Makarov, P. McDonald and H. Trac, *Can sterile neutrinos be the dark matter?*, Phys. Rev. Lett. **97** (2006) 191303 [astro-ph/0602430] [INSPIRE].

[330] A. Boyarsky, J. Lesgourgues, O. Ruchayskiy and M. Viel, *Realistic sterile neutrino dark matter with keV mass does not contradict cosmological bounds*, Phys. Rev. Lett. **102** (2009) 201304 [arXiv:0812.3256] [INSPIRE].

[331] M. Viel, G.D. Becker, J.S. Bolton and M.G. Haehnelt, *Warm dark matter as a solution to the small scale crisis: new constraints from high redshift Lyman-α forest data*, Phys. Rev. D **88** (2013) 043502 [arXiv:1306.2314] [INSPIRE].

[332] M. Viel, G.D. Becker, J.S. Bolton, M.G. Haehnelt, M. Rauch and W.L.W. Sargent, *How cold is cold dark matter? Small scales constraints from the flux power spectrum of the high-redshift Lyman-α forest*, Phys. Rev. Lett. **100** (2008) 041304 [arXiv:0709.0131] [INSPIRE].

[333] P. Bode, J.P. Ostriker and N. Turok, *Halo formation in warm dark matter models*, Astrophys. J. **556** (2001) 93 [astro-ph/0010389] [INSPIRE].

[334] A. Schneider, D. Anderhalden, A.V. Macciò and J. Diemand, *Warm dark matter does not do better than cold dark matter in solving small-scale inconsistencies*, Mon. Not. Roy. Astron. Soc. **441** (2014) 6 [arXiv:1309.5960] [INSPIRE].

[335] A.V. Macciò, S. Paduroiu, D. Anderhalden, A. Schneider and B. Moore, *Cores in warm dark matter haloes: a catch* 22 problem, Mon. Not. Roy. Astron. Soc. **424** (2012) 1105 [arXiv:1202.1282] [INSPIRE].

[336] A.V. Macciò and F. Fontanot, *How cold is dark matter? Constraints from milky way satellites*, Mon. Not. Roy. Astron. Soc. **404** (2010) 16 [arXiv:0910.2460] [INSPIRE].

[337] A. Schneider, R.E. Smith, A.V. Macciò and B. Moore, *Nonlinear evolution of cosmological structures in warm dark matter models*, Mon. Not. Roy. Astron. Soc. **424** (2012) 684 [arXiv:1112.0330] [INSPIRE].

[338] T. Goerdt, B. Moore, J.I. Read, J. Stadel and M. Zemp, *Does the Fornax dwarf spheroidal have a central cusp or core?*, Mon. Not. Roy. Astron. Soc. **368** (2006) 1073 [astro-ph/0601404] [INSPIRE].

[339] B. Moore, T.R. Quinn, F. Governato, J. Stadel and G. Lake, *Cold collapse and the core catastrophe*, Mon. Not. Roy. Astron. Soc. **310** (1999) 1147 [astro-ph/9903164] [INSPIRE].
[340] R. Kennedy, C. Frenk, S. Cole and A. Benson, Constraining the warm dark matter particle mass with milky way satellites, Mon. Not. Roy. Astron. Soc. 442 (2014) 2487 [arXiv:1310.7739] [INSPIRE].

[341] M.R. Lovell, C.S. Frenk, V.R. Eke, A. Jenkins, L. Gao and T. Theuns, The properties of warm dark matter haloes, Mon. Not. Roy. Astron. Soc. 439 (2014) 300 [arXiv:1308.1399] [INSPIRE].

[342] S. Shao, L. Gao, T. Theuns and C.S. Frenk, The phase space density of fermionic dark matter haloes, Mon. Not. Roy. Astron. Soc. 430 (2013) 2346 [arXiv:1209.5563] [INSPIRE].

[343] A. Boyarsky, D. Iakubovskyi and O. Ruchayskiy, Next decade of sterile neutrino studies, Phys. Dark Univ. 1 (2012) 136 [arXiv:1306.4954] [INSPIRE].

[344] K. Abazajian, Production and evolution of perturbations of sterile neutrino dark matter, Phys. Rev. D 73 (2006) 063506 [astro-ph/0511630] [INSPIRE].

[345] A. Boyarsky, A. Neronov, O. Ruchayskiy, M. Shaposhnikov and I. Tkachev, Where to find a dark matter sterile neutrino?, Phys. Rev. Lett. 97 (2006) 261302 [astro-ph/0603660] [INSPIRE].

[346] A. Boyarsky, D. Iakubovskyi, O. Ruchayskiy and V. Savchenko, Constraints on decaying dark matter from XMM-Newton observations of M31, Mon. Not. Roy. Astron. Soc. 387 (2008) 1361 [arXiv:0709.2301] [INSPIRE].

[347] A. Boyarsky, D. Malyshev, A. Neronov and O. Ruchayskiy, Constraining DM properties with SPI, Mon. Not. Roy. Astron. Soc. 387 (2008) 1345 [arXiv:0710.4922] [INSPIRE].

[348] R.E. Shrock, Pure leptonic decays with massive neutrinos and arbitrary Lorentz structure, Phys. Lett. B 112 (1982) 382 [INSPIRE].

[349] A. Kusenko, S. Pascoli and D. Semikoz, New bounds on MeV sterile neutrinos based on the accelerator and Super-Kamiokande results, JHEP 11 (2005) 028 [hep-ph/0405198] [INSPIRE].

[350] PIENU collaboration, M. Aoki et al., Search for massive neutrinos in the decay $\pi \to e\nu$, Phys. Rev. D 84 (2011) 052002 [arXiv:1106.4055] [INSPIRE].

[351] E949 collaboration, A.V. Artamonov et al., Search for heavy neutrinos in $K^+ \to \mu^+\nu_H$ decays, Phys. Rev. D 91 (2015) 052001 [arXiv:1411.3963] [INSPIRE].

[352] A.D. Dolgov, S.H. Hansen, G. Raffelt and D.V. Semikoz, Cosmological and astrophysical bounds on a heavy sterile neutrino and the KARMEN anomaly, Nucl. Phys. B 580 (2000) 331 [hep-ph/0002223] [INSPIRE].

[353] A.D. Dolgov, S.H. Hansen, G. Raffelt and D.V. Semikoz, Heavy sterile neutrinos: bounds from big bang nucleosynthesis and SN1987A, Nucl. Phys. B 590 (2000) 562 [hep-ph/0008138] [INSPIRE].

[354] G.M. Fuller, A. Kusenko and K. Petraki, Heavy sterile neutrinos and supernova explosions, Phys. Lett. B 670 (2009) 281 [arXiv:0806.4273] [INSPIRE].

[355] A.C. Vincent, E.F. Martinez, P. Hernández, M. Lattanzi and O. Mena, Revisiting cosmological bounds on sterile neutrinos, JCAP 04 (2015) 006 [arXiv:1408.1956] [INSPIRE].

[356] G. Gelmini, E. Osoba, S. Palomares-Ruiz and S. Pascoli, MeV sterile neutrinos in low reheating temperature cosmological scenarios, JCAP 10 (2008) 029 [arXiv:0803.2735] [INSPIRE].

[357] M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].

[358] A. Ibarra, D. Tran and C. Weniger, Indirect searches for decaying dark matter, Int. J. Mod. Phys. A 28 (2013) 1330040 [arXiv:1307.6434] [INSPIRE].

[359] R.E. Shrock, Electromagnetic properties and decays of Dirac and Majorana neutrinos in a general class of gauge theories, Nucl. Phys. B 206 (1982) 359 [INSPIRE].
[360] H.E.S.S. collaboration, A. Abramowski et al., Search for photon-linelike signatures from dark matter annihilations with H.E.S.S., Phys. Rev. Lett. 110 (2013) 041301 [arXiv:1301.1173] [INSPIRE].

[361] J. Aleksić et al., Optimized dark matter searches in deep observations of Segue 1 with MAGIC, JCAP 02 (2014) 008 [arXiv:1312.1535] [INSPIRE].

[362] W. Buchmüller and C. Greub, Heavy Majorana neutrinos in electron-positron and electron-proton collisions, Nucl. Phys. B 363 (1991) 345 [INSPIRE].

[363] FERMI-LAT collaboration, M. Ackermann et al., Fermi LAT search for dark matter in gamma-ray lines and the inclusive photon spectrum, Phys. Rev. D 86 (2012) 022002 [arXiv:1205.2739] [INSPIRE].

[364] L. Dugger, T.E. Jeltema and S. Profumo, Constraints on decaying dark matter from Fermi observations of nearby galaxies and clusters, JCAP 12 (2010) 015 [arXiv:1009.5988] [INSPIRE].

[365] M. Garny, A. Ibarra and D. Tran, Constraints on hadronically decaying dark matter, JCAP 08 (2012) 025 [arXiv:1205.6783] [INSPIRE].

[366] I. Cholis, New constraints from PAMELA anti-proton data on annihilating and decaying dark matter, JCAP 09 (2011) 007 [arXiv:1007.1160] [INSPIRE].

[367] PAMELA collaboration, O. Adriani et al., PAMELA results on the cosmic-ray antiproton flux from 60 MeV to 180 GeV in kinetic energy, Phys. Rev. Lett. 105 (2010) 121101 [arXiv:1007.0821] [INSPIRE].

[368] A. Ibarra, A.S. Lamperstorfer and J. Silk, Dark matter annihilations and decays after the AMS-02 positron measurements, Phys. Rev. D 89 (2014) 063539 [arXiv:1309.2570] [INSPIRE].

