Available online at www.sciencedirect.com Nuclear and Particle Physics Proceedings 267 269 (2015) 323 331 www.elsevier.com/locate/nppp Dark Matter Theory Alejandro Ibarra Physik-Department T30d, Technische Universität München, James-Franck-Straße, 85748 Garching, Germany Abstract We review the present theoretical status of particle dark matter, concentrating on two of the most attractive dark matter candidates: sterile neutrinos and weakly interacting massive particles. We review the basic theoretical aspects of each of these two scenarios as well as their observational signatures, with emphasis on the possible signals recently reported by various authors. Keywords: Dark Matter, Sterile Neutrino Dark Matter, WIMP Dark Matter, Indirect Dark Matter Searches 1. Introduction http://dx.doi.org/.16/j.nuclphysbps.2015..126 2405-6014/ 2015 Elsevier B.V. All rights reserved. There is presently mounting evidence for particle dark matter (DM) in a wide range of distance scales. While there is currently no experimental indication for dark matter inside the Solar System, observations of various kinematical tracers in galaxies have revealed that approximately 80% of the total mass of galaxies must be in the form of dark matter. Besides, the lensing images produced by galaxy clusters of distant objects cannot be explained if all the matter were in the form of stars and gas. Instead, it is necessary a dark matter component in order to account for the lensing observations and which again amounts to roughly 80% of the total mass of the cluster. Finally, measurements of the power spectrum of the temperature fluctuations in the cosmic microwave background also require a dark matter component, which once again amounts to approximately 80% of the total matter content of the Universe. The discovery of the dark matter was without any doubt one of the many great discoveries in Physics during the 20th century. However, and despite the existence of dark matter is known since more than eighty years [1], its particle physics properties, such as the mass, the spin or its interaction strength with the ordinary matter, are still largely unconstrained by observations. In fact, the parameter space of viable dark matter models is vast, and covers at least 30 orders of magnitude in the mass and 40 orders of magnitude in the interaction cross section with protons (see, e.g. [2]). It is clearly very difficult, if not impossible, to devise a single experiment which can probe this huge parameter space. Instead, the current strategy consists in exploring the smaller parameter space of the best motivated models. In this talk we review the theory of two particularly well motivated dark matter candidates, as well as the present status of their searches, namely the sterile neutrino and the Weakly Interacting Massive Particle (WIMP). These two candidates are reviewed in Sections 2 and 3, respectively. 2. Sterile neutrinos as dark matter One of the simplest and most economical scenarios that account for the dark matter of the Universe consists in adding to the Standard Model particle content one sterile neutrino, namely a fermion that is a singlet under the Standard Model gauge group and that only interacts with the Standard Model via a Yukawa coupling with the left-handed lepton doublet and the Higgs doublet (for reviews, see [3, 4]). This model contains just two free parameters, the sterile neutrino mass and the mixing angle between the active and the sterile neutrino, which arises after the electroweak symmetry breaking. In this simple scenario, the parameter space is constrained by the following considerations:
324 A. Ibarra / Nuclear and Particle Physics Proceedings 267 269 (2015) 323 331 1. Sterile neutrinos can be produced in the early Universe via the active-steriles neutrino mixing [5]. The requirement that sterile neutrinos should not be overproduced sets an upper limit on the mixing angle as a function of the dark matter mass. 2. The existence of a lepton asymmetry can resonantly enhance the dark matter production [6]. An upper limit on the cosmic lepton asymmetry then implies a lower limit on the active-sterile neutrino mixing angle as a function of the sterile neutrino mass. 3. Sterile neutrinos are fermions and obey the Pauli exclusion principle, hence it is not possible to have an arbitrarily large dark matter number density in a region of space. The determination of the mass and the size of galaxy clusters or dwarf galaxies then allows to set a lower limit on the dark matter mass [7]. 