A Tight Connection Between Direct and Indirect Detection of Dark Matter
through Higgs Portal Couplings to a Hidden Sector
Abstract
We present a hidden abelian extension of the Standard Model including a complex scalar as a dark matter candidate and a light scalar acting as a long range force carrier between dark matter particles. The Sommerfeld enhanced annihilation crosssection of the dark matter explains the observed cosmic ray excesses. The light scalar field also gives rise to potentially large crosssections of dark matter on the nucleon, therefore providing an interesting way to probe this model simultaneously at direct and indirect dark matter search experiments. We constrain the parameter space of the model by taking into account CDMSII exclusion limit as well as PAMELA and FermiLAT data.
pacs:
95.35.+dI Introduction
The existence of dark matter (DM) in the present Universe has been firmly supported by a range of evidences dm_review . The prime among them are galaxy rotation curves, large scale structure, cosmic microwave background and gravitational lensing. However, the identity of DM within the Standard Model (SM) of particle physics is still missing. Therefore, its experimental verification is expected to be a new discovery and a strong indication for physics beyond the SM.
Recently the Cryogenic DM Search (CDMS) Collaboration cdms in the Soudan mine reported the observation of two events compatible with a positive dark matter detection at confidence level (C.L.). The DAMA/LIBRA dama experiment claims an evidence of DM in its modulated signal at C.L. Several other direct detection experiments are running and setting upper bounds, including EDELWEISSII edelweiss , ZEPLINII zeplin , XENON10 xenon2007 and CresstIII cresst . The Xenon collaboration will soon release the data from the first run of the Xenon100 experiment xenonup and superCDMS is planned.
A significant amount of effort has also been devoted to detection of DM through indirect searches. For example, the PAMELA collaboration pamela reported an unexpected rise of the positron fraction compared to that of the galactic background at energies above 10 GeV, while confirming the earlier results of AMS ams and HEAT heat . Similarly the HESS hess and Fermi Large Area Telescope (FermiLAT) fermilat collaborations also reported an excess of electron plus positron flux with respect to the galactic background at energies above 100 GeV, but without confirming the spectral features observed by the balloonbased experiments ATIC atic and PPBBETS ppbbets . It has been widely interpreted that DM could be a viable candidate for the observed cosmic ray anomalies, although they could be explained by astrophysical sources astrophysics .
In light of the above experimental results, several models have been considered in the literature, which leave signatures at either directdirect_detection or indirect indirect_scattering ; indirect_decay DM searches. Typically, for a given model, the predictions for direct and indirect signatures of DM depend on different parts of the parameterspace, and the derived constraints thus do not overlap. However, in some models the same couplings are responsible for both the scattering of DM on the nucleon and large annihilation cross sections, in which case an interesting complementarity between direct and indirect searches exists cfs ; cfs2 .
A simple possibility is to consider singlet extensions of the SM, in which the DM is a singlet scalar Singlet , coupled to the SM Higgs particle through the socalled Higgs portal wilzeck , namely the Higgs to DM quartic coupling (see also doublet extensions of the SM doublet_models ). Depending on the strength of this portal, the singlet can account for the observed relic density, Komatsu:2010fb . Furthermore, through the Higgs portal coupling, DM scatters with the nucleon and is thereby constrained by direct searches, as well as annihilates into SM fermions which can be observed at indirect detection experiments cfs ; cfs2 .
The anomalous positron and electron fluxes observed by PAMELA and FermiLAT require a large enhancement of current DM annihilations. In their minimal versions Singlet , the singlet extensions cannot reproduce such features. Furthermore, in these models, the stability of DM is supported by an ad hoc discrete symmetry. In this paper, we study a model which naturally solves these issues. We introduce a hidden sector gauged under an Abelian HiddenU1 HU1_2 , containing two complex scalars and . While all SM fields are hidden sector singlet, the extra scalars are singlet under the SM but charged under . This model provides all the ingredients for a viable DM model with potentially large direct and indirect detection signals.
