High-energy neutrino signals from the Sun in dark matter scenarios with internal bremsstrahlung
TTUM-HEP 912/13
High-energy neutrino signals from the Sun in dark matter scenarios with internal bremsstrahlung
Alejandro Ibarra, Maximilian Totzauer and Sebastian Wild
Physik-Department T30d, Technische Universit¨at M¨unchen,James-Franck-Straße, 85748 Garching, Germany
October 4, 2018
Abstract
We investigate the prospects to observe a high energy neutrino signal from darkmatter annihilations in the Sun in scenarios where the dark matter is a Majoranafermion that couples to a quark and a colored scalar via a Yukawa coupling. In thisminimal scenario, the dark matter capture and annihilation in the Sun can be studiedin a single framework. We find that, for small and moderate mass splitting between thedark matter and the colored scalar, the two-to-three annihilation q ¯ qg plays a centralrole in the calculation of the number of captured dark matter particles. On the otherhand, the two-to-three annihilation into q ¯ qZ gives, despite its small branching fraction,the largest contribution to the neutrino flux at the Earth at the highest energies. Wecalculate the limits on the model parameters using IceCube observations of the Sunand we discuss their interplay with the requirement of equilibrium of captures andannihilations in the Sun and with the requirement of thermal dark matter production.We also compare the limits from IceCube to the limits from direct detection, antiprotonmeasurements and collider searches. The search for the particles which are presumed to be produced by dark matter annihilationsis one of the primary goals in Astroparticle Physics (see [1, 2] for reviews on particle darkmatter). This search is however hindered by the low fluxes expected from annihilations andby the existence of large, and still poorly understood, astrophysical backgrounds. Therefore,in order to detect a signal from annihilations, it is necessary to devise search strategies thatmildly rely on the modelling of the backgrounds. Up to now, the most promising strategiesto identify a signal from dark matter annihilations consist in i) the search for features in themeasured energy spectrum of the products of annihilation and ii) the search for an excess ofevents following a spatial distribution with the morphology expected from an annihilationsignal.Both strategies have been successfully applied to the search for annihilation signals ingamma-rays [3]. Several spectral features have been identified [4, 5, 6, 7, 8, 9, 10] and1 a r X i v : . [ h e p - ph ] D ec earched for in the gamma-ray sky [11, 12, 13, 14]. Besides, the characteristic morphologyof the signal expected from dark matter annihilations has been searched for in the GalacticCenter region [15, 16], galaxy clusters [17, 18] and, notably, dwarf galaxies [19, 20, 21, 22].Both search strategies already lead to very stringent limits on the annihilation cross sectionwhich rule out some models. Pursuing these two promising strategies is, however, challengingwhen searching for antimatter particles produced in dark matter annihilations, since thepropagation of the charged cosmic rays in the galaxy practically erases any spectral featureat production and any directional information, yielding a rather featureless spectrum anda fairly isotropic distribution of events. As a result, the limits from antimatter searches aretypically weaker than in gamma-rays (see, however, the recent analyses [23, 24]). Lastly, thesearch for dark matter annihilation using neutrinos as messengers shares many similaritieswith gamma-rays: both are electrically neutral particles and therefore the propagation inthe galaxy does not significantly distort the energy spectrum nor the direction of theseparticles. Nevertheless, searches with neutrinos as messengers are limited by the smallneutrino detection rate and by the poor energy and angular resolution of neutrino telescopes,thus making the search for features in the neutrino spectrum challenging. Indeed, the currentlimits on the annihilation cross section for annihilations into ν ¯ ν [25, 26] are significantlyweaker than the limits for annihilations into γγ . Interestingly, if dark matter particlesinteract with nucleons, they can be captured inside the Sun [27] and subsequently annihilate,producing a high-energy neutrino flux in the direction of the center of the Sun [28, 29]. Thevery characteristic spatial morphology of the signal then opens the possibility of probing thescattering cross section of dark matter particles with nucleons. Conversely, the observationof an excess of high-energy neutrinos in the (time-dependent) direction of the Sun would bea clear signal of dark matter annihilations. The same phenomenon of capture might alsooccur in the Earth and other celestial bodies.In this paper we will concentrate in the possibility of detecting a high-energy neutrino fluxoriginated in the annihilations of dark matter particles that have been previously capturedinside the Sun or inside the Earth. Most analyses postulate that the dark matter particleshad been captured and that their population is constant today, due to the equilibrationbetween the processes of capture and annihilation. In this way, it is possible to set stronglimits on the capture cross section from the non-observation of a neutrino flux originatedin annihilations into, for example, ν ¯ ν or W + W − [30]. However, this requires that the darkmatter particle must couple to neutrinos or to weak gauge bosons, but also sizably to quarksto allow their capture. This scenario can be justified in concrete realizations although doesnot necessarily hold in general.We will then discuss the capture and the annihilation in a single Particle Physics frame-work. More concretely, we will consider a toy model where the dark matter particle is aMajorana fermion that couples to a quark and a scalar via a Yukawa coupling. The couplingto the quark leads to the capture of dark matter particles inside the Sun or the Earth. Onthe other hand, and as is well known, in this toy model the annihilation rate into a quark-antiquark pair is helicity- and velocity- suppressed. Hence, in the equilibration the internalbremsstrahlung processes DM DM → q ¯ qV , with V a gauge boson, play a major role and,in fact, determine the minimal value of the coupling that allows equilibration inside theSun or the Earth. Moreover, these processes determine the energy spectrum of neutrinosproduced in the annihilation and accordingly the detection rate at the Earth (neutrino sig-nals from two-to-three annihilations in leptophilic dark matter models have been considered2reviously in [31, 32]). The parameter space of this toy model is further constrained bythe requirement of reproducing the correct dark matter abundance from thermal produc-tion, as well as from direct, indirect and collider dark matter searches. Concretely, we willconsider, following [33, 34], the limits from the XENON100 experiment [35], the PAMELAmeasurements on the antiproton-to-proton fraction [36], as well as collider limits from theCMS experiment [37]. All these limits, together with the requirement of building up a pop-ulation of dark matter particles inside the Sun or the Earth, will then allow us to assess theprospects to observe a high energy neutrino signal from the Sun or the Earth in neutrinotelescopes, concretely in IceCube.The paper is organized as follows. In Section 2 we present the toy model under consider-ation as well as the properties relevant for our analysis. Then, in Section 3 we describe theprocess of capture of dark matter particles in the Sun and in the Earth and we present theconstraints on the parameter space of our toy model from the requirement of equilibrationbetween capture and annihilation. In Section 4 we calculate the neutrino flux from the Sun,emphasizing the role of the internal bremsstrahlung process in generating a high-energycomponent. In Section 5 we present the limits on the parameter space which stem from thenegative searches of a high-energy neutrino excess in the direction of the Sun in IceCubeand we compare our limits to those from other experiments. Lastly, in Section 6 we presentour conclusions. We consider a toy model where the dark matter particle is a Majorana fermion χ , singletunder the Standard Model gauge group, which interacts with a quark and a scalar η via aYukawa interaction with coupling constant f . The Lagrangian of the model is given by: L = L SM + L χ + L η + L int . (1)Here, L SM is the Standard Model Lagrangian, while L χ and L η are the parts of the La-grangian involving just the new fields χ and η and which are given, respectively, by: L χ = 12 ¯ χ c i /∂χ − m χ ¯ χ c χ , and L η = ( D µ η ) † ( D µ η ) − m η η † η − λ ( η † η ) , (2)Here D µ denotes the usual covariant derivative. Lastly, the interaction term in the La-grangian is given by L int = − λ (Φ † Φ)( η † η ) − f ¯ χq R η + h . c . , (3)where Φ is the Standard Model Higgs boson. Here we have assumed for concreteness that thequark is right-handed, hence the quantum numbers of the scalar under SU (3) c × SU (2) L × U (1) Y are (¯3 , , q f ), where q f is the right-handed quark electric charge (which in this casecoincides with minus the hypercharge).This toy model has been thoroughly discussed in relation to indirect dark matter searches.The lowest order annihilation process χχ → q ¯ q is helicity- and velocity- suppressed, result-ing in an annihilation cross section which is far below the reach of present and foreseeable3ndirect dark matter search experiments. Interestingly, the helicity suppression is lifted bythe associated emission of a spin-one boson [7, 8]. More specifically, the annihilation pro-cesses χχ → q ¯ qV , with V being a gluon [8, 39, 40], a Z/W -boson [41, 42, 43, 44, 45, 46, 47](see also [48, 49]) or a photon [7, 8, 9] can dominate over the two-to-two process, providedthe scalar that mediates the interaction is close in mass to the dark matter particle [42].Moreover, in this regime a sharp spectral feature arises in the gamma-ray spectrum which,if observed, would constitute a smoking gun for dark matter detection. Therefore, newopportunities open for indirect dark matter searches using antimatter, gamma-rays and, aswe will discuss in this paper, neutrinos.The relative importance of the various annihilation channels is illustrated in Fig. 1, wherewe show the branching ratios as a function of the dark matter mass for the exemplary cases m η /m χ = 1 .