[369] AMS collaboration, M. Aguilar et al., Precision measurement of the $(e^+ + e^-)$ flux in primary cosmic rays from 0.5 GeV to 1 TeV with the Alpha Magnetic Spectrometer on the International Space Station, Phys. Rev. Lett. 113 (2014) 221102 [INSPIRE].

[370] AMS collaboration, M. Aguilar et al., Electron and positron fluxes in primary cosmic rays measured with the Alpha Magnetic Spectrometer on the International Space Station, Phys. Rev. Lett. 113 (2014) 121102 [INSPIRE].

[371] ICECUBE collaboration, A. Achterberg et al., Multi-year search for a diffuse flux of muon neutrinos with AMANDA-II, Phys. Rev. D 76 (2007) 042008 [Erratum ibid. D 77 (2008) 089904] [arXiv:0705.1315] [INSPIRE].

[372] ICECUBE collaboration, R. Abbasi et al., A search for UHE tau neutrinos with IceCube, Phys. Rev. D 86 (2012) 022005 [arXiv:1202.4564] [INSPIRE].

[373] ICECUBE collaboration, R. Abbasi et al., Constraints on the extremely-high energy cosmic neutrino flux with the IceCube 2008-2009 data, Phys. Rev. D 83 (2011) 092003 [Erratum ibid. D 84 (2011) 079902] [arXiv:1103.4250] [INSPIRE].

[374] PIERRE AUGER collaboration, P. Abreu et al., A search for ultra-high energy neutrinos in highly inclined events at the Pierre Auger observatory, Phys. Rev. D 84 (2011) 122005 [arXiv:1202.1493] [INSPIRE].

[375] ANITA collaboration, P.W. Gorham et al., Observational constraints on the ultra-high energy cosmic neutrino flux from the second flight of the ANITA experiment, Phys. Rev. D 82 (2010) 022004 [Erratum ibid. D 85 (2012) 049901] [arXiv:1011.5004] [INSPIRE].

[376] A. Esmaili, A. Ibarra and O.L.G. Peres, Probing the stability of superheavy dark matter particles with high-energy neutrinos, JCAP 11 (2012) 034 [arXiv:1205.5281] [INSPIRE].

[377] R. Barbieri, D.V. Nanopoulos, G. Morchio and F. Strocchi, Neutrino masses in grand unified theories, Phys. Lett. B 90 (1980) 91 [INSPIRE].
[378] S. Davidson and A. Ibarra, A lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett. B 535 (2002) 25 [hep-ph/0202239] [INSPIRE].

[379] P. Di Bari, Seesaw geometry and leptogenesis, Nucl. Phys. B 727 (2005) 318 [hep-ph/0502082] [INSPIRE].

[380] O. Vives, Flavor dependence of CP asymmetries and thermal leptogenesis with strong right-handed neutrino mass hierarchy, Phys. Rev. D 73 (2006) 073006 [hep-ph/0512160] [INSPIRE].

[381] S. Blanchet and P. Di Bari, New aspects of leptogenesis bounds, Nucl. Phys. B 807 (2009) 155 [arXiv:0807.0743] [INSPIRE].

[382] R. Barbieri, P. Creminelli, A. Strumia and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys. B 575 (2000) 61 [hep-ph/9911315] [INSPIRE].

[383] G. Engelhard, Y. Grossman, E. Nardi and Y. Nir, The importance of $N_2$ leptogenesis, Phys. Rev. Lett. 99 (2007) 081802 [hep-ph/0612187] [INSPIRE].

[384] E. Bertuzzo, P. Di Bari, F. Feruglio and E. Nardi, Flavor symmetries, leptogenesis and the absolute neutrino mass scale, JHEP 11 (2009) 036 [arXiv:0908.0161] [INSPIRE].

[385] S. Antusch, P. Di Bari, D.A. Jones and S.F. King, Leptogenesis in the two right-handed neutrino model revisited, Phys. Rev. D 86 (2012) 023516 [arXiv:1107.6002] [INSPIRE].

[386] E. Nardi, Y. Nir, E. Roulet and J. Racker, The importance of flavor in leptogenesis, JHEP 01 (2006) 164 [hep-ph/0601084] [INSPIRE].

[387] A. Abada, S. Davidson, F.-X. Josse-Michaux, M. Losada and A. Riotto, Flavor issues in leptogenesis, JCAP 04 (2006) 004 [hep-ph/0601083] [INSPIRE].

[388] S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP 03 (2007) 018 [hep-ph/0607330] [INSPIRE].

[389] W. Buchmüller, P. Di Bari and M. Plümacher, The neutrino mass window for baryogenesis, Nucl. Phys. B 665 (2003) 445 [hep-ph/0302092] [INSPIRE].

[390] G.F. Giudice, A. Notari, M. Raidal, A. Riotto and A. Strumia, Towards a complete theory of thermal leptogenesis in the SM and MSSM, Nucl. Phys. B 685 (2004) 89 [hep-ph/0310123] [INSPIRE].

[391] W. Buchmüller, P. Di Bari and M. Plümacher, Leptogenesis for pedestrians, Annals Phys. 315 (2005) 305 [hep-ph/0401240] [INSPIRE].

[392] A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56 (1997) 5431 [hep-ph/9707235] [INSPIRE].

[393] A. Pilaftsis and T.E.J. Underwood, Electroweak-scale resonant leptogenesis, Phys. Rev. D 72 (2005) 113001 [hep-ph/0506107] [INSPIRE].

[394] S. Blanchet, T. Hambye and F.-X. Josse-Michaux, Reconciling leptogenesis with observable $\mu \to e\gamma$ rates, JHEP 04 (2010) 023 [arXiv:0912.3153] [INSPIRE].

[395] E.K. Akhmedov, V.A. Rubakov and A. Yu. Smirnov, Baryogenesis via neutrino oscillations, Phys. Rev. Lett. 81 (1998) 1359 [hep-ph/9803255] [INSPIRE].

[396] K. Dick, M. Lindner, M. Ratz and D. Wright, Leptogenesis with Dirac neutrinos, Phys. Rev. Lett. 84 (2000) 4039 [hep-ph/9907562] [INSPIRE].

[397] L. Canetti, M. Drewes and M. Shaposhnikov, Sterile neutrinos as the origin of dark and baryonic matter, Phys. Rev. Lett. 110 (2013) 061801 [arXiv:1204.3902] [INSPIRE].

[398] L. Canetti, M. Drewes, T. Frossard and M. Shaposhnikov, Dark matter, baryogenesis and neutrino oscillations from right handed neutrinos, Phys. Rev. D 87 (2013) 093006 [arXiv:1208.4607] [INSPIRE].
[399] M. Shaposhnikov, *The νMSM, leptonic asymmetries and properties of singlet fermions*, JHEP 08 (2008) 008 [arXiv:0804.4542] [INSPIRE].

[400] B. Garbrecht, *More viable parameter space for leptogenesis*, Phys. Rev. D 90 (2014) 063522 [arXiv:1401.3278] [INSPIRE].

[401] M. Drewes and B. Garbrecht, *Leptogenesis from a GeV seesaw without mass degeneracy*, JHEP 03 (2013) 096 [arXiv:1206.5537] [INSPIRE].

[402] S. Alekhin et al., *A facility to search for hidden particles at the CERN SPS: the SHiP physics case*, Rept. Prog. Phys. 79 (2016) 124201 [arXiv:1504.04855] [INSPIRE].

[403] G. Cvetič, C.S. Kim and J. Zamora-Saá, *CP violation in lepton number violating semihadronic decays of K, D, Ds, B, Bc*, Phys. Rev. D 89 (2014) 093012 [arXiv:1403.2555] [INSPIRE].

[404] B. Shuve and I. Yavin, *Baryogenesis through neutrino oscillations: a unified perspective*, Phys. Rev. D 89 (2014) 075014 [arXiv:1401.2459] [INSPIRE].

[405] A. Anisimov, *Majorana dark matter*, hep-ph/0612024 [INSPIRE].

[406] A. Anisimov and P. Di Bari, *Cold dark matter from heavy right-handed neutrino mixing*, Phys. Rev. D 80 (2009) 073017 [arXiv:0812.5085] [INSPIRE].

[407] T. Hambye, *Leptogenesis: beyond the minimal type-I seesaw scenario*, New J. Phys. 14 (2012) 012501 [arXiv:1212.2888] [INSPIRE].

[408] G.C. Branco, R. Gonzalez Felipe, F.R. Joaquim and M.N. Rebelo, *Leptogenesis, CP-violation and neutrino data: what can we learn?*, Nucl. Phys. B 640 (2002) 202 [hep-ph/0202030] [INSPIRE].

[409] E.K. Akhmedov, M. Frigerio and A. Yu. Smirnov, *Probing the seesaw mechanism with neutrino data and leptogenesis*, JHEP 09 (2003) 021 [hep-ph/0305322] [INSPIRE].

[410] P. Di Bari and A. Riotto, *Successful type-I leptogenesis with SO(10)-inspired mass relations*, Phys. Lett. B 671 (2009) 462 [arXiv:0809.2285] [INSPIRE].

[411] P. Di Bari and A. Riotto, *Testing SO(10)-inspired leptogenesis with low energy neutrino experiments*, JCAP 04 (2011) 037 [arXiv:1012.2343] [INSPIRE].

[412] P. Di Bari and L. Marzola, SO(10)-inspired solution to the problem of the initial conditions in leptogenesis, Nucl. Phys. B 877 (2013) 719 [arXiv:1308.1107] [INSPIRE].

[413] P. Di Bari, S. King and M. Re Fiorentin, *Strong thermal leptogenesis and the absolute neutrino mass scale*, JCAP 03 (2014) 050 [arXiv:1401.6185] [INSPIRE].

