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Signatures of the Inert Doublet Dark Matter Model
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Nuclear and Particle Physics Proceedings 263–264 (2015) 107–112 www.elsevier.com/locate/nppp
Signatures of the Inert Doublet Dark Matter Model Camilo Garcia-Cely and Alejandro Ibarra Physik-Department T30d, Technische Universit¨at M¨unchen, James-Franck-Straße, 85748 Garching, Germany
Abstract The inert Doublet Model is an extension of the Standard Model by one extra scalar, with identical gauge quantum numbers as the Standard Model Higgs doublet but charged under an unbroken discrete symmetry. The model offers a very rich phenomenology and could lead to signatures in electroweak precision observables or collider experiments. Furthermore, the lightest particle of the extended scalar sector is a dark matter candidate. In this talk we review the dark matter phenomenology of the model, concretely the dark matter thermal production, the direct detection signals and the indirect detection signals, with emphasis on the generation of sharp gamma-ray spectral features via internal bremsstrahlung and via one-loop effects.
1. The Inert Doublet Model The Inert Doublet Model is a simple extension of the Standard Model that accounts for the dark matter (DM) of the Universe [1]. It introduces a new scalar field η, with identical gauge quantum numbers as the Standard Model Higgs boson, and postulates that the vacuum is invariant under a Z2 symmetry, under which η is odd while all the Standard Model particles are even. These two simple assumptions have a number of implications. First, the Z2 symmetry ensures that the doublet η contains an absolutely stable particle which is a DM candidate. Besides, the exotic doublet η does not interact at tree level with any of the Standard Model fermions, hence the name “inert”. However, this does not imply that η is totally decoupled from our visible sector. On the contrary, η communicates with the observable sector via gauge interactions and via the Higgs portal, e.g via terms in the potential such as (Φ† Φ)(η† η), Φ being the Standard Model Higgs doublet. The corresponding two-to-two interactions allow the equilibration of the inert doublet with the Standard Model particles in the early Universe and their freeze-out from the thermal plasma, thus producing a population of the lightest Z2 -odd scalar that might account, for appropriate http://dx.doi.org/10.1016/j.nuclphysbps.2015.04.020 2405-6014/© 2015 Elsevier B.V. All rights reserved.
choices of the parameters, for the observed DM abundance ΩDM h2 = 0.1199 ± 0.0027 [2]. Moreover, these interactions with the Standard Model particles might lead to signatures in direct and indirect DM searches. 2. Relic abundance One of the most popular frameworks for DM production is the freeze-out mechanism. In this framework, DM particles are assumed to interact in pairs with Standard Model particles, with a strength that controls both the DM production and annihilation rates. It is further assumed that, at sufficiently high temperatures, the DM particles were in thermal equilibrium with the Standard Model particles, namely that the production and the annihilation rates were identical. Then, when the temperature dropped below the DM mass, DM particles continued their annihilations but could no longer be regenerated, since the Standard Model particles did not have enough kinetic energy to produce DM particles. Therefore, the number of DM particles exponentially decreased as the Universe cooled down. In a static universe, this process would have continued until no DM particles remained, however, due to the expan-
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sion of the Universe, the population of DM particles became at some epoch so diluted that annihilations could no longer occur. After this epoch the DM density per comoving volume “froze-out” and remained approximately constant until the present epoch. The relic abundance of DM particles is calculable within this framework, the result being Ωh2 3 × 10−27 cm3 s/σv, where σv is the thermally averaged annihilation cross section multiplied by the relative velocity. Therefore, the observed relic abundance ΩDM h2 0.12 can be obtained if σv 3×10−26 cm3 s at the time of freeze-out, which roughly corresponds to an interaction cross section of the order of the weak interaction. This mechanism is naturally implemented in the inert doublet model. The lightest particle of the Z2 -odd sector, that we assume to be the lightest CP-even scalar H 0 , is absolutely stable and annihilates in pairs into weak gauge bosons, Higgs bosons or Standard model fermions. Therefore, we expect in this model choices of parameters where the correct relic density could be