01, namely a scenario with large degeneracy, and m η /m χ = 2. In these plots,and in the rest of the paper, we neglect the quark masses in the calculation of the rates ofthe two-to-three processes. It is worth recalling that when m χ (cid:29) M Z , which is the rangeof masses relevant for neutrino telescopes, the ratios of cross sections of the two-to-threeprocesses are fairly independent of the mass splitting and take the values [41]: σv ( χχ → gu R ¯ u R ) : σv ( χχ → γu R ¯ u R ) = 3 α s ( m DM ) /α em (cid:39) . ,σv ( χχ → Zu R ¯ u R ) : σv ( χχ → γu R ¯ u R ) = tan ( θ W ) = 0 . , (4)for couplings to right-handed up-type quarks and σv ( χχ → gd R ¯ d R ) : σv ( χχ → γd R ¯ d R ) = 12 α s ( m χ ) /α em (cid:39) ,σv ( χχ → Zd R ¯ d R ) : σv ( χχ → γd R ¯ d R ) = tan ( θ W ) = 0 . . (5)for right-handed down-type quarks. The numerical values in these formulas have beenobtained evaluating, for illustration, the strong coupling constant at the scale m χ = 1 TeV.The dark matter interaction to a quark in Eq. (3) not only induces dark matter annihi-lations but also the elastic scattering of dark matter particles with a nucleus in a detector,thus opening the possibility of observing signals also in direct dark matter search experi-ments and, as we will see in Section 3, of capturing dark matter particles inside the Sun orthe Earth. The scattering cross sections for this model were calculated in [53, 54, 55]. Thespin dependent part reads σ p SD = 12 µ p π (∆ q ) f (cid:2) m η − ( m χ + m q ) (cid:3) , (6)where µ p is the reduced mass of the proton-dark matter system and ∆ q parametrizes thequark spin content of the proton for the light quark to which the dark matter couples; forheavy quarks, ∆ q = 0. Besides, the spin independent cross section with protons reads: σ p SI = 4 µ p π f p , (7) The emission of a Higgs boson also lifts the helicity suppression, as recently pointed out in [38]. Thecross section, however, strongly depends on the parameters of the scalar potential, therefore we will neglectthese processes in our analysis for simplicity. Sharp spectral features from internal bremsstrahlung also arise in the annihilation of scalar dark matterparticles [50, 51, 52]. − − − − − − − m χ [GeV] b r a n c h i n g r a t i o Coupling to u -quarks, m η /m χ = 1 . u ¯ uu ¯ uγ u ¯ ugu ¯ uZ − − − − − − − m χ [GeV] b r a n c h i n g r a t i o Coupling to u -quarks, m η /m χ = 2 . u ¯ uu ¯ uγ u ¯ ugu ¯ uZ − − − − − − − m χ [GeV] b r a n c h i n g r a t i o Coupling to b -quarks, m η /m χ = 1 . b ¯ bb ¯ bγb ¯ bg b ¯ bZ − − − − − − − m χ [GeV] b r a n c h i n g r a t i o Coupling to b -quarks, m η /m χ = 2 . b ¯ b b ¯ bγb ¯ bg b ¯ bZ Figure 1: Branching fraction of the annihilation χχ → q ¯ q ( V ), with V a gauge boson and q a right-handed up-quark (upper panels) or bottom-quark (lower panels), for the mass ratios m η /m χ = 1 .
01 (left panels) and 2.0 (right panels).5here f p = m p (cid:32) f pT q m χ f (cid:2) m η − ( m χ + m q ) (cid:3) + 32 m χ f (cid:2) m η − ( m χ + m q ) (cid:3) [ q p (2) + ¯ q p (2)] − πbf pT g (cid:33) , (8)with an analogous expression for the neutron-dark matter cross section (note that we donot assume isospin invariance). Here, b is a function of the masses of the respective quark,the dark matter particle and the scalar mediator η which we take from [54, 56]. Moreover, f p/nT q ( f p/nT g ) parametrizes the scalar quark (gluon) current in the proton/neutron; we use thevalues and uncertainties from [55]. Lastly, q p/n (2) are the second moments of the particledistribution function of the quark inside the nucleon, given in [53]. Note that both thespin independent and the spin dependent cross sections get enhanced when the dark matterparticle and the intermediate scalar η are close in mass, which is precisely the region ofthe parameter space relevant for indirect dark matter searches in this scenario [33]. Theexpressions for the cross sections, Eqs. (6,7), on the other hand, become divergent when m η = m χ + m q and therefore it is necessary to include close to the resonance the width of theexchanged scalar. However, and in order to avoid the model dependence introduced by themodelling of the scalar decay, we will restrict our analysis to values of the model parameterssufficiently away from the resonance, concretely we will only consider m η − m χ ≥ m q . In our toy model we have postulated that the dark matter particle couples to a quark,therefore, a dark matter particle traversing the Sun could scatter-off a nucleus in the solarinterior and lose energy. After subsequent scatterings, the dark matter particles eventuallysink to the solar core where they accumulate. At the same time, the dark matter populationin the solar core is depleted by annihilations and – in case of light dark matter particles –by thermal evaporation. The time evolution of the number of dark matter particles N inthe solar core is then described by the following differential equation [57]: dNdt = Γ C − C A N − C E N , (9)where Γ C is the capture rate, C A the annihilation constant and C E the evaporation constant.For dark matter masses above ∼
10 GeV the evaporation term can be safely neglected[56, 58]. Then, after solving Eq.(9), one finds an annihilation rate as a function of timegiven by Γ A ( t ) = 12 C A N ( t ) = 12 Γ C tanh ( t/τ ) , (10)where τ = 1 √ Γ C C A . (11)The annihilation rate reaches a maximum when t (cid:29) τ . In this regime, captures andannihilations are in equilibrium and the annihilation rate is determined only by the capture6ate: Γ A = Γ C /
2. It is important to note that, despite the Earth and the Sun have beencapturing dark matter particles since their formation approximately 4 . × y ago, for somechoices of the model parameters equilibrium might have not been reached. Whether darkmatter particles are or not in equilibrium in the Sun or the Earth is determined by thevalues of the capture rate and the annihilation constant, cf. Eq. (11). The capture ratecan be calculated from the scattering cross section of the process dark matter-nucleon andrelies on assumptions on the density and velocity distributions of dark matter particles inthe Solar System, as well as on the composition and density distribution of the interiorof the Sun or the Earth. In our analysis we will use DarkSUSY to evaluate the capturerate from the scattering cross sections in Eqs. (6,7), adopting for concreteness a local darkmatter density ρ local = 0 . / cm [59] and a homogeneous Maxwell-Boltzmann darkmatter distribution with velocity dispersion v = 230 ±
30 km / s [60]. On the other hand,the annihilation constant for the Sun is approximately given by [56] C SunA = 1 . × − s − (cid:18) (cid:104) σ A v (cid:105) × − cm s − (cid:19) (cid:16) m χ TeV (cid:17) / , (12)while for the Earth by C EarthA = 5 . × − s − (cid:18) (cid:104) σ A v (cid:105) × − cm s − (cid:19) (cid:16) m χ TeV (cid:17) / , (13)where the annihilation cross sections for χχ → q ¯ q ( V ) are given in [41].Both the capture rate and the annihilation constant depend on the fourth power ofthe Yukawa coupling f , thus allowing to define a lower limit on the coupling constant f from requiring equilibration. Taking for concreteness the case of the Sun, the equilibrationcondition reads t (cid:12) (cid:39) / √ Γ C C A , where t (cid:12) ≈ . × y. More specifically, we define theequilibrium coupling constant f eq from the requirement that the argument of the hyperbolictangent in Eq.(10) is equal to 1 for t = t (cid:12) , namely t (cid:12) (cid:113) Γ f =1C C f =1A f = 1 , (14)where Γ f =1C and C f =1A are, respectively, the capture and annihilation constants for f = 1.This implies that the ratio of annihilation rate and capture rate can be cast as:2Γ A Γ C = tanh (cid:34)(cid:18) ff eq (cid:19) (cid:35) . (15)It follows from this equation that for values of the coupling larger than the equilibriumvalue, the annihilation rate, and hence the signal strength, reaches exponentially fast themaximal value. On the other hand, when the coupling is smaller than the equilibrium value,the annihilation rate exponentially decreases with ( f /f eq ) . For example, for f = f eq /
2, thesignal strength drops to about 0.4% of the maximal (equilibrium) signal strength.We show in Fig. 2 as red solid lines the minimal values of the coupling constant which arerequired to achieve equilibration between capture and annihilation for dark matter particlesthat couple to the right-handed up- (left plot) or bottom-quarks (right plot) as a functionof the dark matter mass, for the mass ratios m η /m χ = 1 .
