Constraining the co-genesis of Visible and Dark Matter with AMS-02 and Xenon-100
aa r X i v : . [ h e p - ph ] J a n KEK-Cosmo-121,KEK-TH-1642
Constraining the co-genesis of Visible and Dark Matter with AMS-02 and Xenon-100
Kazunori Kohri and Narendra Sahu Cosmophysics Group, Theory Centre, IPNS, KEK, Tsukuba 305-0801, JapanThe Graduate University for Advanced Study (Sokendai), Tsukuba 305-0801, Japan Department of Physics, Indian Institute of Technology Hyderabad, Yeddumailaram 502205, AP, India
We study a non-thermal scenario in a two-Higgs doublet extension of the standard model (SM),augmented by an U (1) B − L gauge symmetry. In this set up, it is shown that the decay product ofa weakly coupled scalar field just above the electroweak scale can generate visible and dark matter(DM) simultaneously. The DM is unstable because of the broken B − L symmetry. The lifetimeof DM ( ≈ × sec) is found to be much longer than the age of the Universe, and its decay tothe SM leptons at present epoch can explain the positron excess observed at the AMS-02. The relicabundance and the direct detection constraint from Xenon-100 can rule out a large parameter spacejust leaving the B − L breaking scale around ≈ − I. INTRODUCTION
The observed cosmic ray anomalies at PAMELA [1, 2],Fermi [3, 4], H.E.S.S. [5] and recently at AMS-02 [6, 7](see also [8]) conclusively hint towards a primary sourceof positron in our Galaxy . This gives rise enough mo-tivation to consider a particle physics based dark mat-ter (DM) models, such as annihilation [11–16] or de-cay [12, 16–22] of DM, as the origin of positron excessin the cosmic rays .At present, the relic abundance of DM: Ω DM h ∼ . b h ∼ .
022 arising from a baryon asym-metry: n B /n γ ∼ . × − , has been established bythe Planck [27] and the big-bang nucleosynthesis (BBN)measurements [28]. The fact that the DM abundance isabout a factor of 5 with respect to the baryonic one mighthint towards a common origin behind their genesis.In fact, both baryon and DM abundances could beproduced at the end of inflation, whose origin is usu-ally linked to a scalar field called inflaton [29]. A visiblesector inflaton which carries the Standard Model (SM)charges [30] can naturally create a weakly interactingDM, as it happens in the case of Minimal Supersym-metric SM scenarios, see [31]. However if the inflatonbelongs to a hidden sector, such a SM singlet inflaton,which might as well couple to other hidden sectors, thenit becomes a challenge to create the right abundance forboth DM and the visible matter.In this paper we will consider a simple example of any In fact it has been shown earlier that there is a clean excess ofabsolute positron flux in the cosmic rays at an energy E > ∼ For astrophysical origins, see Ref. [15, 23–26] and referencestherein. generic hidden sector inflaton, which first decays intoscalar fields charged under a U (1) B − L gauge group. Thesubsequent decay of these scalar fields to DM and SMcharged leptons generate asymmetry in the visible andDM sectors, which has to be matched with the observeddata [27]. The stabilty to DM is provided by the B − L gauge symmetry. We assume that all the above phenom-ena happens in a non-thermal scenario right above theelectroweak scale.If we assume that B − L is broken above the TeV scale,then the resulting DM lifetime comes out to be longerthan the age of the universe, i.e. ≈ × sec, and it’sdecay into charged leptons can explain the rising positronspectrum as shown by the AMS-02 data, provided thatthe DM mass is around 1 TeV. Furthermore, we are ableto put constraints on the model parameters by the directdetection experiments, such as Xenon-100 [32]. The null-detetction of DM at Xenon-100 constraints the B − L breaking scale to be around 2 − Z ′ gauge boson.The paper is organized as follows. In section-II, webriefly discuss the model. In section-III, we providethe mechanism of generating visible and DM simultane-ously in a non-thermal set-up. In section-IV we discusspositron anomalies from a decaying DM. In section -V,we discuss compatibility of the DM with the direct detec-tion limits. In section-VI, we conclude our main results. II. THE MODEL