[414] P. Di Bari, L. Marzola and M. Re Fiorentin, *Decrypting SO(10)-inspired leptogenesis*, Nucl. Phys. B 893 (2015) 122 [arXiv:1411.5478] [INSPIRE].

[415] D. Hooper and L. Goodenough, *Dark matter annihilation in the galactic center as seen by the Fermi gamma ray space telescope*, Phys. Lett. B 697 (2011) 412 [arXiv:1010.2752] [INSPIRE].

[416] J.S. Bullock, A.V. Kravtsov and D.H. Weinberg, *Hierarchical galaxy formation and substructure in the galaxy’s stellar halo*, Astrophys. J. 548 (2001) 33 [astro-ph/0007295] [INSPIRE].

[417] A.J. Benson, C.S. Frenk, C.G. Lacey, C.M. Baugh and S. Cole, *The effects of photoionization on galaxy formation*. 2. Satellites in the local group, Mon. Not. Roy. Astron. Soc. 333 (2002) 177 [astro-ph/0108218] [INSPIRE].

[418] J.F. Navarro, C.S. Frenk and S.D.M. White, *A universal density profile from hierarchical clustering*, Astrophys. J. 490 (1997) 493 [astro-ph/9611107] [INSPIRE].

[419] S. Horiuchi et al., *Properties of resonantly produced sterile neutrino dark matter subhaloes*, Mon. Not. Roy. Astron. Soc. 456 (2016) 4346 [arXiv:1512.04548] [INSPIRE].

[420] T. Sawala et al., *Bent by baryons: the low mass galaxy-halo relation*, Mon. Not. Roy. Astron. Soc. 448 (2015) 2941 [arXiv:1404.3724] [INSPIRE].
[421] G. Kauffmann, S.D.M. White and B. Guiderdoni, *The formation and evolution of galaxies within merging dark matter haloes*, Mon. Not. Roy. Astron. Soc. **264** (1993) 201 [INSPIRE].

[422] S. Cole, A. Aragon-Salamanca, C.S. Frenk, J.F. Navarro and S.E. Zepf, *A recipe for galaxy formation*, Mon. Not. Roy. Astron. Soc. **271** (1994) 781 [astro-ph/9402001] [INSPIRE].

[423] P. Monaco, P. Salucci and L. Danese, *Joint cosmological formation of QSOs and bulge-dominated galaxies*, Mon. Not. Roy. Astron. Soc. **311** (2000) 279 [astro-ph/9907095] [INSPIRE].

[424] G. Kauffmann and M. Haehnelt, *A unified model for the evolution of galaxies and quasars*, Mon. Not. Roy. Astron. Soc. **311** (2000) 576 [astro-ph/9906493] [INSPIRE].

[425] G.L. Granato, G. De Zotti, L. Silva, A. Bressan and L. Danese, *A physical model for the co-evolution of QSOs and of their spheroidal hosts*, Astrophys. J. **600** (2004) 580 [astro-ph/0307202] [INSPIRE].

[426] N. Menci, A. Fontana, E. Giallongo, A. Grazian and S. Salimbeni, *The abundance of distant and extremely red galaxies: the role of AGN feedback in hierarchical models*, Astrophys. J. **647** (2006) 753 [astro-ph/0605123] [INSPIRE].

[427] D.J. Croton et al., *The many lives of AGN: cooling flows, black holes and the luminosities and colours of galaxies*, Mon. Not. Roy. Astron. Soc. **365** (2006) 11 [Erratum ibid. **367** (2006) 864] [astro-ph/0602065] [INSPIRE].

[428] R.G. Bower et al., *The broken hierarchy of galaxy formation*, Mon. Not. Roy. Astron. Soc. **370** (2006) 645 [astro-ph/0511338] [INSPIRE].

[429] R.S. Somerville and J.R. Primack, *Semianalytic modeling of galaxy formation. The local universe*, Mon. Not. Roy. Astron. Soc. **310** (1999) 1087 [astro-ph/9802268] [INSPIRE].

[430] S. Cole, C.G. Lacey, C.M. Baugh and C.S. Frenk, *Hierarchical galaxy formation*, Mon. Not. Roy. Astron. Soc. **319** (2000) 168 [astro-ph/0007281] [INSPIRE].

[431] F. Poli, N. Menci, E. Giallongo, A. Fontana, S. Cristiani and S. D'Odorico, *The evolution of the luminosity function in deep fields: a comparison with CDM models*, Astrophys. J. **551** (2001) L45 [astro-ph/0103113] [INSPIRE].

[432] M. Cirasuolo, R.J. McLure, J.S. Dunlop, O. Almaini, S. Foucaud and C. Simpson, *A new measurement of the evolving near-infrared galaxy luminosity function out to $z \sim 4$: a continuing challenge to theoretical models of galaxy formation*, Mon. Not. Roy. Astron. Soc. **401** (2010) 1166 [arXiv:0804.3471] [INSPIRE].

[433] B.L. Faro, P. Monaco, E. Vanzella, F. Fontanot, L. Silva and S. Cristiani, *Faint Lyman-break galaxies as a crucial test for galaxy formation models*, Mon. Not. Roy. Astron. Soc. **399** (2009) 827 [arXiv:0906.4998] [INSPIRE].

[434] S. Salimbeni et al., *The red and blue galaxy populations in the GOODS field: evidence for an excess of red dwarfs*, Astron. Astrophys. (2007) [arXiv:0710.3704] [INSPIRE].

[435] A. Fontana et al., *The galaxy mass function up to $z = 4$ in the GOODS-MUSIC sample: into the epoch of formation of massive galaxies*, Astron. Astrophys. **459** (2006) 745 [astro-ph/0609068] [INSPIRE].

[436] F. Fontanot, G. De Lucia, P. Monaco, R.S. Somerville and P. Santini, *The many manifestations of downsizing: hierarchical galaxy formation models confront observations*, Mon. Not. Roy. Astron. Soc. **397** (2009) 1776 [arXiv:0901.1130] [INSPIRE].

[437] D. Marchesini, P.G. van Dokkum, N.M.F. Schreiber, M. Franx, I. Labbe' and S. Wuyts, *The evolution of the stellar mass function of galaxies from $z = 4.0$ and the first comprehensive analysis of its uncertainties: evidence for mass-dependent evolution*, Astrophys. J. **701** (2009) 1765 [arXiv:0811.1773] [INSPIRE].

[438] Q. Guo et al., *From dwarf spheroidals to cDs: simulating the galaxy population in a $\Lambda$CDM cosmology*, Mon. Not. Roy. Astron. Soc. **413** (2011) 101 [arXiv:1006.0106] [INSPIRE].
[439] P. Santini et al., The evolving slope of the stellar mass function at $0.6 \le z < 4.5$ from deep WFC3 data, *Astron. Astrophys.* **538** (2012) A33 [arXiv:1111.5728] [INSPIRE].

[440] E. Papastergis, A.M. Martin, R. Giovanelli and M.P. Haynes, The velocity width function of galaxies from the 40% ALFALFA survey: shedding light on the cold dark matter overabundance problem, *Astrophys. J.* **739** (2011) 38 [arXiv:1106.0710] [INSPIRE].

[441] J.D. Simon and M. Geha, The kinematics of the ultra-faint milky way satellites: solving the missing satellite problem, *Astrophys. J.* **670** (2007) 313 [arXiv:0706.0516] [INSPIRE].

[442] J.S. Bullock, A.V. Kravtsov and D.H. Weinberg, Reionization and the abundance of galactic satellites, *Astrophys. J.* **539** (2000) 517 [astro-ph/0002214] [INSPIRE].

[443] R.S. Somerville, Can photoionization squelching resolve the sub-structure crisis?, *Astrophys. J.* **572** (2002) L23 [astro-ph/0107507] [INSPIRE].

[444] F. Governato et al., Forming disk galaxies in $\Lambda$CDM simulations, *Mon. Not. Roy. Astron. Soc.* **374** (2007) 1479 [astro-ph/0602351] [INSPIRE].

[445] S. Mashchenko, J. Wadsley and H.M.P. Couchman, Stellar feedback in dwarf galaxy formation, *Science* **319** (2008) 174 [arXiv:0711.4803] [INSPIRE].

[446] A.M. Nierenberg, T. Treu, N. Menci, Y. Lu and W. Wang, The cosmic evolution of faint satellite galaxies as a test of galaxy formation and the nature of dark matter, *Astrophys. J.* **772** (2013) 146 [arXiv:1302.3243] [INSPIRE].

[447] E. Papastergis, R. Giovanelli, M.P. Haynes and F. Shankar, Is there a “too big to fail” problem in the field?, *Astron. Astrophys.* **574** (2015) A113 [arXiv:1407.4665] [INSPIRE].

[448] T. Kimm et al., The correlation of star formation quenching with internal galaxy properties and environment, *Mon. Not. Roy. Astron. Soc.* **394** (2009) 1131 [arXiv:0810.2794] [INSPIRE].

[449] M. Geha, M. Blanton, R. Yan and J. Tinker, A stellar mass threshold for quenching of field galaxies, *Astrophys. J.* **757** (2012) 85 [arXiv:1206.3573] [INSPIRE].

[450] A.R. Wetzel, J.L. Tinker, C. Conroy and F.C. van den Bosch, Galaxy evolution in groups and clusters: satellite star formation histories and quenching timescales in a hierarchical universe, *Mon. Not. Roy. Astron. Soc.* **432** (2013) 336 [arXiv:1206.3571] [INSPIRE].

[451] J.I. Phillips, C. Wheeler, M. Boylan-Kolchin, J.S. Bullock, M.C. Cooper and E.J. Tollerud, A dichotomy in satellite quenching around $L^*$ galaxies, *Mon. Not. Roy. Astron. Soc.* **437** (2014) 1930 [arXiv:1307.3552] [INSPIRE].