01, 1.1 and 2.0. These lines7cale with the mass as m / χ for the spin independent dominated capture (as is the caseof couplings to the bottom quark) and as m / χ for the spin dependent dominated capture(as is the case of couplings to the up-quark). Below these lines the annihilation ratebecomes very suppressed, due to the small number of particles trapped inside the Sun, andtherefore observing a high energy neutrino signal from the Sun becomes very challenging, ifnot impossible in practice.We also show, for comparison, the values of the coupling f calculated in [33], that lead tothe correct dark matter relic density. Note the existence of a lower limit on the dark mattermass from the requirement of reproducing the correct relic abundance when the scalar η ishighly degenerate in mass with the dark matter particle, and which is due to the impactof coannihilations in the mass degenerate regime (for details, see [33],[34]). Concretely, forcouplings to up-quarks this lower limit is roughly 1 TeV and 150 GeV for m η /m χ = 1 . m χ (cid:38) m χ (cid:38)
200 GeVand m χ (cid:46) m η /m χ = 1 .
01, 1.1 and 2.0, respectively. For masses not fulfillingthese conditions, the number of dark matter particles captured in the Sun is suppressedcompared to the equilibrium values and, accordingly, the annihilation rate. Interestingly,for dark matter particles coupling only to bottom quarks, the coupling required to thermallyproduce the dark matter particles is smaller than the lower limit from the equilibrationcondition Eq. (14) (this can be understood from the fact that σ SD = 0). Hence considerablyhigher couplings are needed in order to achieve equilibrium and therefore in this scenariothe commonly used approximation Γ A = Γ C / The quarks and gauge bosons produced in the annihilations χχ → q ¯ q ( V ) will hadronizeand decay, eventually producing a neutrino flux. The dense medium inside the Sun wherethe annihilations take place significantly affects the energy spectrum of neutrinos, since theparticles produced in the annihilations may lose a substantial fraction of their energy dueto electromagnetic and strong interactions with the medium before decaying. We have sim-ulated the energy loss of particles in the interior of the Sun following [61]. We first calculatethe primary spectrum of particles produced in the annihilation with PYTHIA8.1 [62] inter-faced with CalcHEP [63, 64]. We then assume that the muons and light hadrons, such as These scalings follow from the dependence of the annihilation cross section with the mass (cid:104) σv (cid:105) ∼ m − χ ,which implies an annihilation rate C f =1 A ∼ m − / χ , as well as the dependences of the capture cross sections σ SD ∼ m − χ and σ SI ∼ m − χ , which translate into a capture rate Γ f =1 C ∼ m − χ and Γ f =1 C ∼ m − χ for thespin dependent and the spin independent capture, respectively. Inserting these dependences in Eq. (14) oneobtains f eq ∼ m / χ and ∼ m / χ for the spin dependent and the spin independent dominated captures. − − m χ [GeV] f Coupling to u -quarks f suneq . (1 . f suneq . (1 . f suneq . (2 . f thermal ( m η /m χ = 1 . f th . (1 . f th . (2 . SUN − − m χ [GeV] f Coupling to b -quarks f suneq . (1 . f suneq . (2 . f thermal ( m η /m χ = 1 . f th . (2 . SUN − − m χ [GeV] f Coupling to u -quarks f ea . eq . (1 . f ea . eq . (1 . f ea . eq . (2 . f thermal ( m η /m χ = 1 . f th . (1 . f th . (2 . EARTH − − m χ [GeV] f Coupling to b -quarks f ea . eq . (1 . f ea . eq . (2 . f thermal ( m η /m χ = 1 . f th . (2 . EARTH
Figure 2: Minimal values of the coupling f for various mass ratios from the requirement ofequilibration between dark matter captures and annihilations in the Sun (upper panels) andin the Earth (lower panels), for coupling to up-quarks (left panels) and to bottom-quarks(right panels). Also indicated as dashed lines are the values of the couplings that generatethe observed dark matter abundance via thermal production.9ions and kaons, are stopped in the Sun before decaying and hence produce neutrinos withenergies below 1 GeV, which we neglect in our analysis (the low energy neutrino flux fromdark matter annihilations can also be used to probe dark matter models, as discussed in[65],[66]). On the other hand, taus and heavy hadrons, such as charmed or beauty hadrons,decay in flight after losing a fraction of their kinetic energy. We have simulated the energyloss and subsequent decay in flight of these particles in an event-by-event basis followingthe chain of scatterings they undergo inside the Sun from the first scattering to the last(contrary to [67] which follows the chain of scatterings from the last to the first; the dif-ference between both approaches turns out to be, however, negligible for our analysis). Inaddition to the neutrinos produced in hadronic and leptonic decays there is a componentin the spectrum of hard neutrinos produced by the prompt decay of the Z boson from theannihilation χχ → q ¯ qZ . This process, despite having a small branching ratio, can be animportant source of high energy neutrinos from the Sun and can even be the dominantcontribution to the flux at the highest energies, as we will show below.Neutrinos produced in dark matter annihilations then propagate from the solar interiorto the surface, undergoing flavour oscillations and scatterings off solar matter, and thenfrom the solar surface to a neutrino telescope at the Earth, undergoing flavour oscillationsin vacuum. To calculate the fluxes at the Earth, we use WimpSim [67], a publicly availableMonte Carlo code that simulates, in an event-by-event basis, the propagation of neutrinosfrom the production point in the Solar center to the Earth, including the effect of neutrinointeractions in matter and three-flavour neutrino oscillations; for the calculation we haveadopted the most recent best fit values for the neutrino oscillation parameters [68].We show in Fig. 3 the differential flux at Earth of muon neutrinos and antineutrinosproduced in the annihilation in the Sun of dark matter particles with mass m χ = 1 TeVwhich couple only to right-handed up-quarks (top panels) or to right-handed bottom-quarks(bottom panels), for the exemplary cases with mass degeneracy parameter m η /m χ = 1 . m η /m χ = 2 (right panels). In the scenario where the dark matter particlecouples to up-quarks, the contribution to the neutrino flux from annihilations into u ¯ u isnegligible, since this annihilation channel produces mostly light hadrons that, as explainedabove, do not contribute to the high energy neutrino flux and besides the branching fractionfor this process is helicity suppressed. The annihilation into u ¯ uγ is not helicity suppressedand gives a larger contribution to the total flux, although still suppressed since this channelalso produces mostly light hadrons. More relevant is then the annihilation into u ¯ ug , whichhas the largest branching fraction (even when m η /m χ is sizable, cf. Fig. 1) and moreoverhadronizes producing a significant amount of heavy hadrons, which decay in flight contribut-ing to the high energy neutrino flux. Finally, the annihilation channel into u ¯ uZ has, despitethe fairly small branching fraction, a notable impact on the high energy neutrino flux, dueto the hard neutrinos produced in the decay Z → ν ¯ ν . In fact, for m χ = 1000 GeV, thischannel is the dominant source of neutrinos when E (cid:38)