The paper is organized as follows. In Sec. II we present the model, with particular attention to the mass spectrum and mixings in the scalar sector. The model parameter space is then examined in Sec. III and constrained by requiring the relic density of the DM candidate to be in the WMAP7 range. Sections IV and V describe the phenomenology of the model in light of the present DM searches: CDMSII, XENON10, PAMELA and FemiLAT. First, in Sec. IV, we discuss the direct detection bounds constraining the hidden sector parameter space and the interplay with the indirect detection. Then, in Sec. V, we investigate the indirect detection bounds, and give the results in terms of positron and electron excesses. The conclusions are presented in Sec. VI.
Ii The Model
Assuming a nontrivial charge assignment under the hidden Abelian for the extra scalars and , and , the most general scalar potential is given by:
(1)  
The hidden sector couples to the SM via Higgs portals, as schematically depicted in Fig.(1).
We assume that all parameters are real and positive. The field acquires a nonzero vacuum expectation value (vev), which triggers the breaking of to a remnant symmetry under which all fields are even but . The latter does not develop any nonzero vev and hence can be a dark matter candidate, being stabilized by the symmetry.
It is remarkable that almost all the parameters in this model are well constrained by both direct and indirect searches, as we will see in great details below. The relic density of is obtained through its annihilations into and via and , respectively. These two couplings also enter in the spinindependent cross section of DM on nucleon and hence are strongly constrained by direct DM searches. The field gives rise to a long range attractive force between particles, thus boosting the current annihilations, while keeping the relic abundance unchanged. As a result gets strongly constrained from indirect DM searches. After acquires a vev, it mixes with the SM Higgs through . is destabilized and consequently decays into SM fermions through the same coupling. While should not be too small for to decay before the onset of big bang nucleosynthesis (BBN), a too large  mixing is excluded by constraints coming from LEPII on the ratio of the invisibletovisible Higgs decay CBhiggs1 .
ii.1 Masses and Mixings of Hidden Sector Fields
From the scalar potential in Eq. (1), let us derive the quantities relevant for this study. First of all, vacuum stability requires, besides positive quartic couplings, that . The electroweak symmetry breaking occurs when the SM Higgs acquires a vev , while is broken to a surviving symmetry when acquires a vev . In the unitary gauge, the quantum fluctuations around the minimum are parametrized as
(2) 
where and are physical real scalars, the unphysical degrees of freedom being eaten by the longitudinal component of the SM gauge bosons and of the associated with . Minimization of the scalar potential in Eq. (1) enforces
(3) 
This minimum is the global one if . The two real scalars and mix with each other and the mass matrix in the basis spanned by is given by:
(4) 
Assuming , the mixing angle between and is suppressed:
(5) 
In terms of , the mass eigenstates and read:
(6) 
Consequently is mostly the SM Higgs field, while is the light scalar. Their respective masses are:
(7) 
Because of the small mixing, the current experimental bounds CBhiggs1 ; CBhiggs2 on the SM Higgs mass apply on .
Hereafter, in all numerical evaluations we take . However, we note that our results are
quite insensitive to the Higgs Mass. The light scalar field is the main product of
annihilations at the present epoch. In order to avoid overproduction of highenergy gamma rays from the
decay of , is required: we take as numerical reference value.
We then have .
The DM mass is given by:
(8) 
which is varied from to in the following.
The hidden sector is gauged under the Abelian and contains an extra gauge boson . Although SM particles are singlet under , through the kinetic mixing of with the hypercharge gauge boson, they can couple to . The relevant part of the Lagrangian then reads:
(9) 
where is the hidden sector coupling constant, and are the field strength tensors associated with and respectively and parameterizes the kinetic mixing between the symmetries.
For an invisible , the kinetic mixing is expected to be  at the electroweak scale. The mass of is given by and we take 600 GeV as a reference numerical value. The parameter is then lower bounded by the requirement of perturbative gauge coupling: . For the chosen value of the mass, the electroweak precision measurement constraints the kinetic mixing to be kinmix . Through  mixing, the DM can scatter on nuclei. The corresponding cross section may exceed the current experimental bounds for . When the dark gauge boson is produced in annihilations. For large , this would lead to significant antiproton fluxes in the cosmic ray which is in contradiction with PAMELA data pamela_antiproton . In the following we assume and so effects are negligible.
