Dark Nuclei I: Cosmology and Indirect Detection
PPrepared for submission to JCAP
MIT-CTP 4554
Dark Nuclei I: Cosmology and IndirectDetection
William Detmold, Matthew McCullough, and Andrew Pochinsky
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA02139, USAE-mail: [email protected], [email protected], [email protected]
Abstract.
In a companion paper (to be presented), lattice field theory methods are usedto show that in two-color, two-flavor QCD there are stable nuclear states in the spectrum.As a commonly studied theory of composite dark matter, this motivates the considerationof possible nuclear physics in this and other composite dark sectors. In this work, earlyUniverse cosmology and indirect detection signatures are explored for both symmetric andasymmetric dark matter, highlighting the unique features that arise from considerations ofdark nuclei and associated dark nuclear processes. The present day dark matter abundancemay be composed of dark nucleons and/or dark nuclei, where the latter are generated through dark nucleosynthesis . For symmetric dark matter, indirect detection signatures are possiblefrom annihilation, dark nucleosynthesis, and dark nuclear capture and we present a novelexplanation of the galactic center gamma ray excess based on the latter. For asymmetricdark matter, dark nucleosynthesis may alter the capture of dark matter in stars, allowingfor captured particles to be processed into nuclei and ejected from the star through darknucleosynthesis in the core. Notably, dark nucleosynthesis realizes a novel mechanism forindirect detection signals of asymmetric dark matter from regions such as the galactic center,without having to rely on a symmetric dark matter component. a r X i v : . [ h e p - ph ] J un ontents It remains a pressing challenge in particle physics to understand the particle nature of darkmatter (DM). The relentless experimental exploration of the possible interactions betweenDM and Standard Model (SM) fields has revealed a great deal of crucial information aboutpotential interactions. However, as yet no unambiguous signals of DM have emerged, andmany popularly considered DM candidates have come under increasing pressure from nullexperimental results. This situation motivates the continued, and ever-diversifying experi-mental and theoretical efforts to probe the DM frontier. In particular, it is pertinent to mapout the theoretical landscape of DM paradigms, as candidates with exotic properties maymotivate the consideration of non-standard experimental signatures of DM. In recent years,there has been a surge of interest in models of DM with distinctive interactions and/or mul-tiple states. Along these lines, the properties of the SM fields have in some cases guided theexploration of possibilities for the dark sector via analogy. Popular examples include darksectors, or sub-sectors, with dark atomic behavior [1–12] or strongly-coupled dark sectorsleading to composite DM candidates [13–35], which are the focus of this work. Composite DM, which arises due to confining gauge dynamics in the dark sector, hasbeen considered for some time. In all studies thus far, the DM candidate has been assumedto be hadron of the dark sector, such as a dark meson or a dark baryon. However, if theanalogy with the SM is taken seriously there is also the possibility of stable composites of thehadrons themselves: dark nuclei . The nuclei of the SM provide a clear proof-of-principle that See also [36, 37] for treatment of annihilation and scattering dynamics in composite dark sectors whereresonant effects are important. – 1 –uch states may exist. Determining the spectrum of nuclei in any strongly coupled gaugetheory is a difficult task, only now becoming possible through advances in the application oflattice field theory methods [38–40]. This explains why, thus far, only the hadronic spectrumof postulated strongly coupled dark sectors has been studied seriously. In a first step towardsquantitatively exploring the possibility of a dark nuclear spectrum, we will present latticecalculations in a companion paper that demonstrate that in two-color, two-flavor QCD,stable nuclear states are possible with the lowest lying states being a bound states of π and ρ mesons and their baryonic partners. Thus any discussion of DM candidates in this theorynow necessitate some consideration of the nuclear states. Going further, this suggests thepossibility of analogues of nuclei should be considered in any strongly interacting compositemodel. Our work substantially extends, and is complementary to, earlier pioneering latticestudies of DM candidates in such strongly coupled sectors [28, 30–33, 35].As will be demonstrated, the phenomenology of dark sectors exhibiting composite DMcandidates broadens significantly when the possibility of dark nuclei is introduced. In thiswork, we construct a model based on the broad qualitative findings of the lattice study andundertake an exploration of the cosmology and possible indirect detection signatures of darknuclei.The genesis of dark nuclei is achieved through a dark nucleosynthesis processes. Aprototypical example in the SM is the first step of nucleosynthesis, n + p → d + γ , where d is a deuteron. For symmetric dark sectors, dark nuclear capture is also possible, and ananalogous SM example would be p + d → n + γ . Generally speaking, the broad topology ofboth processes is that of so-called semi-annihilation [42–45], which has also arisen in othermodels [46–48]. We will find that the distinguishing features of dark nucleosynthesis arisefrom the small binding energies involved in these reactions ( i.e. , in the SM, M d (cid:39) M n + M p ).In the case of asymmetric DM, the conservation of dark baryon-number also leads to novelpossibilities. For symmetric and asymmetric DM, the early Universe cosmology may bealtered quite radically by dark nucleosynthesis, and in extreme cases it is possible that theinteractions are strong enough such that all the available dark nucleons may be processedinto dark nuclei through a late period of dark nucleosynthesis, much as the available SMneutrons are processed into nuclei in Big Bang Nucleosynthesis.The phenomenology of indirect detection may also be modified significantly. This ismost notable for the case of asymmetric DM. In standard asymmetric DM scenarios, in-direct detection signals are not possible unless some symmetric DM component is present.This effectively makes the indirect detection signature a feature of symmetric, rather thanasymmetric, DM. However, dark nucleosynthesis preserves dark baryon number and is thuspossible for a purely asymmetric dark sector. If the additional neutral states produced indark nucleosynthesis are observable, this leads to a novel mechanism for the indirect detec-tion of asymmetric DM. Again, this may be seen through the analogous SM nucleosynthesisprocess, n + p → d + γ . In the case of symmetric DM, the usual DM annihilation processesare possible, however the new channels of dark nucleosynthesis and dark nuclear capture maygive rise to additional signals. Furthermore, the energy scale associated with dark nucleosyn-thesis is hierarchically smaller than that of annihilation, and this may lead to complementarysignals from the same DM candidates that would have the same spatial morphology, but atvery different energy scales. Some aspects of dark nucleosynthesis have been discussed in Ref. [41] that appeared as we were concludingour study. – 2 –he phenomenology of DM capture in stars and other astrophysical bodies may alsobe significantly altered by dark nucleosynthesis. DM may become captured within stars,with a rate determined by the magnitude of the DM-nucleon scattering cross section. Ifthe DM is asymmetric, then dark nucleosynthesis may lead to indirect detection signatures,in contrast to standard asymmetric DM candidates. Furthermore, even for relatively smallbinding energy fractions, dark nucleosynthesis may result in the dark nucleus being ejectedfrom the Sun, or other bodies. This hinders the buildup of asymmetric DM within stars,leading to significantly different phenomenology from the signatures of standard asymmetricDM. In Sec. 2, we will briefly review the lattice field theory calculations which provide evi-dence for the presence of stable nuclear states in two-color, two-flavor QCD, leaving the fulltechnical details to the companion paper. In Sec. 3, we present a simplified model of thedark sector based on dark π , ρ , fields as well as dark nuclei D (for simplicity, we restrictour discussion to the lightest dark nucleus) and a dark Higgs, h D . This simple effective the-ory serves to mock-up the qualitative (though not necessarily quantitative) behavior of therelevant states and interactions, allowing for an exploration of the particle phenomenology.In Sec. 4, we solve the relevant Boltzmann equations to determine the relic abundance ofthe dark nucleons and dark nuclei for various interaction strengths for both symmetric andasymmetric DM scenarios. In Sec. 5, we explore the indirect detection signatures of themodel. In Sec. 5.1 we discuss a novel explanation of the galactic center gamma ray excessbased on dark nuclear capture. In Sec. 5.2 we present a novel paradigm for asymmetric DMindirect detection through dark-baryon number conserving nucleosynthesis reactions and webriefly sketch potential modifications of the phenomenology of DM capture in stars whicharise due to the introduction of dark nucleosynthesis, leaving detailed study to a dedicatedanalysis. We conclude in Sec. 6. In this work, we focus on a putative model for dark matter involving a strongly interactingSU( N c = 2) gauge theory with N f = 2 degenerate fermions in the fundamental representa-tion. In a companion paper, we undertake a detailed, lattice field-theoretic exploration of thespectroscopy of hadronic states that appear in this model. Importantly, we show that lightstable nuclei (systems with baryon number B ≥
2) appear even in this simple model and weextract the spectrum of the lightest few nuclei for representative values of the fermion masses.In this section, we summarize the main results that are obtained from these calculations.As will be discussed below, this model has a large set of global symmetries that constrainthe dynamics in the limit of vanishing quark masses. It is expected that the theory producesfive degenerate (pseudo-)Goldstone boson states: three mesons analogous to the usual QCDpions, and a baryon and anti-baryon which are (pseudo-)Goldstone bosons carrying baryonnumber. Ref. [29] considered the interesting possibility that dark baryon number is conservedand that dark matter is composed of the Goldstone baryon with a mass parametrically smallcompared to typical strong interactions in the theory that are set by the scale Λ N c =2 . In ournumerical investigations, we focus on a regime of the model in which explicit chiral symmetrybreaking through quark masses is dominant over the effects of dynamical chiral symmetrybreaking. This regime is characterised by having 0 . < M π /M ρ <
1, where M π and M ρ arethe masses of particle in the lightest multiplets containing pseudoscalar and vector mesons(and their baryon partners), respectively. – 3 –fter a careful analysis of the relevant correlation functions of this theory at multiplelattice spacings and multiple volumes, we are able to extract the continuum limit, infinitevolume spectrum of light nuclei for a range of relevant quark masses. While there is somevariation with the quark masses that are used, the overall picture that emerges from thesecalculations is as follows. • Spin J = 1 axial-vector nuclei with baryon number B = 2 and 3 are clearly bound, withenergies below the threshold for breakup into individual baryons. The J = 1, B = 4system is likely bound, but our results are not precise enough to be definitive in thiscase. Higher baryon number states with J = 1 are clearly above the relevant breakupthresholds and do not form bound states. • The binding energies of these systems are quite deep. Measured in units of the dark piondecay constant, f π , we find dimensionless binding energies per baryon ∆ E B /Bf π ∼ . • Spin J = 0 scalar multi-baryon systems are probably not bound states (although thesystematic uncertainties are somewhat large in this case). Baryons with higher spinand in different flavour representations have not been studied. • By performing calculations with a range of quark masses, the Feynman-Hellmann the-orem can be used to extract the σ -terms for the various hadrons that govern the cou-plings of the states of the theory to scalar currents. These couplings are found to be ofa natural size, with f ( H ) q ≡ (cid:104) H | m q qq | H (cid:105) M H ∼ . . Building upon these lattice investigation, a demonstrative model of dark nucleosynthesis isnow presented.