200 GeV. Therefore, this channelwill be particularly important for IceCube, which is mostly sensitive to high energy neutri-nos. Note also that in the limit m χ (cid:29) M Z , which is the relevant one for IceCube, the totalneutrino spectrum is fairly insensitive to the degeneracy parameter, as long as m η /m χ (cid:46) m χ (cid:29) M Z the cross sections for the two-to-threeprocesses are in fixed relations which depend only on the couplings of the gauge bosons to10 − − − − − − − E ν [GeV] E d Φ d E (cid:2) m − y − G e V − (cid:3) Coupling to u -quarks, m η /m χ = 1 . u ¯ uu ¯ uγu ¯ uZ u ¯ ug − − − − − − − E ν [GeV] E d Φ d E (cid:2) m − y − G e V − (cid:3) Coupling to u -quarks, m η /m χ = 2 . u ¯ u u ¯ uγu ¯ uZ u ¯ ug − − − − − − − E ν [GeV] E d Φ d E (cid:2) m − y − G e V − (cid:3) Coupling to b -quarks, m η /m χ = 1 . b ¯ b b ¯ bγb ¯ bZ b ¯ bg − − − − − − − E ν [GeV] E d Φ d E (cid:2) m − y − G e V − (cid:3) Coupling to b -quarks, m η /m χ = 2 . b ¯ bb ¯ bγ b ¯ bZb ¯ bg Figure 3: Sum of the differential ν µ and ¯ ν µ flux at the Earth for m χ = 1000 GeV forcoupling to up-quarks (upper panels) and bottom-quarks (lower panels) for the mass ratios m η /m χ = 1 .
01 (left panels) and 2.0 (right panels).the final fermions. As a result, the total neutrino energy spectrum depends, for a given darkmatter mass, very mildly on the degeneracy parameter.The conclusions for the case of a dark matter particle coupling to the up-quark alsoapply for the coupling to the bottom-quark. In this case, the annihilation cross sectioninto b ¯ b is not as suppressed as into u ¯ u , due to the larger bottom quark mass, althoughfor large dark matter masses the helicity suppression is still very strong and the dominantannihilation channels are the two-to-three processes. As apparent from the plot, also forthe case of a dark matter particle coupling to the b-quark, the largest contribution to theneutrino spectrum at the highest energies is the annihilation b ¯ bZ . The muon (anti-)neutrino flux produced in the dark matter annihilations in the Sun gen-erates a (anti-)muon signal which can be detected in a neutrino telescope. For a givenneutrino spectrum we calculate the induced number of (anti-)muon events in IceCube fol-lowing the approach of [69], using the effective area presented in [70]. The backgroundconsists of muons induced by the atmospheric neutrino flux and is given, together with theactual data, in [30]. For our analysis, it is necessary to choose a cut on the angle betweenthe reconstructed muon direction and the Sun; to optimize the search we use, for each dark11atter mass and mass ratio, the angle that gives the best constraint under a backgroundonly hypothesis. More details of our method of calculating the limits from the IceCube datacan be found in appendix A.The non-observation in IceCube-79 of an excess of events with respect to the expectationsfrom the atmospheric background then allows to exclude regions of the parameter spaceof the model. We show in Fig. 4 as a light red band the limits on the coupling f as afunction of the dark matter mass, in a toy model where the dark matter particle only couplesto the right-handed up-quarks for three exemplary choices of the degeneracy parameter, m η /m χ = 1 .
01, 1.1 and 2.0. The width of the band brackets the sensitivity of the upper limitto systematic uncertainties in the determination of the capture rate, which were estimated tobe 3% (25%) for spin dependent (spin independent) capture [70], as well as to uncertaintiesin the determination of the astrophysical parameter v , the nuclear parameters Σ πn , σ andthe second moments of the quark PDFs. The values of the corresponding uncertainties arechosen as in [33]. We also show for comparison the limits derived in [33] on the coupling f from the non-observation of an excess in the cosmic antiproton-to-proton fraction measuredby PAMELA (grey band), and which in this model stem mostly from the two-to-threeprocess χχ → q ¯ qg , or from the non-observation of a dark matter signal in the XENON100experiment (dark blue band). Again, the width of the band brackets the sensitivity ofthe upper limit to the astrophysical and nuclear uncertainties. As apparent from the plot,IceCube-79 gives limits which are competitive, and for small degeneracies better, than thePAMELA antiproton limits. On the other hand, the IceCube-79 limits are worse than theXENON100 limits, due to the fact that this toy model has both spin dependent and spinindependent interactions with matter, the latter being strongly constrained by direct searchexperiments.We also show in the plot the region of the parameter space where, for this toy model,captures and annihilations are in equilibrium in the Sun and therefore the annihilation ratereaches its maximum value. The shaded blue region then corresponds to model parameterswhere the neutrino signal from the Sun is very suppressed due to the inefficient dark mattercapture and therefore observing an annihilation signal from the Sun becomes very challeng-ing. As can be seen from the plot, IceCube-79, and especially XENON100, already probe afairly large region of the parameter space where a signal of annihilations from the Sun couldbe found, especially for scenarios with large mass degeneracy. The XENON1T experimentwill close in on the parameter space even further, concretely, the factor of ∼
60 increase insensitivity projected in the mass range of interest for our analysis [71], will translate intoan improvement in the limit on the coupling by a factor of 60 / ≈ .
8. Note also thatXENON100 rules out the values of the couplings necessary to achieve equilibriation insidethe Earth, as can be checked from comparing Fig. 2, bottom plot, with Fig. 4. Therefore,the observation of a high energy neutrino signal from the center of the Earth is very unlikelyin this scenario.The limits of the coupling can be straightforwardly translated into limits of the spindependent cross section, as commonly presented in searches for neutrinos from dark matterannihilations in the Sun. The result is shown in Fig. 5 for our exemplary cases m η /m χ =1 .
01, 1.1 and 2.0. We show the limit on the spin dependent cross section that followsfrom assuming annihilations in the Sun only into u ¯ u as well as the limit that results fromconsidering also the two-to-three annihilations. As apparent from the plot, including thethree body annihilations in the Sun dramatically improves the limits on this scenario. We12 − − m χ [GeV] f Coupling to u -quarks, m η /m χ = 1 . t eq . > t (cid:12) f thermal XENON100antiprotonIC-79 XENON1T − − m χ [GeV] f Coupling to u -quarks, m η /m χ = 1 . t eq . > t (cid:12) f thermal XENON100antiprotonIC-79 XENON1T − − m χ [GeV] f Coupling to u -quarks, m η /m χ = 2 . t eq . > t (cid:12) XENON100antiproton IC-79 XENON1T
Figure 4: Upper limits on the Yukawa coupling f for coupling to up-quarks for m η /m χ = 1 . − − − − − − − − m χ [GeV] σ S D [ c m ] m η /m χ = 1 . t eq . > t (cid:12) thermal relicXENON100COUPP u ¯ uX u ¯ u − − − − − − − − m χ [GeV] σ S D [ c m ] m η /m χ = 1 . t eq . > t (cid:12) thermal relicXENON100COUPP u ¯ uX u ¯ u − − − − − − − − m χ [GeV] σ S D [ c m ] m η /m χ = 2 . t eq . > t (cid:12) thermal relicXENON100 COUPP u ¯ uX u ¯ u Figure 5: Upper limit on the spin dependent interaction cross section for couplings to up-quarks for m η /m χ = 1 .