naturally accommodated [3, 4, 5]. We show in Fig.1, left plot, the predicted DM abundance as a function of the DM mass for random choices of the parameters of the model. The points in cyan were generated by letting the quartic couplings of the model vary linearly in the range |λi | 2; the points in orange are the subset of those points which reproduce the correct relic density. It is notable from the plot the existence of a gap at intermediate masses, MW MH 0 500 GeV. The reason for this gap is that for DM masses larger than the W mass, the annihilation channel H 0 H 0 → W + W − is, despite being mediated by a weak interaction, very efficient in depleting the number density of DM particles. As a result, the predicted relic abundance lies below the value required by observations. There are, however, two windows where one finds points reproducing the observed DM abundance, one for MH 0 < MW and another for MH 0 500 GeV. In the light mass window, the dominant annihilation channel is not into ¯ W + W − , since it is kinematically forbidden, but into bb, via the exchange of the Standard Model Higgs in the s-channel. In this region of the parameter space, the annihilation rate is proportional to the quartic couplings of the model, hence, it is possible to reproduce the correct DM abundance by adjusting the values of these couplings. On the other hand, in the heavy DM scenario, due to the suppression of the annihilation cross section with the squared of the DM mass (as required by unitarity), the relic abundance can be again in agreement with observations. If all quartic couplings vanished and the DM particle coupled just to the weak gauge bosons, the strength of the interaction would be fixed and, ac-
cordingly, the DM mass leading to the observed relic abundance, the value being mH 0 500 GeV. For larger DM masses, the cross section would be too small and the relic abundance would be larger than the observed value. Nevertheless, when the quartic couplings are different from zero, new annihilation channels open, which increase the total annihilation cross section. In this case, and by choosing appropriately the value of the coupling, it is possible again to reproduce the observed DM abundance. 3. Direct detection The DM particle can in this model scatter with partons inside a nucleon in two different channels: i) the inelastic channel producing a pseudo-scalar, A0 , in the final state via the exchange of a Z boson, provided the collision is kinematically accessible and ii) the elastic channel via the exchange of a Higgs boson. The inelastic channel yields a too large scattering rate when the DM particle and the pseudo-scalar are very degenerate in mass, while the scattering rate can be safely neglected when mA0 − mH 0 100 keV. We will assume that this is the case in what follows. Then, the only kinematically accessible channel is the elastic scattering via the mediation of the Higgs boson, which has a rate proportional to the quartic coupling between two DM particles and two Higgs bosons, that we denote by λH 0 . More concretely, 2 1 TeV cm2 . (1) σ(H 0 p) 5 × 10−44 λ2H 0 MH 0 Present experiments are sensitive to an interaction cross section of O(10−44 ) cm2 between ∼ 20 − 500 GeV, thus opening the exciting possibility of observing signatures of the inert doublet model in direct detection experiments. We present in Fig. 1, middle plot, the scattering cross section of DM particles with protons for random choices of the parameters of the model. Many of the points in the low mass regime are in fact excluded by the present XENON100 limit [6], except when mH 0 60 GeV, corresponding to the freeze-out via the resonant Higgs s-channel exchange. On the other hand, the high mass regime is currently unconstrained by direct detection experiments, although there exist points in the parameter space that are at the reach of the LUX [7] and XENON1T [8] experiments. 4. Indirect detection The annihilation of DM particles into weak gauge bosons, Higgs bosons and a top-antitop pair in the heavy
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Figure 1: Relic abundance (left plot), scattering cross section with protons (middle plot), and total annihilation cross section (right plot) obtained from scanning the parameter space of the inert doublet model, shown as cyan points, highlighting in orange those points that reproduce the correct DM abundance via thermal freeze-out. We show, together with the predicted scattering cross sections, the limits from XENON100, as well as the projected sensitivity of XENON1T and LUX. Besides, we show together with the total annihilation cross sections the limits from dwarf galaxies (dashed lines) and antiprotons (solid lines) assuming 100% branching fraction into WW (green lines) or hh (blue lines).