Assuming with while implies a strong tuning of the model parameters, with and . Reducing this tuning can be achieved by either increasing the hidden scalar boson mass, or by lowering as well as . However, in those cases, predictions of the model turn out to be very different from those we discuss hereafter. By increasing we possibly face an antiproton overproduction in DM current annihilations, in which case the corresponding cross section should be suppressed compared to PAMELA requirements. In this case, still, the model can afford a viable DM candidate but lacks predictivity. Another way to reduce the tuning is to lower or . With a lighter DM, the PAMELA cosmic ray spectrum cannot be accounted for, while with a lighter the model is in conflict with direct detection experiments. Therefore, in the following, we assume a certain amount of tuning, allowing the model to be predictive and probed by both direct and indirect detection experiments.
ii.2 Astrophysical and collider constraints
We now discuss some relevant constraints on the hidden sector coming from astrophysics and the electroweak precision measurements. The scalar field decays to SM fermions through  mixing; its decay rate is approximately given by:
(10) 
The lifetime of is then estimated as
(11) 
Thus, demanding that decays before the onset of BBN BBN , should be bigger than . Equivalently a lower bound on the Higgs portal coupling is inferred:
(12) 
Assuming that dominantly decays to , a strong constraint on can be obtained from the meson decay. From the branching ratio HU1_2 ,pdg , one infers an upper bound on to be O'Connell:2006wi . This in turn gives
(13) 
Since is very light, the mixing angle never saturates the above bound. For the same reason, the electroweak precision measurements on the S, T and U parameters do not receive any significant contributions from ewpo .
Iii Annihilation crosssection of the DM at freezeout and at present epoch
iii.1 Relic density
In the early universe the particles maintain their thermal equilibrium through the scattering processes: and SM particles. In Fig. (2), we display ratios of the dominant annihilation channels with respect to the total annihilation crosssection , as a function of the DM mass. In case of (left panel) the dominant channel is (blue dashed curve) until the (black dotlong dashed solid) and (black dotdashed) thresholds are reached. These two processes dominate the behavior of annihilations up to 120 GeV, when (green dashed curves) takes the upper hand. The situation is reversed as soon as (central and right panels). The annihilation into is competitive only for equal Higgs portal couplings, while for , (red solid curves) dominates in all the DM mass range, apart from the Higgs pole.
As the universe expands, the temperature of the thermal bath gradually falls; at , gets decoupled and starts redshifting. The relic abundance of DM can be evaluated by solving the Boltzmann equation for the number density:
(14) 
where is the Hubble expansion parameter and is the thermal average of the total annihilation crosssection.
To accurately evaluate the DM relic density, we solve Eq.(14) by using micrOMEGAs micromegas . The model has been implemented in micrOMEGAs through FeynRules FeynRules . The parameter space is chosen as follows. The physical Higgs masses are fixed at and , while the other relevant parameters are varying randomly within their allowed ranges: from to and from to . The portal couplings and vary from to , the perturbative upper bound, while varies from to . We also constrain the lifetime of to be less than s.
Demanding that the relic abundance of DM should satisfy the WMAP7 constraints Komatsu:2010fb at C.L., given by
(15) 
we show in Fig. (3) the resulting scatter plots in the plane of and against .
The requirement of having the correct relic density fixes the balance between the two Higgs portal couplings and and hence between the different annihilation channels. In the left panel of Fig. (3), as long as , we clearly see that the channel dominates. Near the Higgs resonance, , lower values of the portal couplings are allowed, but at the pole, annihilations are too efficient and the relic density gets suppressed. For , the DM dominantly annihilates into light SM fermions, mostly pairs. For , the and channels, mediated by , strongly constrain , as can be seen in Fig. (3) (right panel). For larger DM masses, the annihilation channels and are also allowed. For such large DM masses, is more constrained than . The latter can indeed take values up to the perturbative bound, while the former is upper bounded at .