01 (upper panel), 1.1 (lower left panel) and 2.0 (lower right panel).The red dot-dashed line is the upper limit from IceCube-79 assuming only annihilationsinto u ¯ u , while the solid line includes also the two-to-three annihilations into u ¯ uV , with V a gauge boson. The black solid line is the upper limit on the spin dependent cross sectionof the model from XENON100 and the green dashed line, from COUPP. The shaded blueregion shows the spin dependent cross section corresponding to the model parameters whereequilibration between captures and annihilations does not occur in the Sun, while the dashedline, where the observed dark matter abundance can be generated via thermal production.also show for completeness the experimental limits on the spin dependent cross section ofthis model from the COUPP [72] and the XENON100 [35] experiments. The lines alwayscorrespond, where applicable, to the choice of astrophysical and nuclear parameters givingthe most conservative constraints. It should be stressed that the XENON100 limit in thisplot refers to the limit on the spin dependent cross section from the non-observation ofevents in the XENON100 experiment in this specific model , which produces spin dependentand spin independent dark matter-nucleon interactions. The limits then differs from thosereported in [73, 74], where it was implicitly assumed a model with just spin dependentinteractions.The limits for the scenario where the dark matter particle couples just to the right-handedbottom-quark are shown in Fig. 6. As explained at the end of Section 2, we restrict ouranalysis to m η − m χ > m q , therefore we only show in this case the limits for m η /m χ = 1 . m η /m χ = 2 .
0, for which the previous condition is automatically fulfilled provided14 − − m χ [GeV] f Coupling to b quarks, m η /m χ = 1 . t eq . > t (cid:12) f thermal XENON100 XENON1T antiprotonIC-79 − − m χ [GeV] f Coupling to b quarks, m η /m χ = 2 . t eq . > t (cid:12) f thermal XENON100XENON1T
Figure 6: Same as Fig. 4 but for couplings to bottom-quarks. m χ >
100 GeV. Due to the suppressed spin dependent scattering rate, and as is apparentfrom the plots, for couplings to bottom-quarks the IceCube limits are rather weak, weakerthan the antiproton limits and sensibly weaker than the XENON100 limits. It also followsfrom the plot that the XENON100 limits rule out already a large part of the parameterspace where equilibration in the Sun is possible; the XENON1T experiment will improvethe limit in the coupling f by a factor ∼ .
8, if no signal is found.In deriving these limits we have not made any assumption on how the dark matterparticle was produced. It is then interesting to analyze the limits under the well motivatedassumption that the dark matter particle was produced thermally in the early Universe. Thisfixes one of the three parameters of the toy model, f , m χ or m η . The value of the couplingconstant required to produce the correct dark matter abundance is shown in Figs. 4,6 asa dashed line and lies well below the IceCube-79 limits, although close to, and for somechoices of parameters above, the XENON100 limit.We further investigate in Fig. 7 the complementarity of the various search strategies toprobe this scenario, under the assumption that the observed dark matter abundance wasthermally produced. We have calculated, following [34] (see also [75, 76, 77]), the excludedregions of the parameter space, spanned by the dark matter mass and the mass splittingbetween η and χ , from the XENON100 results (light green) and from the LHC searches ofa colored scalar by the CMS collaboration employing the α T -analysis based on 11.7 fm − at 8 TeV center of mass energy [37] (light red). The present limits for the model withcouplings to just right-handed up- (bottom-) quarks are shown in the upper (lower) leftplots, together with the regions of the parameter space where it is impossible to generatethermally the observed relic abundance of dark matter particles (light gray) and the regionwhere the perturbative calculation is not valid (dark gray). We also show in the plot thelines of constant 2Γ A / Γ C (shown in black) and the line that marks the boundary of theparameter space where equilibration in the Sun is not attained, t eq < t (cid:12) (shown in red).Note that indirect search experiments with antiprotons and with high energy neutrinos arenot yet sensitive to probe thermally produced dark matter particles, cf. Figs.4,6, hencethese experiments do not rule out any point in this parameter space. For couplings to up-quarks, XENON100 is the experiment that gives the strongest constraints on the parameterspace at low mass splittings, and in particular rules out the possibility of observing a signal15rom the Sun for m χ (cid:46)
300 GeV when m η = 1 . m χ ; for larger mass splittings, it is theCMS experiment the one giving the strongest constraints. Future experiments, notably theXENON1T experiment, will cover a much larger region of the parameter space where a darkmatter signal from the Sun could be observed, as apparent from Fig. 7, upper right plot.For couplings to bottom-quarks, limits from present experiments are very weak, as canbe seen in Fig. 7, lower left plot. In particular, the region of the parameter space whereequilibration in the Sun takes place, around m η /m χ (cid:39) . m χ (cid:46)
300 GeV, is barelyconstrained by the XENON100 experiment. Interestingly, the upcoming XENON1T ex-periment will be able to cover the whole region where equilibration is predicted to takeplace in the Sun, cf.
Fig. 7, lower right plot. The non-observation of a dark matter signalat XENON1T will then have important implications for the feasibility of observing a highenergy neutrino signal from the Sun in this concrete scenario.
The observation of an excess of high energy neutrinos in the direction of the Sun would bea clear signature of the annihilation of dark matter particles captured in the solar interior.In this paper we have investigated the prospects to observe this signature in a minimalscenario where the dark matter is a Majorana fermion that couples to a right-handed quark,concretely an up-quark or a bottom-quark, and a colored scalar via a Yukawa coupling. Thisscenario then allows to study the capture and the annihilation in a single Particle Physicsframework. We have found that, for small and moderate mass splitting between the darkmatter and the colored scalar, the most important channel in the calculation of the numberof captured dark matter particles in the Sun is the two-to-three annihilation into q ¯ qg . Wehave determined, for a given dark matter and colored scalar mass, the minimal value of theYukawa coupling necessary to attain equilibrium between capture and annihilation. Uponcomparing with the value of the coupling necessary to thermally produce the observed darkmatter abundance, we conclude that for a thermal relic equilibration is never reached in theinterior of Sun if the dark matter particle only couples to bottom-quarks. Equilibration inthe interior of the Earth is not attained neither for couplings to up-quarks nor to bottom-quarks. Therefore, the observation of a high-energy neutrino flux from the Earth is, althoughnot precluded in theory, very challenging in practice due to the very suppressed annihilationrate.We have also calculated the neutrino flux produced in the dark matter annihilationsincluding the two-to-three annihilations into a quark-antiquark pair and a gauge boson.We have found that the neutrino flux at the Earth is, close to the kinematical endpoint,dominated by the annihilations into q ¯ qZ , despite the rather small branching fraction inthis channel. We have then derived an upper limit on the Yukawa coupling from the non-observation at IceCube of an excess of high-energy neutrino events in the direction of theSun. For couplings to up-quarks, and small mass degeneracies between the dark matterparticle and the colored scalar, the IceCube limits are stronger than the limits on the samemodel parameters from the PAMELA measurements of the cosmic antiproton-to-protonfraction. On the other hand, for couplings to bottom-quarks the IceCube limits are weaker,due to the inefficient capture of dark matter particles in the Sun in this scenario. Bothfor couplings to up- and to bottom-quarks, the direct detection limits on the coupling fromXENON100 are significantly stronger than the IceCube limits and already exclude regions of16 − − m χ [GeV] m η / m χ − Coupling to u -quarks no thermal relic non-pert.XENON100CMS α T /Razor+ISR CMS α T . t (cid:12) = t eq . . . A / Γ C = 0 . − − m χ [GeV] m η / m χ − Coupling to u -quarks, prospects XENON1TExistingconstraintsno thermal relic non-pert. . t (cid:12) = t eq . . . A / Γ C = 0 . − − m χ [GeV] m η / m χ − Coupling to b -quarks A / Γ C = 0 . . . t (cid:12) = t eq . . no thermal relicXENON100 − − m χ [GeV] m η / m χ − Coupling to b -quarks, prospects A / Γ C = 0 . . . t (cid:12) = t eq . . no thermal relicXENON1T Figure 7: Excluded regions of the parameter space of our toy model assuming couplings justto the up-quarks (upper panels) or to the bottom-quarks (lower panels) upon requiring thatthe observed dark matter abundance was thermally generated. The left panels show thepresent constraints from XENON100 (light green) and CMS (light red), as well as contourlines indicating the ratio of twice the annihilation rate over the capture rate in the Sun,which determines whether equilibration between these two processes is reached, cf.
