Dark Matter with a Late Decaying Dark Partner

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Dark matter with a late decaying dark partner

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Please note that terms and conditions apply. JCAP07(2009)001 data − e + + hysics e P mic ray theory le ic t o particle species in the ar n the early universe. While s without the need for large second one is metastable and 10.1088/1475-7516/2009/07/001 a, raints on the parameters of the doi: strop A b,c,d [email protected] , s old. In this model it is simple to accommodate the large 8 − and Jure Zupan osmology and and osmology a,b C dark matter theory, cosmology of theories beyond the SM, cos

We explain the PAMELA positron excess and the PPB-BETS/ATIC [email protected] rnal of rnal

ou An IOP and SISSA journal An IOP and 2009 IOP Publishing Ltd and SISSA Physics, King’s College London, Strand, London WC2R 2LS, U.K. Theory Division, Department ofCH-1211 Physics, Geneva CERN, 23, Switzerland J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia Faculty of mathematics and physics, University of Ljubljan Jadranska 19, 1000 Ljubljana, Slovenia E-mail: b c d a c Received April 16, 2009 Accepted June 14, 2009 Published July 2, 2009 Abstract. Malcolm Fairbairn Dark matter with apartner late decaying dark J using a simple twodark component matter dark sector sector areone model assumed particle is to (2CDS). stable be Thedecays and after in tw is the thermal the universe equilibrium present is i day 10 dark matter, the boost factors required to explain the PAMELA positron exces spikes in the localmodel dark matter and density. comment We on provide possible the signals const at future colliders. Keywords:

JCAP07(2009)001 x ]. 1 2 6 8 − ) a 33 i W (1.2) (1.1) + W 1 TeV [ ∼ e 800 GeV from a − ons with no strong o been suggested as y spectrum which is ] or from DM decaying f 500 le self-annihilation cross ] (or the combination of 15 – 22 4 – predominantly to a [ e PAMELA data using DM gs have so far been obtained. m the ATIC-2 balloon experi- ayload for Antimatter Matter agreement with previous hints 16 iment may represent a break- constraint on dark matter an- with mass around 1 TeV which th the PAMELA observations. If , s required to explain dark matter. . s / of dark matter are largely unknown 2 DM 3 /m cm 26 2 DM − ρ i 10 v ]. A possible explanation for this excess is that A 3 × σ , – 1 – h 3 2 , is due to DM annihilating in the milky way, then + + e ≃ e ] find two explanations for the PAMELA data: ¯ N 5 F i v ∝ ]. In this paper we will focus on the annihilating DM A + 30 σ e ]. h – 8 Φ , 23 7 , 5 ]. PAMELA sees a larger positron fraction in the cosmic ray flu , 1 4 ] 34 ], in agreement with the change of power-law seen by HESS abov ]). Astrophysical sources, such as a nearby pulsar, have als 32 ) a DM particle which annihilates predominantly into SM lept 22 , ii 31 One class of DM candidates are particles that have a weak-sca There are also hints of a positron excess in the energy range o The PAMELA experiment also detects an anti-proton cosmic ra long duration Polar Patrol Balloonment (PPB-BETS) [ flight and fro - only lower limits onIt the has mass been and suggestedExploration upper that limits and the on preliminary Light-nuclei the results Astrophysicsthrough couplin from (PAMELA) in The exper this P situation [ 1 Introduction Other than its gravitational interactions, the properties 3 Particle physics context 4 Discussion and conclusions Contents 1 Introduction 2 Two component dark matter constraint on the DM mass. If one triesannihilations, to it explain seems simultaneously necessaryannihilates both to into these leptons consider [ a data DM and particle th section at freeze-out [ with a decay time much longer than the age of the universe [ interpretation of the excess. it comes from dark matter (DM) annihilating in ourthe own two galaxy [ an explanation of the excess [ at 10 - 80 GeV thanfrom one the expects HEAT in and the AMS-01 galactic experiments environment, [ in heavy DM particle of mass above about 10 TeV that annihilates compatible with the expectednihilation galactic modes. background, The giving authors a of ref. [ The resulting thermal relic abundance isSuch then a close candidate to does what not, i the however, PAMELA fit excess straightforwardly flux wi of positrons, Φ pair or JCAP07(2009)001 1 ]. ]. at he 8 ion 38 – rius F ) for 5 (1.3) . We i [ 5 nding 0 [ and is B > 2 TeV. v , larger s, then F ]. 10 A 1 DM i , ∼ → σ v 3 43 m h m 2 v A – 10 σ /g , h 41 bosons, these [ W and χ (10 m πm /v ∼ 4 1 the average number W, Z has mass B + 1 & 1 and at most a factor ∝ e χ ¯ . In both cases the DM avours. These two DM ≤ N xperiment data. ]. Enhancements are also A F DM i σ + ew force in the DM sector e v 40 with mass below m factor ¯ , A anced DM annihilation cross N rticle true also, if DM is composed σ hancing the local annihilation 00 GeV the PAMELA positron 39 ). If the annihilation proceeds ass of order 2 1. In the case of co-annihilation, eavy, t enhancement comes from states ld [ 1.3 , ) includes among others the effect of 2 i ≪ h and can become large for ) v A 1.2 B < ysical origin of the cosmic ray enhancement, /v DM σ . 2 DM is the number of co-annihilating flavors. 2 h ρ ρ channel, then g (¯ is very large. f 100 GeV seems to exclude a simple single i − v F f N s i > A N v ], with very large Sommerfeld enhancements ]. σ A h 7 6 σ – 2 – , DM h 5 annihilation (usually the DM particle mass and m + e , where ¯ X 2 f N DM meaning that ], in which case → ≡ m v 37 B ∝ χχ B < N A is the average expected local DM density. We can have σ . As a working tool we will present a simple 2-component dark 3 ]. While substructure in simulations is not well understood or if there is a local DM over-density due to substructure in t 10 TeV) respectively, with a variation of a factor of few depe which explain the positron data are roughly , channel annihilation is enhanced by Sommerfeld correction which is larger than the value required at freeze-out cm DM 36 F Analysis of the N-body dark matter only Via Lactea II simulat / 10, while much smaller fluctuations were observed in the Aqua − B i i , today, giving no enhancement in ( m s v v 1 i 35 A A ∼ v σ σ 1 TeV is possible. For DM particles which interact with h A h , B σ F 35 GeV channel then > i . v 0 − i ≃ h p A v ≃ is the local DM density, σ A σ h (100 GeV DM DM ρ ρ ∼ All these explanations require light new degrees of freedom If the annihilation proceeds through the If, however, the i ≫ h v Conventionally, ”boost factor” refers only to this astroph 1 A DM σ boost factors seem tosection. require The a values different of explanation — an enh of positrons produced in a single m of few in more exotic models). The proportionality in ( where Project simulations [ will address the otherthat possibility, namely are that heavier the than apparen on the predominant annihilation channel [ The mismatch is parametrized by a parameter called the boost Alternatively, the Sommerfeld enhancementwhere can a come force frompossible, carrier if a there possesses n exists GeV apossible bound mass if state the [ very annihilation close goes to through thresho a resonance with m positron propagation in galacticexcess medium. suggests For masses a above 1 through the suggests there israte a by 1% a probability of factor density fluctuations en where ¯ if either while we prefer to define it as referring to the combined effect sector (2CDS) model that can explain the PAMELA and balloon e 2 Two component darkIn matter the 2CDSparticles model can the be dark scalars, sector fermions is or composed vectors. of The two first particle DM fl pa the boost factor is bounded by interpretation of the PAMELA data for galactic distribution. freeze-out is Sommerfeld corrections are present if the DM particles are h h Again, large boost factors are excluded unless The annihilation cross section is then enhanced by of many stable components as in [ component thermal relic explanation of the results. This is JCAP07(2009)001 1 χ /T 2 1 (2.2) (2.4) (2.1) (2.3) (2.5) m → 2 = there is a ). In this χ 1 z 2 , is unstable ,A 1 1 ). z A oon data using ( > m /s ) zmann distribution 2 z ( m (see figure , , ). Then the evolution with time as follows eq 2 i 1 z , the larger the enhance- decay. 2 ( n n χ 1eq 2 Y R 2 Y , /s , Γ χ ) 2 rk matter (CDM) relic still , ron excess is proportional to decays too quickly, then the 2 tion for s-wave annihilation, z )= 2 n number density of metastable H Γ dec ( 2eq 2 z p is able to explain PAMELA 2 Y i . ( Y R . χ N Γ has mass n dec . The positron flux excess mea- eq 2 . i rel 2 + − . H Γ N Y log χ are in thermal equilibrium prior to rel decays to . If . d also, through self-annihilation, the Th ) = 1 2 − + F 1 1 2 1 z z Y Th 2 1eq 2 2eq . ( χ 1 χ i i i n n 1 1 . The abundances then first settle into 1 2 Y decay. It is useful to define − dec will therefore be larger than one would 2 , v v − − approaches the values of Γ − − , while 1 1 1 2 N > Y i and i 2 1 2 2 2 2 X A 2 i 1 A A ) n n 2 v + v Γ σ σ R 1 . + h h χ i i ∞ Ai 2 1 A are SM particles. To retain generality we define 1 2 ( 1 2 1 rel . The larger the ratio 2eq 1eq σ ≪ dec . 1 σ Y Y – 3 – v v h χ 1 are possible including a two body decay Y Y h m m for the stable DM component, while 1 2 Y 2 N X 2 2 Th eq A A 1 ) i z dec curve in figure χ = , after which σ σ Y . n N ∞ 1 2 6 1+ ( R rel −h −h A A = . 1 H H )= ≃ Γ Γ Y → = = Th particles produced in a single Ai . i , where = 10 − − ) ∞ 2 1 2 Y 1 ( rel X χ . 1 χ R = = ∞ ( Y + → Hn Hn Th 1 2 1 1 1 i Y Y dz dz χ Y 1 we will have dY dY + 3 + 3 , we find i i 2 1 → z z v 1eq 2eq dt dt 2 Y Y dn dn R > Ai χ σ h / . This is shown on figure . We also assume that both i 1 1 1 v χ ∝ ). Note also that as the value of Γ 1 . A 20 is the freeze out value of ) is the equilibrium number density given by the thermal Bolt ∞ rel t σ ( . ( h ≃ 1 2 eq Th Y is the decay width for i i F 1 . z Y n 2 rel as the average number of . An interesting limit to consider is Γ We can now see why it is possible to explain the PAMELA and ball The number density of each of the dark matter flavours evolves Th 1 dec Y where the annihilation rates are Γ and decays to present today, responsible for galacticPAMELA rotation and curves an balloon results. The second DM particle stable. We assume that it is this particle which is the cold da their thermal relic values, where freeze out. We willand discuss balloon data. under what Many decay conditions modes such of a setu ment of limit we then have where The number density of thedark dark matter matter relic is components. enhancedwhere by Using the an approximate analytic solu the 2CDS model. If and Γ washout effect, as seen for the or multibody decays equations become sured by PAMELA and given by expect in the case of one-component DM model, where the posit N and normalise number density to entropy density, JCAP07(2009)001 . s, n / 3 (2.6) 6 3 = 10 is held cm 10 ). The freezes 10 10 = i = = 26 B 1 = 1 TeV, R 1 R R − 7 2.4 v χ 1, 1, 1, 1 1 10 Y 10 Y Y A 2 m × σ h =3 5 is small enough that r before , the enhancement 2 10 2 CDM ,A i z 1 v A A the DM particle. Through Γ σ cold dark matter scenario h 2 . χ 6 3 . 3 5 4 ≪ ) as denoted. Dashed lines denote 10 10 10 10 100 10 1 10 10 1000 rel = 2 . = = R ∞ R 4 4 ( R R Th 1 2, 10 10 1 2, 2, ) (blue solid line) for Y Y Y Y z Y y with ( 2 Y 10 , in the case where Γ 5 7 9 is held fixed to CDM ∗ 2CDS ∗ 11 13 - - - - - g i g R L