The field content of the model is shown in Table 1 and the Lagrangian is L = L strong − λ (cid:0) v D − H D (cid:1) − (cid:16) κH D ( u † R u L + d † L d R ) + h.c. (cid:17) . (3.1)The strong dynamics of the SU( N c = 2) sector is described implicitly within L strong andcharacterized by a scale Λ QC D . H D is a ‘dark’ Higgs boson as this model could be UVcompleted in such a way that h D is the Higgs boson remaining after spontaneous symmetry– 4 –ield Spin SU(2) L SU(2) R u L / (cid:3) u R / (cid:3) d L / (cid:3) d R / (cid:3) H D : Field content and gauge interactions of the model in the UV.breaking of a dark U(1) gauge symmetry. We assume that v D and the scalar quartic- andYukawa-interactions are sufficiently small that the resulting dark Higgs boson mass and thequark masses are below the strong coupling scale m h D (cid:46) Λ. Approaching the strong couplingscale from above, the relevant interactions are L = L strong − V ( h D ) − (cid:16) m q (1 + h D /v D )( u † R u L + d † L d R ) + h.c. (cid:17) , (3.2)which includes the SU(2) D gauge interactions. In the absence of the Yukawa terms and quarkmasses, there is an SU(2) L × SU(2) R global symmetry which is enlarged to SU(2) L × SU(2) R → SU(4) because the SU(2) D representations are pseudo-real, enabling the right-handed quarksto fall into multiplets alongside the left-handed quarks.We also include a small mixing term between the visible-sector Higgs boson and thedark Higgs boson through the Higgs portal operator | h D | | H | . The dark Higgs boson is aSM gauge singlet, hence below the scale of U(1) D breaking, this coupling mimics the usualmixing between a SM singlet scalar and the SM Higgs boson. This is introduced to enablethe dark Higgs to decay via standard Higgs boson decay channels such as h D → bb . Thereare already strong constraints on the allowed mixing angle, and we thus assume this mixingis small, below the ∼ few% level [49–52].Below the strong-coupling scale, a quark condensate forms and breaks the global sym-metry SU(4) → Sp(4) [53–55]. There are five pseudo-Goldstone bosons corresponding to thebroken generators of SU(4). They obtain mass due to the quark mass terms which break thissymmetry explicitly. Three of these pseudo-Goldstone bosons are familiar from QCD andcan be thought of as the pions ( π , π + , π − ) made up of the u- and d-quarks and anti-quarks.The other two pseudo-Goldstone bosons may be thought of as ud and ud composites carryingbaryon-number. We denote these pseudo-Goldstone bosons as π B and π B . Thus there arein total five pseudo-Goldstone degrees of freedom denoted π , π + , π − , π B , π B .As with the analogous QCD case, the Goldstone manifold for SU(4) / Sp(4) may beparameterized as Σ = U Σ c U T (3.3)where U = exp if π √ π + √ π B √ π − − π −√ π B −√ π B π √ π − √ π B √ π − − π , and Σ c = − − . (3.4)Under chiral rotations, Σ → L Σ R † (where L and R are rotations in the underlying SU(2) L,R ),or equivalently, Σ → G Σ G † where G is an SU(4) rotation. The quark mass matrix can be– 5 –ritten as M q = m q (1+ h D /v D )Σ c and may be thought of as transforming under SU(4) in thesame way as the pion field Σ. The pion masses and Higgs-pion couplings may be determinedfrom the SU(4)-invariant chiral Lagrangian L eff = f ∂ µ Σ ∂ µ Σ † − G π m q (1 + h D /v D ) Tr(Σ c Σ) , (3.5)where G π is an unknown dimensionful constant. As all pions are equally massive, they coupleto the Higgs in the same way.There are also five vector mesons which are odd under the analogue of G -parity. Sincewe choose m q comparable to the strong scale, they have similar masses to the pions. Wecontinue the analogy with QCD and denote these vector bosons ρ µ , ρ + µ , ρ − µ , ρ Bµ , ρ Bµ , with thelatter two carrying baryon number +1 and -1, respectively. The vector bosons and theirinteractions with the pseudo-Goldstone bosons are constrained by chiral symmetry. This canbe implemented in a number of ways including through the ‘heavy-field’ formalism [56–58],since the mass of these particles remains nonzero even for vanishing quark masses. Usingthis approach, we introduce ξ = √ Σ (transforming as ξ → √ R Σ L † ) and parameterize thevector boson fields as a 4 × O µ , in analogy with the pion fields.The leading interactions are parameterized with the Lagrangian L v = − i tr (cid:104) O † µ V · D O µ (cid:105) + ig V tr (cid:104) { O † µ , O ν }A λ (cid:105) v σ (cid:15) µνρσ + M V, tr (cid:104) O † µ O µ (cid:105) + λ tr (cid:104) { O † µ , O µ }M (cid:105) + λ tr (cid:104) O † µ O µ (cid:105) tr [ M ] (3.6)where M = ( ξm q ξ + ξ † m q ξ † ) and D µ O ν = ∂ µ O µ + [ V µ , O ν ] with V µ = ( ξ∂ µ ξ † + ξ † ∂ µ ξ )and A µ = i ( ξ∂ µ ξ † − ξ † ∂ µ ξ ). g V , λ and λ are unknown dimensionless couplings and M V, ∼ Λ QC D is the vector boson mass in the limit of vanishing quark masses.We will only need the lowest-order couplings of the dark Higgs to the composite bosons,and express them as L Int = A π h D (cid:16) ( π ) / π + π − + π B π B (cid:17) + A ρ h D (cid:16) ( ρ ) / ρ + ρ − + ρ B ρ B (cid:17) , (3.7)where the sum over Lorentz indices for the vector mesons is implied. This completes theinteractions necessary for the annihilation processes ππ → h D h D and ρρ → h D h D relevantfor the cosmological abundance and indirect detection signals of these states. We will takethese couplings to be free parameters in what follows, however for a specific choice of quarkmasses they could be calculated from the σ -terms discussed in Sec. 2 where it is found thatthe couplings take perturbative values of O (0 . As demonstrated through the lattice calculation, in this simple model a π boson and a ρ boson may combine to form stable two-body bound states: the dark nucleus, D . In analogyto the visible sector, we will refer to the π and ρ bosons as dark nucleons, and to the D asthe dark deuteron. These dark nuclei have mass M D = M π + M ρ − B D where B D is thebinding energy of the dark nucleus and may take a range of values. In what follows we willassume the isospin symmetric case where any of the five dark π bosons may combine with– 6 –ny of the five dark ρ bosons, leading to a total of 25 dark nuclei which may carry darkbaryon number Q B = 0 , ± , ±
2. Although the lattice calculations give specific values for thebinding energies, we do not wish to restrict ourselves to particular values of masses, bindingenergies, and coupling constants. We thus allow these to be free parameters throughout,taking the lattice values as a rough guide. We will only consider dark nuclei composed oftwo dark nucleons in order to simplify the treatment of the cosmology and indirect detectionphenomenology. The lattice calculations suggest that three- and perhaps four-body statesmay also be stable, which would enrich the phenomenology even further. Other possibileexamples of strongly interacting dynamics may produce higher-body bound states as well.Assuming m h D < B D , dark nucleosynthesis proceeds in this model via the process π + ρ → D + h D , in analogy with the first step of nucleosynthesis in the Standard Model, n + p → d + γ . As discussed in Sec. 1, the reaction π + ρ → D + h D is a semi-annihilationreaction as the number of dark matter states changes by one (stable + stable) → (stable +unstable), followed by (unstable) → (SM). In this work we call this particular realizationof semi-annihilation dark nucleosynthesis to reflect that dark nuclei are forming from darknucleons.In order to estimate the cosmological relic abundance of the dark nuclei, or the indirectdetection signals from dark nucleosynthesis, it is necessary to determine the dark nucleosyn-thesis cross section σ ( πρ → Dh D ). A full nuclear effective field theory estimation would treatthe dark nuclear scattering amplitude as an infinite sum of dark nucleon loops and determinethe corresponding propagator for the dark nucleus from this sum. Such a treatment is wellbeyond the scope of this work and instead we opt for a simplified effective field theory estima-tion which takes the rudimentary assumption of treating the dark nucleus as a fundamentalstate at energies near or below m D . Effective operators for π , ρ , and D interactions are thendetermined from the symmetry structure and dimensional analysis.In terms of the remaining Sp(4) global flavour symmetry, the π and ρ fields both livein the coset space SU(4) / Sp(4). Rather than constraining the interactions using an Sp(4)basis for the D fields, we instead utilize the local isomorphism Sp(4) ∼ = SO(5). The π and ρ bosons transform as fundamentals under the the global SO(5) symmetry. Thus the D fields, which are composites of these two fundamentals, must decompose as the tensorproduct × = + + . These SO(5) representations are at most 2-index, simplifyingthe calculation of vertices relative to the alternative Sp(4) representations. The bosons inSO(5) are real degrees of freedom and do not fall naturally into the classification of pionsand baryons discussed above. However, the two bases for these fields may be simply foundfrom the following unitary rotation π = U · π R , where the subscript R denotes a real SO(5)representation. Specifically, this relationship is π + π − π π B π B = 1 √ +1 + i − i √ i − i · π π π π π , (3.8)and similarly for the ρ mesons. The 25 real degrees of freedom in D furnish an SO(5) singlet,an antisymmetric representation, and a symmetric representation. Using the rotation ofEq. (3.8), we may relate this basis of real fields to a more intuitive basis of 5 real and 10– 7 –omplex vector fields which have varying baryon number. This representation is D µ = S µ + D µ , D µ , D µ , − D µ , D µ , S µ − D µ − , D µ − , − D µ − , D µ , D µ − , S µ D µ , − D µ , D µ , − D µ − , − D µ , − S µB D µ , D µ , D µ − , D µ , + D µ , S µB , (3.9)where all diagonal elements are real and the subscript denotes the states that the diagonalelements couple to in the notation of the pion fields. The off-diagonal elements are complexvectors for which the first subscript denotes the global U(1) D charge and the second subscriptthe dark U(1) B baryon number in the same units as the pions. In this notation the variousreal SO(5) representations may be written as D µ = Tr( D µ ) , (3.10) D µ = i (cid:0) D µ − D µT (cid:1) , (3.11) D µ = 12 (cid:0) D µ + D µT (cid:1) −
15 Tr( D µ ) . (3.12)The lattice calculation considered the nuclei in the symmetric representation, D ,finding bound states for a range of quark masses, but did not investigate the singlet or anti-symmetric representations. To simplify the calculations relevant for phenomenology, we willassume that all nuclei representations are stable and equally massive. This is purely for thesake of simplifying the phenomenology, however if it turned out that the antisymmetric repre-sent were unstable this would only result in minor modifications. There is some contributionto the mass of the dark nuclei from the masses of the constituent hadrons, and some fromtheir interactions. For the regime in which it makes sense to call D a ‘nucleus’, the bind-ing energy should be small, B D (cid:28) M π , M ρ , and the first contribution from the constituentmasses should to be dominant. Since the nuclei are ultimately built from quarks, there is acoupling to the Higgs field which we may write (under the assumption of equal masses) as L Int = 12 A D h D Tr (cid:16) D † D (cid:17) , (3.13)where again A D is taken as a free parameter of O (0 . × Λ QC D ). Also, consistent with theremaining symmetries in the real-field basis the , , and of SO(5) may couple to themesons as L ρπD ∼ π † (¯ λ D µ + ¯ λ D µ + ¯ λ D µ ) ρ µ . (3.14)The remaining symmetry does not constrain these interactions any further, however to sim-plify the calculation of annihilation and semi-annihilation cross sections we make the furtheradditional assumption that ¯ λ = ¯ λ = ¯ λ = ¯ λ , thus the coupling written in terms of thereal degrees of freedom may be simply expressed as L πρD = ¯ λ π † R · D µR · ρ µR where D R is a5 × π + ρ → D + h D , by dressing one of the external propa-gators in three-body scattering with a dark Higgs vertex. If all parameters were known,then these additional couplings and diagrams should be included in a full treatment of semi-annihilation. However, as the energy carried away by h D in the semi-annihilation process– 8 – ⇡⇢ Dh D Figure 1 : A dark nucleosynthesis event. This is realized in the model of Sec. 3 and isanalogous to the SM process n + p → D + γ . Such dark nucleosynthesis processes areimportant in early Universe cosmology as they may alter relic abundances. In the presentday they may also be relevant as they may give rise to observable indirect detection signaturesfrom the galactic center and from stars.is E h D ∼ O ( B D ) (cid:28) M π , M ρ , m D , we may integrate out these interactions to generate aneffective quartic vertex L Eff = λh D π † R · D µR · ρ µR , (3.15)where λ is taken as a free parameter assumed to be λ ∼ O (0 . λ . Thus,Eq. (3.7) and Eq. (3.13) contain all of the information relevant for annihilation, and Eq. (3.15)determines dark nucleosynthesis. The cosmology and possible experimental signatures of dark nuclei, and in particular ofdark nucleosynthesis, are rich subjects. Throughout we aim to stress the differences betweenscenarios with dark nuclei and standard dark matter models, finding that dark nuclei maypossess a very distinctive phenomenology. We will appeal to the specific model of Sec. 3 inorder to illustrate the signatures. We do this to demonstrate that explicit realizations ofthese signatures exist, and also for the pedagogical purposes of providing a familiar example.However, we emphasize that the signatures are common to the broad class of possibilitiesfor dark nuclei and are not restricted to this model. As such, the various cross sections aretaken as free parameters and, motivated by the values of the σ -terms determined from thelattice calculation, they are assumed to be σ ∼ O (0 . / πM π ). We begin by considering theearly Universe cosmology and relic abundance of a sector capable of dark nucleosynthesis. Thermal freeze-out of the coupled system involves the π and ρ nucleons and D nuclei ofSec. 