Eq. (10).The thick red line indicates the parameters where the equilibration time equals the age ofthe Sun; above this line the high-energy neutrino flux from the Sun is strongly suppressed.The dark grey regions are theoretically not accessible, since they do not reproduce theobserved relic abundance or because the Yukawa coupling becomes non-perturbative. Theright panels show the projected sensitivity of XENON1T.17he parameter space where equilibration between capture and annihilation is reached insidethe Sun.We have investigated in detail the limits on the parameter space under the assumptionthat the observed dark matter abundance was thermally generated, calculating the excludedregions from present searches of new physics at LHC and from XENON100. For couplingsto bottom-quarks, the present limits are rather weak, while for couplings to up-quarks, theyalready exclude some regions of the parameter space. Future direct detection experiments,such as LUX and notably XENON1T will continue closing in on the the possibility ofobserving a high energy neutrino flux from the Sun. In particular, in the scenario where thedark matter couples just to right-handed bottom-quarks, XENON1T will cover the wholeregion of the parameter space where equilibration is reached in the solar interior. Therefore,the non-observation of a dark matter signal at XENON1T will then make very unlikely thepossibility of observing a high energy neutrino signal from the Sun in this scenario.
Note Added
After the completion of this work, the LUX experiment released new limits on the spinindependent dark matter-nucleon scattering cross section [78], which are approximately afactor of three better than the XENON100 limits in the range of masses of interest for ourwork. In view of the new results, our limits on the coupling constant f are improved byapproximately 30%. Acknowledgements
We are grateful to Sergio Palomares-Ruiz, Miguel Pato and Stefan Vogl for useful discus-sions. This work was partially supported by the DFG cluster of excellence “Origin andStructure of the Universe,” the Universit¨at Bayern e.V., the TUM Graduate School and theStudienstiftung des Deutschen Volkes.
A Calculation of limits from the IceCube data
In this appendix, we shortly review our method of converting a (anti-)neutrino flux fromdark matter annihilations in the Sun into a number of (anti-)muon events in IceCube aswell as the statistical method of extracting limits from the data, closely following [69].The number of expected muon signal events, θ S , for a given (anti-)neutrino flux dΦ ν/ ¯ ν d E isobtained by [69] θ S = t exp ∞ (cid:90) L ( E, φ cut ) (cid:18) A ν ( E ) dΦ ν d E + A ¯ ν ( E ) dΦ ¯ ν d E (cid:19) d E . (16)Here, t exp is the live-time of the 79-string analysis of IceCube given in [70] and A ν/ ¯ ν ( E )is the effective area for the detection of neutrinos/antineutrinos in IceCube, encapsulating18ll information about the efficiency of the IceCube detector as well as the scattering crosssections of neutrinos and the muon range in rock and ice. We use the total effective area A ν ( E ) + A ¯ ν ( E ) for the IceCube 79-string configuration given in [70] and we convert it intoseparate effective areas for neutrinos and antineutrinos using the method described in [79].Besides, L ( E, φ cut ) is the angular loss factor, defined as the probability that the angle ofthe reconstructed muon track, originated from an incoming neutrino with energy E , withrespect to the direction of the Sun is smaller than a certain cut angle φ cut , namely L ( E, φ cut ) = 1 − exp (cid:34) − (cid:18) φ cut σ θ ( E ) (cid:19) (cid:35) . (17)This assumes a 2D Gaussian point spread function of the muon track directions (see [69]for more details); we extract the corresponding median angle σ θ ( E ) between the neutrinoand the muon track from [70].We then use the standard CL s method for calculating upper limits on θ S , based on ahypothesis test using the likelihood ratio X = L ( n obs | θ S + θ BG ) L ( n obs | θ BG ) . (18)For a definition of the likelihood functions and the corresponding p -values of the hypothesistest we refer to [69]. The number of observed events n obs and the number of off-sourcemeasured background events θ BG as a function of the angle between the muon direction andthe Sun are given in [30].For our analysis we choose the cut angle φ cut such that the limit on the annihilationcross section is optimized. To this end, we use the number of neutrino events observedby IceCube in directions away from the Sun, which are presumably of atmospheric origin,and we make the plausible assumption that the background of atmospheric neutrinos in thedirection of the Sun is identical to the background in these directions. We then calculate,for given m χ and m η /m χ , the limit on the annihilation cross section for eight different cutangles φ cut between 3 ◦ and 8 . ◦ (corresponding to the the bins in φ used in [30]) from therequirement that the dark matter signal would not produce an excess over the atmosphericneutrino background with a significance larger than 95% C.L. In this step of the calculation,we use the off-source measured background events instead of the real data (i.e. the datain the direction of the sun); hence our procedure to determine the optimal cut angle isnot biased by the actual measurements in the direction of the Sun, which might receivean exotic component. Lastly, we select the cut angle that gives the best limit under this“background-only” hypothesis, and use it to calculate the limit on the annihilation crosssection from the actual number of neutrino events measured by the IceCube collaborationin the direction of the Sun.The optimal cut angle as a function of the dark matter mass is shown in Fig. 8 for m η /m χ = 1 . φ cut are favored, as in this case most of the19 m χ [GeV] φ c u t i nd e g r ee s Optimal cone angle φ cut for m η /m χ = 1 . u coupling b coupling Figure 8: Cut angle used in our analysis as a function of the dark matter mass for thescenario with couplings to up-quarks or bottom-quarks and mass ratio m η /m χ = 1 . θ S , n obs and θ BG aswell as its own effective area. The three event selections thereby correspond to different setsof experimental cuts, each optimized for a different signal model; in particular the “Summerlow” data set consists of downward going muons which were detected in DeepCore, using thesurrounding IceCube strings as an active veto against atmospheric muons. While it wouldbe in principle possible to use all three data sets in a combined likelihood for calculating theconstraints, we choose the simpler (and conservative) strategy of calculating for each pointin the parameter space three independent constraints using the three event selections andthen choose the most constraining one. In our model, this turns out to be almost always the“Winter high” data set, except for dark matter masses below 200 GeV, where the “Winterlow” or “Summer low” event selection can be relevant. References [1] G. Bertone, D. Hooper, and J. Silk,
Particle dark matter: Evidence, candidates andconstraints , Phys.Rept. (2005) 279–390, [ hep-ph/0404175 ].[2] L. Bergstrom,
Nonbaryonic dark matter: Observational evidence and detectionmethods , Rept.Prog.Phys. (2000) 793, [ hep-ph/0002126 ].[3] T. Bringmann and C. Weniger, Gamma Ray Signals from Dark Matter: Concepts,Status and Prospects , Phys.Dark Univ. (2012) 194–217, [ arXiv:1208.5481 ].204] M. Srednicki, S. Theisen, and J. Silk, Cosmic Quarkonium: A Probe of Dark Matter , Phys.Rev.Lett. (1986) 263.[5] S. Rudaz, Cosmic production of quarkonium? , Phys.Rev.Lett. (1986) 2128.[6] L. Bergstrom and H. Snellman, Observable monochromatic photons from cosmicphotino annihilation , Phys.Rev.