10 10 10 2

10 10

v i Y s 2 (1), while the last ratio is given in ( 3 3 A and ) labeling contours give boost factors as GeV H σ O 10 10 n 1 h 1 F CDM F 2CDS 1 m m – 4 – z z ≃ 7 3.0 2.4 1.8 1.2 0.6 4.8 4.2 3.6 i 10 F 1 i v v 1 A A σ 100 100 σ = 1 and three diﬀerent values of 5 4 3 1 h ) (black solid line) and h 10

z 10 10 10 100

the predicted boost factors in the limit of small Γ ( 5 dec R = 1 as a function of 2 10 Y N ). On the left ﬁgure . For illustration we also show the right ﬁgure, where z B B 1 z ( χ i Y GeV, 3 6 s. 24 10 / 10 10 3 − = = = 1000 R R R 2 1, cm 1, 1, Y Y Y Y = 10 26 − 2 particles may still have chance to annihilate with each othe 10 1 10 χ . The solution for × . The boost factor 19 13 15 17 11 - - - - -

10 10 10 10 10

i We also show in figure Y = 3TeV, Γ 2 Figure 2 Figure 1 m resulting out completely. If we are not therefore in the limit where Γ quantities labeled CDM areand the 2CDS parameters corresponds for to the the parameters usual of WIMP our model. wash-out can be neglected. The framed numbers ( The first two ratios on the right-hand-side are the thermal relic values of effect is lost. so that without decay this would give correct DM relic densit decay this is transfered to fixed to 3 JCAP07(2009)001 (2.7) (2.8) (2.9) (2.10) ) imply 2.8 is less than 1 measured ≪ decay time can SM 1 TeV suggested 2 M l travel at least a then follows from ) and ( . For a particular dark matter could χ + 1 ∼ i rder to explain the 1 2 2.7 ) is smaller than the scenario, namely the 1 v χ 2 m >m 2.2 A → e small, giving an upper 2 σ h 2 m 2 after the start of structure at that time was the idea χ CDM ances. If on the other hand , ]. Such particles would not and more recently has shown ]. While these problems are , m . 2 nto the idea of decaying dark ed to being dark energy was roblem of the excess positrons ) 2 he value of Ω s (cold or hot) and its heating dark halos making them more by more recent observations of 48 53 implest scenario then is that by F 1 , – – . z 1 i ( 2 1 B P l 1 1 . Equations ( 46 1 51 m 2 v m we need A m m 1 1TeV Γ 1TeV 1 1 10 A 100 GeV, with . χ σ 0 · ∼ ≃ − · ) ) ≃ ∗ 3 g F F ) 2 1 3 i ≪ h z z B F ]. The value of 1 ( ( 10 2 B , the second term in ( z 5 10 v [ ( F 1 2 from nucleosynthesis. One can use the detailed 2eq 1eq z · 1 , the PAMELA and balloon experiment data fix – 5 – A H Y Y 2 3 σ m × ) 20 and h SM ) F 1 particles from the decay are non-relativistic so that ∼ s X ≃ z GeV 7 ) 1 ( dec 1 17 − F 1 F χ 1 N → A z − z ( 1 Γ (10 1 10 χ A 1 ≪ Γ ≫ ) at late times with its freeze-out value) to be larger than 50 χ ≪ z 2 2 1 ( to be able to decay into 2 τ Γ 2 Γ 2 m Y χ as a function of ] to argue that so long as the lifetime of F i is produced in colliders at relativistic velocities, it wil 2 v 45 2 A χ σ h is allowed, this usually does not affect abundances. The ) 1 1 χ ]. Because of this some workers have suggested that decaying m ( 1 50 . This means that at freeze-out, χ B 2 , = → 49 . For large boost factors we have i 2 2 1 To have significant boost factors, the washout effect should b We next discuss the limits on the parameters of our model. In o There also exists a lower bound on Γ More interesting is the situation where the particles decay χ v 1 A σ formation. In the 1980smatter a and significant amount its ofthat effect thought the went on i missing structureactually energy formation. the in relativistic the The universe decay motivation now products usually of subscrib