3. For a symmetric DM scenario, it is useful to return to the real basis of fields. Thisis because all 5 π meson degrees of freedom are equally massive and similarly for the 5 ρ mesons and the 25 nuclei. We will also use the rotated form of the nucleus matrix such thatall of these fields are contained within a 5 × π and ρ combination in the same way. The assumed symmetry reducesthe coupled system of Boltzmann equations down from 35 individual equations to 3 as thenumber density of any π a must be equal to the number density of any other π b and so on– 9 – (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 500 100010 (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 500 100010 (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 500 100010 (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61) Figure 2 : Relic density of nucleons and nuclei in the presence of annihilations and darknucleosynthesis. Nucleon masses are M π = M ρ = 100 GeV, the dark Higgs at 10 GeV, andthe binding energy fraction δ = 0 . B = 10 GeV), thus dark nucleosynthesis occurs preciselyat threshold. The full solutions are shown as solid lines and the equilibrium values as dashedlines. The total DM abundance is shown in solid black. Even a small dark nucleosynthesiscross section may have a dramatic effect on the relic density, most notably as the nuclei mayremain in thermal equilibrium through interactions with nucleons down to the freeze-outtemperature of the lighter nucleons. Interestingly once all of the nuclei and nucleons fall outof thermal equilibrium the nucleus fraction may be repopulated at lower temperatures dueto the continued nucleosynthesis reactions.for the other fields. We thus write n π a = n π / n ρ a = n ρ / n D a = n D /
25. Also, the totalnumber of π degrees of freedom is 5, the total number of ρ degrees of freedom is 5 × × M π = M ρ .If we let ( σv ) be a free parameter describing the typical scale for scattering crosssections in the dark sector which is of order the weak scale, we may write the thermally-,– 10 –nd spin-averaged individual dark nuclear capture cross section as (cid:104) σv ( π a D b → ρ c h D ) (cid:105) = (cid:104) σv ( ρ a D b → π c h D ) (cid:105) = R N ( σv ) where the subscript denotes that this is a nuclear process. If we write the nuclear binding energy as B D = δ M π and the dark Higgs boson mass as M h D = κ M π , the dark nucleosynthesis process π a + ρ b → D c + h D is only possible atzero relative velocity if κ < δ . Even in this case, dark nucleosynthesis must occur close tothe kinematic threshold. It was shown some time ago that in determining the cosmologicalevolution of DM abundances, any near-threshold processes have distinctive features whencompared to more typical processes, such as annihilation to light states [59]. In order tosimplify the presentation of results in this section we choose κ = δ in many instances, suchthat dark nucleosynthesis may only occur exactly on threshold. We have not found an analyticsolution for the thermally averaged cross section in the most general case, and hence choose toprovide an approximate expression. For the case where δ > κ and nucleosynthesis is possibleat zero relative velocity, we calculate the standard velocity-independent cross section. Tothis, we include the thermally averaged cross section when nucleosynthesis is possible exactlyon threshold ( δ = κ ) which we calculate following Ref. [59]. The resulting expression isapproximate, however it is appropriate for the case we will usually consider with δ = κ , andhas the correct limits in the more general case. Thus we find that the thermally-averagednucleosynthesis cross section is (cid:104) σv ( π a ρ b → D c h D ) (cid:105) ≈ (cid:18)(cid:112) δ − κ + 3 √ πx (cid:18) − x (cid:19)(cid:19) R N ( σv ) = f ( x ) R N ( σv ) , (4.1)where x = M π /T , in agreement with the results of [59]. As expected, this cross section van-ishes in the zero temperature limit at threshold ( δ = κ ) and if nucleosynthesis is kinematicallyallowed ( δ > κ ) the correct limit is reached for s-wave scattering in the zero temperaturelimit. The various spin-averaged annihilation cross sections may be parameterized relativeto ( σv ) as (cid:104) σv ( π a π a → h D h D ) (cid:105) / R π ( σv ) , (cid:104) σv ( ρ a ρ a → h D h D ) (cid:105) /
15 = R ρ ( σv ) , (4.2) (cid:104) σv ( D a D a → h D h D ) (cid:105) /
75 = R D ( σv ) , where R π , R ρ and R D are simple rescaling factors introduced to allow different annihilationcross sections for the various fields. The co-moving number densities are written as Y π,ρ,D = n π,ρ,D /s , where n a is the temperature-dependent number density of a particle species and s is the temperature-dependent entropy density. The equilibrium co-moving number densitiesare defined as Y eqf and we use the parameterization λ = 5 x ( σv ) H ( M π ) (cid:12)(cid:12)(cid:12)(cid:12) x =1 . (4.3)With all of these definitions in place the set of coupled Boltzmann equations for all particle Note that this particular capture process only occurs for specific combinations of nucleons and nuclei, forexample π B + D , → ρ B + h D , while other channels are excluded. – 11 –pecies may be rearranged following standard methods [60] and are written dY π dx = − λ (cid:20) R π (cid:0) Y π − Y eqπ (cid:1) + 15 R N ( Y π Y D − Y ρ Y eqρ Y eqπ Y eqD ) (4.4) − R N ( Y ρ Y D − Y π Y eqπ Y eqρ Y eqD ) + R N f ( x )( Y π Y ρ − Y D Y eqD Y eqπ Y eqρ ) (cid:21) ,dY ρ dx = − λ (cid:20) R ρ (cid:0) Y ρ − Y eqρ (cid:1) + 15 R N ( Y ρ Y D − Y π Y eqπ Y eqρ Y eqD ) − R N ( Y π Y D − Y ρ Y eqρ Y eqπ Y eqD ) + R N f ( x )( Y ρ Y π − Y D Y eqD Y eqρ Y eqπ ) (cid:21) ,dY D dx = − λ (cid:20) R D (cid:16) Y D − Y eqD (cid:17) − R N f ( x )( Y π Y ρ − Y D Y eqD Y eqπ Y eqρ )+ 15 R N (cid:18) ( Y π + Y ρ ) Y D − (cid:18) Y ρ Y eqρ Y eqπ + Y π Y eqπ Y eqρ (cid:19) Y eqD (cid:19) (cid:21) , where the various multiplicities of the species have been taken into account. Further, inany given nucleosynthesis reaction the symmetry structure requires that only one nucleus isproduced for any particular combination of π and ρ . This can be seen clearly in the SO(5)basis. These coupled Boltzmann equations may then be solved to determine the total relicabundance of dark matter, and also the relative abundances of the dark nucleons, ρ, π , andthe dark nuclei D . The energy density in any particle relative to the critical density may bedetermined from the particle mass and the current entropy density.Fig. 2 shows some typical solutions to the Boltzmann equations. It is clear that darknucleosynthesis may have a pronounced effect on the final relic density, with the greatesteffect coming from the additional destruction of nuclei through the dark nuclear captureprocesses π a + D b → ρ c + h D . It is clarifying to break the evolution of the dark nuclei intoa number of smaller steps: • T > M π / : The number density of dark nucleons and nuclei tracks the equilibriumdensity due to efficient annihilations. • M π / < T < M π / : The dark nuclei are kept at equilibrium density below thetemperature of dark nuclei annihilation freeze out due to efficient dark nuclear captureinteractions with the dark nucleons which are themselves still efficiently annihilating.Freeze out of the dark nuclei is paused until the lighter dark nucleons freeze out, hencethe greatly suppressed number density of dark nuclei. This can be seen from Fig. 2where in cases with dark nucleosynthesis, the freeze out of the dark nuclei is pauseduntil dark nucleon freeze out. • B D / < T < M π / : In this regime, all annihilations have effectively frozen out,and the only remaining interactions are dark nucleosynthesis interactions. The possiblereaction types are nucleosynthesis, π + ρ → D + h D , and nuclear capture, D + ( π, ρ ) → h D + ( ρ, π ). The cross section for the former is suppressed due to the reduced phasespace, however the interaction rate for the latter is suppressed to a greater degree dueto the extremely small number density of dark nuclei. Hence during this era the dark There may also be capture processes such as D + ρ → ρ + h D , however these would be p-wave suppressedand thus subdominant to the s-wave processes that we consider. – 12 –uclei effectively ‘freeze in’ [61] as their number density increases exponentially whilethe total energy density in DM slowly bleeds off through dark nucleosynthesis. • T < B D / : In this era all reactions, including dark nucleosynthesis, have effectivelyfrozen out and the number density of all species is now fixedThis completes our discussion of cosmological evolution of the symmetric scenario fordark nuclei. We now consider more directly the analogy with standard nucleosynthesis and consider anasymmetric DM (ADM) scenario. Recent years have seen a resurgence in the study of ADM[13, 14, 62–75], and this has led to the realization of a large number of models which maygenerate a DM asymmetry through a variety of mechanisms. Thus there are many plausiblescenarios in which an asymmetry may be generated in the dark sector. In this work, wewill focus on heavy asymmetric DM [78, 79] which is a complementary scenario to the usual M ∼ M ∼ n π B (cid:29) n π B . Also, for the sakeof simplicity we will assume that the only relevant fields are the dark Higgs h D , the darkbaryon-number carrying mesons π B , π B , ρ B , ρ B and the dark baryon-number charge 2 fields D B , and D B (note the change in notation for convenience). It may be possible to realizethis in a full scenario as an appropriate splitting between quark masses may explicitly breakthe global SU(4) symmetry sufficiently that M π ± (cid:29) M π , M π B,B . In turn, this makes allnuclei containing M π ± heavy as well. As the π field is neutral under the remaining globalsymmetries we may introduce new decay channels for this field, hence the dominant DM phe-nomenology may be determined by considering only the dark baryon-number 1 nucleons anddark baryon-number 2 nuclei. However, we have chosen to make this assumption primarilyto simplify the treatment of the phenomenology.In order for the relic abundance to be dominated by an asymmetry, the annihilationcross-section for all states must exceed the thermal relic annihilation cross section which,given that the dark sector is strongly coupled, seems plausible. In this case, the relic abun-dance of the symmetric component is suppressed by a factor ∼ exp( σ Ann /σ Th ) where the lat-ter is the standard thermal DM cross section [80]. This is a result of continued annihilationswith the asymmetric component. With the symmetric DM component mostly annihilatedaway, the dominant component of DM is comprised of the baryon-number carrying statesshown in Table 2. State π B ρ B D B Dark Baryon Number +1 +1 +2
Table 2 : Relic DM states carrying dark baryon-number in the asymmetric scenario.If we consider the production of an asymmetry in dark baryon number in the earlyUniverse, then at later times this asymmetry may be understood by considering the chemicalpotential for dark baryon number µ D . If the dark nucleosynthesis interactions π B + ρ B → See [76, 77] for recent reviews. – 13 – (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 500 100010 (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 500 100010 (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 500 100010 (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61) Figure 3 : Relic density of dark nucleons and nuclei in the presence of annihilations and darknucleosynthesis for the case of asymmetric DM. Nucleon masses are M π = M ρ = 100 GeV, thedark Higgs at 10 GeV, and the binding energy fraction δ = 0 .