D37 (1988) 3737–3741.[7] L. Bergstrom,
Radiative processes in dark matter photino annihilation , Phys.Lett.
B225 (1989) 372.[8] R. Flores, K. A. Olive, and S. Rudaz,
Radiative processes in LSP annihilation , Phys.Lett.
B232 (1989) 377–382.[9] T. Bringmann, L. Bergstrom, and J. Edsjo,
New Gamma-Ray Contributions toSupersymmetric Dark Matter Annihilation , JHEP (2008) 049,[ arXiv:0710.3169 ].[10] A. Ibarra, S. Lopez Gehler, and M. Pato,
Dark matter constraints from box-shapedgamma-ray features , JCAP (2012) 043, [ arXiv:1205.0007 ].[11]
Fermi-LAT Collaboration , M. Ackermann et. al. , Search for Gamma-ray SpectralLines with the Fermi Large Area Telescope and Dark Matter Implications , arXiv:1305.5597 .[12] H.E.S.S. Collaboration , A. Abramowski et. al. , Search for photon line-likesignatures from Dark Matter annihilations with H.E.S.S , Phys.Rev.Lett. (2013)041301, [ arXiv:1301.1173 ].[13] T. Bringmann, X. Huang, A. Ibarra, S. Vogl, and C. Weniger,
Fermi LAT Search forInternal Bremsstrahlung Signatures from Dark Matter Annihilation , arXiv:1203.1312 .[14] A. Ibarra, H. M. Lee, S. Lopez Gehler, W.-I. Park, and M. Pato, Gamma-ray boxesfrom axion-mediated dark matter , JCAP (2013) 016, [ arXiv:1303.6632 ].[15]
LAT Collaboration , M. Ackermann et. al. , Fermi LAT Search for Dark Matter inGamma-ray Lines and the Inclusive Photon Spectrum , Phys.Rev.
D86 (2012) 022002,[ arXiv:1205.2739 ].[16]
H.E.S.S.Collaboration , A. Abramowski et. al. , Search for a Dark Matterannihilation signal from the Galactic Center halo with H.E.S.S , Phys.Rev.Lett. (2011) 161301, [ arXiv:1103.3266 ].[17] M. Ackermann, M. Ajello, A. Allafort, L. Baldini, J. Ballet, et. al. , Constraints onDark Matter Annihilation in Clusters of Galaxies with the Fermi Large AreaTelescope , JCAP (2010) 025, [ arXiv:1002.2239 ].[18]
HESS Collaboration , A. Abramowski et. al. , Search for Dark Matter AnnihilationSignals from the Fornax Galaxy Cluster with H.E.S.S , Astrophys.J. (2012) 123,[ arXiv:1202.5494 ]. 2119]
Fermi-LAT Collaboration , M. Ackermann et. al. , Dark Matter Constraints fromObservations of 25 Milky Way Satellite Galaxies with the Fermi Large Area Telescope , arXiv:1310.0828 .[20] A. Geringer-Sameth and S. M. Koushiappas, Exclusion of canonical WIMPs by thejoint analysis of Milky Way dwarfs with Fermi , Phys.Rev.Lett. (2011) 241303,[ arXiv:1108.2914 ].[21]
MAGIC Collaboration , J. Aleksic et. al. , Searches for Dark Matter annihilationsignatures in the Segue 1 satellite galaxy with the MAGIC-I telescope , JCAP (2011) 035, [ arXiv:1103.0477 ].[22]
HESS Collaboration , A. Abramowski et. al. , H.E.S.S. constraints on Dark Matterannihilations towards the Sculptor and Carina Dwarf Galaxies , Astropart.Phys. (2011) 608–616, [ arXiv:1012.5602 ].[23] L. Bergstrom, T. Bringmann, I. Cholis, D. Hooper, and C. Weniger, New limits ondark matter annihilation from AMS cosmic ray positron data , Phys.Rev.Lett. (2013)[ arXiv:1306.3983 ].[24] A. Ibarra, A. S. Lamperstorfer, and J. Silk,
Dark matter annihilations and decaysafter the AMS-02 positron measurements , arXiv:1309.2570 .[25] IceCube collaboration , R. Abbasi et. al. , Search for Neutrinos from AnnihilatingDark Matter in the Direction of the Galactic Center with the 40-String IceCubeNeutrino Observatory , arXiv:1210.3557 .[26] IceCube Collaboration , M. Aartsen et. al. , The IceCube Neutrino ObservatoryPart IV: Searches for Dark Matter and Exotic Particles , arXiv:1309.7007 .[27] W. H. Press and D. N. Spergel, Capture by the sun of a galactic population of weaklyinteracting massive particles , Astrophys.J. (1985) 679–684.[28] J. Silk, K. A. Olive, and M. Srednicki,
The Photino, the Sun and High-EnergyNeutrinos , Phys.Rev.Lett. (1985) 257–259.[29] A. Gould, Resonant Enhancements in WIMP Capture by the Earth , Astrophys.J. (1987) 571.[30]
IceCube collaboration , M. Aartsen et. al. , Search for dark matter annihilations inthe Sun with the 79-string IceCube detector , Phys.Rev.Lett. (2013) 131302,[ arXiv:1212.4097 ].[31] N. F. Bell, A. J. Brennan, and T. D. Jacques,
Neutrino signals from electroweakbremsstrahlung in solar WIMP annihilation , JCAP (2012) 045,[ arXiv:1206.2977 ].[32] K. Fukushima, Y. Gao, J. Kumar, and D. Marfatia,
Bremsstrahlung signatures of darkmatter annihilation in the Sun , Phys.Rev.
D86 (2012) 076014, [ arXiv:1208.1010 ].2233] M. Garny, A. Ibarra, M. Pato, and S. Vogl,
Closing in on mass-degenerate darkmatter scenarios with antiprotons and direct detection , JCAP (2012) 017,[ arXiv:1207.1431 ].[34] M. Garny, A. Ibarra, M. Pato, and S. Vogl,
Internal bremsstrahlung signatures in lightof direct dark matter searches , arXiv:1306.6342 .[35] XENON100 Collaboration , E. Aprile et. al. , Dark Matter Results from 225 LiveDays of XENON100 Data , Phys.Rev.Lett. (2012) 181301, [ arXiv:1207.5988 ].[36]
PAMELA Collaboration , O. Adriani et. al. , PAMELA results on the cosmic-rayantiproton flux from 60 MeV to 180 GeV in kinetic energy , Phys.Rev.Lett. (2010)121101, [ arXiv:1007.0821 ].[37]
CMS Collaboration , S. Chatrchyan et. al. , Search for supersymmetry in hadronicfinal states with missing transverse energy using the variables AlphaT and b-quarkmultiplicity in pp collisions at 8 TeV , Eur.Phys.J.
C73 (2013) 2568,[ arXiv:1303.2985 ].[38] F. Luo and T. You,
Enhancement of Majorana Dark Matter Annihilation ThroughHiggs Bremsstrahlung , arXiv:1310.5129 .[39] M. Drees, G. Jungman, M. Kamionkowski, and M. M. Nojiri, Neutralino annihilationinto gluons , Phys.Rev.
D49 (1994) 636–647, [ hep-ph/9306325 ].[40] V. Barger, W.-Y. Keung, H. E. Logan, and G. Shaughnessy,
Neutralino annihilationto q anti-q g , Phys.Rev.