dark matter [ limit on Γ h by the ATIC excess. For assumed annihilation channel cuspy halo problem and the small scale power problem [ around a second thereonly will be no change to light element abund Because of this, if and the annihilation rate at freeze-out is approximately then be very long, ofthe order time the of cosmological time structure scale. formation The the s few meters before decaying. cluster below 100 Mpc and therefore would not contribute to t have a bearing upon two apparent possible problems with the Λ an upper bound on Γ first one (we approximate PAMELA data one needs they are cold dark matter. figure where in the last equality we used or results presented in [ on scales smaller thanH(z) 100 and Mpc. structure formation This and scenariowe would are not is addressing anyway disfavoured solve in the this p that work. the However, decay work of done at darkin the matter that time into decay another has darkdiffuse interesting [ matter effects specie on structure, puffing out JCAP07(2009)001 . , 1 is ∼ 2 in Y χ χ are ) 1 1 that π (3.1) (3.2) χ g 1 05 at . 1 , while U(1) . Then m 0 2 χ ′ (16 2 χ × Z ∼ carries an m/ L and v 2 × ross section 2 χ 2 g 2 Z m ∼ is decays are not. If ′ 2 Z X components, × → 2 ]), which for 2 Z is p-wave suppressed. The , 44 1 lained by the hierarchy 2 would be that e do not pursue here is that χ χ . . sections in the non-relativistic ′ 2 4 2 suffices). The other possibility 2 1 ed, though (for instance for a Z χ , χ under 1 A simple possibility is that 5 exist, it is certainly true that the ) 1 × g n of can have. For simplicity we focus c es has a rich phenomenology when 1 2 H . 2 are singlets under SU(2) † ≫ + is a Majorana fermion. Yet another Z 0 χ 4 1 2 2 1 2 2 2 H , SM ( ∼ 1 χ χ Λ Λ ), and the decay width Γ 2 4 χ 2 c 4 4 c 1 2 and g g g 2 1 1 2.9 is metastable in agreement with the 2CDS + 1 + , 2 1 χ − 4 χ 2 2 2 2 2 m m χ χ χ , while the SM is neutral under without any fine-tunings. This is easily realized ) 2 1 ′ are allowed, while 2 1 1 1 1 1 suppressed (see e.g. [ , eq. ( ∼ – 6 – χ 3 Z 2 χ H is the dominant annihilation channel for 1 − 2 † i i X c 10 1 1 2 v H v v χ of exchanged particles. The hierarchy of annihilation + ( 1 2 → ∼ 1 1 TeV, ′ 2 2 3 2 A A , χ 2 c are scalars. If . The charges under Z Z 1 σ σ kin of the second one (here the hierarchy need not to be very field χ ≫ h h 2 + 2 L 2 → can be obtained for instance, if the typical coupling 2 1 g χ is then χ ). Another elegant possibility is that the annihilation of 2 i = 2 m m , 2 2 χ χ Λ proceeds through a heavier state than the annihilation of v 2 χ 2 2 L Table 1 χ and 1 SM − A χ is a Dirac fermion, while 1 σ X under a different 10 χ 1 2 χ → ∼ and masses Λ χ 1 1 2 i ≫ h , χ annihilation is phase space suppressed. For instance, if 1 1 1 v , Λ g that is metastable, can explain the enhanced annihilation c 2 and 1 χ 4 A 2 2 m σ χ Z h We next discuss the possible interactions More severe is the hierarchy between Γ is broken at some high scale Λ could be charged under a gauge group broken at a high scale. can also annihilate to SM. ′ 2 2 1 few GeV typical for a weakly coupled theory. One explanation the first DM sector is larger than controversial in that not everybodypossibility of actually dark agrees matter if decayingit they into comes another dark to speci structure formation. 