[452] C.T. Slater and E.F. Bell, The mass dependence of dwarf satellite galaxy quenching, *Astrophys. J.* **792** (2014) 141 [arXiv:1407.6006] [INSPIRE].

[453] C. Wheeler, J.I. Phillips, M.C. Cooper, M. Boylan-Kolchin and J.S. Bullock, The surprising inefficiency of dwarf satellite quenching, *Mon. Not. Roy. Astron. Soc.* **442** (2014) 1396 [arXiv:1402.1498] [INSPIRE].

[454] R.B. Larson, B.M. Tinsley and C.N. Caldwell, The evolution of disk galaxies and the origin of S0 galaxies, *Astrophys. J.* **237** (1980) 692 [INSPIRE].

[455] M.L. Balogh, J.F. Navarro and S.L. Morris, The origin of star formation gradients in rich galaxy clusters, *Astrophys. J.* **540** (2000) 113 [astro-ph/0004078] [INSPIRE].

[456] D. Kawata and J.S. Mulchaey, Strangulation in galaxy groups, *Astrophys. J.* **672** (2008) L103 [arXiv:0707.3814] [INSPIRE].

[457] I.G. McCarthy et al., Ram pressure stripping the hot gaseous halos of galaxies in groups and clusters, *Mon. Not. Roy. Astron. Soc.* **383** (2008) 593 [arXiv:0710.0964] [INSPIRE].

[458] M. Hirschmann, R.S. Somerville, T. Naab and A. Burkert, Origin of the anti-hierarchical growth of black holes, *Mon. Not. Roy. Astron. Soc.* **426** (2012) 237 [arXiv:1206.6112] [INSPIRE].
[459] R.G. Bower, A.J. Benson and R.A. Crain, *What shapes the galaxy mass function? Exploring the roles of supernova-driven winds and AGN*, Mon. Not. Roy. Astron. Soc. **422** (2012) 2816, [arXiv:1112.2712] [INSPIRE].

[460] S.M. Weinmann et al., *A fundamental problem in our understanding of low mass galaxy evolution*, Mon. Not. Roy. Astron. Soc. **426** (2012) 2797 [arXiv:1204.4184] [INSPIRE].

[461] R. Dave, B.D. Oppenheimer and K. Finlator, *Galaxy evolution in cosmological simulations with outflows I: stellar masses and star formation rates*, Mon. Not. Roy. Astron. Soc. **415** (2011) 11 [arXiv:1103.3528] [INSPIRE].

[462] M. Hirschmann et al., *The effect of metal enrichment and galactic winds on galaxy formation in cosmological zoom simulations*, Mon. Not. Roy. Astron. Soc. **436** (2013) 2929 [arXiv:1309.2946] [INSPIRE].

[463] L. Wang, S.M. Weinmann and E. Neistein, *A modified star formation law as a solution to open problems in galaxy evolution*, Mon. Not. Roy. Astron. Soc. **421** (2012) 3450 [arXiv:1107.4419] [INSPIRE].

[464] B. Henriques et al., *Simulations of the galaxy population constrained by observations from z = 3 to the present day: implications for galactic winds and the fate of their ejecta*, Mon. Not. Roy. Astron. Soc. **431** (2013) 3373 [arXiv:1212.1717] [INSPIRE].

[465] V. Simha, D.H. Weinberg, R. Dave, O.Y. Gnedin, N. Katz and D. Keres, *The growth of central and satellite galaxies in cosmological smoothed particle hydrodynamics simulations*, Mon. Not. Roy. Astron. Soc. **399** (2009) 650 [arXiv:0809.2999] [INSPIRE].

[466] A.S. Font et al., *The colours of satellite galaxies in groups and clusters*, Mon. Not. Roy. Astron. Soc. **389** (2008) 1619 [arXiv:0807.0001] [INSPIRE].

[467] G. De Lucia, S. Weinmann, B. Poggianti, A. Aragon-Salamanca and D. Zaritsky, *The environmental history of group and cluster galaxies in a ΛCDM universe*, Mon. Not. Roy. Astron. Soc. **423** (2012) 1277 [arXiv:1111.6590] [INSPIRE].

[468] D. Coe et al., *CLASH: precise new constraints on the mass profile of Abell 2261*, Astrophys. J. **757** (2012) 22 [arXiv:1201.1616] [INSPIRE].

[469] M. Hirschmann et al., *The influence of the environmental history on quenching star formation in a Λ cold dark matter universe*, Mon. Not. Roy. Astron. Soc. **444** (2014) 2938 [arXiv:1407.5621] [INSPIRE].

[470] S.P. Fillingham, M.C. Cooper, C. Wheeler, S. Garrison-Kimmel, M. Boylan-Kolchin and J.S. Bullock, *Taking care of business in a flash: constraining the time-scale for low-mass satellite quenching with ELVIS*, Mon. Not. Roy. Astron. Soc. **454** (2015) 2039 [arXiv:1503.06803] [INSPIRE].

[471] A.J. Benson et al., *Dark matter halo merger histories beyond cold dark matter: I — methods and application to warm dark matter*, Mon. Not. Roy. Astron. Soc. **428** (2013) 1774 [arXiv:1209.3018] [INSPIRE].

[472] A. Schneider, *Structure formation with suppressed small-scale perturbations*, Mon. Not. Roy. Astron. Soc. **451** (2015) 3117 [arXiv:1412.2133] [INSPIRE].

[473] N. Menci, F. Fiore and A. Lamastra, *Galaxy formation in WDM cosmology*, Mon. Not. Roy. Astron. Soc. **421** (2012) 2384 [arXiv:1201.1617] [INSPIRE].

[474] F. Calura, N. Menci and A. Gallazzi, *The ages of stellar populations in a warm dark matter universe*, Mon. Not. Roy. Astron. Soc. **440** (2014) 2066 [arXiv:1402.4828] [INSPIRE].

[475] N. Drory et al., *The Munich Near-Infrared Cluster Survey (MUNICS) — 6. The stellar masses of k-band selected field galaxies to z ~ 1.2*, Astrophys. J. **608** (2004) 742 [astro-ph/0403041] [INSPIRE].
[476] P. Monaco, F. Fontanot and G. Taffoni, *The MORGANA model for the rise of galaxies and active nuclei*, Mon. Not. Roy. Astron. Soc. **375** (2007) 1189 [astro-ph/0610805] [INSPIRE].

[477] G. De Lucia, V. Springel, S.D.M. White, D. Croton and G. Kauffmann, *The formation history of elliptical galaxies*, Mon. Not. Roy. Astron. Soc. **366** (2006) 499 [astro-ph/0509725] [INSPIRE].

[478] R.S. Somerville et al., *An explanation for the observed weak size evolution of disk galaxies*, Astrophys. J. **672** (2008) 776 [astro-ph/0612428] [INSPIRE].

[479] P. Dayal, A. Mesinger and F. Pacucci, *Early galaxy formation in warm dark matter cosmologies*, Astrophys. J. **806** (2015) 67 [arXiv:1408.1102] [INSPIRE].

[480] K.N. Abazajian, *Resonantly produced 7 keV sterile neutrino dark matter models and the properties of milky way satellites*, Phys. Rev. Lett. **112** (2014) 161303 [arXiv:1403.0954] [INSPIRE].

[481] F. Pacucci, A. Mesinger and Z. Haiman, *Focusing on warm dark matter with lensed high-redshift galaxies*, Mon. Not. Roy. Astron. Soc. **435** (2013) L53 [arXiv:1306.0009] [INSPIRE].

[482] E. Polisensky and M. Ricotti, *Constraints on the dark matter particle mass from the number of milky way satellites*, Phys. Rev. D **83** (2011) 043506 [arXiv:1004.1459] [INSPIRE].

[483] V. Belokurov et al., *Big fish, small fish: two new ultra-faint satellites of the milky way*, Astrophys. J. **712** (2010) L103 [arXiv:1002.0504] [INSPIRE].

[484] K.N. Abazajian et al., *Cosmological and astrophysical neutrino mass measurements*, Astropart. Phys. **35** (2011) 177 [arXiv:1103.5083] [INSPIRE].

[485] C.R. Watson, Z.-Y. Li and N.K. Polley, *Constraining sterile neutrino warm dark matter with Chandra observations of the Andromeda galaxy*, JCAP **03** (2012) 018 [arXiv:1111.4217] [INSPIRE].

[486] C. Schultz, J. Oñorbe, K.N. Abazajian and J.S. Bullock, *The high-z universe confronts warm dark matter: galaxy counts, reionization and the nature of dark matter*, Mon. Not. Roy. Astron. Soc. **442** (2014) 1597 [arXiv:1401.3769] [INSPIRE].

[487] J. Diemand, M. Zemp, B. Moore, J. Stadel and M. Carollo, *Cusps in cold dark matter haloes*, Mon. Not. Roy. Astron. Soc. **364** (2005) 665 [astro-ph/0504215] [INSPIRE].

[488] J.J. Binney and N.W. Evans, *Cuspy dark-matter haloes and the galaxy*, Mon. Not. Roy. Astron. Soc. **327** (2001) L27 [astro-ph/0108505] [INSPIRE].

[489] N. Bissantz and O. Gerhard, *Spiral arms, bar shape and bulge microlensing in the milky way*, Mon. Not. Roy. Astron. Soc. **330** (2002) 591 [astro-ph/0110368] [INSPIRE].

[490] F.C. van den Bosch and R.A. Swaters, *Dwarf galaxy rotation curves and the core problem of dark matter halos*, Mon. Not. Roy. Astron. Soc. **325** (2001) 1017 [astro-ph/0006048] [INSPIRE].