The positron excess seen in PAMELA [1, 2], Fermi [3,4], AMS-02 [6, 7] experiments hint towards a leptophilicorigin of the DM [18, 33]. A simple non-supersymmetricorigin of this DM can be explained in a two Higgs dou-blet extension of the SM with an introduction of an U (1) B − L gauge symmetry [18, 34]. We also add three sin-glet fermions N L (1 , , − ψ R (1 , , −
1) and S R (1 , , − SU (2) L × U (1) Y × U (1) B − L . We need to check the axial-vector anomaly [35], which requires the following condi-tions to be satisfied for its absence: SU (3) C U (1) B − L : 3 (cid:20) × − − (cid:21) = 0 SU (2) L U (1) B − L : 2 (cid:20) × − (cid:21) = 0 U (1) Y U (1) B − L : 3 " × (cid:18) (cid:19) × − "(cid:18) (cid:19) ×
13 + (cid:18) − (cid:19) × + (cid:2) − ( − − − ( − (cid:3) = 0 U (1) Y U (1) − L : 3 " × × (cid:18) (cid:19) − " × (cid:18) (cid:19) + (cid:18) − (cid:19) × (cid:18) (cid:19) + (cid:2) − − − − − (cid:3) = 0 U (1) − L : 3 " × (cid:18) (cid:19) − (cid:18) (cid:19) − (cid:18) (cid:19) + (cid:2) × ( − − ( − (cid:3) + (cid:2) ( − − ( − − ( − (cid:3) = 0where the number 3 in front is the color factor. Thusthe model is shown to be free from B − L anomaly andhence can be gauged by introducing an extra gauge boson Z ′ . Since N L is a singlet under SU (2) L , and it doesnot carry any charge under U (1) Y , its electromagneticcharge is zero. As a result the lightest one can be a viablecandidate of the DM. The stability to DM is provided bythe gauged B − L symmetry.However, we also add two massive charged scalars: η − (1 , − ,
0) and χ − (1 , − , −
2) in the particle spectrumsuch that their interaction in the effective theory breakslepton number by two units and hence introduces a pro-longed lifetime for the lightest N L , which is the candidatefor DM. As we show later the extremely slow decay of DMcan explain the positron excess observed at PAMELA [1],Fermi [4] and recently at AMS-02 [6]. Furthermore, weassume that these particles are produced non-thermallyfrom the cascade decay of the hidden sector inflaton field φ (1 , ,
0) just above the EW scale as pictorially depictedin Fig. 1. The particle content and their quantum num-bers are summarised in table I.The main interactions are given by the effective La-grangian: L eff ⊇
12 ( M N ) αβ ( N αL ) c N βL + 12 ( M ψ ) αβ ( ψ αR ) c ψ βR + 12 ( M S ) αβ ( S αR ) c S βR + ( g S ) αβ (cid:0) S αR Hℓ βL (cid:1) + ( g ψ ) αβ (cid:0) ψ αR Hℓ βL (cid:1) + µηH H + m η † χ TABLE I: Particle content and their quantum numbers.Particle SU (2) L × U (1) Y U (1) B − L Mass range ℓ L (2,-1) -1 MeV to GeV ℓ − R (1,-2) -1 MeV to GeV H , H (2,1) 0 100 GeV → O (TeV) φ (1,0) 0 O (10 TeV) χ − (1,-2) -2 O (10 TeV) η − (1,-2) 0 O (10 TeV) N L (1,0) -1 O (TeV) ψ R , S R (1,0) -1 O (TeV) χηη χ + − + − NN ll l LL e R e R + −+ − l φ H H H H
FIG. 1: Decay of hidden sector inflaton to SM degrees offreedom through η and χ fields. + h αβ η † N αL ℓ βR + f αβ χ † ℓ αL ℓ βL + h.c. (1)where m = µ ′ v B − L , M i = F i v B − L , (2)with “ v B − L ” is the vacuum expectation value (vev) ofthe U (1) B − L breaking scalar field which carries B − L charges by two units and F i is the coupling between B − L breaking scalar field and the singlet fermions. InEq. (1), H , H are two Higgs doublets and ℓ L (2 , − , − ℓ R (1 , − , −
