Hunting for Dark Matter and New Physics with (a) GECCO
Adam Coogan, Alexander Moiseev, Logan Morrison, Stefano Profumo
PPrepared for submission to JHEP
Hunting for Dark Matter and New Physicswith (a) GECCO
Adam Coogan, a Alexander Moiseev, b Logan Morrison, and c,d
Stefano Profumo c,d a GRAPPA, Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands b CRESST, Greenbelt and NASA, Goddard and Maryland University c Department of Physics, 1156 High St., University of California Santa Cruz, Santa Cruz, CA95064, USA d Santa Cruz Institute for Particle Physics, 1156 High St., Santa Cruz, CA 95064, USA
E-mail: [email protected] , [email protected] , [email protected] , [email protected] Abstract:
We outline the science opportunities in the areas of searches for dark matterand new physics offered by a proposed future MeV gamma-ray telescope, the GalacticExplorer with a Coded Aperture Mask Compton Telescope (GECCO). We point out thatsuch an instrument would play a critical role in opening up a discovery window for par-ticle dark matter with mass in the MeV or sub-MeV range, in disentangling the originof the mysterious 511 keV line emission in the Galactic Center region, and in potentiallydiscovering Hawking evaporation from light primordial black holes. a r X i v : . [ a s t r o - ph . H E ] J a n ontents It is in not an overstatement that the MeV gamma-ray energy range remains one of the leastexplored frontiers in observational astronomy, with important implications for the under-standing of high-energy astrophysical phenomena. With the most recent data dating backseveral decades, the photon band in between hard x-rays and the gamma rays detectablewith the Fermi Large Area Telescope quite literally offers some of the richest opportunitiesfor discovery across the electromagnetic spectrum. It is therefore not a surprise that muchactivity has resumed in recent years around a next-generation MeV telescope. Withoutattempting to be exhaustive, a partial list of such missions under consideration, in no spe-cial order, includes AdEPT [1], AMEGO [2], eASTROGAM [3] , MAST [5], PANGU [6, 7]and GRAMS [8, 9].The scientific significance of a new space-borne observatory in the MeV range in-cludes a very broad range of topics such as identifying the hadronic versus leptonic natureand the acceleration processes underpinning jets outflows, studying the role of magneticfields in powering the jets associated with gamma-ray bursts, pinning down the sources ofgravitational wave events, understanding the electromagnetic counterparts of astrophysicalneutrinos. Lower energy phenomena will also be clarified by new capabilities in the MeV:for instance, cosmic-ray diffusion in interstellar clouds, and the role cosmic rays play in gas This has since been scaled back to All-Sky-ASTROGAM [4]. – 1 –ynamics and wind outflows, as well as nucleosynthesis and chemical enrichment via thestudy of nuclear emission lines.Here, we focus on a proposed mid-size class mission, the Galactic Explorer with aCoded Aperture Mask Compton Telescope (GECCO) and consider its capabilities in thesearch for new physics beyond the Standard Model. We describe GECCO in some detail inthe following section 2. We then explore GECCO’s potential in searching for dark matterannihilation and decay for dark matter particle masses in the MeV range in section 3; indiscovering the products of Hawking evaporation of primordial black holes in section 4 (seealso Ref. [10]); and in identifying the origin of the 511 keV emission line from the GalacticCenter (section 5).
The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO) is anovel concept for a next-generation γ -ray telescope that will cover the hard x-ray to soft γ -ray region, and is currently being considered for a future NASA Explorer mission.GECCO will conduct high-sensitivity measurements of the cosmic γ -radiation in theenergy range from 100 keV to ∼
10 MeV and create intensity maps with high spectral andspatial resolution, with a focus on the separation of diffuse and point-source components.As we show in this study, such observational capabilities will be of paramount importantin e.g. disentangling astrophysical and dark matter explanations of emission from theGalactic Center and potentially providing a key to discovering as-of-yet unexplored darkmatter candidates.The instrument is based on a novel CdZnTe Imaging calorimeter and a deployablecoded aperture mask. It utilizes a heavy-scintillator shield and plastic scintillator anti-coincidence detectors. The unique feature of GECCO is that it combines the advantagesof two techniques – the high-angular resolution possible with coded mask imaging anda Compton telescope mode providing high sensitivity measurements of diffuse radiation.With this combined “mask + Compton” operation GECCO will separate diffuse and point-sources components in the Galactic Center radiation with high sensitivity. GECCO willbe operating mainly in pointing mode, focusing on the Galactic Center and other regionsof interest. The observatory can be quickly re-pointed to any other region when alarmed.The expected GECCO performance is as follows: energy resolution <
1% at 0 . − ∼ − ◦ field-of-view, ∼ effective area), and 3 − ◦ in the Compton mode (15 − ◦ field-of-view, ∼
500 cm effectivearea). The sensitivity is expected to be better than 10 − MeV / cm / s at 1 MeV. Theseparameters are particularly promising for searching for dark matter particles with O (MeV)-scale masses as well as for evaporating primordial black holes with O (10 grams) masses(a viable dark matter candidate), as explained below.– 2 – Searches for Annihilating and Decaying Sub-GeV Dark Matter
In this section we demonstrate that GECCO will be especially well-suited to search forparticle dark matter (DM) in the MeV mass range. After reviewing DM indirect detectionand explaining how we set limits using existing gamma-ray data and make projections forGECCO, we study the instrument’s capabilities to detect the annihilation and decay ofDM into specific Standard-Model final states. We also project GECCO’s sensitivity reachfor three specific, well-motivated DM models: one with an additional scalar mediating theDM’s interaction with the Standard Model, a second one with a vector mediator and a thirdone in which the DM is an unstable right-handed neutrino. Throughout we utilize our code hazma , which we previously developed to analyze DM models producing MeV-scale gammarays [11].