mass regime of the inert doublet model produces a flux of antimatter particles, neutrinos and gamma-rays that could be detected at the Earth. The non-observation of an excess in the antiproton-to-proton fraction measured by the PAMELA experiment [9] with respect to the expectations from secondary production allows to set limits on the annihilation cross section (see, for example, [10]). Besides, the excellent fit of the AMS02 data on the positron flux and fraction [11] by a model consisting on secondary production plus a primary source, following a simple power law with an exponential cut-off, allows to set stringent limits on the DM annihilation cross section into W + W − /ZZ and hh [12]. These annihilation channels are further constrained by gamma-ray observations of the diffuse background [13] and of dwarf galaxies [14, 15]. More specifically, the non-observation of a significant excess of gamma-rays from dwarf galaxies allows to set the approximate limit of the total annihilation cross-section (σv) 5.0 × 10−30 cm3 s−1 GeV−2 (8πMH2 0 /Nγtot ) [16], where Nγtot is the number of photons that are produced per annihilation with energies between 1 and 100 GeV. The limits on the annihilation cross section from antiprotons and dwarf galaxies are shown in Fig. 1, right plot, and lie one or two orders of magnitude above the expected values in the inert doublet model.
5. Sharp gamma-ray spectral features The observation of sharp spectral features in the gamma-ray sky would constitute an unambiguous signal for DM annihilations, since no known astrophysical process can produce a similar signature. So far, three
different gamma-ray spectral features have been identified in DM scenarios: gamma-ray lines [17, 18, 19], internal electromagnetic bremsstrahlung [20, 21, 22] and gamma-ray boxes [23]. Interestingly, the three spectral features arise in the inert doublet model. Gamma ray lines are generated through the W ± bosons or the charged Higgs component of the inert doublet that appear in loops, and correspond to a monochromatic line at an energy equal to the DM mass. In the low mass regime, the predicted cross section ranges between σvγγ 6 × 10−29 cm3 s−1 at mH0 = 45 GeV and 4 × 10−28 cm3 s−1 at mH0 = 75 GeV [24]. Notably, these cross sections lie in the ballpark of the currently excluded cross section in this channel by the Fermi collaboration [25]. The calculation of the cross section in the high-mass regime will be presented in [26]. Gamma ray boxes appear in scenarios where the DM particle annihilates into two scalar (or pseudo-scalar) particles, which in turn decay in flight into two photons. In the rest frame of the scalar, the two photons are monoenergetic. However, in the Galactic frame the scalar possesses some momentum. Therefore, photons emitted in the forward direction gain energy, while those emitted in the backward direction, lose energy. Finally, since the decay is isotropic, the energy spectrum in the galactic frame has the shape of a box. In the limit where the scalar mass is close to the DM mass, the box is very narrow and resembles a gamma-ray line. As the mass difference increases, the box becomes wider and wider. Nevertheless, a sharp feature remains consisting in a flat energy spectrum with a sudden dropoff, which is easily distinguishable from the monotonically decreasing, and relatively soft, energy spectrum
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from the astrophysical background. As a consequence, even in the wide-box scenario, present limits from the Fermi-LAT and H:E.S.S. exclude the thermal cross section σv = 3 × 10−26 cm3 s−1 for mDM 700 GeV, assuming a branching fraction of the scalar into two photons equal to 1 [27]. A gamma-ray box is naturally produced in the inert doublet model, from the annihilation into two Higgs bosons on shell, which then decay into two photons. This process corresponds, in the high mass regime, to the wide box scenario, due to the large difference between the DM mass and the Higgs mass. Present measurements are, however, not yet sensitive to the gamma-ray box produced in the inert doublet model, due to the small branching fraction of the Higgs into gamma-gamma, BR(h → γγ) 2 × 10−3 , and which translates into a signal about two orders of magnitude fainter than the present experimental sensitivity. Finally, a sharp spectral feature also arises from the three body annihilation H 0 H 0 → W + W − γ, dubbed internal bremsstrahlung [28]. This process is generated through the exchange of a charged scalar in the tchannel and therefore produces, as discussed in [22], a bump close to the kinematical endpoint of the gammaray spectrum when the mass of the particle in the tchannel is degenerated to the DM mass. This situation naturally occurs in the high mass regime of the inert doublet model, therefore this signature is generically expected to appear. This is illustrated in Fig.2, where we show the photon multiplicity