[491] D. Marchesini et al., *Hα rotation curves: the soft core question*, Astrophys. J. **575** (2002) 801 [astro-ph/0202075] [INSPIRE].

[492] S.-H. Oh, W.J.G. de Blok, F. Walter, E. Brinks and R.C. Kennicutt Jr., *High-resolution dark matter density profiles of THINGS dwarf galaxies: correcting for non-circular motions*, Astron. J. **136** (2008) 2761 [arXiv:0810.2119] [INSPIRE].

[493] S.-H. Oh, W.J.G. de Blok, E. Brinks, F. Walter and R.C. Kennicutt Jr., *Dark and luminous matter in THINGS dwarf galaxies*, Astron. J. **141** (2011) 193 [arXiv:1011.0899] [INSPIRE].

[494] W.J.G. de Blok, S.S. McGaugh and V.C. Rubin, *High-resolution rotation curves of low surface brightness galaxies. II. Mass models*, Astron. J. **122** (2001) 2396 [INSPIRE].

[495] M.A. Breddels, A. Helmi, R.C.E. van den Bosch, G. van de Ven and G. Battaglia, *Orbit-based dynamical models of the Sculptor dSph galaxy*, Mon. Not. Roy. Astron. Soc. **433** (2013) 3173 [arXiv:1205.4712] [INSPIRE].
[496] J.T. Kleyna, M.I. Wilkinson, N.W. Evans and G. Gilmore, Dark matter in dwarf spheroidals. 2. *Observations and modeling of Draco, Mon. Not. Roy. Astron. Soc.* **330** (2002) 792 [astro-ph/0109450] [INSPIRE].

[497] M.G. Walker, M. Mateo, E.W. Olszewski, J. Penarrubia, N.W. Evans and G. Gilmore, A universal mass profile for dwarf spheroidal galaxies, *Astrophys. J.* **704** (2009) 1274 [Erratum ibid. **710** (2010) 886] [arXiv:0906.0341] [INSPIRE].

[498] J. Wolf et al., Accurate masses for dispersion-supported galaxies, *Mon. Not. Roy. Astron. Soc.* **406** (2010) 1220 [arXiv:0908.2995] [INSPIRE].

[499] N.W. Evans, J. An and M.G. Walker, Cores and cusps in the dwarf spheroidals, *Mon. Not. Roy. Astron. Soc.* **393** (2009) 50 [arXiv:0811.1488] [INSPIRE].

[500] M.G. Walker and J. Penarrubia, A method for measuring (slopes of) the mass profiles of dwarf spheroidal galaxies, *Astrophys. J.* **742** (2011) 20 [arXiv:1108.2404] [INSPIRE].

[501] N.C. Amorisco and N.W. Evans, Dark matter cores and cusps: the case of multiple stellar populations in dwarf spheroidals, *Mon. Not. Roy. Astron. Soc.* **419** (2012) 184 [arXiv:1106.1062] [INSPIRE].

[502] A. Agnello and N.W. Evans, A virial core in the Sculptor dwarf spheroidal galaxy, *Astrophys. J.* **754** (2012) L39 [arXiv:1205.6673] [INSPIRE].

[503] N.C. Amorisco, A. Agnello and N.W. Evans, The core size of the Fornax dwarf spheroidal, *Mon. Not. Roy. Astron. Soc.* **429** (2013) L89 [arXiv:1210.3157] [INSPIRE].

[504] L.E. Strigari, C.S. Frenk and S.D.M. White, Dynamical models for the Sculptor dwarf spheroidal in a $\Lambda$CDM universe, arXiv:1406.6079 [INSPIRE].

[505] O.Y. Gnedin and H. Zhao, Maximum feedback and dark matter profiles of dwarf galaxies, *Mon. Not. Roy. Astron. Soc.* **333** (2002) 299 [astro-ph/0108108] [INSPIRE].

[506] J.I. Read and G. Gilmore, Mass loss from dwarf spheroidal galaxies: the origins of shallow dark matter cores and exponential surface brightness profiles, *Mon. Not. Roy. Astron. Soc.* **356** (2005) 107 [astro-ph/0409565] [INSPIRE].

[507] F. Governato et al., Cuspy no more: how outflows affect the central dark matter and baryon distribution in $\Lambda$CDM galaxies, *Mon. Not. Roy. Astron. Soc.* **422** (2012) 1231 [arXiv:1202.0554] [INSPIRE].

[508] A. Pontzen and F. Governato, How supernova feedback turns dark matter cusps into cores, *Mon. Not. Roy. Astron. Soc.* **421** (2012) 3464 [arXiv:1106.0499] [INSPIRE].

[509] R. Kuzio de Naray and K. Spekkens, Do baryons alter the halos of low surface brightness galaxies?, *Astrophys. J.* **741** (2011) L29 [arXiv:1109.1288] [INSPIRE].

[510] F. Villaescusa-Navarro and N. Dalal, Cores and cusps in warm dark matter halos, JCAP **03** (2011) 024 [arXiv:1010.3008] [INSPIRE].

[511] V. Springel et al., The Aquarius project: the subhalos of galactic halos, *Mon. Not. Roy. Astron. Soc.* **391** (2008) 1685 [arXiv:0809.0898] [INSPIRE].

[512] J. Diemand, M. Kuhlen and P. Madau, Formation and evolution of galaxy dark matter halos and their substructure, *Astrophys. J.* **667** (2007) 859 [astro-ph/0703337] [INSPIRE].

[513] J. Wang, C.S. Frenk, J.F. Navarro and L. Gao, The missing massive satellites of the milky way, *Mon. Not. Roy. Astron. Soc.* **424** (2012) 2715 [arXiv:1203.4097] [INSPIRE].

[514] C.A. Vera-Ciro, A. Helmi, E. Starkenburg and M.A. Breddels, Not too big, not too small: the dark halos of the dwarf spheroidals in the milky way, *Mon. Not. Roy. Astron. Soc.* **428** (2013) 1696 [arXiv:1202.6061] [INSPIRE].

[515] C.W. Purcell and A.R. Zentner, Bailing out the milky way: variation in the properties of massive dwarfs among galaxy-sized systems, JCAP **12** (2012) 007 [arXiv:1208.4602] [INSPIRE].
[516] E.J. Tollerud, M. Boylan-Kolchin and J.S. Bullock, M31 satellite masses compared to $\Lambda$CDM subhaloes, Mon. Not. Roy. Astron. Soc. 440 (2014) 3511 [arXiv:1403.6469] [INSPIRE].

[517] L.E. Strigari and R.H. Wechsler, The cosmic abundance of classical milky way satellites, Astrophys. J. 749 (2012) 75 [arXiv:1111.2611] [INSPIRE].

[518] A. Rodriguez-Puebla, V. Avila-Reese and N. Drory, The massive satellite population of milky-way sized galaxies, Astrophys. J. 773 (2013) 172 [arXiv:1306.4328] [INSPIRE].

[519] A. Zolotov et al., Baryons matter: why luminous satellite galaxies have reduced central masses, Astrophys. J. 761 (2012) 71 [arXiv:1207.0007] [INSPIRE].

[520] A.M. Brooks, M. Kuhlen, A. Zolotov and D. Hooper, A baryonic solution to the missing satellites problem, Astrophys. J. 765 (2013) 22 [arXiv:1209.5394] [INSPIRE].

[521] E.N. Kirby, J.S. Bullock, M. Boylan-Kolchin, M. Kaplinghat and J.G. Cohen, The dynamics of isolated local group galaxies, Mon. Not. Roy. Astron. Soc. 439 (2014) 1015 [arXiv:1401.1208] [INSPIRE].

[522] S. Garrison-Kimmel, M. Boylan-Kolchin, J.S. Bullock and E.N. Kirby, Too big to fail in the local group, Mon. Not. Roy. Astron. Soc. 444 (2014) 222 [arXiv:1404.5313] [INSPIRE].

[523] S. Garrison-Kimmel, M. Boylan-Kolchin, J. Bullock and K. Lee, ELVIS: Exploring the Local Volume in Simulations, Mon. Not. Roy. Astron. Soc. 438 (2014) 2578 [arXiv:1310.6746] [INSPIRE].

[524] I. Ferrero, M.G. Abadi, J.F. Navarro, L.V. Sales and S. Gurovich, The dark matter halos of dwarf galaxies: a challenge for the $\Lambda$CDM paradigm?, Mon. Not. Roy. Astron. Soc. 425 (2012) 2817 [arXiv:1111.6609] [INSPIRE].

[525] Q. Guo, S. White, C. Li and M. Boylan-Kolchin, How do galaxies populate dark matter halos?, Mon. Not. Roy. Astron. Soc. 404 (2010) 1111 [arXiv:0909.4305] [INSPIRE].

[526] M.P. Haynes et al., The Arecibo legacy fast ALFA survey: the $\alpha$-40 HI source catalog, its characteristics and their impact on the derivation of the HI mass function, Astron. J. 142 (2011) 170 [arXiv:1109.0027] [INSPIRE].

[527] T. Sawala et al., The abundance of (not just) dark matter haloes, Mon. Not. Roy. Astron. Soc. 431 (2013) 1366 [arXiv:1206.6495] [INSPIRE].

[528] F. Governato et al., At the heart of the matter: the origin of bulgeless dwarf galaxies and dark matter cores, Nature 463 (2010) 203 [arXiv:0911.2237] [INSPIRE].

[529] A. Di Cintio, C.B. Brook, A.A. Dutton, A.V. Macciò, G.S. Stinson and A. Knebe, A mass-dependent density profile for dark matter haloes including the influence of galaxy formation, Mon. Not. Roy. Astron. Soc. 441 (2014) 2986 [arXiv:1404.5959] [INSPIRE].