3 Particle physics context To recapitulate, we have found that the 2CDS model with two DM freeze out can lead to a boost factor of is that the annihilation of is stable, and large, for instance even for a boost factor of 10 where we have denoted schematicallylimit the on dependence couplings of cross cross sections observed by PAMELA. The large boost factors observed are exp approximately conserved charge that suppresses its decay. For large boostboost factors factor a of 10 relatively large hierarchy is need annihilation cross section for in a concrete model, if proceeds through and s-wave process, while the annihilatio the annihilations possibility is, if explanation of the PAMELA data. Another possibility which w χ on the case, where both charged under then the most general renormalizable Lagrangian invariant Z almost mass degenerate and χ JCAP07(2009)001 2 4 ) χ 2 are p/p (3.4) (3.3) (3.5) (3.6) 2 χ andard leading v/m are 10 TeV so d but not 2 need to be Z 2 ∼ , , is needed, for 1 2 1 gh four scalar | and/or χ χ 3 for simplicity) 2 m , 1 , ) 1 2 2 c χ , 1 H GeV, an intriguing χ † but not 2 1 hh, W W, ZZ m 15 χ ′ 2 H rk sector, for instance . Even then the terms | ≫ | 2 ≡ Z 10 2 Λ Y 1 c Λ m 2 | . sector that then mediates ) m are fermions, while leaving . U(1) d, would exclude this simple 2 et must also exist to cancel chy 2 ∼ / 3.4 is most conveniently chosen to 1 χ 1 × . L m m 2 2 / = 0, which for instance is trivially , e SM, the fermionic 3 1 fields. Renormalizable interactions annihilate into i ) excess as well as the absence of ¯ 2 1 , 2 m . 1TeV are weak doublets so that the neutral 2 − χ and/or , ) χ χ h 2 e 2 2 χ 2 1 1 2 decay that break χ Λ χ m + / χ ) works. Also, in order to prevent “fast” χ 1TeV 1 π 2 . µ | + H χ 3 e ∂ † , ( 3 mass has to be large enough, 1 (16 1 or two / (so that BBN constraints are fulfilled regardless c / H χ B 1 | 10 3 2 vev (i.e. + W, Z 1 µ s 2 – 7 – χ and/or GeV e 2 ∂ 1 χ 2 − m Λ 1 · 15 1 χ m Λ < 10 ) give decay widths that are additionally ( χ ≃ 10 2 ) includes the see-saw scale 2 are fermions or vectors. · . τ 3.3 Γ | 2 GeV 5 , ) we then have (taking 3.6 2 1 c 12 | < χ 3.4 ), ( 10 have masses in the 10 TeV range as in the scalar case. Again, Λ 2 3.5 ≫ small enough. χ , 2 2 Λ c χ ) and ( only rescales the definition of Λ). Decays into all massive st , decays with will contain two 2 2 ′ 2 ψ χ m 2.9 χ 2 1 } Z a hierarchy can explain both the and/or 5 only to the higgs or to χ 4 − 1 × 2 , γ † , χ 2 10 1 1 in the dark sector. In the milky way W { Z χ 0). These qualitative conclusions do not change even if 5 under an extra U(1) under which also the SM leptons are charge thermalise through interactions with the SM higgs and throu + ¯ ∼ , ψ HH 4 1 2 , should not be broken by a > W 1 B χ χ ′ 2 c 1 Λ m Λ i ]. It is possible to avoid this constraint by enlarging the da Z c → 5 (the choice of are the SM fermions. The dimensionful parameter 1 and 2 χ ψ 1 1 m To get large boost factors in this simple scenario the hierar We also briefly comment on the case where If we assume that The dimension 5 operators relevant to the χ χ ∼ by charging signal by PAMELA (whilescenario) the [ balloon experiments, if confirme model particles are possible with partial decay widths the quarks, while keeping The last and the first operator in ( suppressed. From eq. ( to leptonic and hadronic final states. Thus instance, for where be The decay, the This general limit applies also, if Note that the allowed range ( interactions possibility in view of the leptonic-only signal in PAMELA. true if all that of the decay mode), this then implies an upper limit on Λ in ( detailed analysis for future. In order to thermalise with th neutral components of someinvariant higher under representation of SU(2) either charged under thewith SM the gauge SM. groups The or simplest couple case to is a that hidden can thus couple components are massiveanomalies). “dark Then neutrinos” (some dark multipl this can be avoided by enlarging the dark matter sector. JCAP07(2009)001 is ]. SM is a eak 2 X χ 1 e not χ . How a weak → ]. − ]. 