1) are SM lepton doublet and singlet respec-tively.We demand M i = F i v B − L , with i = N, S, ψ , to be ofthe order of TeV scale in order to explain the cosmic rayanomalies as discussed in section IV. Since the interac-tions of S and ψ break B − L by two units, the neutrinomass, after electroweak phase transition, can be gener-ated via the dimension five operators: ℓℓHH/M S and ℓ L ℓ L HH/M ψ and is given by: M ν = g S h H i M S + g ψ h H i M ψ . (3)Taking M S , M ψ ∼ O (TeV), the sub-eV neutrino massimply g S , g ψ ∼ O (10 − ). Therefore, the decay of S and e R N L η e R N L η η HH FIG. 2: The interference of tree-level and self-energy correc-tion diagrams which give rise to CP violation. ψ can not produce any lepton asymmetry even thoughtheir interactions break B − L by two units. Moreover,the number density of these particles are Boltzmann sup-pressed as the reheat temperature is around 100 GeV.As we will show in section (III), the lepton number con-serving decay: η → N L + ℓ R generates visible and DM( N L ) simultaneously. However, note that the interactionbetween η and χ violates the lepton number by two units.Therefore, the DM is no more stable and decays slowlyto SM fields. Since the DM carry a net leptonic charge,it only decays to leptons without producing any quarks.As we will discuss in section (IV) the lifetime of the DMis much longer than the age of the Universe. As a re-sult it could explain the observed positron anomalies atPAMELA [1, 2], Fermi [3, 4] and AMS-02 [6, 7] withoutconflicting with the antiproton data. III. CO-GENESIS OF VISIBLE AND DARKMATTERA. Baryon asymmetry
In this section we explain the details of simultaneouslycreating the observed baryon asymmetry and the relicabundance of DM in our model. We assume that thehidden sector inflaton φ with mass m φ decays into theSM degrees of freedom through η and χ as depicted inFig. 1. We further assume this gives rise to a reheattemperature: T R ∼ . p Γ φ M Pl > ∼ . (4)To generate baryon asymmetry we need CP violation forwhich we assume that there exist two η fields: η and η of masses M and M . Since their couplings with N L and ℓ R are in general complex, the B − L conserving decayof the lightest one can give rise to CP violation throughthe interference of tree level and self energy correctiondiagrams as shown in the Fig. 2. The CP violation dueto the decay of the lightest η can be estimated to be [36], ǫ L = I m h ( µ µ ∗ ) P αβ h αβ h ∗ αβ i π ( M − M ) (cid:20) M Γ (cid:21) = − ǫ N L , (5) where Γ = 18 πM µ µ ∗ + M X i,j h αβ h ∗ αβ . (6)Now assuming µ ∼ µ ∼ M ∼ M and h αβ ∼ h αβ ∼O (10 − ) we get from Eqs. (5) and (6) the CP asymmetry | ǫ L | = | ǫ N L | ≃ − .Since the decay of the lightest η does not violate leptonnumber, so it can not produce a net B − L asymmetry.But it will produce an equal and opposite B − L asym-metry between N L and ℓ R [34, 37, 38]. The two asym-metries, which remain isolated from each other beforeelectroweak phase transition, can be given by: Y B − L = B η ǫ L n φ s | T = T R = −Y asy N L (7)where n φ = ρ φ /m φ is the inflaton density and s =(2 π / g ∗ T is the entropy density. The branching frac-tion in the above equation is defined by: B η = Γ( φ → η + η − )Γ( φ → all) . (8)Using ρ φ | T = T R = ( π / g ∗ T R in Eq. (7) we get Y B − L = 34 B η ǫ L T R m φ = −Y asy N L . (9)The B − L asymmetry in ℓ R can be transformed to ℓ L through the lepton number conserving process: ℓ R ℓ cR ↔ ℓ L ℓ cL mediated via the SM Higgs as it remains equilib-rium above electroweak phase transition. As a result the B − L asymmetry in the lepton sector can be converted tobaryon asymmetry through the SU (2) L sphalerons whileleaving an equal and opposite