Resuming, on the whole range of DM mass, typically takes values of the same order or larger than . This corresponds to middle and right plots of Fig.(2), and implies that the DM is preferably annihilating into , as can be inferred from the approximate crosssections:
(16) 
Thus we see that both portal couplings and are constrained from the requirement of obtaining the right DM relic density. Interestingly, these couplings also enter in the tchannel Higgsmediated scattering , which is relevant for the direct detection of DM, as we discuss in the next section.
iii.2 Sommerfeld enhancement
The observed relic density of DM can be obtained for an annihilation crosssection at the decoupling epoch, . However, at the present epoch, such a crosssection is too small to explain the anomalous cosmic ray fluxes observed by PAMELA and FermiLAT. Several mechanisms have been invoked in the literature to boost it. A natural enhancement may occur due to the local overdensities of DM in clumps Lavalle:1900wn , but estimates show that the resulting boost of the annihilation crosssection is too small to account for the observed cosmic ray fluxes. Two different mechanisms, arising from particle physics, also exist: either a BreitWigner resonance of the annihilation crosssection HU1_2 ,BreitWigner , or the Sommerfeld effect Sommerfeld . In this model, the latter naturally occurs because of the presence of . The light scalar acts as a long range attractive force carrier between the DM particles. If kinetic energy is small enough, the attractive interaction becomes relevant and induces an enhancement of the annihilation cross section. Defining the reduced DM boundstate wavefunction as , the corresponding boost is computed by solving the radial Schrödinger equation:
(17) 
where is the DM relative velocity, and is the attractive Yukawa potential:
(18) 
We solve Eq.(17) using the boundary condition . The Sommerfeld boost is then given by
(19) 
To consider the enhancement at present time, one should integrate over the velocity distribution of DM in the Earth’s neighborhood:
(20) 
with mean velocity km/s, escape velocity km/s and a normalization factor for a smooth maxwellian halo. The boost factor is then only a function of , and . Therefore, for a given DM mass, is degenerate with respect to and , the hidden sector breaking scale. The effective DM annihilation crosssection then reads
(21) 
In Fig. (3) the region of the parameters giving rise to boost factors from 20 up to 2000 is displayed by a green (gray) region. This is the range of enhancement required to explain the observed cosmic ray anomalies for a DM of mass (100  1000) GeV, compatible with current cosmological and astrophysical constraints, as discussed in Sec. V. On the left panel we see that only large values for are allowed, ranging from up to . This is expected by the behavior of the Sommerfeld enhancement . As mentioned before, the requirement of having a good relic density fixes the balance between the two portal couplings. In the right panel of Fig.(3), the values of in the green (gray) region correspond to the values of giving rise to a correct boost factor, although the Sommerfeld effect does not depend on . For , the largest values of are not allowed because they dominate annihilations, which in turn corresponds to lower values of .
Iv CDMSII Events and Dark Matter
iv.1 Experimental upper bounds
The CDMS collaboration has recently published the analysis of the final run of the CDMSII experiment cdms . After the background subtraction and cuts, two events survive, respectively at 12.3 keV and 15.5 keV recoil energies. The significance of the two events being a DM signal is at C.L., namely there is probability that these are of more common origin, such as cosmogenic or neutron background. In Ref. cdmsanalysis , it has been shown that if the two events are taken to be DM signal, the region will prefer light dark matter candidates, with an upper bound on the mass around 6080 GeV. If we consider the 90 C.L. region to constraint the DM mass, then only an upper bound can be set. We approach the analysis of the two events of the CDMSII in a conservative way, finding a 90 C.L. exclusion limit with the maximum gap method mgm .
In addition the upper bound from the XENON10 experiment xenon2007 is taken into account, which is the most constraining one together with CDMSII, in the case of spinindependent elastic interaction on nucleon. Using the data of the 2007 run, reanalyzed as in Ref. xenon2009 , and the maximum gap method, we infer the C.L. upper bound. We also consider the prediction for the first run of the XENON100 experiment, following Ref. xenonup .
iv.2 The elastic spinindependent crosssection
The interaction of on the nucleon gives rise to a coherent spinindependent elastic scattering, mediated at tree level by the scalars of the model, the SM Higgs particle and . This cross section reads:
(22) 
where is the nucleon mass and is the nucleonDM reduced mass. The parameter indicates the effective Higgs nucleon interaction, , where the sum runs over all the quark flavor. The factor introduces hadronic uncertainties in the elastic cross section: its value vary within a wide range , as quoted in Refs. fn_factor . Hereafter we take to be 1/3, the central value.