The prompt gamma-ray flux from DM annihilating or decaying in a region of the skysubtending a solid angle ∆Ω is given bydΦd E γ (cid:12)(cid:12)(cid:12) ¯ χχ ( E γ ) = ∆Ω4 π m aχ · (cid:20) (cid:90) ∆Ω dΩ (cid:90) LOS d l [ ρ ( r ( l, ψ ))] a (cid:21) · Γ · d N d E γ (cid:12)(cid:12)(cid:12) ¯ χχ ( E γ ) , (3.1)where “LOS” indicates the integral along the observation’s direction line of sight. Fordecaying (annihilating) DM a = 1 ( a = 2). The integral in the bracketed term ranges overlines of sight within a solid angle ∆Ω from the target region direction. This is referred toas the ¯ D factor for decaying DM and ¯ J factor for annihilating DM. It is proportional tothe angle-averaged number of particles (pairs of particles) in the target available to decay(annihilate). The third term is the DM interaction rate. This is 1 /τ for decaying DM,where τ is the DM’s lifetime. For annihilating DM, Γ = (cid:104) σv (cid:105) ¯ χχ / f χ , where f χ = 1 ifthe DM is self-conjugate and 2 otherwise (we assume the latter in this work). The lastterm is the photon spectrum per decay or annihilation. The calculation of this spectrumin hazma accounts for the radiative decay chains of the charged pion and muon as wellas model-dependent final-state radiation from annihilations that produce electrons, muonsand pions relevant for studying specific particle DM models.To connect the gamma-ray flux with existing and future gamma-ray observations, wedefine the “convolved” fluxd ¯Φd E γ (cid:12)(cid:12)(cid:12) ¯ χχ ( E γ ) ≡ (cid:90) d E (cid:48) γ R (cid:15) ( E γ | E (cid:48) γ ) dΦd E γ ( E (cid:48) γ ) . (3.2)In the equation above, R (cid:15) ( E γ | E (cid:48) γ ) is the telescope’s energy resolution function, specifyingthe probability that a photon with true energy E (cid:48) γ is detected with energy E γ . This iswell-approximated as a normal distribution R (cid:15) ( E γ ) = N ( E γ | E (cid:48) γ , (cid:15)E (cid:48) γ ) [12], which defines (cid:15) . To set an upper limit on the DM contribution to gamma-ray observations we perform Note that the energy resolution of detectors is also sometimes given in terms of the full width at halfmaximum of this distribution. – 3 – χ test with the quantity χ = (cid:88) i max (cid:104) ¯Φ ( i )¯ χχ − Φ ( i )obs , (cid:105) σ ( i ) , (3.3)where the sum ranges over energy bins, the flux in the numerator is the integral “convolved”flux over bin i and the denominator is the upper error bar on the observed integrated flux.Including an explicit background model would introduce significant systematic uncertain-ties since there is a paucity of MeV gamma-ray data, and in practice we expect it wouldonly strengthen our constraints by less than an order of magnitude [13]. We project GECCO’s discovery reach by finding the smallest dark matter interactionrate such that the signal-to-noise for different targets is significant at the 5 σ level. Wedefine the signal-to-noise ratio as SN ≡ max E min , E max N γ | ¯ χχ (cid:112) N γ | bg , (3.4)where the numerator and denominator contain the number of signal and background pho-tons respectively, and the energy window used for the analysis is chosen to maximize theratio. The number of signal photons depends on the energy window along with GECCO’sobserving time and effective area: N γ | ¯ χχ = (cid:90) E max E min d E γ T obs A eff ( E γ ) d ¯Φd E γ . (3.5)While T obs is in general energy-dependent, we fix it to 10 s ≈ . Φd E γ dΩ = 2 . × − (cid:18) E MeV (cid:19) − cm − s − sr − MeV − . (3.6)For the Galactic Center we adopt the model from Ref. [15]. This consists of several spectraltemplates computed with GALPROP [16] and an analytic component, tailored to fit existinggamma-ray data in the inner part of the Milky Way. The background fluxes per solidangle can be converted to photon counts using eq. (3.5).The ¯ J and ¯ D factors for the GECCO targets are shown in table 1. These are derivedfrom fits of dark matter density profiles to measurements of the targets rotation curves,surface brightnesses and velocity dispersions. We employ a Navarro-Frenk-White (NFW)density profile [17] for all targets and additionally consider an Einasto profile [18] for theGalactic Center to bracket the uncertainties in our analysis stemming from assumptions For final states containing monochromatic gamma rays the resulting constraints depend on the binningof the data. In the figures that follow we manually smooth out constraints in this case to account fordifferent possible ways the data could have been binned. http://galprop.stanford.edu In practice, this model’s flux is approximately the one in eq. (3.6) rescaled by a factor of 7. – 4 –bout the dark matter distribution. For our analysis of annihilating DM we select a 1 (cid:48) observing region (roughly GECCO’s angular resolution) to maximize the signal-to-noiseratio. In the case of decaying DM we instead find the best strategy is to use a larger5 ◦ field of view, since the ¯ D factor depends much less strongly on the observing region’ssize. The observing regions and ¯ J / ¯ D factors used to collect existing gamma-ray data arepresented in table 2. Secondary photons are also produced by dark matter processes that create electronsand positrons. These can produce energetic photons via inverse-Compton scattering againstambient CMB, starlight and dust-reprocessed infrared photons [19, 20]. Their spectrum, forupscattered initial photon energy E γ peaks near E peak (cid:39) E γ ( E e /m e ) (cid:39) E γ ( m DM / (10 m e )) which for sub-GeV DM masses and for the highest energy background photon from starlight( E γ ∼ (cid:46)
100 keV upscattered photon energy, thus well below GECCO’s ex-pected energy threshold. Also, the calculation of the secondary radiation carries inherentlydifficult systematics ranging from the effects of diffusion to the morphology of the back-ground radiation fields. While Ref. [21] recently studied constraints from INTEGRAL onsecondary photons produced by MeV-scale DM, we omit these from our plots. Uncer-tainties in the astrophysics of secondary emission can relax their bounds by an order ofmagnitude, bringing them into line with constraints on primary emission obtained usingother telescopes.Observations of the cosmic microwave background (CMB) constrain the amount ofpower DM annihilations and decays are allowed to inject in the form of ionizing particlesduring recombination [22–26]. hazma contains functions for calculating this constraint forannihilating DM. To review, given a DM model the constraint is set by p ann = f χ eff (cid:104) σv (cid:105) ¯ χχ, CMB m χ , (3.7)where f χ eff is the fraction of energy per DM annihilation imparted to the plasma and p ann is an effective parameter measured from observations bounding the energy that can beinjected per unit volume and time. In turn f χ eff depends on the photon and electron/positronspectrum per DM annihilation. When DM annihilation is velocity-suppressed (as in theHiggs portal model