4. Sterile neutrinos are not absolutely stable particles but decay via quantum effects into an active neutrino and a photon, with a rate proportional to the fifth-power of the mass and to the second power of the active-sterile mixing angle [8]. The photon produced in the decay could be detected in X- or γ-ray telescopes, thus leading to an upper limit on the mixing angle as a function of the mass. The allowed parameter space of the model is shown in Fig. 2. As apparent from the plot, X-ray observations play a pivotal role in constraining the parameter space of the model. Conversely, the observation of a line in the X-ray sky would constitute a hint for sterile neutrino decay. Interestingly, two groups [9, ] have recently found indications for an unidentified X-ray line signal at an energy of 3.5 kev in the data taken with the XMM-Newton X-ray observatory, see Fig. 2. The line was detected in different data sets at an energy consistent with their redshift and it was not observed in a deep blank sky data set, suggesting that the line is not an instrumental artifact. Moreover, these authors claim that no known atomic transition could explain the 3.5 kev line with the observed intensity. Therefore, in the absence of an explanation of this line in terms of conventional physics, the authors of [9, ] speculated that it could be originated by the decay of a sterile neutrino with mass m s 7 kev and a mixing angle with the active neutrino O( 11 ). The exotic interpretation of the 3.5 kev line, however, has been questioned by various authors over the last year. With the parameters favored in [9, ], a signal should have been detected in the Milky Way center with the Chandra X-ray observatory [11], in the Coma, Virgo and Ophiuchus galaxy clusters with the Suzaku satellite [12], in a stacked spectra of dwarf galaxies with the XMM-Newton observatory [13] and in a stacked spectra of a sample of 81 selected galaxies using the Chandra observatory, or in a sample of 89 galaxies using the XMM-Newton observatory [14]. However, no signal was detected in any of these analyses. There is moreover a debate on whether the strength of the potassium and chlorine lines was underestimated in the first analyses [15, 16, 17, 18]. Future X-ray telescopes, such as Astro-H [19], will be able to refute the existence of this line and possibly shed more light on its origin. 3. WIMPs as dark matter A very simple and compelling framework to generate a population of dark matter particles in our Universe is the freeze-out mechanism. It assumes that dark matter particles are long lived in cosmological time scales and that they interact in pairs with two Standard Model particles. Moreover, It assumes that the strength of this interaction is large enough to keep the dark matter particles in thermal equilibrium with the Standard Model at very high temperatures, and weak enough to allow the dark matter particles to drop out of equilibrium at sufficiently early times. After this time, dubbed the freezeout time, the number density per comoving volume of dark matter particles remains practically constant until today, thus constituting a dark matter population. The density of dark matter particles today can be readily calculated from the Boltzmann-equation, the result being Ωh 2 3 27 cm 3 s 1. (1) σv Therefore, the predicted dark matter abundance matches the observed value Ω DM h 2 = 0.1198 ± 0.0015, as measured by the Planck satellite [20], when σv 3 26 cm 3 s 1, which can be also be cast as σv 1pb c. Considering that the dark matter particles had at the time of freeze-out velocities comparable to the speed of light, the previous argument reveals that the interaction strength between dark matter particles and Standard Model particles should be O(0.1 1) pb, i.e. the typical cross section for a weak interaction. For this reason, this dark matter candidate is commonly called Weakly Interacting Massive Particle (WIMP). If one now considers the full theory giving rise to this effective interaction, for instance by the exchange of a mediator in the t-channel, the cross section will typically read σ g 4 /m 2 DM, where g is the coupling constant of the dark matter to the Standard Model. Assuming that the coupling constant is g g weak 0.1, one
A. Ibarra / Nuclear and Particle Physics Proceedings 267 269 (2015) 323 331 325-6 -7 Ω N1 > Ω DM NRP -8 X-ray constraints sin 2 (2θ 1 ) -9 - -11-12 -13 Phase-space density constraints L 6 =25 L 6 =70 L 6 max =700 BBN limit: L 6 BBN = 2500-14 -15 Ω N1 < Ω DM 1 5 50 M 1 [kev] Figure 1: Allowed parameter space of the sterile neutrino dark matter scenario, spanned by the sterile neutrino mass and the active-sterile mixing angle. Figure taken from [4]. obtains, from requiring σ 0.1 1 pb, a range for the dark matter mass which is m DM 0 GeV 1 TeV. This simple and natural mechanism to generate the observed dark matter abundance then suggests dark matter particles with masses in the range m DM 0 GeV 1 TeV and annihilation cross sections σ 0.1 1 pb. Interestingly, this range for WIMP parameters is now being probed by different experiments using very different approaches. First, direct detection experiments aim to