From the Lagrangian in Eq. (9), the particle couples directly to the hidden gauge boson and through the kinetic mixing it communicates to the SM fermions. This results in an additional DMnucleon scattering. Neglecting terms of order , the corresponding spinindependent cross section is approximately:
(23) 
where and are the mass and the atomic number of the nucleus and is the coupling. The cross section is slightly dependent on the DM mass, through the reduced mass . For , the values of we scanned over and for a maximal kinetic mixing , the crosssection value ranges from cm up to cm. As stated above, we fixed , and consequently the cross section varies from cm up to cm, and is therefore a negligible correction to and contributions. It is then possible to constrain Higgs portal couplings thanks to direct detection searches.
The behavior of as a function of the Higgs portal couplings is rather involved. Owing to the large mass differences between the two scalars, cf. Eq. (5), the mixing angle between and is small, of the order of . Even though , the second term in Eq. (22) is not negligible in the whole mass range. With respect to the standard Higgs exchange, the contribution is enhanced due to its small mass, which compensates the smallness of its coupling to the nucleon. Note that this result is valid in general in models where a scalar with mass lighter than , typically the light force carrier of the Sommerfeld enhancement mechanism, mixes with the SM Higgs cfs ; cfs2 .
The predictions for are shown in Fig. (4) as a function of , with all the points having a relic abundance in the WMAP7 range. The crosssection is enhanced respect to the standard Higgs exchange: a large region (red region) of the parameter space is not allowed by CDMSII experiment. In the low mass range a portion of the parameter space is incompatible with the XENON10 upper bound, denoted by the blue (light gray) band. The green (gray) region describes the parameter space that leads to a large sommerfeld effect and boosts . As described in the previous section, a large Sommerfeld enhancement calls for large coupling. We can therefore constraint the parameter space yielding such a large boost factor with the direct detection bounds. As shown in Fig. (4), a large portion of the green (gray) region is excluded, but nonetheless a large portion is found compatible with direct detection constraints. We also show the prediction for the upcoming XENON100 first run (blue line): while it can probe a bigger portion of the hidden sector parameter space compatible with indirect detection, a large part can give DM to nucleon crosssection below the expected sensitivity.
On the left of Fig. (5), we show an illustrative example of the balance between the two contributions in Eq. (22), for a fixed DM mass . The maximum value of the elastic cross section compatible with CDMSII is plotted, as a function of and . In this plot, three different values of the mixing angle are depicted, (blue dashed line), (orange dotted line), and (green long dashed line). First of all, for , the SM Higgs exchange dominates and is rather insensitive to . As decreases towards smaller values, the contribution becomes the leading one. For , from Eq. (22) we see that only depends on the product . For , we then have that different values of the mixing angle imply different maximum values of . Notice that, from Eqs. (18) and (20), the Sommerfeld enhancement is sensitive to the same combination . The right panel of Fig. (5) shows the points giving the right relic abundance in the plane vs , where again a green (gray) region highlights the values of interest for the indirect detection. For , a small mixing angle allows for , which is compatible with indirect detection constraints. Indeed, we see that for , should be in the range. Increasing calls for smaller values of , and consequently lower can be obtained. For , we see that , a value for which the boost factor is too small to account for the whole cosmic ray excesses. The situation is even worst for for which .
V Electron, Positron and Antiproton Fluxes from Annihilation
As described in Sec. III, the annihilation of and will generate both positrons and antiprotons in the present Universe and could have been detected by various experiments such as PAMELA, HESS and FermiLAT. In the case annihilates into , the final products are dominantly muons and antimuons resulting from the decay of , while in the latter case the final products are mostly hadrons. From Eq.(III.1), the ratio of annihilation cross sections into to is
(24) 
As we see from Fig.(3), we typically have when we require that the annihilation crosssection is enhanced by a nonnegligible boost factor. This is sufficient to suppress the antiproton flux over the positron one. Therefore, in what follows we will focus on the production and propagation of positrons in the Galactic medium.
v.1 Production and propagation of positrons
From annihilations, is produced which then decays to muon and antimuon. They ultimately decay to electrons, positrons and neutrinos. As a result, equal numbers of electrons and positrons are produced from the annihilation of particles. However, the background flux of electrons in the Galactic medium is significantly larger than the positron one. Therefore, it is easier to find signature of DM, if any, in the Galactic positron flux.