B − L asymmetry in N L .The conversion of B − L asymmetry to the baryon asym-metry is obtained by : Y B = 2492 B η ǫ L T R m φ . (10)For T R /m φ ≈ − and ǫ L ≈ − , we can achieve theobserved baryon asymmetry Y B ≈ O (10 − ). This leadsto the DM to baryon abundance: Y asy N L Y B = 9232 . (11)A crucial point to note here is that the asymmetric com-ponent of DM and baryon asymmetry are produced bya non-thermal decay of the φ decay products, η and χ .An obvious danger of washing out this asymmetry comesfrom the B − L violating process N L ℓ R → ℓ L ℓ L throughthe mixing between η and χ . However, this process issuppressed by a factor ( m /M η M χ ) for m ≪ M η , M χ and hence it cannot compete with the Hubble expansionparameter at T R ∼
100 GeV. Another lepton number vio-lating process is ℓ L ℓ L → HH mdeiated by S and ψ . How-ever, the rate of this process: Γ ∼ M ν T R / h H i is muchless than the Hubble expansion parameter at T R ∼ B − L asymmetry produced bythe decay of η will be converted to the required baryonasymmetry without suffering any washout. B. Dark Matter abundance
Let us now calculate the required DM to baryon ratio:Ω N L Ω B = Y asy N L Y B M N m n , (12)where m n is the mass of a nucleon, and M N is the Ma-jorana mass of the DM candidate N L .As we discuss in section (IV), N L mass is required tobe O (TeV) to explain the observed cosmic ray anomaliesat PAMELA [1, 2], Fermi [3, 4] and recently at AMS-02 [6, 7]. However, for O (TeV) mass of N L , Eq. (12)gives Ω N L >> Ω B . Fortunately this is not be the case,because of the Majorana mass of N L which give rise torapid oscillation between N L and N cL [39]. As a resultthe N L asymmetry can be further reduced through theannihilation process: N L N cL → Z B − L → f ¯ f , where f isthe SM fermion.Note that the decay of η also give rise to a dominant B − L symmetric abundance of N L and is given by: Y sym N L = 34 B η T R m φ (13)which is larger than the asymmetric component Y asy N L byfive orders of magnitude and hence required further de-pletion to match with the observed DM abundance.The total N L abundnace Y N L = Y sym N L + Y asy N L ≈ Y sym N L ,thus produced non-thermally, can be matched with theobserved DM abundance by requiring that the annihila-tion cross-section: h σ | v |i ann ≡ h σ | v |i ( N L N L → Z B − L → P f f ¯ f ) ≈ π M N v − L , (14)is larger than the freeze-out value h σ | v |i F = 2 . × − GeV − . Note that in the above equation we haveused the mass of Z B − L boson to be: M Z ′ = g B − L v B − L , (15)with v B − L is the B − L symmetry breaking scale. In anexpanding Universe, the annihilation cross-section (14)has to compete with the Hubble expansion parameter: H = 1 . g / ∗ T M pl , (16)and the details of dynamics can be obtained by solvingthe relevant Boltzmann equations: dn η dt + 3 n η H = − Γ η n η ,dn N L dt + 3 n N L H = −h σ | v |i ann n N L + Γ η n η . (17) If we omit the production term from the thermal bath,i.e., Γ η n η → dn NL dt << n N L H . Inthis approximation we obtain, Y N L ≡ n N L s ≃ H h σ | v |i ann s , (18)where s is the entropy density. In the above equation Y N L has to be matched with the observed DM abundance:( Y N L ) obs = 4 × − (cid:18) M N (cid:19) (cid:18) Ω DM h . (cid:19) . (19)The matching of Eqs. (18) and (19) at T = T R , gives aconstraint on the annihilation cross-section to be: h σ | v |i ann h σ | v |i F = 2 . (cid:18) M N (cid:19) (cid:18) . DM h (cid:19)(cid:18) T R (cid:19) . (20)The above equation implies that the annihilation cross-section (14) is a few times larger than the freeze-out valuefor a reheat temperature of 100 GeV. Now combiningEqs. (14) and (20) we can get a constraint on the B − L breaking scale to be v B − L = 3 .