the observation of the nuclear recoil induced by the scattering with a dark matter particle. The experiments which currently have the highest sensitivities are LUX and XENON0 (for a review of the latest experimental results, see [21]). On the other hand, indirect detection experiments aim to the observation of the photons, antimatter particles or neutrinos hypothetically produced in dark matter annihilations or decays. Some experiments following this approach are Fermi-LAT, H.E.S.S., MAGIC and VERITAS, for gamma-rays, PAMELA and AMS-02, for antimatter and IceCube and ANTARES for neutrinos. Finally, collider searches aim to the production at a collider of dark matter particles, and their subsequent detection through the observation of large amounts of missing transverse momentum in the final state. The leading experiments in this search strategy are currently the LHC detectors ATLAS and CMS. In this talk I will concentrate on the indirect dark matter searches, which have witnessed a huge improvement in sensitivity in the last few years thanks in particular to a new generation of space-based missions. The annihilation of dark matter particles with mass m DM produces Standard Model particles at the position r, at a rate per unit energy E and unit volume given by Q(E, r) = 1 ρ 2 DM ( r) dn i (σv) i 2 de, (2) m 2 DM i where (σv) i is the annihilation cross section times the relative dark matter velocity in the annihilation channel i, producing an energy spectrum of Standard Model particles dn i /de, and ρ DM ( r) is the dark matter density at the position r. Unfortunately, in this expression none of the parameters involved is positively known. It is common in the literature to fix the annihilation final state, so that dn/de is fixed. Besides, the distribution of dark matter particles in the Milky Way is not precisely known, although it can be inferred from numerical N-body simulations. Some popular choices for the dark matter density profile are the Navarro-Frenk-White (NFW) profile [22, 23], the Einasto profile [24, 25, 26] or the much shallower isothermal profile [27]. Under these assumptions, the parameter space of WIMP indirect searches is spanned by the dark matter mass m DM and the annihilation cross section in that channel (σv). In this parameter space, the region favored by the freeze-out mechanism is (σv) 3 26 cm 3 s 1, hence the goal of indirect search experiments is to probe this region. 3.1. Indirect dark matter searches with antimatter The AMS-02 experiment has recently published data of exquisite quality on the positron fraction [28, 29], de-
326 A. Ibarra / Nuclear and Particle Physics Proceedings 267 269 (2015) 323 331 Data - model [cts/sec/kev] Normalized count rate [cts/sec/kev] 0.36 0.34 0.32 0.30 0.28 0.26 0.24 0.22 1-2 8-3 6-3 4-3 2-3 0 0-2 -3 M31 ON-center No line at 3.5 kev No line at 3.5 kev Line at 3.5 kev -4-3 3.0 3.2 3.4 3.6 3.8 4.0 Energy [kev] Figure 2: Left plot. X-ray flux, residuals and effective area between 3 and 4 kev of the stacked spectrum of 73 galaxy clusters obtained in [9] using data from XMM-Newton. Right plot: Folded count rate and residuals for the spectrum of the central region of M31 obtained in [] using data from XMM-Newton. In the plots for the residuals, the red (blue) points show the residual before (after) a Gaussian line is added. fined as the flux of positrons divided by the total flux of electrons plus positrons, as well as on the separate electron and positron fluxes [30]. The data confirm the raise in the positron fraction hinted by HEAT [31] and positively discovered by PAMELA [32, 33], and has been attributed by some authors to dark matter annihilations. Unfortunately, the positron background fluxes are not well understood and could receive, in addition to the secondary component from spallation of high energy cosmic rays on the interstellar medium, a primary component from sources, such as the positrons produced by the interactions of high-energy photons in the strong magnetic fields of pulsars [34, 35, 36] or by hadronic interactions inside the same sources that accelerate galactic cosmic rays [37, 38]. As a result, it is not possible at the moment to conclusively attribute the raise in the positron fraction to WIMP annihilations. On the other hand, the excellent quality of the positron data can be used to set stringent limits on the dark matter annihilation cross section [39, 40]. The current limits on some selected annihilation final states are shown in Fig. 3, taken from [40], where it was adopted the propagation parameters of the MED model defined in [41]. Here, the solid lines show limits which were derived using data at all energies, while the dashed lines only data at E > GeV, for which the uncertainties from the modeling of solar modulation effects are expected be very small. Notably, the positron data currently