from internal bremsstrahlung in the limit where the charged scalar is degenerate in mass with the DM particle, for different values of the absolute value of the quartic coupling λ3 from the potential term V ⊃ 12 λ3 (Φ† Φ)(η† η). As apparent from the plot, the model produces, for a wide range of parameters, a very sharp spectral feature. To study the prospects to observe the signal from internal bremsstrahlung in gamma-ray telescopes a series of benchmark points were proposed in [28], which correctly reproduce the observed cold DM density and which are consistent with current direct and indirect DM searches. We show in Fig.3 the photon spectrum for two of these benchmark points, BMP2 and BMP5, which correspond to mH 0 = 938 GeV and mH 0 = 4.21 TeV (for details, see [28]). The total spectrum (shown as a black line) includes the hard photon contribution from the two-to-three process H 0 H 0 → W + W − γ (blue line), as well as the soft photons from the two-to-two processes H 0 H 0 → W + W − , Z 0 Z 0 , hh, tt¯ (red line). We then calculate the photon flux received at the Earth considering a J-factor given by J = 1.2 × 1025 GeV2 cm−5 , corresponding to the search region adopted by the H.E.S.S. collaboration for the search for
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Figure 2: Contributions to the total multiplicity of the hard photon corresponding to the internal bremsstrahlung process H 0 H 0 → W + W − γ, when the charged scalar is degenerate in mass with the DM particle and mH 0 = 0.5 TeV (top plot), 1 TeV (middle plot) and 5 TeV (bottom plot). The different darkness of the lines correspond to varying the absolute value of the quartic coupling |λ3 | between 0 (darkest lines) and 2 (lightest lines) in intervals of 0.4.
line-like gamma-ray features in the central part of the Milky Way halo with energies between ∼ 500 GeV and ∼ 25 TeV [29]. The predicted integrated flux of the hard photon emitted in the internal bremsstrahlung process H 0 H 0 → W + W − γ is shown in Fig. 4 for random choices of the parameters of the model (cyan points); those points shown in orange are the subset of those points which reproduce the correct relic density, and among them we highlight the benchmark scenarios of [28]. We also show the limits derived by the H.E.S.S. collaboration for the BM4 benchmark point of [22], corresponding to the neutralino annihilation χ0 χ0 → W + W − γ and which produces a similar spectrum as H 0 H 0 → W + W − γ. As apparent from the plot, the predicted signal lies a factor O(10 − 100) below the sensitivity of present gamma-ray telescopes. Nevertheless, future in-
C. Garcia-Cely, A. Ibarra / Nuclear and Particle Physics Proceedings 263–264 (2015) 107–112 BMP 2
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Figure 3: Predicted photon spectrum from DM annihilations in the inert doublet model for the benchmark points BMP2 and BMP5 defined in [28].
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rect DM searches. We have argued that the low mass regime is in tension with the current limits from the XENON100 experiment, while the high mass regime is mostly unconstrained. Remarkably, the future experiments LUX and XENON1T will be able to explore large regions of the parameter space. We have also found that limits on the annihilation cross section from antiprotons, positrons or diffuse gamma-rays typically are one or two orders of magnitude weaker than the expected values for thermally produced DM particles. The model also produces sharp spectral features in the form of gamma-ray lines, gamma-ray boxes and internal bremsstrahlung. The signal from internal bremsstrahlung naturally emerges in this model and give limits which are competitive with those stemming from other indirect search strategies, despite being a higher order annihilation process. Future searches for gamma-ray spectral features by DAMPE, GAMMA400 or CTA will continue closing in on the parameter space of the inert doublet DM model.
Acknowledgements struments, such as DAMPE [30], GAMMA-400 [31] or CTA [32] will close in on the signal of internal bremsstrahlung from the inert doublet model. 6. Conclusions The inert doublet model is a simple extension of the Standard Model which accounts for the DM of the Universe. It offers a rich phenomenology and predicts potentially observable effects in collider searches, electroweak precision tests, as well as in direct and indirect DM searches. In this talk we have focused on the signatures of the inert doublet model in direct and indi-
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Figure 4: Same as Fig. 1, but for the integrated flux of the internal bremsstrahlung feature. We also show for reference the flux upper limit derived in [29] by the H.E.S.S. collaboration for the spectral feature χ0 χ0 → W + W − γ from neutralino annihilation (red line) and the predicted flux for H 0 H 0 → W + W − γ, assuming |λ3 | = 0, 1, 2 (black lines).