we will consider in section 3.3), the present-day thermally-averagedself-annihilation cross section is related to the one in eq. (3.7) by the squared ratio ofthe DM velocity at present and at recombination, ( v χ, /v χ, CMB ) . Computing v χ, CMB requires the DM’s kinetic decoupling temperature as input, which typically falls between(10 − − − ) m χ [13]. While this can be calculated self-consistently for a given DM model,we instead leave it as a parameter in our analysis and fix its value when necessary. ForDM masses above ∼ p -wave annihilation are found to be weakerthan for s -wave annihilation. For constraints on decaying DM we reuse the results fromRef. [27]. We first consider GECCO’s discovery reach for “simplified” dark matter models where thedark matter particles annihilate or decay into exclusive, single final states, namely the– 5 –arget ¯ J (1 (cid:48) ) ¯ J (5 ◦ ) ¯ D (1 (cid:48) ) ¯ D (5 ◦ )Galactic Center (NFW) [28] 6 . × . × . × . × Galactic Center (Einasto) [28] 5 . × . × . × . × Draco (NFW) [29] 3 . × . × . × . × M31 (NFW) [30] 1 . × . × . × . × Table 1 : ¯ J and ¯ D factors for various circular targets, in units of MeV cm − sr − and MeV cm − sr − respectively. The dark matter profile parameters are taken from theindicated references. For the Milky Way, we use the values from Table III of Ref. [28]. TheEinasto profile parameters are adjusted within their 1 σ uncertainty bands to maximize the¯ J and ¯ D factors. For all other targets we use the parameters’ central values. The distancefrom Earth to the Galactic Center is set to 8.12 kpc [28, 31]. For reference, the angularextents of the 1 (cid:48) and 5 ◦ regions are 2 . × − sr and 2 . × − sr respectively.Experiment Region ∆Ω [sr] ¯ J ¯ D COMPTEL [32] | b | < ◦ , | l | < ◦ . × . × EGRET [33] 20 ◦ < | b | < ◦ , | l | < ◦ . × . × Fermi [34] 8 ◦ < | b | < ◦ , | l | < ◦ . × . × INTEGRAL [
AC: ref] | b | < ◦ , | l | < ◦ . × . × Table 2 : ¯ J and ¯ D factors for observing regions in the Milky Way used bypast experiments, in units of MeV cm − sr − and MeV cm − sr − respectively. Theregions are specified in Galactic coordinates. We again use the NFW profile parametersfrom Table III of ref. [28].diphoton, dielectron and dimuon final states. The existing gamma-ray constraints andGECCO projections on the branching fraction times self-annihilation cross section (forannihilating DM) are shown in fig. 1 and on the lifetime (for decaying DM) in fig. 2. In thefigures we shade regions of parameter space ruled out by observations taken with previousor existing telescopes, namely COMPTEL, EGRET, Fermi-LAT, and INTEGRAL. Wealso indicate constraints from CMB distortions with dashed and dot-dashed black lines(the regions excluded are above those lines).The GECCO sensitivity is shown for four distinct cases, listed here from top to bottomin the order the lines appear in fig. 1 (the order is inverted for the lifetime in the case ofdecay shown in fig. 2): the grey line corresponds to observations, within an angular regionof 1 (cid:48) , of the Draco dSph; the magenta line for observations of M31, within the same angularregion of 1 (cid:48) ; finally the brown and purple lines correspond to observations of the GalacticCenter, again within 1 (cid:48) , assuming an NFW profile (brown line) and an Einasto profile(purple line). The results for annihilation into two pions are weaker than the results for the dimuon final state by anorder one factor, but otherwise nearly identical, so we do not plot them separately. – 6 – m χ [MeV]10 -32 -30 -28 -26 -24 -22 B r × › σ v fi ¯ χχ , [ c m / s ] e + e − -1 m χ [MeV]10 -36 -34 -32 -30 -28 γγ m χ [MeV]10 -30 -28 -26 -24 -22 B r × › σ v fi ¯ χχ , [ c m / s ] µ + µ − GECCO (GC , Einasto)GECCO (GC , NFW)GECCO (M31 )GECCO (Draco )CMB ( s -wave)CMB ( p -wave)COMPTELEGRET Fermi INTEGRAL Figure 1 : Constraints on annihilation into different final states. The shaded regions showconstraints from existing gamma ray data. The dashed black line shows the CMB constraintassuming the DM annihilation are p -wave and have a kinetic decoupling temperature of10 − m χ . Higher kinetic decoupling temperatures would give weaker constraints. Thedot-dashed line gives the CMB constraint for s -wave DM annihilations.We find that the greatest gains a telescope such as GECCO will bring in the searchfor MeV dark matter are for final states producing monochromatic gamma ray (i.e. lines).In this case the improvements to the sensitivity across the range between 0.1 and 10 MeVare forecast to be as large as four orders of magnitude in the annihilation rate, or over twoorders of magnitude in lifetime. Signals will potentially be visible across different targets.The entire parameter space testable with GECCO is compatible with constraints fromCMB for p -wave DM annihilations. GECCO observations have the potential to discoverDM annihilating in an s -wave to two photons. While the s -wave CMB bounds for thedielectron and dimuon final states are more stringent, GECCO still has the potential touncover DM annihilation in the Galactic Center depending on the DM mass and spatialdistribution. We note that the jagged lines for the GECCO predicted sensitivity are due– 7 – D M li f e t i m e τ [ s ] e + e − γγ m χ [MeV]10 D M li f e t i m e τ [ s ] µ + µ − GECCO (GC ◦ , Einasto)GECCO (GC ◦ , NFW)GECCO (M31 ◦ )GECCO (Draco ◦ )CMBCOMPTELEGRET Fermi INTEGRAL Figure 2 : Constraints on the DM particle’s lifetime for decays into different final states.The CMB constraint on decays into e + e − is taken from Ref. [27]. While constraints forthe µ + µ − final state are not provided, we estimate they lie around 10 − s since thesubsequent muon decays produces electrons with energy ∼ / m χ . The constraint fordecays into γγ lies below the axis range. See the caption of fig. 1 for more details.to the energy window optimization described below eq. (3.4).The electron-positron final state also offers highly promising prospects, especially atlow masses around 1-10 MeV, with improvements to the current sensitivity of up to fiveorders of magnitude in annihilation rate (two in lifetime) but will improve by almost twoorders of magnitude even at large masses, around 10 GeV; detection of an annihilationsignal outside the Milky Way center will be possible again, but only for masses below 30MeV or so, with similar prospects for decay.Finally, in the muon pair case, the optimal dark matter candidate would have a massof around the muon mass, offering an improvement of three orders of magnitude for anni-hilation, and over one in decay. However, in the µ + µ − case current constraints exclude thepossibility of detecting a signal from M31 or Draco, in either annihilation or decay.