1, thus dark nucleosynthesisoccurs precisely at threshold. The dark baryon densities are shown as full lines and theanitbaryon densities as dashed lines. The total DM abundance is shown in solid black. Onceagain, dark nucleosynthesis may have a pronounced effect on the relic density of the variousspecies. Many of the features, including the timeline of the various freeze-out epochs, aresimilar to the symmetric DM case. However, due to the preservation of the asymmetrylarger dark nucleosynthesis cross sections may be tolerated while maintaining the observedDM abundance, and in this case the majority of available dark nucleons may be processedinto dark nuclei. D B + h D are efficient, then we obtain the relationship between chemical potentials µ π + µ ρ = µ D . Similarly, we will assume that at high temperatures around the strong coupling scalewe would have µ π = µ ρ , however it is not possible to determine the full details of chemicalequilibrium in practice at these scales without evolving through the strong coupling scale.Before considering the Boltzmann equations, it is illuminating to consider general fea-– 14 –ures of dark nucleosynthesis in the asymmetric case. If we specify the number densities ofthe various DM species relative to the number density of photons as η a = n a /n γ , we mayrelate the total asymmetric dark number density to the cosmological abundance of DM bytaking the ratio of the known baryon asymmetry and baryon abundance η N D = η π + η ρ + 2 η D ≈ . × − × (cid:18) Ω DM h Ω B h M H M π (cid:19) , (4.5)where M H is the mass of hydrogen. From this, denoting the fractional asymmetry in a givenspecies as X a = Q B a n a / ( n π + n ρ + 2 n D ), we have the fractional asymmetry carried in darknuclei X D = 13 X π η N D (cid:18) − B D M π (cid:19) / (cid:18) πM π T (cid:19) / exp B D /T . (4.6)For temperatures well above the binding energy, T (cid:38) B D , the exponential is small and X D (cid:28) X π . However, if chemical equilibrium is maintained to temperatures T (cid:28) B D suchthat the exponential overcomes the small value of the asymmetry in either π or ρ , which is η N D ∼ O (10 − ), then the majority of the asymmetric component will actually be carried inthe dark nuclei. In fact, this is already familiar from nucleosynthesis in the SM where thestrong interactions maintain chemical equilibrium to temperatures well below the bindingenergy of helium and all available neutrons are processed into nuclei. However, if the darknucleosynthesis interactions freeze out at temperatures close to, or even a factor of a fewbelow the binding energy, then the dominant asymmetry will remain tied up in the π and ρ nucleons. Thus, already from Eq. (4.6), it is clear that the final asymmetry carried in darknuclei may vary greater from being a tiny fraction up to the dominant component, dependingprecisely on when the dark nucleosynthesis interactions freeze out.In order to study this scenario quantitatively, it is necessary to solve the Boltzmannequations. In total there are six equations, one for the each baryon and anti-baryon out ofeach nucleon π and ρ and the nuclei D . These equations may be found directly from theBoltzmann equations of Eq. (4.5) by dressing these equations with a label for whether eachspecies carries positive or negative dark baryon number. In this instance it is crucial toensure that baryon number is conserved in each interaction, i.e. Y π → Y π B Y π B etc. For the π and ρ carrying positive dark baryon number, we have dY π B dx = − λ (cid:20) R π (cid:16) Y π B Y π B − Y eqπ B Y eqπ B (cid:17) + R N (cid:32) Y π B Y D B − Y ρ B Y eqρ B Y eqπ B Y eqD B (cid:33) (4.7) − R N (cid:32) Y ρ B Y D B − Y π B Y eqπ B Y eqρ B Y eqD B (cid:33) + R N f ( x ) (cid:32) Y π B Y ρ B − Y D B Y eqD B Y eqπ B Y eqρ B (cid:33) (cid:21) ,dY ρ B dx = − λ (cid:20) R ρ (cid:16) Y ρ B Y ρ B − Y eqρ B Y eqρ B (cid:17) + R N (cid:32) Y ρ B Y D B − Y π B Y eqπ B Y eqρ B Y eqD B (cid:33) (4.8) − R N (cid:32) Y π B Y D B − Y ρ B Y eqρ B Y eqπ B Y eqD B (cid:33) + R N f ( x ) (cid:32) Y π B Y ρ B − Y D B Y eqD B Y eqπ B Y eqρ B (cid:33) (cid:21) , (4.9)– 15 –nd for the dark nucleus dY D B dx = − λ (cid:20) R D (cid:16) Y D B Y D B − Y eqD B Y eqD B (cid:17) − R N f ( x ) (cid:32) Y π B Y ρ B − Y D B Y eqD B Y eqπ B Y eqρ B (cid:33) + R N (cid:32)(cid:16) Y π B + Y ρ B (cid:17) Y D B − (cid:32) Y ρ B Y eqρ B Y eqπ B + Y π B Y eqπ B Y eqρ B (cid:33) Y eqD B (cid:33) (cid:21) . For the species carrying anti-baryon number, the equations are identical with the exceptionof the replacement B ↔ B . Considering all six Boltzmann equations and taking the sum Y B = Y π B + Y ρ B + 2 Y D B and then by taking the difference Y η = Y B − Y B , it is also clear thatthe dark asymmetry is constant dY η /dx = 0, as expected.In Fig. 3, we show the evolution of the DM abundances in the presence of an asymmetrywhere we have set the chemical potential in order to generate the observed DM abundance ineach case. As with the symmetric case, dark nuclear capture and dark nucleosynthesis maysignificantly alter the relic abundance of both the nucleons and the nuclei. In particular, inthe presence of a large dark nucleosynthesis cross section all of the dark π -mesons may beprocessed into dark nuclei, leaving only the dark ρ -mesons and dark nuclei as the dominantconstituents. As there are three ρ degrees of freedom for every π degree of freedom, onceall of the pions are processed into dark nuclei some dark ρ mesons remain. If they hadequal numbers of degrees of freedom, it would be possible for all of the dark nucleons to beprocessed, leaving only dark nuclei. This picture is in some ways familiar from the SM wheremost of the neutrons are processed into nuclei during Big Bang nucleosynthesis, leaving onlyprotons and nuclei. We will first depart from committing to the specific model of Sec. 3 and instead considerthe indirect detection possibilities of dark nucleosynthesis broadly. In generic scenarios, darknucleosynthesis may occur via processes such as n n,a + n n,b → N D,c + X where n n is a darknucleon, N D is a dark nucleus and X is some other state. If X is a SM state, or if it may decayto SM states, then dark nucleosynthesis occurring presently in DM halos may be observablethrough the contribution of X to the cosmic ray spectrum. Considering a particular SM finalstate SM , the spectrum generated in dark nucleosynthesis may be determined from d Φ d Ω dE γ = 18 π βγ ζ J ( θ ) (cid:90) E SM /γ (1 − β ) E SM /γ (1+ β ) d (cid:101) E SM (cid:101) E SM dNd (cid:101) E SM (cid:12)(cid:12)(cid:12)(cid:12) X , (5.1)where J ( θ ) is the line-of-sight integral over the DM density-squared and dN/dE SM | X is thespectrum of SM states obtained from X in the rest frame of X , either from X directly or fromits decays. In Eq. (5.1), γ and β are Lorentz factors associated with the fact that X is typicallyproduced with non-zero speed and the integral accommodates the modification of the rest-frame spectrum due to the boosting. Specifically, for the process n n,a + n n,b → N D,c + X these factors are given by γ = ( M a + M b ) − M c + M X M a + M b ) M X , β = (cid:114) − γ . (5.2)– 16 – is a factor which is equivalent to ζ Ann = 2 (cid:104) σv (cid:105) /M DM in the case of DM annihilation wherethe extra factor of 2 arises as two X states are produced. In the general case includingannihilations and dark nucleosynthesis, this is modified to ζ = κ A (cid:88) a,b,c f a f b M a M b (cid:104) σv (cid:105) ( n n,a + n n,b → N D,c + X ) , (5.3)where κ A = 1 for dark nucleosynthesis instead of the usual κ A = 2 for annihilation. f a isthe fraction of the DM energy density made up by species a and (cid:104) σv (cid:105) is the thermally-, andspin-averaged cross section and velocity.If the DM abundance is symmetric, then in general one would also expect nucleonannihilation signatures from processes such as n n,a + n n,a → X + X and also nuclei annihilationprocess N D,a + N D,a → X + X . In addition, there could be dark nuclear capture signatures n n,a + N D,b → n n,c + X . If the nucleon mass is M n the nucleus mass is M N = 2 M n − B D where B D (cid:28) M n is the nuclear binding energy. This provides the main ‘smoking gun’ signature ofdark nucleosynthesis which is that in dark nucleosynthesis the energy carried away by X is E X ∼ O ( B D (cid:28) M n ), however in annihilation or dark nuclear capture the energy carried awayis E X ∼ O ( M n ). Thus, if an excess of gamma rays were observed which may be attributedto dark nucleosynthesis (annihilation or capture), then an excess due to the annihilationor capture (dark nucleosynthesis) should also be observable at higher (lower) energies withexactly the same spatial morphology. Whether or not the other excess is observable dependson both the typical energy scales, and model parameters such as the relative cross sectionsfor dark nucleosynthesis and annihilation.If the DM abundance is asymmetric, then we are also led to a novel feature of darknucleosynthesis: in asymmetric DM scenarios it is typically assumed that indirect signa-tures of DM annihilation cannot be accommodated unless some symmetric DM componentis present in the halo. However, in the case of dark nucleosynthesis if the DM abundance iscompletely asymmetric then indirect signatures of dark nucleosynthesis are possible and thisleads to a novel, and well-motivated, mechanism for generating indirect detection signaturesfrom asymmetric DM. Specifically, dark baryon number may be conserved in the reaction n n,a + n n,b → N D,c + X , allowing for indirect signatures from asymmetric DM without theneed for a symmetric component. Having discussed the broad indirect detection features of dark nucleosynthesis, we will nowshow the utility of this process by entertaining the possibility that the gamma ray excess atthe galactic center is due to DM [81–89], specifically considering an interpretation in terms ofdark nucleosynthesis or capture. With regard to dark sector-SM interactions, we envisagethe model of Sec. 3 in which X is a light singlet scalar with a small mixing with the SM Higgsboson, identified previously as a dark Higgs h D . For masses M h D > m b and M h D < m W the dominant decay mode of the dark Higgs will be to a pair of b -quarks.To fit the spectrum, we employ the prompt gamma ray spectrum from b -quarks obtainedin Ref. [92]. We calculate the J -factor for the best-fit NFW [94] profile of Ref. [81] with It should be noted that plausible interpretations based on SM physics have also been suggested [90, 91],and thus we use this DM hint as an interesting scenario with which to demonstrate the possible indirectdetection signatures of dark nuclei, but not as the main motivation for this work. We do not include final-state effects such as bremsstrahlung for this analysis, but note that these effectsmay lead to small quantitative changes to the spectrum [93]. – 17 – .5 1.0 5.0 10.0 50.0 (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) (cid:180) (cid:45) E Γ (cid:64) GeV (cid:68) E d N (cid:144) d E (cid:72) G e V (cid:144) c m (cid:144) s (cid:144) s r (cid:76) Γ(cid:61) h D (cid:61)