Once the positrons are produced in the Galactic halo where the DM concentration is large, they travel under the influence of the Galactic magnetic field which is assumed to be of the order of a few microgauss. The motion of positrons can then be thought of as a random walk. In the vicinity of the Solar System, the positron flux can be obtained by solving the diffusion equation delahayeetal:2007
(25) 
where is the number density of positrons per unit energy, is the energy of positron, is the diffusion constant, is the energyloss rate and is the positron source term. The latter, due to annihilations, is given by:
(26) 
In the above equation the fragmentation function represents the number of positrons with energy which are produced from the annihilation of particles. We assume that the positrons are in steady state, i.e. . Then from Eq. (25), the positron flux in the vicinity of the solar system can be obtained in a semianalytical form delahayeetal:2007 ; hisanoetal:PRD2006 ; cireli&strumia:NPB2008
(27) 
where is the diffusion length from energy to energy and is the halo function which is independent of particle physics. An analogous solution for the electron flux can also be obtained.
v.2 Background fluxes of electron and positron
Positrons in our galaxy are not only produced by particle annihilations but also by the scattering of cosmicray protons with the interstellar medium moskalenko&strong:astro1998 . The positrons produced from the later sources thus act as background for the positrons produced from DM annihilations. The background positron fraction can be defined as
(28) 
where the primary and secondary electron fluxes, as well as the secondary positron flux, can be parameterized as baltz&edsjo:prd1998 :
(29) 
where =E/(1 GeV) is a dimensionless parameter.
v.3 Results and Discussions
The net positron flux in the galactic medium is given by
(30) 
The second term in the above equation is given by Eq. (27), which depends on various factors: , , , , and the injection spectrum . The energy loss (due to inverse Compton scattering and synchrotron radiation with Galactic magnetic field) term is determined by the photon density, and the strength of magnetic fields. Its value is taken to be baltz&edsjo:prd1998 . The number density of DM in the Solar System is given by , where . In the energy range we are interested in, the value of is taken approximately to be , the velocity of light. The values of diffusion length and the corresponding halo function are based on astrophysical assumptions delahayeetal:2007 ; cireli&strumia:NPB2008 . By considering different heights of the Galactic plane and different DM halo profiles the results may vary slightly. In the following, the Galactic plane height is taken to be less than kpc, which is referred to as the "MED" model delahayeetal:2007 ; cireli&strumia:NPB2008 , and we have used the NavarroFrenkWhite (NFW) DM halo profile NFW
(31) 
to determine the halo function , where and .
We use the program DARKSUSY darksusy to compute electron and positron fluxes from annihilations . We then determine, for , what is the maximum annihilation cross section allowed for the fluxes not to exceed PAMELA observations. In this range, we found the approximate empirical upper bound:
(32) 
The constraint Eq. (32) only tells us that bigger boost factor are excluded. If one wants to fully account for the anomalous cosmic ray fluxes through DM annihilations, the boost factor gets lowerbounded, again in the range:
(33) 
If both Eqs. (32) and (33) are fulfilled, then cosmic ray fluxes are within 1 standard deviation of PAMELA data. Of course, if all PAMELA data have to be explained, is required, given the annihilation channel .
Actually several constraints exist on large annihilation cross sections, relying on different physics, but all sensitive to DM annihilation products. When compared to the fiducial value of the annihilation cross section, these constraints apply in turn to the Sommerfeld enhancement . At high redshift, the energy deposition of the charged leptons may induce perturbations of the cosmic microwave background photon spectra CMB1 , reionization and heating of the intergalactic medium reion , providing strong constraints. At the recombination time during which DM relative velocity is , a bound on is inferred CMB1 :
(34) 
Stringent constraints arise from inverse Compton gamma rays in the Galaxy. The muons produced in DM annihilations subsequently decay into electrons. This population of electron yields irreducible highenergy gamma rays through inverse Compton on the Galactic radiation field. We consider the Fermi data released in Abdo:2010nz , at galactic latitude and the analysis of Ref. Hutsi:2010ai . For a NFW profile and a final state into , the allowed boost factor is for a dark matter mass of 400 GeV. Notice that Ref. Papucci:2009gd considers a Galactic latitude closer to the Galactic center and is therefore more sensitive to the DM density profile. In this case and for a NFW profile the maximum allowed boost factor at is . The model is thus in great tension with the Pamela anomaly. However with an isothermal profile instead, a boost factor up to is allowed, attenuating the constraints on the model parameter space. As for the extragalactic gamma ray constraints, discussed in Refs. Abdo:2010dk ; Hutsi:2010ai , they strongly depend on the assumptions on the history of structure formation. It turns out that the parameter space we are considering is allowed for a conservative choice of the halo concentration parameter, see Fig. 4 of Hutsi:2010ai and Fig. 6 of Ref.Abdo:2010dk (which considers a twomuon final state case). For the cases we consider, constraints from recombination and from diffuse gamma rays are of the same order. In Figs.(3)(5), we depicted the boost factor satisfying the constraints Eqs.(3234) within a green (gray) band.