16 TeV (cid:18) Ω DM h . (cid:19) / (cid:18) M N (cid:19) / × (cid:18) T R
100 GeV (cid:19) / . (21) IV. DECAYING DM AND COSMIC RAYANOMALIES
The lepton number is violated through the mixing be-tween η and χ as defined by m η † χ . Therefore, the light-est N L , which is the candidate of DM, is not stable. Weassume that m << M η , M χ . This gives a suppression inthe decay rate of DM. In other words the lifetime of DMis longer than the age of the Universe. The only availablechannel for the decay of lightest N L is three body decay: N L → e − αR e + βL ν γL , (22)with β = γ . Since the coupling of χ to two lepton dou-blets is antisymmetric, i.e., β = γ , the decay of N L isnot necessarily to be flavor conserving. In particular thedecay mode: N L → τ − R τ + L ν eL ( ν µL ), violates L e ( L µ ) byone unit while it violates L = L e + L µ + L τ by two units.In the mass basis of N L the lifetime can be estimatedto be τ N = 8 . × s (cid:18) − h (cid:19) (cid:18) − . f (cid:19) (cid:18)
50 GeV m (cid:19) (cid:16) m φ GeV (cid:17) (cid:18) M N (cid:19) , (23)where we assume that M η ≃ M χ ≈ m φ in order to geta lower limit on the lifetime of N L . The prolonged life-time of N L may explain the current cosmic ray anoma-lies observed by PAMELA [1, 2], Fermi [3, 4] and re-cently at AMS-02 [6, 7]. The electron and positron en-ergy spectrum can be estimated by using the same set-up as in Ref. [17]. In Figs. 3 and 4 we have shown theintegrated electron and positron fluxes in a typical de-cay mode: N L → τ − τ + ¯ ν up to the maximum availableenergy M N / τ N = 4 × sec and τ N = 5 × sec. . From thereit can be seen that the decay of N L can nicely explainthe observed cosmic ray excesses at PAMELA, Fermi andat AMS-02. While doing so we assume that the branch-ing fraction in the decay of N L to τ − τ + ¯ ν is significantlylarger than the other viable decay modes: N L → µ − µ + ¯ ν and N L → e − e + ¯ ν . Φ / ( Φ + Φ ) eee +++ FIG. 3: Positron excess from lightest N L → τ − τ + ¯ ν with M N = 3 TeV. The red-solid (top) and Blue-dashed (bottom)lines are shown for τ N = 4 × sec and τ N = 5 × secrespectively. The fragmentation function has been calculatedusing PYTHIA [40]. Another potential signature of this scenario is the emis-sion of energetic neutrinos from the Galactic center [41]which can be checked by future experiments such as Ice-Cube DeepCore [42] and KM3NeT [43]. The constraints on the τ + + τ − emission modes by gamma-rayemissions from the Galactic center and dwarf spheroidals withinthe Galaxy depends on the density profile. Since we adopt acored profile, the constraints are much weaker than those fromthe Galactic center and dwarf spheroidals [15] E ( G e V c m - s - S r - ) FermiHESS:08HESS:09ATIC:08PPB-BETS:08AMS:13PAMELA:11
Background Φ e + + e - FIG. 4: Total electron plus positron flux from lightest N L → τ − τ + ¯ ν with M N = 3 TeV. The Black-solid (top) and Blue-dashed (bottom) lines are shown for τ N = 4 × sec and τ N = 5 × sec respectively. The fragmentation functionhas been calculated using PYTHIA [40]. V. DIRECT DETECTION OF DARK MATTERAND CONSTRAINTS
The interaction of N L on the nucleons can give rise toa coherent spin-independent elastic scattering, mediatedby the Z B − L gauge boson, through t -channel process. Inthe limit of zero-momentum transfer the resulting cross-section is given by: σ N L n = µ N L n πv − L (cid:16) Y q B − L Y N L B − L (cid:17) (cid:18) Z f p f n + ( A − Z ) (cid:19) f n (24)where f n and f p introduces the hadronic uncertainties inthe elastic cross-section and µ N L n is the reduced mass ofDM-nucleon system, given by µ N L n = M N m n M N + m n . (25)Since M N >> m n , one gets µ N L n ≈ m n . In Eq. (24),the symbols Y q B − L and Y N L B − L represent B − L charge ofquark and N L respectively. The value of f n vary withina wide range: 0 . < f n < .