16 GeV
Ζ (cid:61) (cid:180) (cid:45) cm (cid:144) s (cid:144) GeV Figure 4 : DM parameters which allow an interpretation of the galactic center gamma rayexcess. The red data points show the excess extracted in Ref. [81] and the black line is thespectrum from boosted h D decays. The possible realization of these parameters in specificmodels is discussed in the text.scale-radius r S = 20 kpc, and choose the overall density parameter such that the local DMdensity at 8 . . − . We also choose the NFW profile parameter γ = 1 . θ = 5 ◦ and we find J (5 ◦ ) = 6 . × GeV cm − . There are many parameter choices which may give a reasonable fit to thedata and in Fig. 4 we show one parameter choice allowing a good fit to the data where M h D = 16 GeV and the dark Higgs is produced at a boost of γ = 2 .
8. This explanationrequires ζ = 2 . × − cm s − GeV − , providing a target for an interpretation of thisexcess. However, it is worth emphasizing that all of these numbers may change with differentchoices of local DM density, halo profiles, different template fitting procedures to extract thegamma ray excess, and also with different SM final states, thus it should be kept in mindthat the required parameters are a good qualitative guide but are subject to a number ofuncertainties. If the DM is symmetric, then it is possible for indirect detection signals to arise in a number ofways. The first, and very well known, possibility is for DM annihilations. In this context, thegamma ray excess in the galactic center may be easily accommodated through the annihilationof nucleons, or nuclei, of mass ∼
45 GeV into pairs of dark Higgs bosons which eventuallydecay to bb pairs. As this scenario is very well known we will not dwell on it any further.Another scenario, which has not been considered previously, is relevant if a symmetriccomponent of dark nuclei is regenerated in the early Universe as in Fig. 2. In this case, itis possible for indirect detection signals to arise through dark nuclear capture processes suchas π a + D b → ρ c + h D , followed by h D → bb . In this case the dark nucleosynthesis processis critically important, both for regenerating the dark nuclei in the early Universe and alsofor the capture which leads to potential signals. Some of the indirect detection signaturespossible in this scenario are depicted in Fig. 6 and their associated energy scales are given in– 18 – (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 200 500 10000.0010.010.11 m Π T Ζ (cid:64) (cid:45) c m s (cid:45) G e V (cid:45) (cid:68) Figure 5 : Evolution of cosmological relic DM densities (left panel) and the ζ -factor forindirect detection defined in Eq. (5.3) (right panel). This is a particular parameter choicewhich gives rise to the galactic center gamma ray excess from dark nucleus destructionprocesses occurring in the center of the galaxy. The full solutions are shown as solid linesand the equilibrium values as dashed lines.Table 3.In Fig. 5, we consider a scenario that is motivated by the model of Sec. 3. The nucleonmasses are both taken to be M π = M ρ = 40 GeV. The dark Higgs mass is M h D = 16 GeV andwe allow for dark nucleosynthesis only at the kinematic threshold such that δ = M h D /M π . The masses are chosen such that in dark nuclear capture the dark Higgs bosons are producedwith a boost factor of 2 .
8, as desired.In Fig. 5, we show the additional parameters of the model. In the left panel it is shownthat the observed relic density may be achieved for these parameters, and in the right panelthe ζ -factor for indirect detection is shown. From this we see that the ζ -factor is too low byapproximately a factor of four, however (as argued in Ref. [95], for example) specific choicesabout the form of the halo lead to the required value of ζ = 2 . × − cm s − GeV and thusa different choice of DM halo profile, particularly in the center of the galaxy, could accountfor this additional factor of four. Other final states could also be considered, which mayaccommodate smaller cross sections.Thus we see that nuclear processes in a symmetric dark sector may lead to a novelcosmology and a novel interpretation of the galactic center gamma ray excess. Furthermorein this scenario additional, but greatly subdominant, nucleon and nucleus annihilation sig-natures would also be present with greater boost factors ( O (3 . This binding energy is quite large, of O (40%) the nucleon mass and may thus not lie strictly withinthe confines of the SU(2) model, however in this section we wish to explore general possibilities for darknucleosynthesis and choose this binding such that the on-threshold Boltzmann equations of Sec. 4.1 may beused. – 19 – ⇡⇢ Dh D ⇢⇢ h D h D h D h D ⇡⇡ ⇡⇢ Dh D ⇢⇢ h D h D h D h D ⇡⇡ ⇡⇢ Dh D ⇢⇢ h D h D h D h D ⇡⇡ Figure 6 : Annihilation and dark nucleosynthesis processes leading to indirect detectionsignatures of symmetric DM. Rearrangements of the final diagram involving dark nuclearcapture D + ( π, ρ ) → h D + ( ρ, π ) are also possible. ⇡⇢ Dh D ⇢⇢ h D h D h D h D ⇡⇡ ⇡⇢ Dh D ⇢⇢ h D h D h D h D ⇡⇡ ⇡⇢ Dh D ⇢⇢ h D h D h D h D ⇡⇡ Figure 7 : Indirect detection signatures of asymmetric DM. Rearrangements of the finaldiagram involving dark nuclear destruction D + π, ρ → h D + ρ, π are not possible due to darkbaryon number conservation. The diagrams with crosses are forbidden in asymmetric DMscenarios, however dark nucleosynthesis is still possible.Signature Collider Direct Detection Annihilation Nucleosynthesis CaptureSym-DM M, M M, M M, M E (cid:28)
M M
Asym-DM M, M M, M — E (cid:28) M — Table 3 : Typical energy scales associated with symmetric and asymmetric DM signatures,where the mass M denotes the typical nucleon mass. Unlike symmetric DM, annihilationsignals are absent for purely asymmetric DM, however indirect signals may still arise for darknucleosynthesis in this model, or more general multi-component asymmetric DM models. An interesting feature which is raised by (but not restricted to) dark nucleosynthesis is thepossibility of indirect signals of purely asymmetric dark matter. In single-component modelsof purely asymmetric dark matter it has long been known that indirect detection signalsare not possible as annihilation of thermal relics is not compatible with a conserved globalU(1) symmetry in the dark sector. Some authors have considered annihilations involvinga small relic, or regenerated, symmetric DM component, but this is not possible in strictlyasymmetric DM scenarios [96–100].However, if the dark sector involves more than one stable state it is possible to haveindirect detection signals for purely asymmetric dark matter while conserving the global DMsymmetry. A classic analogue of this arises in the SM where the nucleosynthesis process n + p → D + γ conserves baryon number. Following this analogy, in ADM scenarios suchprocesses may still be observable in the current epoch, raising the intriguing possibilityof indirect detection signals from a fully asymmetric dark sector. In the specific model– 20 – (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) m Π T (cid:87) h ΡΠ D (cid:72) Σ v (cid:76) (cid:61) (cid:180) (cid:45) cm (cid:144) s R N (cid:61) R Π (cid:61) R Ρ (cid:61) R D (cid:61)
20 50 100 200 500 10000.0010.010.11 m Π T Ζ (cid:64) (cid:45) c m s (cid:45) G e V (cid:45) (cid:68) Figure 8 : Evolution of cosmological relic DM densities (left panel) and the ζ -factor forindirect detection defined in Eq. (5.3) (right panel) for asymmetric DM. This is a particularparameter choice aimed at explaining the galactic center gamma ray excess from dark nucleusdestruction processes occurring in the center of the galaxy. In the left panel the dark baryonsare shown as solid lines and dark anti-baryons as dashed lines. The right panel demonstratesthat within this model for these chosen parameters an explanation of the galactic centerexcess based on dark nucleosynthesis is unlikely.considered here, the analogous process is π B + ρ B → D B + h D . In this section, we willstudy possible signals from this process, however it should be emphasized that these signalsare possible in a great variety of asymmetric DM models and are not restricted to nuclearor composite DM. The full range of possibilities is deserving of a dedicated study and herewe just consider a variant of the dark nuclear model of Sec. 3. Indirect detection signaturespossible in this scenario are depicted in Fig. 7 and their associated energy scales are given inTable 3. For the sake of simplicity, we will consider the same asymmetric DM model of Sec. 3 wherethe only states are the dark baryon number carrying states π B , ρ B , and the dark nucleus D B which carries dark baryon number two. Attempting to explain the gamma ray excess as inSec. 5.1.1, we choose the same parameters as before, with m h D = 16 GeV and boost factor γ = 2 .