[530] A. Di Cintio et al., The dependence of dark matter profiles on the stellar-to-halo mass ratio: a prediction for cusps versus cores, Mon. Not. Roy. Astron. Soc. 437 (2014) 415 [arXiv:1306.0898] [INSPIRE].

[531] C.B. Brook and A. Di Cintio, Expanded haloes, abundance matching and too-big-to-fail in the local group, Mon. Not. Roy. Astron. Soc. 450 (2015) 3920 [arXiv:1410.3825] [INSPIRE].

[532] C.R. Christensen et al., The effect of models of the interstellar media on the central mass distribution of galaxies, Mon. Not. Roy. Astron. Soc. 440 (2014) 2843 [arXiv:1211.0326] [INSPIRE].

[533] J. Zavala et al., The velocity function in the local environment from $\Lambda$CDM and $\Lambda$WDM constrained simulations, Astrophys. J. 700 (2009) 1779 [arXiv:0906.0585] [INSPIRE].

[534] M.R. Lovell et al., Satellite galaxies in semi-analytic models of galaxy formation with sterile neutrino dark matter, Mon. Not. Roy. Astron. Soc. 461 (2016) 60 [arXiv:1511.04078] [INSPIRE].

[535] M.R. Lovell et al., Properties of local group galaxies in hydrodynamical simulations of sterile neutrino dark matter cosmologies, arXiv:1611.00010 [INSPIRE].
[536] D. Anderhalden, A. Schneider, A.V. Macciò, J. Diemand and G. Bertone, *Hints on the nature of dark matter from the properties of milky way satellites*, JCAP 03 (2013) 014 [arXiv:1212.2967] [INSPIRE].

[537] M.R. Lovell et al., *Addressing the too big to fail problem with baryon physics and sterile neutrino dark matter*, arXiv:1611.00005 [INSPIRE].

[538] A. Garzilli, A. Boyarsky and O. Ruchayskiy, *Cutoff in the Lyman-α forest power spectrum: warm IGM or warm dark matter?, arXiv:1510.07006 [INSPIRE].

[539] A. Klypin, I. Karachentsev, D. Makarov and O. Nasonova, *Abundance of field galaxies*, Mon. Not. Roy. Astron. Soc. 454 (2015) 1798 [arXiv:1405.4523] [INSPIRE].

[540] U. Maio and M. Viel, *The first billion years of a warm dark matter universe*, Mon. Not. Roy. Astron. Soc. 446 (2015) 2760 [arXiv:1409.6718] [INSPIRE].

[541] F. Governato et al., *Faint dwarfs as a test of DM models: WDM vs. CDM*, Mon. Not. Roy. Astron. Soc. 448 (2015) 792 [arXiv:1407.0022] [INSPIRE].

[542] M.-Y. Wang, L.E. Strigari, M.R. Lovell, C.S. Frenk and A.R. Zentner, *Mass assembly history and infall time of the Fornax dwarf spheroidal galaxy*, Mon. Not. Roy. Astron. Soc. 457 (2016) 4248 [arXiv:1509.04308] [INSPIRE].

[543] L.E. Strigari, C.S. Frenk and S.D.M. White, *Kinematics of milky way satellites in a Λ cold dark matter universe*, Mon. Not. Roy. Astron. Soc. 408 (2010) 2364 [arXiv:1003.4268] [INSPIRE].

[544] P.S. Behroozi, R.H. Wechsler and C. Conroy, *The average star formation histories of galaxies in dark matter halos from $z=0-8$*, Astrophys. J. 770 (2013) 57 [arXiv:1207.6105] [INSPIRE].

[545] P.S. Behroozi, R.H. Wechsler, H.-Y. Wu, M.T. Busha, A.A. Klypin and J.R. Primack, *Gravitationally consistent halo catalogs and merger trees for precision cosmology*, Astrophys. J. 763 (2013) 18 [arXiv:1110.4370] [INSPIRE].

[546] D.S. Gorbunov and V.A. Rubakov, *Introduction to the theory of the early universe: hot big bang theory*, World Scientific, Hackensack U.S.A. (2011).

[547] D. Gorbunov, A. Khmelnitsky and V. Rubakov, *Is gravitino still a warm dark matter candidate?*, JHEP 12 (2008) 055 [arXiv:0805.2836] [INSPIRE].

[548] A.A. Meiksin, *The physics of the intergalactic medium*, Rev. Mod. Phys. 81 (2009) 1405 [arXiv:0711.3358] [INSPIRE].

[549] H. Bi and A.F. Davidsen, *Evolution of structure in the intergalactic medium and the nature of the Ly-α forest*, Astrophys. J. 479 (1997) 523 [astro-ph/9611062] [INSPIRE].

[550] M. Viel, S. Matarrese, H.J. Mo, M.G. Haehnelt and T. Theuns, *Probing the intergalactic medium with the Lyman-α forest along multiple lines of sight to distant QSOs*, Mon. Not. Roy. Astron. Soc. 329 (2002) 848 [astro-ph/0105233] [INSPIRE].

[551] N.G. Busca et al., *Baryon acoustic oscillations in the Ly-α forest of BOSS quasars*, Astron. Astrophys. 552 (2013) A96 [arXiv:1211.2616] [INSPIRE].

[552] A. Slosar et al., *Measurement of baryon acoustic oscillations in the Lyman-α forest fluctuations in BOSS data release 9*, JCAP 04 (2013) 026 [arXiv:1301.3459] [INSPIRE].

[553] K. Markovič and M. Viel, *Lyman-α forest and cosmic weak lensing in a warm dark matter universe*, Publ. Astron. Soc. Austral. 31 (2014) e006 [arXiv:1311.5223] [INSPIRE].

[554] J.R. Bond, G. Efstathiou and J. Silk, *Massive neutrinos and the large scale structure of the universe*, Phys. Rev. Lett. 45 (1980) 1980 [INSPIRE].

[555] V.K. Narayanan, D.N. Spergel, R. Dave and C.-P. Ma, *Constraints on the mass of warm dark matter particles and the shape of the linear power spectrum from the Ly-α forest*, Astrophys. J. 543 (2000) L103 [astro-ph/0005095] [INSPIRE].
[556] R.A.C. Croft et al., Towards a precise measurement of matter clustering: Lyman-α forest data at redshifts 2–4, Astrophys. J. 581 (2002) 20 [astro-ph/0012324] [INSPIRE].

[557] A. Klypin, S. Borgani, J. Holtzman and J. Primack, Damped Lyman-α systems versus cold + hot dark matter, astro-ph/9410022 [INSPIRE].

[558] M. Viel, M.G. Haehnelt and V. Springel, Inferring the dark matter power spectrum from the Lyman-α forest in high-resolution QSO absorption spectra, Mon. Not. Roy. Astron. Soc. 354 (2004) 684 [astro-ph/0404600] [INSPIRE].

[559] J. McDonald, F-term inflation Q-balls, Phys. Rev. D 73 (2006) 043501 [hep-th/0509141] [INSPIRE].

[560] K. Abazajian and S.M. Koushiappas, Constraints on sterile neutrino dark matter, Phys. Rev. D 74 (2006) 023527 [astro-ph/0605271] [INSPIRE].

[561] M. Viel, K. Markovic, M. Baldi and J. Weller, The non-linear matter power spectrum in warm dark matter cosmologies, Mon. Not. Roy. Astron. Soc. 421 (2012) 50 [arXiv:1107.4094] [INSPIRE].

[562] I.P. Carucci, F. Villaescusa-Navarro, M. Viel and A. Lapi, Warm dark matter signatures on the 21 cm power spectrum: intensity mapping forecasts for SKA, JCAP 07 (2015) 047 [arXiv:1502.06961] [INSPIRE].

[563] R. Shrock, Decay $L^0 \to \nu_e\gamma$ in gauge theories of weak and electromagnetic interactions, Phys. Rev. D 9 (1974) 743 [INSPIRE].

[564] W.J. Marciano and A.I. Sanda, Exotic decays of the muon and heavy leptons in gauge theories, Phys. Lett. B 67 (1977) 303 [INSPIRE].

[565] S.T. Petcov, The processes $\mu \to e\gamma$, $\mu \to ee\bar{e}$, $\nu' \to \nu\gamma$ in the Weinberg-Salam model with neutrino mixing, Sov. J. Nucl. Phys. 25 (1977) 340 [Erratum ibid. 25 (1977) 698] [Yad. Fiz. 25 (1977) 641] [Erratum ibid. 25 (1977) 1336] [INSPIRE].

[566] K. Abazajian, G.M. Fuller and W.H. Tucker, Direct detection of warm dark matter in the X-ray, Astrophys. J. 562 (2001) 593 [astro-ph/0106002] [INSPIRE].

[567] J.W. den Herder et al., The search for decaying dark matter, arXiv:0906.1788 [INSPIRE].

[568] M. Mapelli and A. Ferrara, Background radiation from sterile neutrino decay and reionization, Mon. Not. Roy. Astron. Soc. 364 (2005) 2 [astro-ph/0508413] [INSPIRE].

[569] A. Boyarsky, A. Neronov, O. Ruchayskiy and M. Shaposhnikov, Constraints on sterile neutrino as a dark matter candidate from the diffuse X-ray background, Mon. Not. Roy. Astron. Soc. 370 (2006) 213 [astro-ph/0512509] [INSPIRE].

[570] D.E. Gruber, J.L. Matteson, L.E. Peterson and G.V. Jung, The spectrum of diffuse cosmic hard X-rays measured with HEAO-1, Astrophys. J. 520 (1999) 124 [astro-ph/9903492] [INSPIRE].