– 8 –n what follows we illustrate with explicit model realizations the physics reach ofGECCO for the detection of dark matter annihilation in the Higgs portal (section 3.3)and vector portal/dark photon (section 3.4) cases, and of dark matter decay in the casethe right-handed neutrino dark matter (section 3.5). In this model, we extend the Standard Model by adding a new scalar singlet ˜ S . The darkmatter interacts only with this scalar, through a Yukawa interaction: L ⊃ g Sχ ˜ S ¯ χχ . Thenew scalar mixes with the real neutral scalar component of the Higgs with a mixing angle θ providing a portal through which the dark matter can interact with the Standard Model. This results in a Lagrangian density of the form: L = L SM + ¯ χ ( i (cid:19) ∂ − m χ ) χ − S (cid:0) ∂ + m S (cid:1) S (3.10) − g Sχ ( h sin θ + S cos θ ) ¯ χχ + ( h cos θ − S sin θ ) (cid:88) f m f ¯ f f + · · · where f is a massive SM fermion and the · · · contain pure scalar interactions. This La-grangian density is only valid for energies E (cid:38) Λ EW while our interest lies in sub-GeVenergies. To obtain a Lagrangian valid for sub-GeV energies, we first need to find a La-grangian valid above the QCD confinement scale and then match onto the chiral Lagrangian(see Ref. [35] for a detailed review of chiral perturbation theory). We omit the details here(to be provided in a forthcoming paper) and simply give the result: L Int( S ) = 2 sin θ v h S (cid:2) ( ∂ µ π )( ∂ µ π ) + 2( ∂ µ π + )( ∂ µ π − ) (cid:3) (3.11)+ 4 ie sin θ v h SA µ (cid:2) π − ( ∂ µ π + ) − π + ( ∂ µ π − ) (cid:3) − m π ± sin θ v h (cid:18) S + sin θ v h S (cid:19) (cid:2) ( π ) + 2 π + π − (cid:3) − e sin θ v h Sπ + π − A µ A µ − g Sχ S ¯ χχ − sin θS (cid:88) (cid:96) = e,µ y (cid:96) √ (cid:96)(cid:96). In the equation above, we have made the redefinition g Sχ cos θ → g Sχ . The terms relevantfor indirect detection are those involving an S field interacting with pions (along with a This is achieved by modifying the scalar potential to be: V ( ˜ S, H ) = − µ H H † H + λ (cid:16) H † H (cid:17) + 12 µ S ˜ S + g SH ˜ SH † H + · · · (3.8)where H is the SM Higgs doublet, ˜ S is a new, neutral scalar singlet and the · · · represent interaction termswith more than a single ˜ S . After diagonalizing the scalar mass matrix we find two neutral scalars h and S which are related to the original scalars through a mixing angle: (cid:32) ˜ h ˜ S (cid:33) = (cid:32) cos θ − sin θ sin θ cos θ (cid:33)(cid:32) hS (cid:33) . (3.9) – 9 –hoton), leptons or dark matter. The S ππ and SππAA terms are subdominant since theyhave additional factors of sin θ , the Higgs vev and/or the electron charge.As discussed in our previous work [11], this leading-order chiral perturbation theoryapproach has a limited regime of validity. To avoid the f (500) resonance [36] and theresulting final-state interactions between pairs of pions as well as (500 MeV / Λ QCD ) ∼ m χ <
250 MeVwhen the DM annihilates into SM particles, and m S <
500 MeV when it predominantlyannihilates into mediators.The thermally-averaged DM self-annihilation cross section for this model is p -wavesuppressed: (cid:104) σv (cid:105) ¯ χχ ∝ T χ /m for low DM temperatures T χ . Since this assumption holdsfor all our targets, under the assumption that the DM particles’ speeds follow a Maxwell-Boltzmann distribution we can approximate (cid:104) σv (cid:105) ¯ χχ ∝ σ v , where σ v is the velocity disper-sion in the target. We take σ v = 10 − c for the Milky Way targets [38] and M31 [39] and σ v = 3 × − c for Draco [40]. The constraints from current gamma-ray data, our projections for GECCO’s reachusing different targets and the CMB bounds for this model are displayed in fig. 3, withtwo ratios of m S to m χ . We have rescaled the constraints on (cid:104) σv (cid:105) ¯ χχ for each targetinto constraints on (cid:104) σv (cid:105) ¯ χχ, , the thermally-averaged self-annihilation cross section in theMilky Way. GECCO’s projected reach exceeds the CMB bound for all targets exceptDraco, on account of the p -wave suppression in the self-annihilation cross section. GECCOobservations of M31 and the Galactic Center will improve over previous telescopes by oneto four orders of magnitude.An array of terrestrial, astrophysical and cosmological observations constrain this Higgsportal model (see e.g. Ref. [41]). Depending on the DM and mediator masses the mostrelevant ones for this work include rare and invisible decays of B and K mesons and beamdumps sensitive to visible S decays. How these complement indirect detection boundsdepends strongly on whether the DM annihilates into mediator pairs ( m χ > m S , leftpanel) or SM particles ( m χ < m S , right panel). In the first case, the DM self-annihilationcross section scales as (cid:104) σv (cid:105) ¯ χχ, ∼ g Sχ . As a result, the conservative interpretation of otherbounds on this model is that they do not constrain the strength of the possible gamma-raysignals. This is because all other constraints involve the coupling sin θ , and for each DMand mediator mass combination at least some values of sin θ are allowed. In the left panel ofthe figure we show contours of constant g Sχ to give a sense of reasonable values of the crosssection. GECCO observations of the Galactic Center will probe down to g Sχ ∼ × − for low DM masses.When the SS final state is not accessible, the DM’s annihilations are strongly sup-pressed since the cross section scales as (cid:104) σv (cid:105) ¯ χχ, ∼ g Sχ sin θ y , where y (cid:28) g Sχ , sin θ ) = (4 π,
1) (very A more careful treatment would average over the position-dependent velocity distribution in the target.In the case of the Milky Way, this should only change our results by a factor of (cid:46) – 10 –oughly the maximum coupling values consistent with unitarity). GECCO can probe thiscross section for most masses and targets we consider.Each point in the ( m χ , (cid:104) σv (cid:105) ¯ χχ, ) plane corresponds to a range of possible sin θ values.The lower end of this range is determined by setting g Sχ ∼ π while the upper end issin θ = 1. We can conservatively map constraints on the Higgs portal model at each pointin this plane by checking whether any of the sin θ values in this range are permitted.Applying this procedure using the constraints from [41] leads to the orange region in theright panel of fig. 3. At all points, these constraints are a few orders of magnitude morestringent than GECCO’s discovery reach. This conclusion holds for other mediator masses m S > m χ above and below the resonance region around m S = 2 m χ .To guide the eye, we also plot curves corresponding to values of the coupling that givethe correct DM relic abundance. GECCO can discover this benchmark Higgs portal modelwhen the mediator is lighter than the DM and decays into photons or electrons, dependingon the observing region. For both DM-mediator mass ratios shown, the process relevantfor the standard relic abundance calculation is ¯ χχ → SS . While this is not kinematicallypermitted for m χ < m S when the DM is nonrelativistic, it contributes dominantly tothe thermal average involved in the relic abundance calculation since annihilations intoSM final states are