8. Assuming heavy DM, M π = M ρ = 250 GeV, then the correct boost factor may beachieved with a nuclear binding energy fraction of δ ≈ . π B have been processed into nuclei by the time the evolutionstabilizes. In the right hand plot, we show the ζ -factor relevant for the galactic gamma rayexcess. For this case, we see that this factor is too small by two orders of magnitude. Thisis due to a number of factors. First, the total energy released in dark nucleosynthesis is thebinding energy which is B D = δ M π (cid:28) M π . To boost a 16 GeV dark Higgs by a sufficientamount while keeping the binding energy fraction small enough to identify D B as a bound– 21 –tate of two nucleons requires relatively heavy DM, M π (cid:29) m h D . Since the number density isinversely proportional to the square of this number, this significantly suppresses the signal.Second, for the asymmetric DM scenario, the dark nucleosynthesis cross section may not betaken arbitrarily large as then all of the available π B mesons will be processed into nuclei inthe early Universe and too few π B will remain in the current epoch to nucleosynthesize andgenerate the observed gamma ray excess.Overall, it seems that within the confines of this simplest version of a dark nuclei model,an explanation of the galactic center gamma ray excess appears difficult for an asymmetricDM scenario with dark nucleosynthesis. It should be emphasized that this is only within thisspecific model and an asymmetric DM interpretation is not precluded on general grounds.It would be interesting to explore this scenario by considering other halo profiles and/or SMfinal states. Indeed, this example demonstrates that dark nucleosynthesis allows for indirectsignals of asymmetric DM even in the absence of any symmetric DM component. If DM scatters on SM nucleons, it may become captured in astrophysical hosts, such asplanets, stars such as the Sun [101–109], neutron stars and white dwarfs [110–112]. In thecontext of asymmetric DM, it is assumed that because of the lack of DM annihilations,the abundance of asymmetric DM will gradually build up in these objects and eventuallyalter their properties [113–119], in some cases quite spectacularly through modifications ofhelioseismology or even the premature gravitational collapse of neutron stars. However, ifthe possibility of dark nucleosynthesis is introduced, the phenomenology of asymmetric DMcapture may be altered radically. We leave a full quantitative study to future work and onlydiscuss potential qualitative signatures here.If they scatter on SM nucleons, dark nucleons and nuclei would steadily build up withina star as in standard DM models. However, unlike standard asymmetric DM scenarios, darknucleosynthesis would also occur within the star due to the increasing density of DM. Inthis case, dark nucleosynthesis may lead to observable indirect detection signatures from theEarth or the Sun if the neutral dark nucleosynthesis final states include SM particles thatcan subsequently produce observable neutrinos through decay or rescattering, as depicted inFig. 9. This is not possible for standard asymmetric DM candidates.Another interesting feature of dark nucleosynthesis is that even for very small bindingenergies, the produced dark nuclei may have a semi-relativistic velocity allowing it to escapethe astrophysical host. In general, this occurs for β > β
Escape . For dark nucleosynthesiswith binding fraction δ and with a massless neutral final state particle, the outgoing speedof the nucleus is β ≈ δ/
2, thus for a binding energy fraction δ (cid:38) .
01, the dark nucleuswould be ejected from the Sun by dark nucleosynthesis. Dark matter ejection due to darknucleosynthesis could thus have a significant effect as the usual build up of asymmetric DMmay be obstructed. For the Sun, the expected modifications of helioseismology may bereduced. For more compact objects, the build up of a large DM component would be slowed,or even avoided, due to the steady ejection of DM from the star. Furthermore, it maybe possible to search for these ejected dark nuclei in Earth-based laboratory experimentsby searching for neutral-current scattering events in low-background detectors where thescattering energy is at an energy scale of E ∼ δM DM and the incoming dark nucleus pointstowards the Sun or the center of the Earth. This signature would motivate similar searchesas recently proposed in [120, 121], however at potentially lower energy scales.– 22 – ⇡ D ⇡ D ⌫⇡ D D D ⇢ D Figure 9 : Capture of asymmetric DM in astrophysical bodies such as planets, the Sun,white dwarfs, and neutron stars (left panel). Dark nucleosynthesis in these astrophysicalbodies is catalyzed by the enhanced density of DM (right panel). Dark nucleosynthesis maylead to observable signatures if the end-products produce neutrinos either through decay orrescattering. Even if the binding energy fraction is small, the produced dark nucleus maybe ejected from the astrophysical body because the resulting semi-relativistic velocity of thedark nucleus would typically be greater than the escape velocity. This may drastically alterthe phenomenology of asymmetric DM capture in comparison to standard asymmetric DMmodels, and the ejected dark nuclei could be searched for in new laboratory experiments.There is also a very pleasing synergy between DM and the visible sector in this case asthe capture of asymmetric DM in stars leads to the dark nucleons being processed into darknuclei, in a tenuous analogy with the processes which occur in the visible sector. If thereare additional dark nuclei with larger dark baryon number, further dark nucleosynthesis mayalso occur, processing the dark nucleons into more massive dark nuclei. In essence, thestar would lead to a co-located dark protostar, burning dark nucleons into dark nuclei. Allof these features require a detailed study for a full exploration of the capture and ejectionprocesses, and a dedicated study of the experimental requirements for detecting the ejecteddark nuclei is also required. However, our brief discussion is suggestive of a very rich andnovel phenomenology which could lead to experimental signatures significantly different fromthose expected of standard DM candidates.
To ensure that possible experimental signatures of DM are not missed, it is crucial to considerthe broad scope of possible realizations of DM, in addition to the more well-studied DMcandidates. From a theoretical perspective, the possibility of dark nuclear physics is wellmotivated. In fact, in the two strongly-coupled theories for which nuclear states have beenstudied, the SM and two-color two-flavor QCD, nuclei are seen to exist. For QCD, nucleihave also been shown to occur for heavier-than-physical quark masses [38–40]. As far asquantitatively studied strongly-coupled composites are concerned, this hints towards theubiquity of nuclei. Thus, if DM consists of composites of a strongly coupled gauge sector,then it is very possible that there is an entire dark nuclear sector.In this work, motivated by the lattice results to be presented in a companion paper, andby analogy with the SM, some aspects of dark nuclear phenomenology have been explored.For symmetric and asymmetric DM, it is possible that the abundance may be composed of– 23 – range of admixtures of dark nucleons and dark nuclei. New indirect detection possibilitieshave been found, and an illustrative explanation of the galactic center gamma ray excessbased on dark nuclear capture has been presented. For asymmetric DM, the consequences ofdark nuclei are striking. Dark nucleosynthesis accommodates indirect detection signaturesof asymmetric DM, even for a vanishing symmetric component. This opens new avenues forasymmetric DM model building.The phenomenology of DM capture in astrophysical bodies may also be significantlymodified. Not only are indirect detection signals of captured asymmetric DM possible, butdark nucleosynthesis may also radically alter the process of capture. Even for small bindingenergy fractions, dark nucleosynthesis may lead to the ejection of asymmetric dark nucleifrom stars, suppressing the build up asymmetric DM in these objects. There is also possiblyan attractive synergy between the dark and visible sectors in which visible stars essentiallycatalyze the production of dark nuclei.By touching upon the broad phenomenological features of dark nuclei, important de-partures from the standard signatures of DM have been demonstrated, particularly for thescenario of asymmetric DM. It has also been argued that dark nuclear physics is a well-motivated consideration for the dark sector. It would be interesting to map out furtherpossibilities by considering different models, particularly with guidance from lattice fieldtheory methods, which may exhibit different confining gauge symmetries, different globalsymmetry breaking patterns, different flavor symmetries, and also heavier nuclei. It wouldalso be interesting to study more broadly the early Universe cosmology, indirect detection,solar capture, and direct detection possibilities. Our current studies suggest that the generalphenomenology of dark nuclei is rich.
Acknowledgments
We thank Timothy Cohen, Patrick Fox, Michael Ramsey-Musolf, Jesse Thaler, Martin Sav-age, Brian Shuve, Tracey Slatyer, James Unwin, Neal Weiner and the participants of theKITP ‘Particlegenesis’ program for useful conversations. M.M. is grateful for the hospitalityof the KITP during the completion of this work and is supported by a Simons Postdoc-toral Fellowship, W.D by a US Department of Energy Early Career Research Award DE-SC0010495 and the Solomon Buchsbaum Fund at MIT and AVP by Department of Energygrant DE-FG02-94ER40818.
References [1] D. Spier Moreira Alves, S. R. Behbahani, P. Schuster, and J. G. Wacker,
The Cosmology ofComposite Inelastic Dark Matter , JHEP (2010) 113, [ arXiv:1003.4729 ].[2] S. R. Behbahani, M. Jankowiak, T. Rube, and J. G. Wacker,
Nearly Supersymmetric DarkAtoms , Adv.High Energy Phys. (2011) 709492, [ arXiv:1009.3523 ].[3] D. E. Kaplan, G. Z. Krnjaic, K. R. Rehermann, and C. M. Wells,
Dark Atoms: Asymmetryand Direct Detection , JCAP (2011) 011, [ arXiv:1105.2073 ].[4] K. Kumar, A. Menon, and T. M. Tait,
Magnetic Fluffy Dark Matter , JHEP (2012) 131,[ arXiv:1111.2336 ].[5] M. Y. Khlopov,
Physics of Dark Matter in the Light of Dark Atoms , Mod.Phys.Lett.
A26 (2011) 2823–2839, [ arXiv:1111.2838 ]. – 24 –
6] J. M. Cline, Z. Liu, and W. Xue,
Millicharged Atomic Dark Matter , Phys.Rev.
D85 (2012)101302, [ arXiv:1201.4858 ].[7] F.-Y. Cyr-Racine and K. Sigurdson,
Cosmology of atomic dark matter , Phys.Rev.