probe the region σv 3 26 cm 3 s 1 for m DM 190 GeV (80 GeV) for dark matter annihilations into e + e (μ + μ ). The status on antiproton searches from dark matter annihilations has not changed significantly since the latest release of data by the PAMELA collaboration in 20 [42], however, data from the AMS-02 experiment [43] are expected to be released in the near future with better statistics than PAMELA. Current data on the antiproton flux and the antiproton-to-proton ratio agree reasonably well with the expectations from secondary production of antiprotons from spallation of cosmic ray nuclei on the interstellar medium [44, 45]. This allows to set stringent constraints on a possible primary contribution generated from dark matter annihilations, see e.g. [46, 47], even for leptophilic scenarios, due to the electroweak bremsstrahlung, see e.g [48, 49, 50, 51]. The production of antiprotons in dark matter annihilations leads to the possibility of producing antinuclei, such as antideuterium [52] or antihelium [53, 54]. This channel is particularly interesting due to the very small background flux of antideuterons [55, 56] and antihelium [53, 54] expected at the energies relevant for experiments. In fact, the expected flux lies more than three orders of magnitude below the best present limit by BESS [57] and more than one order of magnitude below the expected sensitivity of AMS-02 and GAPS [58], therefore, the observation of a few antideuterons in experiments will constitute a strong hint for their exotic origin. The antideuteron flux at the Earth from dark matter annihilations is, on the other hand, strongly constrained by the non-observation of an excess in antiprotons [59]. Given the strong limits from the PAMELA experiment mentioned above, and despite the various sources of uncertainty in the modeling of the antideuteron production, the observation of an antideuteron flux at AMS-02 or GAPS from dark matter annihilations will be challenging [59].
A. Ibarra / Nuclear and Particle Physics Proceedings 267 269 (2015) 323 331 327 22 23 Σv cm 3 s 24 25 26 27 28 thermal e e E GeV Μ Μ E GeV Τ Τ E GeV b b E GeV W W E GeV 20 50 0 200 500 00 m DM GeV Figure 3: Limits on the annihilation cross section derived in [40] using the AMS-02 data on the positron fraction from [29] assuming the final states e + e, μ + μ, τ + τ, b b and W + W. The solid line shows limits derived using data at all energies, while the dashed lines only data at E > GeV, which are less affected by solar modulation effects. 3.2. Indirect dark matter searches with gamma-rays In contrast to antimatter particles, which propagate from their production point to the Earth in a complicated way, gamma-rays propagate in straight lines and practically without losing energy. This allows to concentrate the search in regions of the sky with the largest signalto-background ratio and hence with the largest discovery potential. Furthermore, the fairly good energy resolution of current gamma-ray telescopes allows to search for the characteristic gamma-ray spectrum produced in some annihilation channels. For these reasons, gammarays from self-annihilations are a promising and unique channel for dark matter detection. The observation of sharp gamma-ray spectral features in the gamma-ray sky is considered to be a smoking gun for dark matter detection, since no known astrophysical process can mimic such a signal in the GeV-TeV energy range. So far, three different gamma-ray spectral features have been identified in dark matter scenarios: gamma-ray lines [60, 61, 62], internal electromagnetic bremsstrahlung [63, 64] and gamma-ray boxes [65]. Gamma-ray lines arise in two-body annihilation DM DM γγ or γx, with X = Z 0, h, and produce, respectively, two monoenergetic photons at E γ = m DM or one monoenergetic photon at E γ = m DM (1 MX 2 /4m2 DM ) [60, 61, 62]. Besides, the two-to-three annihilation DM DM f f γ [63, 64, 66] and DM DM W + W γ [66, 67] give rise, in scenarios where the annihilation is mediated by a charged scalar in the t-channel and when the mass of the mediator is close to the dark matter mass, to a photon with an energy close to the kinematical end-point of the spectrum, producing a signal that resembles a distorted gamma-ray line. Finally, gamma-ray boxes appear when the dark matter particle annihilates producing a monoenergetic scalar, which then decays in flight into γγ (or γz, γh). The photons are monoenergetic in the rest frame of the scalar, then, when boosting to the galactic frame where the scalars have some non-vanishing momentum, the photon energy spectrum becomes box-shaped [65]. Gamma-ray lines have been searched for by the Fermi-LAT collaboration between 5 and 300 GeV [68] and by the H.E.S.S. collaboration between 500 GeV and 25 TeV [69], resulting in strong limits on the annihilation cross section which