66, as quoted in ref. [44].Here after we take f n ≃ , the central value.At present the strongest constraint on spin-independent DM-nucleon cross-section is given byXenon-100, which assumes f p /f n = 1 with Z = 54, while A varies between 74 to 80. This is the case of iso-spinconserving case. For a 3 TeV DM, Xenon-100 gives anupper bound on the DM-nucleon cross-section to be σ N L n < O (10 − )cm at 90% confidence level [32]. FromEq.(24) we can estimate the DM-nucleon cross-section: σ N L n = 2 . × − cm (cid:16) µ N L n GeV (cid:17) (cid:18) v B − L (cid:19) . (26)Thus the σ N L n cross-section is in the right order of mag-nitude and it is compatible with the latest Xenon-100limit [32]. However, from Eq. (14) we see that for v B − L = 5 TeV and M N = 3 TeV, the annihilation cross-section: h σ | v |i ann < h σ | v |i F = 2 . × − GeV − . Thisimplies that we get DM abundance more than the ob-served value and hence v B − L ≥ v B − L < v B − L arenot allowed by Xenon-100 constraint as they give largeDM-nucleon cross-section. These features can be easilyread from Fig. 5, where we have shown the compatibiltyof B − L breaking scale with relic abundance (dashedblack line) and direct detection constraint (solid red foriso-spin conserving and dot-dashed blue for iso-spin vio-lating) from Xenon-100.From Eqs.(14) and (24) we see that both the cross-sections: h σ | v |i ann and σ N L n vary inversely as 4 th powerof B − L breaking scale. Therefore, we need large h σ | v |i ann to get the right amount of relic abundance ofDM, while small σ N L n is required to be compatible withthe direct detection limits from Xenon-100. In otherwords, we need small v B − L to get the right amount ofrelic abundance, while large v B − L is required to be com-patible with the direct detection limits.From Fig. 5, we see that for iso-spin conserving case(solid red line) we don’t get any value of v B − L , whichis compatible with the relic abundance and the directdetection constraint on DM. However, this constraintscan be evaded by considering an iso-spin violating DM-nucleon interaction [45] as shown in the Fig. 5 by dot-dashed blue line. From there we see that a small windowof B − L breaking scale: v B − L = (2.5 TeV - 4 TeV) cangive h σ | v |i ann > ∼ h σ | v |i F and σ N L n < σ Xenon100 for M N =3 TeV.Thus we saw that the DM satisfy the direct detectionconstraints from Xenon-100 only in case of iso-spin vi-olation and within a small window of B − L breakingscale: v B − L = (2.5 TeV - 4 TeV). It is worth mentioningthat the model though involves many parameters to ex-plain the cosmic ray anomalies from decaying DM, butthe relic abundance and the compatibility with direct de-tection constraints of the latter involves a single param-eter, i.e. the B − L breaking scale: v B − L . In one hand,if v B − L > v B − L < B-L <-Allowed-> <-------Ruled out---------> byRelic abundance of DM<------Ruled out by Xenon-100 constraint------> values of v
B-L
FIG. 5: h σ | v |i ann / h σ | v |i F , shown by dashed black and σ DMn /σ xenon100 shown by solid red (iso-spin conserving) andblue dot-dashed (iso-spin violating) as function of v B − L for atypical value of the DM mass: M N = 3 TeV. ray anomalies and baryon asymmetry. Therefore, ourscenario is strongly constrained in terms of the modelparameter and can be checked at the future terrestrialexperiments such as Xenon-1T. VI. CONCLUSIONS
We studied a non-thermal scenario in a gauged B − L extension of the SM to explain a common origin behindDM abundance and baryon asymmetry. The B − L sym-metry is broken at a TeV scale which gives a Majoranamass to the DM, while the baryon asymmetry is createdvia lepton number conserving leptogenesis mechanismand therefore it does not depend on the B − L break-ing scale. Since the lepton number is violated, the DM isno longer stable and slowly decays into the lepton sectoras it carries a net leptonic charge. Since the decay rate ofDM is extremely slow, it could explain the positron ex-cess observed at PAMELA, Fermi and recently at AMS-02 without conflicting with the antiproton data.We also checked the compatibility of a TeV scaleDM with the spin-independent DM-nucleon scatteringat Xenon-100, which at present gives the strongest con-straint on DM-nucleon cross-section. We have found thatin the case of iso-spin conserving, the spin independentDM-nucleon cross-section is incompatible with the relicabundance of DM. On the other hand, by assuming theiso-spin violation interaction, we found a small windowof B − L breaking scale: v B − L = (2.5 TeV - 4 TeV), whichcan yield right amount of DM abundance while explain-ing the positron excess. This implies the corresponding B − L gauge boson ( i.e. Z ′ -gauge boson) is necessarilyto be at a TeV scale which can be searched at the LHC. VII. ACKNOWLEDGEMENTS
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