Yukawa-suppressed, making this an example of forbidden DM [42].Translating the value of g Sχ that gives the correct relic abundance for this scenario into (cid:104) σv (cid:105) ¯ χχ, additionally requires fixing sin θ , which we set to 1 in the right panel of fig. 3. If the DM freezes out purely through annihilations into SM particles (as is the case for m S (cid:29) m χ ), nonperturbatively large values of the DM-mediator coupling are required togive the correct relic abundance ( g Sχ (cid:38) θ = 1.Given that we do not know the thermal history of the universe before big bang nucle-osynthesis (BBN), the thermal relic cross sections we show can be evaded. For example, ifthe DM freezes out over-abundantly before BBN ( m χ / (cid:38) T BBN ∼ Our vector-portal model is the well-known “dark photon” model in which we add a newU(1) D gauge group and charge the DM under this group. We connect the dark sector andSM sector by letting the U(1) D gauge boson mix with the Standard Model photon through Note that there is a weak lower bound on sin θ coming from requiring that the DM and mediatorthermalize with the SM bath at early times. – 11 – -1 m χ [MeV]10 -40 -36 -32 -28 -24 › σ v fi ¯ χχ , [ c m / s ] g S χ = g S χ = − g Sχ =10 − m S = 0 . m χ -1 m χ [MeV]10 -40 -36 -32 -28 -24 ( g Sχ ,s θ )=(4 π, m S = 1 . m χ CMBThermal relicGECCO (GC , Einasto)GECCO (GC , NFW)GECCO (M31 )GECCO (Draco )Other constraints γ -ray telescopes Figure 3 : Constraints on the thermally-averaged DM self-annihilation cross section in theMilky Way for the Higgs portal model. The case where the indirect detection signal comesfrom annihilations into mediators (SM particles) is shown on the left (right). The thin reddotted lines are contours of constant coupling strength. The orange region in the rightpanel is a conservative exclusion region from experiments besides gamma-ray telescopes.The CMB constraint was computed assuming a kinetic decoupling temperature of 10 − m χ .Taking this to be higher would weaken the constraint. (cid:15) V µν F µν where (cid:15) is a small mixing parameter and V µν and F µν are the dark photon andSM photon field strength tensors. The Lagrangian density is: L = L SM − V µν V µν + (cid:15) V µν F µν + ¯ χ ( i (cid:19) ∂ − m χ ) χ + g χV V µ ¯ χγ µ χ (3.12)where V µ is the dark-photon. The kinetic terms for the U(1) fields are diagonalized byshifting the SM-photon field by A µ → A µ + (cid:15)V µ and ignoring terms O (cid:0) (cid:15) (cid:1) . The resultis that all electrically-charged SM fields receive a small dark charge and the DM receivesa small electric charge. After integrating out the heavy SM field and matching onto thechiral Lagrangian, we end up with the following interaction Lagrangian between the darkphoton and the light SM fields and meson: L V − SM = − eV µ (cid:88) (cid:96) ¯ (cid:96)γ µ (cid:96) + i(cid:15)eV µ (cid:2) π − ∂ µ π + − π + ∂ µ π − (cid:3) − e π (cid:15) µναβ F µν V αβ (cid:18) π f π (cid:19) (3.13)where (cid:96) is either the electron or muon. The first two terms come from the covariantderivatives of the leptons and charge pion. The last term is a shift in the neutral piondecay, stemming from the Wess-Zumino-Witten Lagrangian [49, 50].In our analysis, we focus on the regime where the mediator is heavier than the darkmatter mass, taking 3 m χ = m V . With this choice, we are able to recycle previously studiedconstraints produced by non-astrophysical experiments. The strongest constraints on darkphoton models for the masses we are interested in come from the B -factory BaBar [51]and beam-dump experiments such as LSND [52]. Studies using the datasets of theseexperiments were able to constraint the dark photon model by looking for the productionof dark photons which then decay into dark matter (see, for example Ref. [53–55]); inthe case of BaBar, the relevant process is Υ(2 S ) , Υ(3 S ) → γ + V → γ + invisible, while– 12 – m χ [MeV] − − − − − − h σ v i [ c m s − ] CMBThermal RelicGECCO (GC 1 , Einasto)GECCO (GC 1 , NFW)GECCO (M31 1 )GECCO (Draco 1 ) γ -ray telescopesOther constraints Figure 4 : Projected constraints on the dark matter annihilation cross section for the darkphoton model from GECCO (solid lines). The light blue shaded region shows the combinedconstraints from COMPTEL, EGRET, FERMI and INTEGRAL. The orange region showsthe region excluded by BaBar and LSND. We show the contour yielding the correct darkmatter relic density with the dotted black line.the relevant process for LSND is π → γ + V → γ + invisible. We adapt the constraintscomputed in Ref. [55] (see Fig.(201) for the constraints and the text and references thereinfor details).In fig. 4, we show the combined constraints from BaBar and LSND in orange. Asin section 3.3, we show the constraints from existing gamma-ray telescope constraints (inblue), constraints from CMB (dashed black) and a contour where we find the correct relicdensity for the dark matter through standard thermal freeze-out through annihilation intoStandard Model particles (dotted black). While our results show that the dark photonmodel is which dark matter is produced via standard thermal freeze out is already wellexcluded, we again point out that there are mechanisms for producing DM through non-thermal processes; see the end of the previous section for further discussion and Ref. [56]for a specific example using entropy dilution for a dark photon-mediated DM model. Theprojected constraints for GECCO for various targets and DM profiles are shown with solidlines. Our results demonstrate that GECCO’s potential to significantly extend currentconstraints, and, more importantly, to offer opportunities for discovery of this class ofwell-motivated dark matter candidates. The decaying DM model we investigate is one in which the DM is given by a right-handed(RH) neutrino (i.e. a Weyl spinor transforming as a singlet under all Standard Model gaugegroups) featuring a non-zero mixing with left-handed “active” neutrinos. We assume the– 13 –H neutrino mixes with a single left-handed neutrino flavor, ν kL , where ν kL is an electron,muon or tau neutrino. The Lagrangian density describing the interactions of the RH-neutrino with the SM is the 4-fermion effective Lagrangian obtained by integrating out the W ± and Z : L N(int) = − G F √ (cid:104) J + µ J − µ + (cid:0) J Zµ (cid:1) (cid:105)(cid:12)(cid:12)(cid:12)(cid:12) ν kL → sin θN − i cos θν kL (3.15)Where G F is Fermi’s constant and J ± µ and J Zµ are the charged and neutral weak fermioncurrents, given by: J + µ = (cid:88) i ¯ ν iL γ µ (cid:96) iL + (cid:88) i,j V CKM ij ¯ u iL γ µ d jL (3.16) J Zµ = 12 c W (cid:88) i =1 (cid:20)(cid:18) − s W (cid:19) ¯ u i γ µ u i + (cid:18) − s W (cid:19) ¯ d i γ µ d i + ¯ ν iL γ µ ν iL − (cid:0) s W (cid:1) ¯ (cid:96) i γ µ (cid:96) i (cid:21) with s W and c W being the sine and cosine of the weak mixing angle.In order to calculate the interactions between the RH neutrino and mesons, we firstneed to determine the interaction Lagrangian written in terms of light quarks. Groupingthe up, down and strange into a light-quark vector q = ( u d s ) T , we can write the relevantinteractions terms of the expanded 4-Fermi Lagrangian as: − √ G f L N(int) = ¯ q γ µ (cid:2) G R ( L µ + R µ ) (cid:3) P R q + ¯ q γ µ (cid:104)(cid:16) V † L − µ + h . c . (cid:17) + 2 G L (cid:0) L µ + R µ (cid:1)(cid:105) P L q + L + µ L − µ + ( L µ + R µ ) + · · · (3.17)Here the · · · contain terms without the RH-neutrino. The charged and neutral left andright handed currents which the light quarks interact with are given by: R µ = 12 c W ( i cos θ ¯ ν kL + sin θ ¯ N ) γ µ ( − i cos θν kL + sin θN ) + · · · (3.18) L µ = 12 c W ( i cos θ ¯ ν kL + sin θ ¯ N ) γ µ ( − i cos θν kL + sin θN ) + · · · (3.19) L − µ = − i cos θν kL γ µ (cid:96) kL + sin θ ¯ N γ µ (cid:96) kL + · · · (3.20) This can be achieved by the following Lagrangian density: L = L SM + i ˆ N † ¯ σ µ ∂ µ N −