This work was partially supported by the DFG cluster of excellence “Origin and Structure of the Universe” and by the Graduiertenkolleg “Particle Physics at the Energy Frontier of New Phenomena”.
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Nuclear and Particle Physics Proceedings 263–264 (2015) 107–112 www.elsevier.com/locate/nppp
Signatures of the Inert Doublet Dark Matter Model Camilo Garcia-Cely and Alejandro Ibarra Physik-Department T30d, Technische Universit¨at M¨unchen, James-Franck-Straße, 85748 Garching, Germany
Abstract The inert Doublet Model is an extension of the Standard Model by one extra scalar, with identical gauge quantum numbers as the Standard Model Higgs doublet but charged under an unbroken discrete symmetry. The model offers a very rich phenomenology and could lead to signatures in electroweak precision observables or collider experiments. Furthermore, the lightest particle of the extended scalar sector is a dark matter candidate. In this talk we review the dark matter phenomenology of the model, concretely the dark matter thermal production, the direct detection signals and the indirect detection signals, with emphasis on the generation of sharp gamma-ray spectral features via internal bremsstrahlung and via one-loop effects.
1. The Inert Doublet Model The Inert Doublet Model is a simple extension of the Standard Model that accounts for the dark matter (DM) of the Universe [1]. It introduces a new scalar field η, with identical gauge quantum numbers as the Standard Model Higgs boson, and postulates that the vacuum is invariant under a Z2 symmetry, under which η is odd while all the Standard Model particles are even. These two simple assumptions have a number of implications. First, the Z2 symmetry ensures that the doublet η contains an absolutely stable particle which is a DM candidate. Besides, the exotic doublet η does not interact at tree level with any of the Standard Model fermions, hence the name “inert”. However, this does not imply that η is totally decoupled from our visible sector. On the contrary, η communicates with the observable sector via gauge interactions and via the Higgs portal, e.g via terms in the potential such as (Φ† Φ)(η† η), Φ being the Standard Model Higgs doublet. The corresponding two-to-two interactions allow the equilibration of the inert doublet with the Standard Model particles in the early Universe and their freeze-out from the thermal plasma, thus producing a population of the lightest Z2 -odd scalar that might account, for appropriate http://dx.doi.org/10.1016/j.nuclphysbps.2015.04.020 2405-6014/© 2015 Elsevier B.V. All rights reserved.
choices of the parameters, for the observed DM abundance ΩDM h2 = 0.1199 ± 0.0027 [2]. Moreover, these interactions with the Standard Model particles might lead to signatures in direct and indirect DM searches. 2. Relic abundance One of the most popular frameworks for DM production is the freeze-out mechanism. In this framework, DM particles are assumed to interact in pairs with Standard Model particles, with a strength that controls both the DM production and annihilation rates. It is further assumed that, at sufficiently high temperatures, the DM particles were in thermal equilibrium with the Standard Model particles, namely that the production and the annihilation rates were identical. Then, when the temperature dropped below the DM mass, DM particles continued their annihilations but could no longer be regenerated, since the Standard Model particles did not have enough kinetic energy to produce DM particles. Therefore, the number of DM particles exponentially decreased as the Universe cooled down. In a static universe, this process would have continued until no DM particles remained, however, due to the expan-
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sion of the Universe, the population of DM particles became at some epoch so diluted that annihilations could no longer occur. After this epoch the DM density per comoving volume “froze-out” and remained approximately constant until the present epoch. The relic abundance of DM particles is calculable within this framework, the result being Ωh2 3 × 10−27 cm3 s/σv, where σv is the thermally averaged annihilation cross section multiplied by the relative velocity. Therefore, the observed relic abundance ΩDM h2 0.12 can be obtained if σv 3×10−26 cm3 s at the time of freeze-out, which roughly corresponds to an interaction cross section of the order of the weak interaction. This mechanism is naturally implemented in the inert doublet model. The lightest particle of the Z2 -odd sector, that we assume to be the lightest CP-even scalar H 0 , is absolutely stable and annihilates in pairs into weak gauge bosons, Higgs bosons or Standard model fermions. Therefore, we expect in this model choices of parameters