range between 29 and 2 27 cm 3 s 1 for 5-300 GeV, and 5 28 and 2 26 cm 3 s 1 for 500 GeV - 25 TeV. These values are below the canonical value of the cross section, σv = 3 26 cm 3 s 1, however most models predict an annihilation cross section into monoenergetic photons which is much smaller than this value, since this process necessarily arises at the quantum level. More concretely, the expected cross section for gamma-ray lines is (σv) γγ O(α 2 )(σv) thermal 30 cm 3 s 1, i.e. orders of magnitude below the current sensitivity of experiments. On the other hand, a search for the signal of internal electromagnetic bremsstrahlung was conducted in [70] using Fermi-LAT data and in [69] using H.E.S.S. data, again finding strong limits on the cross section,
328 A. Ibarra / Nuclear and Particle Physics Proceedings 267 269 (2015) 323 331 which are comparable, or for low masses better, than the canonical value σv = 3 26 cm 3 s 1. In this case, the theory prediction for the cross section is (σv) f f γ O(α/π)(σv) thermal 28 cm 3 s 1, since this process involves the electromagnetic coupling and is suppressed, compared to the two-to-two annihilation which dominates the freeze-out, by the three-body phase space. The predicted value of the cross section into sharp gammaray spectral features also in this case lags well below the current limits, although interestingly for some choices of parameters it is only necessary a boost in the flux from annihilations by a factor of 5- to produce an observable signal. Finally, a search for gamma-ray boxes was conducted in [71] using Fermi-LAT and H.E.S.S. data. The limits in this case are remarkably strong and can even rule out models where the annihilation cross section into scalars is of the order of the canonical value σv = 3 26 cm 3 s 1, provided the decay branching fraction of the scalar into monoenergetic photons is sizable. A complementary way to search for dark matter annihilations consists in exploiting the morphology of the expected signal, due to the directional information carried by the gamma-rays arriving at the detector. The most promising targets for dark matter detection following this approach are dwarf spheroidal galaxies and the Milky Way center region. Astronomical observations demonstrate that dwarf galaxies have most of its mass in the form of dark matter. Moreover, these objects present very little astrophysical activity, which translates into a negligible gamma-ray emission from astrophysical sources. As a result, the observation of a gamma-ray excess correlated to the direction of dwarf galaxies would be a very strong indication for dark matter annihilations. Searches for gamma-rays from annihilations have been conducted in a stacked set of 15 dwarf galaxies by the Fermi-LAT collaboration [72] and in Segue 1 by the MAGIC [73] and VERITAS [74] collaborations. No signal has been detected, allowing to set fairly strong limits on the annihilation cross section, which are better than the canonical value of the cross section, σv = 3 26 cm 3 s 1 for masses below GeV for the b b final state and below 15 GeV for the τ + τ final state [72]. Another promising target is the Milky Way center, although this region presents large background fluxes from sources and from the diffuse galactic emission, as well as from the worse understood Fermi bubbles and extragalactic components. Interestingly, a subtraction of all the known components of the background emission revealed a very significant excess of gamma-rays in the galactic center region, peaked at an energy of a few GeV [75, 76, 77, 78, 79, 80, 81]. This excess implies that there must exist an additional source of gammarays not taken into account in the templates. An exciting possibility is that this excess could originate in dark matter annihilations. Remarkably, the observed spectrum and intensity of the excess are in excellent agreement with the expectations from dark matter annihilating into b b with mass 35 GeV and annihilation cross section σv = 1.0 26 cm 3 s 1 [81] (see Fig.4, left panel), very close to the expected value for a thermal relic. Reproducing the correct morphology of the signal requires moreover a density distribution close to the Galactic Center with a radial distribution approximately proportional to r 1.3. Since the galactic center might be populated with unresolved sources, not taken into account in the analysis and which could explain this emission, the authors of [81] undertook a similar analysis away from the central region. Intriguingly, a search in the inner galaxy, defined as the region with 1 < b < 20 and l < 20, also revealed an excess with very similar spectral characteristics as the one found in the galactic center region, defined with b < 5 and l < 5. Namely, the excess in the inner galaxy could be explained by dark matter annihilations into b b with