D87 (2013),no. 10 103515, [ arXiv:1209.5752 ].[8] J. Fan, A. Katz, L. Randall, and M. Reece,
Double-Disk Dark Matter , Phys.Dark Univ. (2013) 139–156, [ arXiv:1303.1521 ].[9] J. Fan, A. Katz, L. Randall, and M. Reece, Dark-Disk Universe , Phys.Rev.Lett. (2013),no. 21 211302, [ arXiv:1303.3271 ].[10] M. McCullough and L. Randall,
Exothermic Double-Disk Dark Matter , JCAP (2013)058, [ arXiv:1307.4095 ].[11] J. M. Cline, Z. Liu, G. Moore, and W. Xue,
Scattering properties of dark atoms andmolecules , Phys.Rev.
D89 (2014) 043514, [ arXiv:1311.6468 ].[12] K. Belotsky, M. Khlopov, C. Kouvaris, and M. Laletin,
Decaying Dark Atom constituents andcosmic positron excess , Adv.High Energy Phys. (2014) 214258, [ arXiv:1403.1212 ].[13] S. Nussinov,
TECHNOCOSMOLOGY: COULD A TECHNIBARYON EXCESS PROVIDE A’NATURAL’ MISSING MASS CANDIDATE? , Phys.Lett.
B165 (1985) 55.[14] S. M. Barr, R. S. Chivukula, and E. Farhi,
Electroweak Fermion Number Violation and theProduction of Stable Particles in the Early Universe , Phys.Lett.
B241 (1990) 387–391.[15] M. Y. Khlopov,
Composite dark matter from 4th generation , Pisma Zh.Eksp.Teor.Fiz. (2006) 3–6, [ astro-ph/0511796 ].[16] S. B. Gudnason, C. Kouvaris, and F. Sannino, Towards working technicolor: Effective theoriesand dark matter , Phys.Rev.
D73 (2006) 115003, [ hep-ph/0603014 ].[17] S. B. Gudnason, C. Kouvaris, and F. Sannino,
Dark Matter from new Technicolor Theories , Phys.Rev.
D74 (2006) 095008, [ hep-ph/0608055 ].[18] M. Y. Khlopov and C. Kouvaris,
Composite dark matter from a model with composite Higgsboson , Phys.Rev.
D78 (2008) 065040, [ arXiv:0806.1191 ].[19] T. A. Ryttov and F. Sannino,
Ultra Minimal Technicolor and its Dark Matter TIMP , Phys.Rev.
D78 (2008) 115010, [ arXiv:0809.0713 ].[20] R. Foadi, M. T. Frandsen, and F. Sannino,
Technicolor Dark Matter , Phys.Rev.
D80 (2009)037702, [ arXiv:0812.3406 ].[21] D. S. Alves, S. R. Behbahani, P. Schuster, and J. G. Wacker,
Composite Inelastic DarkMatter , Phys.Lett.
B692 (2010) 323–326, [ arXiv:0903.3945 ].[22] J. Mardon, Y. Nomura, and J. Thaler,
Cosmic Signals from the Hidden Sector , Phys.Rev.
D80 (2009) 035013, [ arXiv:0905.3749 ].[23] G. D. Kribs, T. S. Roy, J. Terning, and K. M. Zurek,
Quirky Composite Dark Matter , Phys.Rev.
D81 (2010) 095001, [ arXiv:0909.2034 ].[24] M. T. Frandsen and F. Sannino, iTIMP: isotriplet Technicolor Interacting Massive Particle asDark Matter , Phys.Rev.
D81 (2010) 097704, [ arXiv:0911.1570 ].[25] M. Lisanti and J. G. Wacker,
Parity Violation in Composite Inelastic Dark Matter Models , Phys.Rev.
D82 (2010) 055023, [ arXiv:0911.4483 ].[26] M. Y. Khlopov, A. G. Mayorov, and E. Y. Soldatov,
Composite Dark Matter and Puzzles ofDark Matter Searches , Int.J.Mod.Phys.
D19 (2010) 1385–1395, [ arXiv:1003.1144 ].[27] A. Belyaev, M. T. Frandsen, S. Sarkar, and F. Sannino,
Mixed dark matter from technicolor , Phys.Rev.
D83 (2011) 015007, [ arXiv:1007.4839 ]. – 25 –
28] R. Lewis, C. Pica, and F. Sannino,
Light Asymmetric Dark Matter on the Lattice: SU(2)Technicolor with Two Fundamental Flavors , Phys.Rev.
D85 (2012) 014504,[ arXiv:1109.3513 ].[29] M. R. Buckley and E. T. Neil,
Thermal Dark Matter from a Confining Sector , Phys.Rev.
D87 (2013), no. 4 043510, [ arXiv:1209.6054 ].[30] A. Hietanen, C. Pica, F. Sannino, and U. I. Sondergaard,
Isotriplet Dark Matter on theLattice: SO(4)-gauge theory with two Vector Wilson fermions , PoS
LATTICE2012 (2012)065, [ arXiv:1211.0142 ].[31] A. Hietanen, C. Pica, F. Sannino, and U. I. Sondergaard,
Orthogonal Technicolor withIsotriplet Dark Matter on the Lattice , Phys.Rev.
D87 (2013), no. 3 034508,[ arXiv:1211.5021 ].[32]
Lattice Strong Dynamics (LSD) Collaboration
Collaboration, T. Appelquist et. al. , Lattice calculation of composite dark matter form factors , Phys.Rev.
D88 (2013), no. 1014502, [ arXiv:1301.1693 ].[33] A. Hietanen, R. Lewis, C. Pica, and F. Sannino,
Composite Goldstone Dark Matter:Experimental Predictions from the Lattice , arXiv:1308.4130 .[34] J. M. Cline, Z. Liu, G. Moore, and W. Xue, Composite strongly interacting dark matter , arXiv:1312.3325 .[35] T. Appelquist, E. Berkowitz, R. C. Brower, M. I. Buchoff, G. T. Fleming, et. al. , Compositebosonic baryon dark matter on the lattice: SU(4) baryon spectrum and the effective Higgsinteraction , arXiv:1402.6656 .[36] E. Braaten and H. W. Hammer, Universal Two-body Physics in Dark Matter near an S-waveResonance , Phys.Rev.
D88 (2013) 063511, [ arXiv:1303.4682 ].[37] R. Laha and E. Braaten,
Direct detection of dark matter in universal bound states , Phys.Rev.
D89 (2014) 103510, [ arXiv:1311.6386 ].[38] S. Beane, E. Chang, S. Cohen, W. Detmold, H. Lin, et. al. , Light Nuclei and Hypernucleifrom Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry , Phys.Rev.
D87 (2013), no. 3 034506, [ arXiv:1206.5219 ].[39] W. Detmold and K. Orginos,
Nuclear correlation functions in lattice QCD , Phys.Rev.
D87 (2013), no. 11 114512, [ arXiv:1207.1452 ].[40] T. Yamazaki, K.-i. Ishikawa, Y. Kuramashi, and A. Ukawa,
Helium nuclei, deuteron anddineutron in 2+1 flavor lattice QCD , Phys.Rev.
D86 (2012) 074514, [ arXiv:1207.4277 ].[41] G. Krnjaic and K. Sigurdson,
Big Bang Darkleosynthesis , arXiv:1406.1171 .[42] F. D’Eramo and J. Thaler, Semi-annihilation of Dark Matter , JHEP (2010) 109,[ arXiv:1003.5912 ].[43] F. D’Eramo, L. Fei, and J. Thaler,
Dark Matter Assimilation into the Baryon Asymmetry , JCAP (2012) 010, [ arXiv:1111.5615 ].[44] F. D’Eramo, M. McCullough, and J. Thaler,
Multiple Gamma Lines from Semi-Annihilation , JCAP (2013) 030, [ arXiv:1210.7817 ].[45] G. Belanger, K. Kannike, A. Pukhov, and M. Raidal,
Impact of semi-annihilations on darkmatter phenomenology - an example of ZN symmetric scalar dark matter , JCAP (2012)010, [ arXiv:1202.2962 ].[46] C. Arina, T. Hambye, A. Ibarra, and C. Weniger,
Intense Gamma-Ray Lines from HiddenVector Dark Matter Decay , JCAP (2010) 024, [ arXiv:0912.4496 ].[47] T. Hambye and M. H. Tytgat,
Confined hidden vector dark matter , Phys.Lett.
B683 (2010)39–41, [ arXiv:0907.1007 ]. – 26 –
48] T. Hambye,
Hidden vector dark matter , JHEP (2009) 028, [ arXiv:0811.0172 ].[49] D. Bertolini and M. McCullough,
The Social Higgs , JHEP (2012) 118,[ arXiv:1207.4209 ].[50] G. Belanger, B. Dumont, U. Ellwanger, J. Gunion, and S. Kraml,
Status of invisible Higgsdecays , Phys.Lett.
B723 (2013) 340–347, [ arXiv:1302.5694 ].[51] P. P. Giardino, K. Kannike, I. Masina, M. Raidal, and A. Strumia,
The universal Higgs fit , JHEP (2014) 046, [ arXiv:1303.3570 ].[52] J. Ellis and T. You,
Updated Global Analysis of Higgs Couplings , JHEP (2013) 103,[ arXiv:1303.3879 ].[53] M. E. Peskin,
The Alignment of the Vacuum in Theories of Technicolor , Nucl.Phys.
B175 (1980) 197–233.[54] J. Preskill,
Subgroup Alignment in Hypercolor Theories , Nucl.Phys.
B177 (1981) 21–59.[55] D. Kosower,
SYMMETRY BREAKING PATTERNS IN PSEUDOREAL AND REALGAUGE THEORIES , Phys.Lett.
B144 (1984) 215–216.[56] S. R. Coleman, J. Wess, and B. Zumino,
Structure of phenomenological Lagrangians. 1. , Phys.Rev. (1969) 2239–2247.[57] J. Callan, Curtis G., S. R. Coleman, J. Wess, and B. Zumino,
Structure of phenomenologicalLagrangians. 2. , Phys.Rev. (1969) 2247–2250.[58] E. E. Jenkins, A. V. Manohar, and M. B. Wise,
Chiral perturbation theory for vector mesons , Phys.Rev.Lett. (1995) 2272–2275, [ hep-ph/9506356 ].[59] K. Griest and D. Seckel, Three exceptions in the calculation of relic abundances , Phys.Rev.
D43 (1991) 3191–3203.[60] E. W. Kolb and M. S. Turner,
The Early Universe , Front.Phys. (1990) 1–547.[61] L. J. Hall, K. Jedamzik, J. March-Russell, and S. M. West, Freeze-In Production of FIMPDark Matter , JHEP (2010) 080, [ arXiv:0911.1120 ].[62] G. Gelmini, L. J. Hall, and M. Lin,
What Is the Cosmion? , Nucl.Phys.
B281 (1987) 726.[63] R. S. Chivukula and T. P. Walker,
TECHNICOLOR COSMOLOGY , Nucl.Phys.