Point  

1  0.82  500  195  
2  0.1  800  8 
In Fig. (6), we show the comparison between the positron fraction obtained from annihilations with the positron fraction observed by PAMELA, AMS and HEAT, for the two typical points defined in Table 1 at GeV. The quoted values of the couplings are inferred from Fig. (5), and provide a relic density in the WMAP7 range as well as saturate current direct detection bound. The first set of parameters is in a good agreement with the anomalous positron fraction observed by PAMELA. However, the corresponding boost factor is at the border line of gamma ray constraints coming from FermiLAT Hutsi:2010ai Abdo:2010dk and reionization reion . The second set cannot entirely account for the excess measured by PAMELA since the largest boost factor allowed by direct detection is about 8. We conclude that in order to fully explain the positron fraction together with an observable cross section on nucleon, bigger values of , and conversely lower values of the mixing angle are mandatory.
Concerning the electron plus positron flux observed by FermiLAT, is necessary if the flux stems only from DM annihilations. However, for such high masses, the required boost factor is . Such a high value is in great tension with reionization constraints reion . In Fig. (7), we compare FermiLAT, HESS, PPBBETS and ATIC data on electron plus positron fluxes with the predictions of this model for the representative points mentioned in Table 1, for which . The first point, depicted by a red solid line, yields and can fit PAMELA data as well as the low energy flux observed by FermiLAT. Of course, with , not all the energy range can be explained. The second point, depicted by a dashed black line and for which , cannot account neither for the PAMELA results nor for the FermiLAT ones. In both cases, FermiLAT electron plus positron flux can only explained by adding an extra source of astrophysical origin.
Vi Conclusions
In this paper we studied a hidden Abelian extension of the standard model. The DM is a complex scalar, singlet under the SM gauge group but charged under the hidden sector. We also introduce a light scalar , whose nonzero vev breaks to a symmetry under which all fields but are even. As a result is a stable DM candidate, with mass ranging from the GeV to the TeV scale. The three fields , and couple together via three Higgs portal couplings. The physical scalars and mix together with the mixing angle .
The relic density of mainly results from the annihilation channel through . All three portal couplings enter in the spinindependent DMnucleon cross section. While the usual Higgsmediated channel depends on , the mixing between and provides an additional channel, mediated by the light scalar , which is . Given the mass scales we consider, the main contribution to the direct detection signal actually comes from this mixing term. For the parameter space we scanned over, solutions are found saturating or exceeding current experimental bounds from XENON10 and CDMSII, or are in the reach of sensitivity of XENON100. The model also provides indirect signatures of through cosmic ray flux measurements. The main annihilation channel , followed by fast decays, ends up in highenergy electron and positron fluxes. The suppression of annihilations into standard Higgs compared to our dominant channel, together with the light mass of , entail that no antiproton flux is expected at a significant level. A Sommerfeld enhancement of the current DM annihilation cross section occurs through the light exchange, which explains cosmic ray excess observations. This enhancement depends on .
Interestingly, in this model, direct and indirect DM searches constrain same part of the parameter space. More precisely, in order to fully account for the anomalous positron fraction observed by PAMELA, large values of are required. Such large values give rise to large direct detection signals, saturating the current experimental exclusion limits. From this, an upper bound on the mixing angle is inferred. As an example, for and , should be less than in order to satisfy simultaneously the current direct and indirect detection limits. We stress that in all models where the Sommerfeld enhancement occurs thanks to a light scalar that mixes with the Higgs particle, direct and indirect detection of dark matter are tightly connected.
Acknowledgements.
N.S. would like to thank K. Kohri, J. McDonald and C. Balazs for useful discussions. This work is supported by the IISN and the Belgian Science Policy (IAP VI11).References

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