mass 35 GeV and cross section σv = 1.7 26 cm 3 s 1 (see Fig.4, right panel), which are in remarkable agreement with the parameters found for the galactic center region. Moreover, the morphology of the signal requires a dark matter distribution close to the center roughly proportional to r 1.26, also very close to the value found in the galactic center region. A possible caveat for this conclusion is that these analyses used a very specific template for the Galactic diffuse emission, based on the conventional model. Therefore, the excess might simply be a consequence of a wrong modeling of the diffuse gamma-ray emission. To address this question, the authors of [82, 83] extracted the residual emission from the galactic center using 60 different Galactic diffuse models, and found an excess in all of them, with similar characteristics to the one found in [81]. Moreover, in order to analyze the morphology of the residual, they divided the galactic center region into ten segments, and found a non-vanishing residual in all of them, with similar spectra, and with an intensity consistent with annihilations of dark matter with density distribution approximately proportional to r 1.3 close to the Galactic Center. The best fit value of the dark matter mass was found to be 50 GeV and the annihilation cross section σv = 1.8 26 cm 3 s 1.
A. Ibarra / Nuclear and Particle Physics Proceedings 267 269 (2015) 323 331 329 Figure 4: Spectrum of the residual emission of gamma-rays in the Galactic Center (left plot) and in the Inner Galaxy (right plot), together with the expected spectrum from dark matter annihilations into b b with mass 35.25 GeV and cross section σv = 1.0 26 cm 3 s 1 (for the Galactic Center) and σv = 1.7 26 cm 3 s 1 (for the Inner Galaxy). Figures taken from [81]. While the dark matter interpretation of the GeV excess is a very exciting possibility, other explanations using conventional physics have also been proposed, notably unresolved millisecond pulsars (see e.g. [84, 85, 86]. The dark matter interpretation of the galactic center gamma-ray excess, on the other hand, may be tested in the near future using gamma-ray observations [87], antiproton data [88, 89], radio measurements [88] or direct detection experiments [90]. 4. Conclusions The search for dark matter particles has entered a golden era. Many experiments are currently operating in direct searches, indirect searches and collider searches with a sensitivity which might be sufficiently good to detect signals in theoretically well motivated scenarios. This is in particular the case for two of the most popular dark matter candidates: sterile neutrinos and weakly interacting massive particles. Sterile neutrinos could be detected through the monoenergetic photon produced in their decay. The excellent sensitivity of current X-ray observations implies a very long lifetime for the sterile neutrino which rules out already the region of the parameter space where a signal is expected in the simplest models of dark matter production in the early Universe. Interestingly, an X-ray line with an energy of 3.5 kev was recently found using data from XMM-Newton and which is consistent with being produced in sterile neutrino decay, although this framework would require more complicated dark matter production mechanisms. The future Astro- H mission will hopefully be able to shed more light on the origin of this unidentified line. Weakly Interacting Massive Particles could annihilate in regions of the Universe with an overdensity of dark matter particles, producing gamma-rays, antimatter and neutrinos. Remarkably, the exquisite measurements of the positron flux and fraction by the AMS- 02 collaboration and of the gamma-ray flux from dwarf galaxies by the Fermi-LAT collaboration allow to probe already some dark matter scenarios with thermal production. Besides, the Fermi-LAT data from the Milky Way center and inner region are also of very high quality and start to probe the region of the WIMP parameter space where a signal could be found, although this search still suffers from large uncertainties in the modeling of the background. Some authors have recently claimed the existence of a residual gamma-ray emission, which is compatible with dark matter annihilations, and for parameters well consistent with the theory expectations. Future measurements, notably from dwarf galaxies, will elucidate whether this excess is of astrophysical origin or has a dark matter origin. Acknowledgements The author would like to thank the organizers of the X The Latin American Symposium on High Energy Physics (SILAFAE) for their kind invitation to participate in this event and for their warm hospitality. This work was partially supported by the DFG cluster of excellence Origin and Structure of the Universe.
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