2 − 1 SPIRES χ W χ ] [ + + 1 o hierarchies o 100 GeV in ]; χ , l SPIRES − SPIRES → riment? If ] [ ] [ W 2 + 1 χ χ , SPIRES mimic the large boost ome ways reminiscent 1 ] [ χ ntract No. MRTN-CT- → 2 cross sections need to be ysics, it may be necessary 2 C anomaly. An important 2 on through the Marie Curie → χ be observed directly. Let us thermal relics. Rather, their odified and relaxed from the χ astro-ph/0703154 2 , [ ders. In this way 2CDS model χ nstance decays of gravitinos or is not a thermal relic, but rather or weakly coupled moduli decays ysics. The 2CDS setup represents n more detail. and arXiv:0810.4994 is a singlet scalar and [ astro-ph/9703192 1 1 νh, νZ χ χ arXiv:0810.4995 → [ (2007) 145 are possible. If on the other hand are both weak doublet fermions, then the 2 χ 2 , 1 , (MRTN-2006-035863). The work of J. Z. was χ Z B 646 An anomalous positron abundance in cosmic rays may be will depend on the actual masses and 1 Measurements of the cosmic-ray positron fraction (2009) 051101 (1997) L191 [ – 8 – Cosmic-ray positron fraction measurement from 2 ν,νZ,νγ (2009) 607 χ 1 h, χ 102 482 1 χ χ 458 ]. Also in these two cases the correlation between the → 2 → 54 Phys. Lett. χ , Universenet 2 is a singlet scalar, the decays χ Nature 2 are possible. If , χ Astrophys. J. ¯ interactions governing its abundance (before the decay) ar qq decay width needs to be much smaller than for normal electrow , , 2 Phys. Rev. Lett. − 2 l χ , χ + A new measurement of the antiproton-to-proton flux ratio up t , l − l + 1 collaboration, O. Adriani et al., collaboration, M. Aguilar et al., ν,χ 1 collaboration, S.W. Barwick et al., χ needed to explain the PAMELA and balloon experiment data. Tw , and ii) the B B → ∼ 2 What would be the signatures of a 2CDS model in a collider expe In conclusion, we have presented a simple 2CDS model that can AMS-01 HEAT 1 GeV to 30 GeV with AMS-01 from 1 GeV to 50 GeV O. Adriani et al., the cosmic radiation PAMELA with energies 1.5.100 GeV χ [3] [2] [1] annihilation cross section of DM and the relic abundance is m thermal relic relation. Incan this give way large also enoughdifference decaying ”boost with gravitino 2CDS factors” is toabundance that (before explain the neither PAMELA-ATI decay) gravitino isthe reflective nor of other moduli Planck scale limit, are ph where Planck suppressed and canis possibly much be closer probed to the at simple future thermal colli relic scenario. produced near threshold, itbe can more decay in specific the with detector a and few may illustrative examples. If factors are needed for this proposal to work: i) the ratio of doublet fermion, then the decays large, 2006-035482 (FLAVIAnet). References supported in part by the European Commission RTN network, Co decays. If theto PAMELA revisit data the cannot kind be of explained scenario using outlined astroph inAcknowledgments this manuscript i The work of MF isResearch partially and supported Training by Network the European Comissi weak doublet fermion, while challenging the experimental search for of situations already discussedoriginates in from the literature, decays where ofweakly DM a coupled heavier moduli state. into Examples DM are [ for i branching ratios. 4 Discussion and conclusions The proposed 2CDS explanation of PAMELA/ATIC anomaly is in s possible two body decays are and JCAP07(2009)001 , ]. ]; , , ]. , SPIRES [ (2009) 1 ]. SPIRES (2009) 004 ] [ and SPIRES ]. ]. [ 02 ]; ]. ]; B 813 SPIRES [ , MSSM SPIRES SPIRES JCAP [ arXiv:0810.5557 , ] [ The Case for a 700+ SPIRES SPIRES arXiv:0901.2925 SPIRES , DM [ , ] [ ] [ N arXiv:0810.5397 Nucl. Phys. ]. A Theory of Dark Matter , arXiv:0802.3378 High Energy Positrons From einer, [ , r, r, arXiv:0811.3641 ]. ter , ]. PAMELA and dark matter ]. 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