where the correct relic density could be naturally accommodated [3, 4, 5]. We show in Fig.1, left plot, the predicted DM abundance as a function of the DM mass for random choices of the parameters of the model. The points in cyan were generated by letting the quartic couplings of the model vary linearly in the range |λi | 2; the points in orange are the subset of those points which reproduce the correct relic density. It is notable from the plot the existence of a gap at intermediate masses, MW MH 0 500 GeV. The reason for this gap is that for DM masses larger than the W mass, the annihilation channel H 0 H 0 → W + W − is, despite being mediated by a weak interaction, very efficient in depleting the number density of DM particles. As a result, the predicted relic abundance lies below the value required by observations. There are, however, two windows where one finds points reproducing the observed DM abundance, one for MH 0 < MW and another for MH 0 500 GeV. In the light mass window, the dominant annihilation channel is not into ¯ W + W − , since it is kinematically forbidden, but into bb, via the exchange of the Standard Model Higgs in the s-channel. In this region of the parameter space, the annihilation rate is proportional to the quartic couplings of the model, hence, it is possible to reproduce the correct DM abundance by adjusting the values of these couplings. On the other hand, in the heavy DM scenario, due to the suppression of the annihilation cross section with the squared of the DM mass (as required by unitarity), the relic abundance can be again in agreement with observations. If all quartic couplings vanished and the DM particle coupled just to the weak gauge bosons, the strength of the interaction would be fixed and, ac-
cordingly, the DM mass leading to the observed relic abundance, the value being mH 0 500 GeV. For larger DM masses, the cross section would be too small and the relic abundance would be larger than the observed value. Nevertheless, when the quartic couplings are different from zero, new annihilation channels open, which increase the total annihilation cross section. In this case, and by choosing appropriately the value of the coupling, it is possible again to reproduce the observed DM abundance. 3. Direct detection The DM particle can in this model scatter with partons inside a nucleon in two different channels: i) the inelastic channel producing a pseudo-scalar, A0 , in the final state via the exchange of a Z boson, provided the collision is kinematically accessible and ii) the elastic channel via the exchange of a Higgs boson. The inelastic channel yields a too large scattering rate when the DM particle and the pseudo-scalar are very degenerate in mass, while the scattering rate can be safely neglected when mA0 − mH 0 100 keV. We will assume that this is the case in what follows. Then, the only kinematically accessible channel is the elastic scattering via the mediation of the Higgs boson, which has a rate proportional to the quartic coupling between two DM particles and two Higgs bosons, that we denote by λH 0 . More concretely, 2 1 TeV cm2 . (1) σ(H 0 p) 5 × 10−44 λ2H 0 MH 0 Present experiments are sensitive to an interaction cross section of O(10−44 ) cm2 between ∼ 20 − 500 GeV, thus opening the exciting possibility of observing signatures of the inert doublet model in direct detection experiments. We present in Fig. 1, middle plot, the scattering cross section of DM particles with protons for random choices of the parameters of the model. Many of the points in the low mass regime are in fact excluded by the present XENON100 limit [6], except when mH 0 60 GeV, corresponding to the freeze-out via the resonant Higgs s-channel exchange. On the other hand, the high mass regime is currently unconstrained by direct detection experiments, although there exist points in the parameter space that are at the reach of the LUX [7] and XENON1T [8] experiments. 4. Indirect detection The annihilation of DM particles into weak gauge bosons, Higgs bosons and a top-antitop pair in the heavy
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Figure 1: Relic abundance (left plot), scattering cross section with protons (middle plot), and total annihilation cross section (right plot) obtained from scanning the parameter space of the inert doublet model, shown as cyan points, highlighting in orange those points that reproduce the correct DM abundance via thermal freeze-out. We show, together with the predicted scattering cross sections, the limits from XENON100, as well as the projected sensitivity of XENON1T and LUX. Besides, we show together with the total annihilation cross sections the limits from dwarf galaxies (dashed lines) and antiprotons (solid lines) assuming 100% branching fraction into WW (green lines) or hh (blue lines).