12 ˆ m N (cid:16) ˆ N ˆ N + ˆ N † ˆ N † (cid:17) − y (cid:96) (cid:16) ˆ L † (cid:96) ˜ H ˆ N + h . c . (cid:17) (3.14)where N is the 2-component Weyl spinor for the RH neutrino and ˆ L (cid:96) = (ˆ ν (cid:96) ˆ e (cid:96) ) T is one of the SM leptondoublets. For non-zero ˆ m N , diagonalizing the neutrino mass matrix yields two majorana spinors. Thediagonalization can be performed by constructing a neutrino mass matrix from the neutrino interactionsstates ν = (cid:16) ˆ ν (cid:96) ˆ N (cid:17) and performing a Takagi diagonalization [57]. The unitary Takagi transformation matrixis: Ω = (cid:32) − i cos θ sin θi sin θ cos θ (cid:33) , sin θ = vy √ m N − O (cid:18) vy ˆ m N (cid:19) , cos θ = 1 − O (cid:18) vy ˆ m N (cid:19) . – 14 –he G R and G L are the right and left light-quark coupling matrices to the Z boson, givenby: G R = 12 c W diag(1 , − , −
1) + G L , G L = − s W c W diag( − , ,
1) (3.21)and V is CKM coupling matrix for the light quarks: V = V ud V us (3.22)These interactions terms are easily matched onto the chiral Lagrangian. The terms in-volving the light-quarks that look like ¯ q γ µ J µL,R P L,R q are matched onto the “covariant”derivative of the meson matrix of the chiral Lagrangian while the terms without quarkssimply carry straight over. The result is: L = f π (cid:104) ( D µ Σ ) † ( D µ Σ ) (cid:105) + L + µ L − µ + (cid:0) L µ + R µ (cid:1) + · · · (3.23)where f π is the pion decay constant f π ∼
92 MeV and the Σ field is the pseudo-Goldstonematrix containing the meson made from u, d and s quarks: Σ = π + η/ √ √ π + √ K + √ π − − π + η/ √ √ K √ K − √ K − η/ √ (3.24)and the covariant derivative is: D µ Σ = ∂ µ Σ − ir µ Σ + i Σ l µ (3.25) r µ = 2 G R R µ (3.26) l µ = (cid:16) V † L − µ + h . c . (cid:17) + 2 G L (cid:0) L µ + R µ (cid:1) (3.27)RH neutrinos are well-known and well-motivated DM candidates (for a recent reviewsee e.g. Ref. [58]). For the range of masses and lifetimes of interest here, the mixing anglemust be extremely small: the dominant decay widths corresponding to a RH neutrino of– 15 –ass m N with mixing angle with active neutrinos θ reads [59]Γ( N → π ν (cid:96) ) = f π G F m N θ π (1 − s W ) (cid:18) − m π m N (cid:19) , (3.28)Γ( N → π ± (cid:96) ∓ ) = f π G F | V ud | θ πm N λ / ( m N , m (cid:96) , m π ± ) (3.29) × (cid:104)(cid:0) m N − m (cid:96) (cid:1) − m π ± (cid:0) m (cid:96) + m N (cid:1)(cid:105) , Γ( N → ν (cid:96) γ ) = 9 e G F m N θ π , (3.30)Γ( N → ν (cid:96) ) = G F m N θ π , (3.31)Γ( N → ν (cid:96) (cid:96) + (cid:96) − ) = G F m N θ π (cid:20) s W + 8 s W − µ (cid:96) (cid:0) s W + 6 s W (cid:1) + 24 µ (cid:96) (cid:0) s W + 12 s W − µ (cid:96) ) (cid:1) (3.32)+ O (cid:0) µ (cid:96) (cid:1)(cid:21) , where s W is the sine of the weak mixing angle, λ ( a, b, c ) = a + b + c − ab − ac − bc and µ (cid:96) = m (cid:96) /m N . For RH neutrino masses below the pion threshold, the three-body final statedecay modes are dominant. In this regime, photons are produced via the one-loop decayof the RH-neutrino into νγ and through radiation off a charged lepton, if N → ν(cid:96) + (cid:96) − iskinematically accessible. Once the pion threshold is crossed, the two body finals states N → π ν (cid:96) and N → π ± ν ∓ (cid:96) dominate and photons are produced via the decay of pions andradiation off charged states.We show contours of constant θ on the lifetime versus mass plot in fig. 5. We do notassume here any specific RH neutrino production mechanism in the early universe. In themass range of interest, the most natural, although by all means not the only, scenario isnon-thermal production from the decay of a heavy species φ coupled to the RH neutrinovia a Yukawa term of the form yφ ¯ N N (see e.g. Ref. [60]). The yield depends on a variety ofassumptions, including whether the φ is in thermal equilibrium or not, which other decaychannels it possesses, and the number of degrees of freedom that populate the universeas a function of time/temperature. However, production of RH neutrinos with the rightabundance is generically possible across the parameter space we show in fig. 5.The phenomenological constraints for RH neutrinos are weak for the masses and mixingangles of interest here. We refer the Reader to fig. 4 of Ref. [61] for an extensive review.In short, the most stringent constraints occur for mixing with the electron-type activeneutrino, for a non-trivial CP phase and lepton-flavor violation structure. The strongestconstraints, from neutrino-less double-beta decay, do not constrain values of the mixingangle to be smaller than θ ∼ − , even in the most favorable case. In the case of muonmixing, at or below 100 MeV the constraints are never stronger than θ ∼ − . Finally, inthe weakest constraints case, that with tau neutrino mixing, the constraints on the mixingangle occur only for θ (cid:38) − . We conclude that there are essentially no meaningful– 16 –henomenological constraints on the parameter space shown in fig. 5, in contrast to thesituation for O (keV)-scale sterile neutrinos (see e.g. Ref. [58]). − m N [MeV] τ [ s ] ‘ = e θ = − θ = − θ = − θ = − θ = − θ = − GECCO (GC ◦ , Einasto)GECCO (GC ◦ , NFW)GECCO (M31 ◦ )GECCO (Draco ◦ ) γ -ray telescopes − m N [MeV] ‘ = µ θ = − θ = − θ = − θ = − θ = − θ = − Figure 5 : Projected constraints on the RH-neutrino lifetime. The area shaded in lightblue is excluded by current observations, as in the previous plots. We also show, withdot-dashed contours, the mixing angle corresponding to parameter space shown in thefigure.Our results in fig. 5 indicate that a signal from sterile neutrino dark matter decay willbe detectable from the Galactic Center over a wide range of masses and lifetimes. Limitswill improve, for RH neutrinos in the few hundreds of keV range, by up to three ordersof magnitude. A signal will also possibly be detectable for masses up to 100 MeV, andfrom targets different from the Galactic Center, such as M31 and Draco, for short enoughlifetimes. Constraints from CMB observations are negligible [13].