B329 (1990)445.[64] D. B. Kaplan,
A Single explanation for both the baryon and dark matter densities , Phys.Rev.Lett. (1992) 741–743.[65] S. D. Thomas, Baryons and dark matter from the late decay of a supersymmetric condensate , Phys.Lett.
B356 (1995) 256–263, [ hep-ph/9506274 ].[66] D. Hooper, J. March-Russell, and S. M. West,
Asymmetric sneutrino dark matter and theOmega(b) / Omega(DM) puzzle , Phys.Lett.
B605 (2005) 228–236, [ hep-ph/0410114 ].[67] R. Kitano and I. Low,
Dark matter from baryon asymmetry , Phys.Rev.
D71 (2005) 023510,[ hep-ph/0411133 ].[68] K. Agashe and G. Servant,
Baryon number in warped GUTs: Model building and (dark matterrelated) phenomenology , JCAP (2005) 002, [ hep-ph/0411254 ].[69] N. Cosme, L. Lopez Honorez, and M. H. Tytgat,
Leptogenesis and dark matter related? , Phys.Rev.
D72 (2005) 043505, [ hep-ph/0506320 ].[70] G. R. Farrar and G. Zaharijas,
Dark matter and the baryon asymmetry , Phys.Rev.Lett. (2006) 041302, [ hep-ph/0510079 ].[71] D. Suematsu, Nonthermal production of baryon and dark matter , Astropart.Phys. (2006)511–519, [ hep-ph/0510251 ]. – 27 –
72] M. H. Tytgat,
Relating leptogenesis and dark matter , hep-ph/0606140 .[73] T. Banks, S. Echols, and J. Jones, Baryogenesis, dark matter and the Pentagon , JHEP (2006) 046, [ hep-ph/0608104 ].[74] R. Kitano, H. Murayama, and M. Ratz,
Unified origin of baryons and dark matter , Phys.Lett.
B669 (2008) 145–149, [ arXiv:0807.4313 ].[75] D. E. Kaplan, M. A. Luty, and K. M. Zurek,
Asymmetric Dark Matter , Phys.Rev.
D79 (2009)115016, [ arXiv:0901.4117 ].[76] K. Petraki and R. R. Volkas,
Review of asymmetric dark matter , Int.J.Mod.Phys.
A28 (2013)1330028, [ arXiv:1305.4939 ].[77] K. M. Zurek,
Asymmetric Dark Matter: Theories, Signatures, and Constraints , Phys.Rept. (2014) 91–121, [ arXiv:1308.0338 ].[78] M. R. Buckley and L. Randall,
Xogenesis , JHEP (2011) 009, [ arXiv:1009.0270 ].[79] J. March-Russell and M. McCullough,
Asymmetric Dark Matter via Spontaneous Co-Genesis , JCAP (2012) 019, [ arXiv:1106.4319 ].[80] M. L. Graesser, I. M. Shoemaker, and L. Vecchi,
Asymmetric WIMP dark matter , JHEP (2011) 110, [ arXiv:1103.2771 ].[81] T. Daylan, D. P. Finkbeiner, D. Hooper, T. Linden, S. K. N. Portillo, et. al. , TheCharacterization of the Gamma-Ray Signal from the Central Milky Way: A Compelling Casefor Annihilating Dark Matter , arXiv:1402.6703 .[82] L. Goodenough and D. Hooper, Possible Evidence For Dark Matter Annihilation In TheInner Milky Way From The Fermi Gamma Ray Space Telescope , arXiv:0910.2998 .[83] D. Hooper and L. Goodenough, Dark Matter Annihilation in The Galactic Center As Seen bythe Fermi Gamma Ray Space Telescope , Phys.Lett.
B697 (2011) 412–428, [ arXiv:1010.2752 ].[84] D. Hooper and T. Linden,
On The Origin Of The Gamma Rays From The Galactic Center , Phys.Rev.
D84 (2011) 123005, [ arXiv:1110.0006 ].[85] K. N. Abazajian and M. Kaplinghat,
Detection of a Gamma-Ray Source in the GalacticCenter Consistent with Extended Emission from Dark Matter Annihilation and ConcentratedAstrophysical Emission , Phys.Rev.
D86 (2012) 083511, [ arXiv:1207.6047 ].[86] D. Hooper and T. R. Slatyer,
Two Emission Mechanisms in the Fermi Bubbles: A PossibleSignal of Annihilating Dark Matter , Phys.Dark Univ. (2013) 118–138, [ arXiv:1302.6589 ].[87] C. Gordon and O. Macias, Dark Matter and Pulsar Model Constraints from Galactic CenterFermi-LAT Gamma Ray Observations , Phys.Rev.
D88 (2013) 083521, [ arXiv:1306.5725 ].[88] W.-C. Huang, A. Urbano, and W. Xue,
Fermi Bubbles under Dark Matter Scrutiny. Part I:Astrophysical Analysis , arXiv:1307.6862 .[89] K. N. Abazajian, N. Canac, S. Horiuchi, and M. Kaplinghat, Astrophysical and Dark MatterInterpretations of Extended Gamma Ray Emission from the Galactic Center , arXiv:1402.4090 .[90] E. Carlson and S. Profumo, Cosmic Ray Protons in the Inner Galaxy and the Galactic CenterGamma-Ray Excess , arXiv:1405.7685 .[91] J. Petrovic, P. D. Serpico, and G. Zaharijas, Galactic Center gamma-ray ”excess” from anactive past of the Galactic Centre? , arXiv:1405.7928 .[92] M. Cirelli, G. Corcella, A. Hektor, G. Hutsi, M. Kadastik, et. al. , PPPC 4 DM ID: A PoorParticle Physicist Cookbook for Dark Matter Indirect Detection , JCAP (2011) 051,[ arXiv:1012.4515 ]. – 28 –
93] M. Cirelli, P. D. Serpico, and G. Zaharijas,
Bremsstrahlung gamma rays from light DarkMatter , JCAP (2013) 035, [ arXiv:1307.7152 ].[94] J. F. Navarro, C. S. Frenk, and S. D. White,
The Structure of cold dark matter halos , Astrophys.J. (1996) 563–575, [ astro-ph/9508025 ].[95] C. Boehm, M. J. Dolan, and C. McCabe,
A weighty interpretation of the Galactic Centreexcess , arXiv:1404.4977 .[96] M. R. Buckley and S. Profumo, Regenerating a Symmetry in Asymmetric Dark Matter , Phys.Rev.Lett. (2012) 011301, [ arXiv:1109.2164 ].[97] M. Cirelli, P. Panci, G. Servant, and G. Zaharijas,
Consequences of DM/antiDM Oscillationsfor Asymmetric WIMP Dark Matter , JCAP (2012) 015, [ arXiv:1110.3809 ].[98] S. Tulin, H.-B. Yu, and K. M. Zurek,
Oscillating Asymmetric Dark Matter , JCAP (2012) 013, [ arXiv:1202.0283 ].[99] N. Okada and O. Seto,
Originally Asymmetric Dark Matter , Phys.Rev.
D86 (2012) 063525,[ arXiv:1205.2844 ].[100] E. Hardy, R. Lasenby, and J. Unwin,
Annihilation Signals from Asymmetric Dark Matter , arXiv:1402.4500 .[101] D. Spergel and W. Press, Effect of hypothetical, weakly interacting, massive particles onenergy transport in the solar interior , Astrophys.J. (1985) 663–673.[102] W. H. Press and D. N. Spergel,
Capture by the sun of a galactic population of weaklyinteracting massive particles , Astrophys.J. (1985) 679–684.[103] J. Silk, K. A. Olive, and M. Srednicki,
The Photino, the Sun and High-Energy Neutrinos , Phys.Rev.Lett. (1985) 257–259.[104] M. Srednicki, K. A. Olive, and J. Silk, High-Energy Neutrinos from the Sun and Cold DarkMatter , Nucl.Phys.
B279 (1987) 804.[105] A. Gould,
WIMP Distribution in and Evaporation From the Sun , Astrophys.J. (1987) 560.[106] A. Gould,
Resonant Enhancements in WIMP Capture by the Earth , Astrophys.J. (1987)571.[107] A. Gould,
Direct and Indirect Capture of Wimps by the Earth , Astrophys.J. (1988)919–939.[108] G. Steigman, C. Sarazin, H. Quintana, and J. Faulkner,
Dynamical interactions andastrophysical effects of stable heavy neutrinos , .[109] A. Bottino, G. Fiorentini, N. Fornengo, B. Ricci, S. Scopel, et. al. , Does solar physics provideconstraints to weakly interacting massive particles? , Phys.Rev.
D66 (2002) 053005,[ hep-ph/0206211 ].[110] I. V. Moskalenko and L. L. Wai,
Dark matter burners , Astrophys.J. (2007) L29–L32,[ astro-ph/0702654 ].[111] G. Bertone and M. Fairbairn,
Compact Stars as Dark Matter Probes , Phys.Rev.
D77 (2008)043515, [ arXiv:0709.1485 ].[112] M. McCullough and M. Fairbairn,
Capture of Inelastic Dark Matter in White Dwarves , Phys.Rev.
D81 (2010) 083520, [ arXiv:1001.2737 ].[113] M. T. Frandsen and S. Sarkar,
Asymmetric dark matter and the Sun , Phys.Rev.Lett. (2010) 011301, [ arXiv:1003.4505 ].[114] C. Kouvaris and P. Tinyakov,
Constraining Asymmetric Dark Matter through observations ofcompact stars , Phys.Rev.
D83 (2011) 083512, [ arXiv:1012.2039 ]. – 29 – Constraints on Scalar Asymmetric DarkMatter from Black Hole Formation in Neutron Stars , Phys.Rev.
D85 (2012) 023519,[ arXiv:1103.5472 ].[116] C. Kouvaris and P. Tinyakov,
Excluding Light Asymmetric Bosonic Dark Matter , Phys.Rev.Lett. (2011) 091301, [ arXiv:1104.0382 ].[117] F. Iocco, M. Taoso, F. Leclercq, and G. Meynet,
Main sequence stars with asymmetric darkmatter , Phys.Rev.Lett. (2012) 061301, [ arXiv:1201.5387 ].[118] I. Lopes and J. Silk,
Solar constraints on asymmetric dark matter , Astrophys.J. (2012)130, [ arXiv:1209.3631 ].[119] N. F. Bell, A. Melatos, and K. Petraki,
Realistic neutron star constraints on bosonicasymmetric dark matter , Phys.Rev.
D87 (2013), no. 12 123507, [ arXiv:1301.6811 ].[120] J. Huang and Y. Zhao,
Dark Matter Induced Nucleon Decay: Model and Signatures , JHEP (2014) 077, [ arXiv:1312.0011 ].[121] K. Agashe, Y. Cui, L. Necib, and J. Thaler, (In)direct Detection of Boosted Dark Matter , arXiv:1405.7370 ..