D74 (2006) 075005, [ hep-ph/0608215 ].[41] M. Garny, A. Ibarra, and S. Vogl,
Dark matter annihilations into two light fermionsand one gauge boson: General analysis and antiproton constraints , JCAP (2012) 033, [ arXiv:1112.5155 ].[42] M. Garny, A. Ibarra, and S. Vogl,
Antiproton constraints on dark matter annihilationsfrom internal electroweak bremsstrahlung , JCAP (2011) 028,[ arXiv:1105.5367 ].[43] P. Ciafaloni, M. Cirelli, D. Comelli, A. De Simone, A. Riotto, et. al. , On theImportance of Electroweak Corrections for Majorana Dark Matter Indirect Detection , JCAP (2011) 018, [ arXiv:1104.2996 ].[44] P. Ciafaloni, M. Cirelli, D. Comelli, A. De Simone, A. Riotto, et. al. , Initial StateRadiation in Majorana Dark Matter Annihilations , JCAP (2011) 034,[ arXiv:1107.4453 ].[45] P. Ciafaloni, D. Comelli, A. De Simone, A. Riotto, and A. Urbano,
ElectroweakBremsstrahlung for Wino-Like Dark Matter Annihilations , JCAP (2012) 016,[ arXiv:1202.0692 ].[46] N. F. Bell, J. B. Dent, A. J. Galea, T. D. Jacques, L. M. Krauss, et. al. , W/ZBremsstrahlung as the Dominant Annihilation Channel for Dark Matter, Revisited , Phys.Lett.
B706 (2011) 6–12, [ arXiv:1104.3823 ].2347] N. F. Bell, J. B. Dent, T. D. Jacques, and T. J. Weiler,
Dark Matter AnnihilationSignatures from Electroweak Bremsstrahlung , Phys.Rev.
D84 (2011) 103517,[ arXiv:1101.3357 ].[48] M. Kachelriess, P. Serpico, and M. A. Solberg,
On the role of electroweakbremsstrahlung for indirect dark matter signatures , Phys.Rev.
D80 (2009) 123533,[ arXiv:0911.0001 ].[49] P. Ciafaloni, D. Comelli, A. Riotto, F. Sala, A. Strumia, et. al. , Weak Corrections areRelevant for Dark Matter Indirect Detection , JCAP (2011) 019,[ arXiv:1009.0224 ].[50] T. Toma,
Internal Bremsstrahlung Signature of Real Scalar Dark Matter andConsistency with Thermal Relic Density , Phys.Rev.Lett. (2013) 091301,[ arXiv:1307.6181 ].[51] F. Giacchino, L. Lopez-Honorez, and M. H. G. Tytgat,
Scalar Dark Matter Modelswith Significant Internal Bremsstrahlung , arXiv:1307.6480 .[52] C. Garcia-Cely and A. Ibarra, Novel Gamma-ray Spectral Features in the InertDoublet Model , JCAP (2013) 025, [ arXiv:1306.4681 ].[53] J. Hisano, K. Ishiwata, and N. Nagata,
Gluon contribution to the dark matter directdetection , Phys.Rev.
D82 (2010) 115007, [ arXiv:1007.2601 ].[54] M. Drees and M. Nojiri,
Neutralino - nucleon scattering revisited , Phys.Rev.
D48 (1993) 3483–3501, [ hep-ph/9307208 ].[55] J. R. Ellis, K. A. Olive, and C. Savage,
Hadronic Uncertainties in the ElasticScattering of Supersymmetric Dark Matter , Phys.Rev.
D77 (2008) 065026,[ arXiv:0801.3656 ].[56] G. Jungman, M. Kamionkowski, and K. Griest,
Supersymmetric dark matter , Phys.Rept. (1996) 195–373, [ hep-ph/9506380 ].[57] K. Griest and D. Seckel,
Cosmic Asymmetry, Neutrinos and the Sun , Nucl.Phys.
B283 (1987) 681.[58] G. Busoni, A. De Simone, and W.-C. Huang,
On the Minimum Dark Matter MassTestable by Neutrinos from the Sun , JCAP (2013) 010, [ arXiv:1305.1817 ].[59] R. Catena and P. Ullio,
A novel determination of the local dark matter density , JCAP (2010) 004, [ arXiv:0907.0018 ].[60] M. Pato, L. Baudis, G. Bertone, R. Ruiz de Austri, L. E. Strigari, et. al. , Complementarity of Dark Matter Direct Detection Targets , Phys.Rev.
D83 (2011)083505, [ arXiv:1012.3458 ].[61] S. Ritz and D. Seckel,
Detailed Neutrino Spectra From Cold Dark MatterAnnihilations in the Sun , Nucl.Phys.
B304 (1988) 877.2462] T. Sjostrand, S. Mrenna, and P. Z. Skands,
A Brief Introduction to PYTHIA 8.1 , Comput.Phys.Commun. (2008) 852–867, [ arXiv:0710.3820 ].[63] A. Pukhov, E. Boos, M. Dubinin, V. Edneral, V. Ilyin, et. al. , CompHEP: A Packagefor evaluation of Feynman diagrams and integration over multiparticle phase space , hep-ph/9908288 .[64] A. Pukhov, CalcHEP 2.3: MSSM, structure functions, event generation, batchs, andgeneration of matrix elements for other packages , hep-ph/0412191 .[65] C. Rott, J. Siegal-Gaskins, and J. F. Beacom, New Sensitivity to Solar WIMPAnnihilation using Low-Energy Neutrinos , Phys.Rev.
D88 (2013) 055005,[ arXiv:1208.0827 ].[66] N. Bernal, J. Martin-Albo, and S. Palomares-Ruiz,
A novel way of constrainingWIMPs annihilations in the Sun: MeV neutrinos , JCAP (2013) 011,[ arXiv:1208.0834 ].[67] M. Blennow, J. Edsjo, and T. Ohlsson,
Neutrinos from WIMP annihilations using afull three-flavor Monte Carlo , JCAP (2008) 021, [ arXiv:0709.3898 ].[68]
Particle Data Group , J. Beringer et. al. , Review of Particle Physics (RPP) , Phys.Rev.
D86 (2012) 010001.[69]
IceCube Collaboration , P. Scott et. al. , Use of event-level neutrino telescope datain global fits for theories of new physics , JCAP (2012) 057, [ arXiv:1207.0810 ].[70] M. Danninger, PhD thesis, Stockholm University.[71]
XENON1T collaboration , E. Aprile,
The XENON1T Dark Matter SearchExperiment , arXiv:1206.6288 .[72] COUPP Collaboration , E. Behnke et. al. , First Dark Matter Search Results from a4-kg CF I Bubble Chamber Operated in a Deep Underground Site , Phys.Rev.
D86 (2012) 052001, [ arXiv:1204.3094 ].[73] M. Garny, A. Ibarra, M. Pato, and S. Vogl,
On the spin-dependent sensitivity ofXENON100 , Phys.Rev.
D87 (2013), no. 5 056002, [ arXiv:1211.4573 ].[74]
XENON100 Collaboration , E. Aprile et. al. , Limits on spin-dependentWIMP-nucleon cross sections from 225 live days of XENON100 data , Phys.Rev.Lett. (2013) 021301, [ arXiv:1301.6620 ].[75] H. An, L.-T. Wang, and H. Zhang,
Dark matter with t -channel mediator: a simplestep beyond contact interaction , arXiv:1308.0592 .[76] Y. Bai and J. Berger, Fermion Portal Dark Matter , arXiv:1308.0612 .[77] A. DiFranzo, K. I. Nagao, A. Rajaraman, and T. M. P. Tait, Simplified Models forDark Matter Interacting with Quarks , arXiv:1308.2679 .2578] LUX Collaboration , D. Akerib et. al. , First results from the LUX dark matterexperiment at the Sanford Underground Research Facility , arXiv:1310.8214 .[79] C. A. Arguelles and J. Kopp, Sterile neutrinos and indirect dark matter searches inIceCube , JCAP (2012) 016, [ arXiv:1202.3431arXiv:1202.3431