The discovery of gravitational radiation from binary black hole mergers ushered a renewedinterest in black holes of primordial rather than stellar origin as dark matter candidates(for recent reviews, see e.g. Refs. [62, 63]). In a recent study, we considered Hawkingevaporation from primordial black holes with lifetimes on the order of the age of the universeto 10 times the age of the universe [10]. There we corrected shortcomings of similar pastanalysis pertaining to the treatment of final state radiation and to the extrapolation ofhadronization results outside proper energy ranges. We carried out a complete calculationof particle emission for Hawking temperatures in the MeV, and of the resulting gamma-rayand electron-positron spectrum.Our key finding is that MeV gamma-ray telescopes are ideally poised to potentiallydiscover Hawking radiation from light but sufficiently long-lived primordial black holes,specifically in the mass range between 10 and 10 grams. The Hawking temperaturescales with the holes’ mass as T H ≈ (10 g /M ) MeV. As a result, especially towards themore massive end of that mass range, the bulk of the emission stems from prompt primary– 17 – M PBH [g]10 -6 -5 -4 -3 -2 -1 f P B H GC ◦ , EinastoGC ◦ , NFWM31 ◦ Draco ◦ Existing
Figure 6 : GECCO’s 5 σ discovery reach for detecting Hawking radiation from evaporatingprimordial black hole dark matter. We assume a monochromatic mass function. The thinpurple and brown lines near 10 M (cid:12) show how the constraints would change if GECCO’senergy threshold was lowered from 100 keV to 50 keV.photon emission at higher energy, and from secondary emission from electrons at lowerenergy.Emission from the central region of the Galaxy and from nearby astrophysical systemswith significant amounts of dark matter can be detectable with GECCO, as we showhere. The calculation of the flux from black hole evaporation is as follows: a non-rotatingblack hole with mass M and corresponding Hawking temperature T H = 1 / (4 πG N M ) (cid:39) . g /M ) MeV, with G N Newton’s gravitational constant, emits a differential fluxof particles per unit time and energy given by ∂ N i ∂E i ∂t = 12 π Γ i ( E i , M ) e E i /T H − ( − s , (4.1)where Γ i is the species-dependent grey-body factor, and E i indicates the energy of theemitted particle of species i . Unstable particles decay and produce stable secondary parti-cles, including photons. The resulting differential photon flux per solid angle from a regionparameterized by an angular direction ψ is obtained by summing the photon yield N γ fromall particle species the hole evaporates to:d φ γ d E γ = 14 π M (cid:90) LOS d l ρ DM ( l, ψ ) f PBH ∂ N γ ∂E∂t . (4.2)Notice that upon integrating over the appropriate solid angle this expression is analogousto the one for the gamma-ray flux from decaying DM, containing the same ¯ D factor (c.f.eq. (3.1)).As for the calculation of the grey-body factors, we employ the publicly available code BlackHawk [64].
BlackHawk provides primary spectra of photons, electrons and muons. We– 18 –hen model the final-state radiation off the charged final state particles by convolving theprimary particle spectrum with the Altarelli-Parisi splitting functions at leading order inthe electromagnetic fine-structure constant α EM [65, 66]. For the unstable particles, suchas pions, we use hazma to compute the photon spectrum from decays. The total resultingphoton spectrum is then given by: ∂ N γ ∂E γ ∂t = ∂ N γ, primary ∂E γ ∂t (4.3)+ (cid:88) i = e ± ,µ ± ,π ± (cid:90) d E i ∂ N i, primary ∂E i ∂t d N FSR i d E γ + (cid:88) i = µ ± ,π ,π ± (cid:90) d E i ∂ N i, primary ∂E i ∂t d N decay i d E γ , where the FSR spectra are given by:d N FSR i d E γ = α EM πQ f P i → iγ ( x ) (cid:20) log (cid:18) (1 − x ) µ i (cid:19) − (cid:21) ,P i → γi ( x ) = (cid:40) − x ) x , i = π ± − x ) x , i = µ ± , e ± , (4.4)with x = 2 E γ /Q f , µ i = m i /Q f and Q f = 2 E f . We give for explicit expressions of dN decay /dE γ for the muon, neutral and charged pions in Ref. [11].In evaluating GECCO’s discovery reach we consider the same targets as in the preced-ing section: the Galactic Center with an NFW and an Einasto dark matter density profile,M31, and Draco. Assumptions on observing time are identical as before, and we use thesame procedures to set limits and make projections as described in section 3.1.In summary, we show in fig. 6 that GECCO will enable the revolutionary possibility ofdirectly detecting Hawking evaporation from primordial black holes, for instance if theseobjects constitute at least 0.001% of the dark matter and have a mass of 10 grams, orif they are a larger fraction of the dark matter and a mass up to 10 grams. Underoptimistic circumstances (e.g. the black holes weigh around 10 grams and they are morethan 10% of the dark matter), GECCO will detect Hawking evaporation from multipletargets besides the Galactic Center, such as from nearby dSph (e.g. Draco) and galaxies(e.g. M31). This reach in PBH mass is an order-of-magnitude improvement over existingbounds. The discovery of 511 keV line emission from positron-electron pair annihilation in thecentral region of the Galaxy dates back to balloon-borne experiments since the 1970s(see e.g. Ref. [67]). Space telescopes, specifically OSSE on the Compton Gamma-RayObservatory [68] and, more recently, the SPI spectrometer [69, 70] and the IBIS imager onboard INTEGRAL [71] have significantly increased the amount of information about the– 19 –11 keV emission. The overall intensity of the line is around 10 − photons cm − s − , andit originates from a region of approximately 10 ◦ radius around the Galactic Center. Theemission does not appear to have any significant time variability, and its spatial smoothness,combined with the point-source sensitivity of the IBIS imager, places a lower limit of atleast eight discrete sources contributing to the signal [70].Measurements of the diffuse emission at energies below and above 511 keV constrainthe injection energy of the positrons and the