mass regime of the inert doublet model produces a flux of antimatter particles, neutrinos and gamma-rays that could be detected at the Earth. The non-observation of an excess in the antiproton-to-proton fraction measured by the PAMELA experiment [9] with respect to the expectations from secondary production allows to set limits on the annihilation cross section (see, for example, [10]). Besides, the excellent fit of the AMS02 data on the positron flux and fraction [11] by a model consisting on secondary production plus a primary source, following a simple power law with an exponential cut-off, allows to set stringent limits on the DM annihilation cross section into W + W − /ZZ and hh [12]. These annihilation channels are further constrained by gamma-ray observations of the diffuse background [13] and of dwarf galaxies [14, 15]. More specifically, the non-observation of a significant excess of gamma-rays from dwarf galaxies allows to set the approximate limit of the total annihilation cross-section (σv) 5.0 × 10−30 cm3 s−1 GeV−2 (8πMH2 0 /Nγtot ) [16], where Nγtot is the number of photons that are produced per annihilation with energies between 1 and 100 GeV. The limits on the annihilation cross section from antiprotons and dwarf galaxies are shown in Fig. 1, right plot, and lie one or two orders of magnitude above the expected values in the inert doublet model.
5. Sharp gamma-ray spectral features The observation of sharp spectral features in the gamma-ray sky would constitute an unambiguous signal for DM annihilations, since no known astrophysical process can produce a similar signature. So far, three
different gamma-ray spectral features have been identified in DM scenarios: gamma-ray lines [17, 18, 19], internal electromagnetic bremsstrahlung [20, 21, 22] and gamma-ray boxes [23]. Interestingly, the three spectral features arise in the inert doublet model. Gamma ray lines are generated through the W ± bosons or the charged Higgs component of the inert doublet that appear in loops, and correspond to a monochromatic line at an energy equal to the DM mass. In the low mass regime, the predicted cross section ranges between σvγγ 6 × 10−29 cm3 s−1 at mH0 = 45 GeV and 4 × 10−28 cm3 s−1 at mH0 = 75 GeV [24]. Notably, these cross sections lie in the ballpark of the currently excluded cross section in this channel by the Fermi collaboration [25]. The calculation of the cross section in the high-mass regime will be presented in [26]. Gamma ray boxes appear in scenarios where the DM particle annihilates into two scalar (or pseudo-scalar) particles, which in turn decay in flight into two photons. In the rest frame of the scalar, the two photons are monoenergetic. However, in the Galactic frame the scalar possesses some momentum. Therefore, photons emitted in the forward direction gain energy, while those emitted in the backward direction, lose energy. Finally, since the decay is isotropic, the energy spectrum in the galactic frame has the shape of a box. In the limit where the scalar mass is close to the DM mass, the box is very narrow and resembles a gamma-ray line. As the mass difference increases, the box becomes wider and wider. Nevertheless, a sharp feature remains consisting in a flat energy spectrum with a sudden dropoff, which is easily distinguishable from the monotonically decreasing, and relatively soft, energy spectrum
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from the astrophysical background. As a consequence, even in the wide-box scenario, present limits from the Fermi-LAT and H:E.S.S. exclude the thermal cross section σv = 3 × 10−26 cm3 s−1 for mDM 700 GeV, assuming a branching fraction of the scalar into two photons equal to 1 [27]. A gamma-ray box is naturally produced in the inert doublet model, from the annihilation into two Higgs bosons on shell, which then decay into two photons. This process corresponds, in the high mass regime, to the wide box scenario, due to the large difference between the DM mass and the Higgs mass. Present measurements are, however, not yet sensitive to the gamma-ray box produced in the inert doublet model, due to the small branching fraction of the Higgs into gamma-gamma, BR(h → γγ) 2 × 10−3 , and which translates into a signal about two orders of magnitude fainter than the present experimental sensitivity. Finally, a sharp spectral feature also arises from the three body annihilation H 0 H 0 → W + W − γ, dubbed internal bremsstrahlung [28]. This process is generated through the exchange of a charged scalar in the tchannel and therefore produces, as discussed in [22], a bump close to the kinematical endpoint of the gammaray spectrum when the mass of the particle in the tchannel is degenerated to the DM mass. This situation naturally occurs in the high mass regime of the inert doublet model, therefore this signature is generically expected to appear. This is illustrated in Fig.2, where we show