[571] E. Churazov et al., INTEGRAL observations of the cosmic X-ray background in the 5–100 keV range via occultation by the earth, Astron. Astrophys. (2006) [astro-ph/0608250] [INSPIRE].

[572] K.N. Abazajian, M. Markevitch, S.M. Koushiappas and R.C. Hickox, Limits on the radiative decay of sterile neutrino dark matter from the unresolved cosmic and soft X-ray backgrounds, Phys. Rev. D 75 (2007) 063511 [astro-ph/0611144] [INSPIRE].

[573] A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi, A.V. Macciò and D. Malyshev, New evidence for dark matter, arXiv:0911.1774 [INSPIRE].

[574] A. Boyarsky, A. Neronov, O. Ruchayskiy and I. Tkachev, Universal properties of dark matter halos, Phys. Rev. Lett. 104 (2010) 191301 [arXiv:0911.3396] [INSPIRE].

[575] A.J. Cuesta et al., Dark matter decay and annihilation in the local universe: CLUES from Fermi, Astrophys. J. 726 (2011) L6 [arXiv:1007.3469] [INSPIRE].
[576] A. Cavaliere and R. Fusco-Femiano, X-rays from hot plasma in clusters of galaxies, *Astron. Astrophys.* **49** (1976) 137 [INSPIRE].

[577] R.F. Mushotzky, X-ray emission from clusters of galaxies, *Phys. Scripta T 7* (1984) 157 [INSPIRE].

[578] C.L. Sarazin, X-ray emission from clusters of galaxies, *Rev. Mod. Phys.* **58** (1986) 1 [INSPIRE].

[579] U.G. Briel and J.P. Henry, X-ray emission from a complete sample of Abell clusters of galaxies, *Astron. Astrophys.* **278** (1993) 379.

[580] M. Bonamente, R. Lieu, M.K. Joy and J.H. Nevalainen, The soft X-ray emission in a large sample of galaxy clusters with ROSAT Position Sensitive Proportional Counter, *Astrophys. J.* **576** (2002) 688 [astro-ph/0205473] [INSPIRE].

[581] A. Boyarsky, A. Neronov, O. Ruchayskiy and M. Shaposhnikov, *Restrictions on parameters of sterile neutrino dark matter from observations of galaxy clusters*, Phys. Rev. D **74** (2006) 103506 [astro-ph/0603368] [INSPIRE].

[582] G.W. Pratt, J.H. Croston, M. Arnaud and H. Böhringer, *Galaxy cluster X-ray luminosity scaling relations from a representative local sample (REXCESS)*, *Astron. Astrophys.* **498** (2009) 361 [arXiv:0809.3784] [INSPIRE].

[583] C.L. Sarazin and J.N. Bahcall, X-ray line emission for clusters of galaxies. II — numerical models, *Astrophys. J. Suppl.* **34** (1977) 451.

[584] J.N. Bahcall and C.L. Sarazin, X-ray line spectroscopy for clusters of galaxies. I, Astrophys. J. **219** (1978) 781.

[585] R.K. Smith, N.S. Brickhouse, D.A. Liedahl and J.C. Raymond, *Collisional plasma models with APEC/APED: emission line diagnostics of hydrogen-like and helium-like ions*, Astrophys. J. **556** (2001) L91 [astro-ph/0106478] [INSPIRE].

[586] M. Mateo, Dwarf galaxies of the local group, Ann. Rev. Astron. Astrophys. **36** (1998) 435 [astro-ph/9810070] [INSPIRE].

[587] A. Boyarsky, J. Nevalainen and O. Ruchayskiy, *Constraints on the parameters of radiatively decaying dark matter from the dark matter halo of the milky way and Ursa minor*, Astron. Astrophys. **471** (2007) 51 [astro-ph/0610961] [INSPIRE].

[588] M. Loewenstein, A. Kusenko and P.L. Biermann, New limits on sterile neutrinos from Suzaku observations of the Ursa minor dwarf spheroidal galaxy, Astrophys. J. **700** (2009) 426 [arXiv:0812.2710] [INSPIRE].

[589] S. Riemer-Sorensen and S.H. Hansen, *Decaying dark matter in Draco*, Astron. Astrophys. **500** (2009) L37 [arXiv:0901.2569] [INSPIRE].

[590] M. Loewenstein and A. Kusenko, Dark matter search using Chandra observations of Willman 1 and a spectral feature consistent with a decay line of a 5 keV sterile neutrino, Astrophys. J. **714** (2010) 652 [arXiv:0912.0552] [INSPIRE].

[591] A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi, M.G. Walker, S. Riemer-Sorensen and S.H. Hansen, *Searching for dark matter in X-rays: how to check the dark matter origin of a spectral feature*, Mon. Not. Roy. Astron. Soc. **407** (2010) 1188 [arXiv:1001.0644] [INSPIRE].

[592] N. Mirabal and D. Nieto, Willman 1: an X-ray shot in the dark with Chandra, arXiv:1003.3745 [INSPIRE].

[593] N. Mirabal, *Swift observation of Segue 1: constraints on sterile neutrino parameters in the darkest galaxy*, Mon. Not. Roy. Astron. Soc. **409** (2010) 128 [arXiv:1010.4706] [INSPIRE].

[594] M. Loewenstein and A. Kusenko, Dark matter search using XMM-Newton observations of Willman 1, Astrophys. J. **751** (2012) 82 [arXiv:1203.5229] [INSPIRE].

[595] A. Kusenko, M. Loewenstein and T.T. Yanagida, Moduli dark matter and the search for its decay line using Suzaku X-ray telescope, Phys. Rev. D **87** (2013) 043508 [arXiv:1209.6403] [INSPIRE].
[596] D. Malyshev, A. Neronov and D. Eckert, *Constraints on 3.55 keV line emission from stacked observations of dwarf spheroidal galaxies*, Phys. Rev. D 90 (2014) 103506 [arXiv:1408.3531] [INSPIRE].

[597] E. Sonbas, B. Rangelov, O. Kargaltsev, K.S. Dhuga, J. Hare and I. Volkov, *X-ray sources in the dwarf spheroidal galaxy Draco*, Astrophys. J. 821 (2016) 54 [arXiv:1505.00216] [INSPIRE].

[598] S. Riemer-Sorensen, K. Pedersen, S.H. Hansen and H. Dahle, *Probing the nature of dark matter with cosmic X-rays: constraints from dark blobs and grating spectra of galaxy clusters*, Phys. Rev. D 76 (2007) 043524 [astro-ph/0610034] [INSPIRE].

[599] A. Boyarsky, O. Ruchayskiy and M. Markevitch, *Constraints on parameters of radiatively decaying dark matter from the galaxy cluster 1E0657-56*, Astrophys. J. 673 (2008) 752 [astro-ph/0611168] [INSPIRE].

[600] C.R. Watson, J.F. Beacom, H. Yuksel and T.P. Walker, *Direct X-ray constraints on sterile neutrino warm dark matter*, Phys. Rev. D 74 (2006) 033009 [astro-ph/0605424] [INSPIRE].

[601] H. Yuksel, J.F. Beacom and C.R. Watson, *Strong upper limits on sterile neutrino warm dark matter*, Phys. Rev. Lett. 101 (2008) 121301 [arXiv:0706.4084] [INSPIRE].

[602] A. Boyarsky, J.W. den Herder, A. Neronov and O. Ruchayskiy, *Search for the light dark matter with an X-ray spectrometer*, Astropart. Phys. 28 (2007) 303 [astro-ph/0612219] [INSPIRE].

[603] S. Horiuchi, K.C.Y. Ng, J.M. Gaskins, M. Smith and R. Preece, *Improved limits on sterile neutrino dark matter from full-sky observations by the Fermi-GBM*, in *Fifth International Fermi Symposium*, Nagoya Japan October 20-24 2014 [arXiv:1502.03399] [INSPIRE].

[604] D.A. Prokhorov and J. Silk, *Can the excess in the Fe XXVI Ly-γ line from the galactic center provide evidence for 17 keV sterile neutrinos?*, Astrophys. J. 725 (2010) L131 [arXiv:1001.0215] [INSPIRE].

[605] K. Koyama et al., *Iron and nickel line diagnostics for the galactic center diffuse emission*, Publ. Astron. Soc. Jap. 59 (2007) 245 [astro-ph/0609215] [INSPIRE].

[606] E. Borriello, M. Paolillo, G. Miele, G. Longo and R. Owen, *Constraints on sterile neutrino dark matter from XMM-Newton observation of M33*, Mon. Not. Roy. Astron. Soc. 425 (2012) 1628 [arXiv:1109.5943] [INSPIRE].

[607] D. Iakubovskyi, *Constraining properties of dark matter particles using astrophysical data*, Ph.D. thesis, Leiden University, Leiden The Netherlands (2013).

[608] A. Boyarsky, J. Franse, D. Iakubovskyi and O. Ruchayskiy, *Checking the dark matter origin of a 3.53 keV line with the milky way center*, Phys. Rev. Lett. 115 (2015) 161301 [arXiv:1408.2503] [INSPIRE].

[609] S. Riemer-Sorensen, *Constraints on the presence of a 3.5 keV dark matter emission line from Chandra observations of the galactic centre*, Astron. Astrophys. 590 (2016) A71 [arXiv:1405.7943] [INSPIRE].

[610] T.E. Jeltema and S. Profumo, *Discovery of a 3.5 keV line in the galactic centre and a critical look at the origin of the line across astronomical targets*, Mon. Not. Roy. Astron. Soc. 450 (2015) 2143 [arXiv:1408.1699] [INSPIRE].

[611] M.E. Anderson, E. Churazov and J.N. Bregman, *Non-detection of X-ray emission from sterile neutrinos in stacked galaxy spectra*, Mon. Not. Roy. Astron. Soc. 452 (2015) 3905 [arXiv:1408.4115] [INSPIRE].