properties of the medium where injectionand annihilation occur. Most notably for constructing new physics interpretations of thesignal, the absence of significant emission at energies higher than 511 keV indicates thatthe positron injection energy is bounded from above in the few MeV (at most 4 − . N src sources each with a luminosity L src at an average distance of 8.5 kpc.Given that the 511 keV signal is approximately φ (cid:39) × − ∆Ω cm s − sr − over anangular region of 10 degrees, i.e. ∆Ω (cid:39) . d src reads φ src = L src πd (cid:39) φ N src (cid:18) . d src (cid:19) . (5.1)We can thus compare the narrow line flux sensitivity of GECCO, which in the best-casescenario is 7 . × − cm − ss − and in the worse case scenario 3 . × − cm − s − with theflux expected for a given putative source class point source. Specifically, we calculate theGECCO sensitivity on the plane of N src vs d src . In the plot we indicate with vertical linesthe closest known WR star, LMXB, and MSP, and with a horizontal line an estimate forthe number of LMXB that could be responsible for the 511 keV line according to Ref. [95]( N LXMB (cid:39) N MSP (cid:39) (9 . ± . × ) and an estimate for the total number of Wolf-Rayet starsin the Milky Way from Ref. [101] ( N WR (cid:39) ± × − cm − s − [95].Notice that certain types of new physics explanations such as dark matter decay wouldfollow a similar scaling. Other new physics explanations such as e.g. eXcited dark mat-ter [91] would not, a critical factor being the typical velocity dispersion in a given system:no signal at all would be predicted from e.g. small galaxies such as Draco or Ursa Minor.The predictions for galaxies versus clusters of galaxies would depend upon the details ofthe model, but generally scale similarly to what reported in table 3.– 21 – − d src (kpc) N s r c MSPLMXBWolf-Rayet W o l f - R a y e t L M X B U + M S P J - GECCO (best-case)GECCO (conservative) M M D r a c o U r s a M i n o r F o r n a x C l. C o m a C l. − − − − φ ( c m − s − ) GECCO (best-case)GECCO (conservative)
Figure 7 : Left: the GECCO sensitivity to 511 keV individual point source on the planedefined by the number of sources contributing to the signal at the Galactic Center (as-sumed to all contribute the same 511 keV luminosity), versus the distance of the closestsuch source; we also indicate with vertical dashed lines the distance to the closest MSP,Wolf-Rayet star, and LMXB, and with horizontal dark green bands the estimates for thetotal number of MSP and Wolf-Rayet stars potentially contributing to the signal. Right:predictions for the 511 keV flux from a variety of nearby astrophysical objects, based on asignal scaling proportional to mass over distance squared. The horizontal dashed and solidlines correspond to GECCO’s point source sensitivity best-case and conservative case.We use the estimate of Ref. [103] for the Milky Way bulge total mass, and the fluxquoted in Ref. [94] for the 511 keV flux from the bulge. We take the value for the totaldynamical mass of M31 from Ref. [104], while the distance is from Ref. [105]; the totalmass of M33 is from Ref. [106] and the distance from Ref. [107]. For the dSph we take datafrom Ref. [102]. Data for the Fornax cluster are from Ref. [108], while for the Coma clusterfrom Ref. [109] and Ref. [110]. We propagate errors including those on masses, distances,and the observed 511 keV flux, and show our results in the right panel of fig. 7.
We explored and elucidated the scientific portfolio that would be enabled by the deploymentof the proposed mid-scale NASA mission GECCO as it pertains to dark matter and newphysics. GECCO is ideally suited to explore MeV dark matter candidates as long as theydecay and/or pair-annihilate. The new instrument would unveil dark matter signals up– 22 –arget Mass [ M (cid:12) ] Distance [kpc] φ [cm − s − ]Milky Way (1 . ± . × . ± . × − M31 (8 . ± × ±
33 (5 . ± . × − M33 (1 . ± . × ±
73 (8 . ± . × − Draco (2 . ± . × ± . ± . × − Ursa Minor (5 . ± . × ± . ± . × − Fornax Cl. (7 ± × (18 . ± . × (7 . ± . × − Coma Cl. (5 . ± . × (106 . ± . × (1 . ± . × − Table 3 : Predicted brightness of a 511 keV signal assuming a scaling proportional to massover distance squared for a variety of astrophysical targets (see main text for references tothe quoted masses, distances, and fluxes).to four orders of magnitude fainter than the current observational sensitivity, and wouldmake it possible to detect a dark matter signal from multiple astrophysical targets, reducingthe intrinsic background and systematic effects that could otherwise obscure a conclusivediscovery.GECCO would enable the exciting possible direct detection of Hawking evaporationfrom primordial black holes with masses in the 10 − grams range, if they constitute asizable fraction of the cosmological dark matter. Under favorable circumstances, GECCOmight detect Hawking evaporation from more than one astrophysical target as well.Finally, we showed the potential of GECCO to elucidate the nature of the 511 keVline, by virtue of its unprecedented line sensitivity and point-source angular resolution.We found that GECCO should be able to observe a 511 keV line from a variety of extra-Galactic targets, such as nearby clusters and massive galaxies and, potentially, even fromnearby dwarf galaxies; in addition, GECCO should be able to detect single sources of the511 keV emission, as long as they are reasonably close.In summary, we have shown that GECCO would push the observational frontier ofMeV gamma rays in ways that would enormously benefit the quest for fundamental ques-tions in cosmology and particle physics, chiefly the nature and particle properties of thecosmological dark matter, and the origin of the mysterious 511 keV line emission from thecenter of the Galaxy. Acknowledgements
This work is partly supported by the U.S. Department of Energy grant number de-sc0010107.A.C. is partially supported by the Netherlands eScience Center, grant number ETEC.2019.018.
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