the photon multiplicity from internal bremsstrahlung in the limit where the charged scalar is degenerate in mass with the DM particle, for different values of the absolute value of the quartic coupling λ3 from the potential term V ⊃ 12 λ3 (Φ† Φ)(η† η). As apparent from the plot, the model produces, for a wide range of parameters, a very sharp spectral feature. To study the prospects to observe the signal from internal bremsstrahlung in gamma-ray telescopes a series of benchmark points were proposed in [28], which correctly reproduce the observed cold DM density and which are consistent with current direct and indirect DM searches. We show in Fig.3 the photon spectrum for two of these benchmark points, BMP2 and BMP5, which correspond to mH 0 = 938 GeV and mH 0 = 4.21 TeV (for details, see [28]). The total spectrum (shown as a black line) includes the hard photon contribution from the two-to-three process H 0 H 0 → W + W − γ (blue line), as well as the soft photons from the two-to-two processes H 0 H 0 → W + W − , Z 0 Z 0 , hh, tt¯ (red line). We then calculate the photon flux received at the Earth considering a J-factor given by J = 1.2 × 1025 GeV2 cm−5 , corresponding to the search region adopted by the H.E.S.S. collaboration for the search for
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Figure 2: Contributions to the total multiplicity of the hard photon corresponding to the internal bremsstrahlung process H 0 H 0 → W + W − γ, when the charged scalar is degenerate in mass with the DM particle and mH 0 = 0.5 TeV (top plot), 1 TeV (middle plot) and 5 TeV (bottom plot). The different darkness of the lines correspond to varying the absolute value of the quartic coupling |λ3 | between 0 (darkest lines) and 2 (lightest lines) in intervals of 0.4.
line-like gamma-ray features in the central part of the Milky Way halo with energies between ∼ 500 GeV and ∼ 25 TeV [29]. The predicted integrated flux of the hard photon emitted in the internal bremsstrahlung process H 0 H 0 → W + W − γ is shown in Fig. 4 for random choices of the parameters of the model (cyan points); those points shown in orange are the subset of those points which reproduce the correct relic density, and among them we highlight the benchmark scenarios of [28]. We also show the limits derived by the H.E.S.S. collaboration for the BM4 benchmark point of [22], corresponding to the neutralino annihilation χ0 χ0 → W + W − γ and which produces a similar spectrum as H 0 H 0 → W + W − γ. As apparent from the plot, the predicted signal lies a factor O(10 − 100) below the sensitivity of present gamma-ray telescopes. Nevertheless, future in-
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rect DM searches. We have argued that the low mass regime is in tension with the current limits from the XENON100 experiment, while the high mass regime is mostly unconstrained. Remarkably, the future experiments LUX and XENON1T will be able to explore large regions of the parameter space. We have also found that limits on the annihilation cross section from antiprotons, positrons or diffuse gamma-rays typically are one or two orders of magnitude weaker than the expected values for thermally produced DM particles. The model also produces sharp spectral features in the form of gamma-ray lines, gamma-ray boxes and internal bremsstrahlung. The signal from internal bremsstrahlung naturally emerges in this model and give limits which are competitive with those stemming from other indirect search strategies, despite being a higher order annihilation process. Future searches for gamma-ray spectral features by DAMPE, GAMMA400 or CTA will continue closing in on the parameter space of the inert doublet DM model.
Acknowledgements struments, such as DAMPE [30], GAMMA-400 [31] or CTA [32] will close in on the signal of internal bremsstrahlung from the inert doublet model. 6. Conclusions The inert doublet model is a simple extension of the Standard Model which accounts for the DM of the Universe. It offers a rich phenomenology and predicts potentially observable effects in collider searches, electroweak precision tests, as well as in direct and indirect DM searches. In this talk we have focused on the signatures of the inert doublet model in direct and indi-
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Figure 4: Same as Fig. 1, but for the integrated flux of the internal bremsstrahlung feature. We also show for reference the flux upper limit derived in [29] by the H.E.S.S. collaboration for the spectral feature χ0 χ0 → W + W − γ from neutralino annihilation (red line) and the predicted flux for H 0 H 0 → W + W − γ, assuming |λ3 | = 0, 1, 2 (black lines).
This work was partially supported by the DFG cluster of excellence “Origin and Structure of the Universe” and by the Graduiertenkolleg “Particle Physics at the Energy Frontier of New Phenomena”.
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