[612] O. Urban, N. Werner, S.W. Allen, A. Simionescu, J.S. Kaastra and L.E. Strigari, *A Suzaku search for dark matter emission lines in the X-ray brightest galaxy clusters*, Mon. Not. Roy. Astron. Soc. 451 (2015) 2447 [arXiv:1411.0050] [INSPIRE].
[631] HITOMI collaboration, F.A. Aharonian et al., *Hitomi constraints on the 3.5 keV line in the Perseus galaxy cluster*, arXiv:1607.07420 [INSPIRE].

[632] K.J.H. Phillips, B. Sylwester and J. Sylwester, *The X-ray line feature at 3.5 keV in galaxy cluster spectra*, Astrophys. J. 809 (2015) 50 [INSPIRE].

[633] L. Gu et al., *A novel scenario for the possible X-ray line feature at ~3.5 keV: charge exchange with bare sulfur ions*, Astron. Astrophys. 584 (2015) L11 [arXiv:1511.06557] [INSPIRE].

[634] O. Dragoun and D. Vénos, *Constraints on the active and sterile neutrino masses from beta-ray spectra: past, present and future*, J. Phys. 3 (2016) 77 [arXiv:1504.07496] [INSPIRE].

[635] C.S. Cook, L.M. Langer and H.C. Price Jr., *The β-spectrum of $^{35}$S and the mass of the neutrino*, Phys. Rev. 73 (1948) 1395.

[636] K.-E. Bergkvist, *A high-luminosity, high-resolution study of the end-point behaviour of the tritium beta-spectrum (i). Basic experimental procedure and analysis with regard to neutrino mass and neutrino degeneracy*, Nucl. Phys. B 39 (1972) 317 [INSPIRE].

[637] G. Drexlin, V. Hannen, S. Mertens and C. Weinheimer, *Current direct neutrino mass experiments*, Adv. High Energy Phys. 2013 (2013) 293986 [arXiv:1307.0101] [INSPIRE].

[638] O. Dragoun, *Internal conversion-electron spectroscopy*, Adv. Electron. Electron Phys. 60 (1983) 1.

[639] K. Schreckenbach, G. Colvin and F. Von Feilitzsch, *Search for mixing of heavy neutrinos in the β+ and β− spectra of the $^{64}$Cu decay*, Phys. Lett. B 129 (1983) 265 [INSPIRE].

[640] J. Deutsch, M. Lebrun and R. Prieels, *Searches for admixture of massive neutrinos into the electron flavor*, Nucl. Phys. A 518 (1990) 149 [INSPIRE].

[641] J.J. Simpson, *Evidence of heavy neutrino emission in beta decay*, Phys. Rev. Lett. 54 (1985) 1891 [INSPIRE].

[642] E. Holzschuh, W. Kundig, L. Palermo, H. Stussi and P. Wenk, *Search for heavy neutrinos in the beta spectrum of $^{63}$Ni*, Phys. Lett. B 451 (1999) 247 [INSPIRE].

[643] T. Ohi et al., *Search for heavy neutrinos in the beta decay of $^{35}$S: an evidence against the 17 keV heavy neutrino*, Phys. Lett. B 160 (1985) 322 [INSPIRE].

[644] J. Markey and F. Boehm, *Search for admixture of heavy neutrinos with masses between 5 keV and 55 keV*, Phys. Rev. C 32 (1985) 2215 [INSPIRE].

[645] T. Altzitzoglou et al., *Experimental search for a heavy neutrino in the beta spectrum of $^{35}$S*, Phys. Rev. Lett. 55 (1985) 799 [INSPIRE].

[646] D.W. Hetherington, R.L. Graham, M.A. Lone, J.S. Geiger and G.E. Lee-Whiting, *Upper limits on the mixing of heavy neutrinos in the beta decay of $^{63}$Ni*, Phys. Rev. C 36 (1987) 1504 [INSPIRE].

[647] T.J. Radcliffe, M. Chen, D.A. Imel, H. Henrikson and F. Boehm, *New limits on the 17 keV neutrino*, in *Progress in Atomic Physics, Neutrinos and Gravitation*, G. Chardin, O. Fackler and J. Trân Thanh Vân eds., *Editions Frontieres, Gif-sur-Yvette France (1992)*, pg. 217–224 [INSPIRE].

[648] F.E. Wietfeldt and E.B. Norman, *The 17 keV neutrino*, Phys. Rept. 273 (1996) 149 [INSPIRE].

[649] S. Muller et al., *Search for an admixture of a 17 keV neutrino in the β decay of $^{35}$S*, Z. Naturforsch. 49a (1994) 874.

[650] C. Kraus, A. Singer, K. Valerius and C. Weinheimer, *Limit on sterile neutrino contribution from the Mainz neutrino mass experiment*, Eur. Phys. J. C 73 (2013) 2323 [arXiv:1210.4194] [INSPIRE].

[651] A.I. Belesev et al., *The search for an additional neutrino mass eigenstate in the 2–100 eV region from ‘Troitsk nu-mass’ data: a detailed analysis*, J. Phys. G 41 (2014) 015001 [arXiv:1307.5687] [INSPIRE].
[652] M. Galeazzi, F. Fontanelli, F. Gatti and S. Vitale, Limits on the existence of heavy neutrinos in the range 50–1000 eV from the study of the $^{187}$Re beta decay, Phys. Rev. Lett. 86 (2001) 1978 [INSPIRE].

[653] K.H. Hiddemann, H. Daniel and O. Schwentker, Limits on neutrino masses from the tritium beta spectrum, J. Phys. G 21 (1995) 639 [INSPIRE].

[654] J.J. Simpson, Measurement of the beta energy spectrum of $^3H$ to determine the anti-neutrino mass, Phys. Rev. D 23 (1981) 649 [INSPIRE].

[655] T. Ohshima et al., No 17 keV neutrino: admixture < 0.073% (95% C.L.), Phys. Rev. D 47 (1993) 4840 [INSPIRE].

[656] J.L. Mortara et al., Evidence against a 17 keV neutrino from $^{35}$S beta decay, Phys. Rev. Lett. 70 (1993) 394 [INSPIRE].

[657] O. Dragoun et al., Search for an admixture of heavy neutrinos in the beta-decay of $^{241}$Pu, J. Phys. G 25 (1999) 1839 [INSPIRE].

[658] O. Dragoun et al., Improved methods of measurement and analysis of conversion electron and β-particle spectra, Appl. Radiat. Isot. 52 (2000) 387.

[659] M.-C. Chen, M. Ratz and A. Trautner, Nonthermal cosmic neutrino background, Phys. Rev. D 92 (2015) 123006 [arXiv:1509.00481] [INSPIRE].

[660] K.N. Abazajian and G.M. Fuller, Bulk QCD thermodynamics and sterile neutrino dark matter, Phys. Rev. D 66 (2002) 023526 [astro-ph/0204293] [INSPIRE].

[661] A.D. Dolgov and F.L. Villante, BBN bounds on active sterile neutrino mixing, Nucl. Phys. B 679 (2004) 261 [hep-ph/0308083] [INSPIRE].

[662] T. Asaka, M. Shaposhnikov and A. Kusenko, Opening a new window for warm dark matter, Phys. Lett. B 638 (2006) 401 [hep-ph/0602150] [INSPIRE].

[663] A. Kusenko, Sterile neutrinos, dark matter and the pulsar velocities in models with a Higgs singlet, Phys. Rev. Lett. 97 (2006) 241301 [hep-ph/0609081] [INSPIRE].

[664] M. Shaposhnikov and I. Tkachev, The $\nu$MSM, inflation and dark matter, Phys. Lett. B 639 (2006) 414 [hep-ph/0604236] [INSPIRE].

[665] D. Boyanovsky and C.M. Ho, Sterile neutrino production via active-sterile oscillations: the quantum Zeno effect, JHEP 07 (2007) 030 [hep-ph/0612092] [INSPIRE].

[666] D. Boyanovsky, Production of a sterile species via active-sterile mixing: an exactly solvable model, Phys. Rev. D 76 (2007) 103514 [arXiv:0706.3167] [INSPIRE].

[667] D. Gorbunov and M. Shaposhnikov, How to find neutral leptons of the $\nu$MSM?, JHEP 10 (2007) 015 [Erratum ibid. 11 (2013) 101] [arXiv:0705.1729] [INSPIRE].

[668] C.T. Kishimoto and G.M. Fuller, Lepton number-driven sterile neutrino production in the early universe, Phys. Rev. D 78 (2008) 023524 [arXiv:0802.3377] [INSPIRE].

[669] K. Petraki, Small-scale structure formation properties of chilled sterile neutrinos as dark matter, Phys. Rev. D 77 (2008) 105004 [arXiv:0801.3470] [INSPIRE].

[670] K. Petraki and A. Kusenko, Dark-matter sterile neutrinos in models with a gauge singlet in the Higgs sector, Phys. Rev. D 77 (2008) 065014 [arXiv:0711.4646] [INSPIRE].

[671] F. Bezrukov, H. Hettmansperger and M. Lindner, keV sterile neutrino dark matter in gauge extensions of the Standard Model, Phys. Rev. D 81 (2010) 085032 [arXiv:0912.4415] [INSPIRE].

[672] A. Kusenko, F. Takahashi and T.T. Yanagida, Dark matter from split seesaw, Phys. Lett. B 693 (2010) 144 [arXiv:1006.1731] [INSPIRE].

[673] M. Nemevšek, G. Senjanović and Y. Zhang, Warm dark matter in low scale left-right theory, JCAP 07 (2012) 006 [arXiv:1205.0844] [INSPIRE].