JCAP03(2015)011 -Ray Γ Hysics P Le Ic T a Ar Doi:10.1088/1475-7516/2015/03/011 Strop a Debasish Majumdar a B

JCAP03(2015)011 -ray γ hysics P le ic t a ar doi:10.1088/1475-7516/2015/03/011 strop A Debasish Majumdar a b . Content from this work may be used 3 osmology and and osmology C 1312.7488 dark matter theory, dark matter experiments We promote the idea of multi-component Dark Matter (DM) to explain results rnal of rnal Article funded byunder SCOAP the terms of the Creative Commons Attribution 3.0 License . , these candidates have larger annihilation cross-sections compared to the single- DM ou An IOP and SISSA journal An IOP and -ray excess from galactic centre and Astroparticle Physics and Cosmology1/AF Division, Bidhannagar, Saha Kolkata Institute 700064, of India Discipline Nuclear of Physics, Physics, IndianIET-DAVV Institute Campus, of Indore Technology 452017, Indore, India E-mail: , [email protected] [email protected], [email protected] b a Any further distribution ofand this the work must title maintain of attribution the to work, the author(s) journal citation and DOI. Kamakshya Prasad Modak, Fermi bubble by awith Dark two Matter real model scalars A possible explanation ofγ low energy J and Subhendu Rakshit Received March 6, 2014 Revised December 6, 2014 Accepted January 15, 2015 Published March 9, 2015 Abstract. from both directeach and DM candidate indirect to detection relicof abundance experiments. Ω is summed up Incomponent to DM these meet models. WMAP/Planck models measurements Wesingle illustrate as this real contribution fact scalar by of DM introducingbounds, model. an perturbative extra We unitarity scalar also and toexperimental present triviality the detailed results constraints popular calculations on still for thisent show the model. scenarios some vacuum with As stability conflict, directinteresting different we detection observation: DM kept mass the ourCRESST zones. existing options II, direct open, XENON In detection 100 discussing the experimentsfrom or galactic framework differ- like centre LUX and CDMS of together Fermi II, bubble ourhave with by the CoGeNT, model the Fermi Gamma-ray capability observation Space we to of Telescope make (FGST) distinguish excess already between an low different energy DM haloKeywords: profiles. ArXiv ePrint: JCAP03(2015)011 4 4 26.5% of the content ∼ 2 0 2 – 1 – Z Z searches 11 × × 2 2 X Z Z 2.1 Lagrangian invariant under 3.1 Vacuum3.2 stability conditions5 Perturbative3.3 unitarity bounds6 Triviality bound3.48 Constraints3.5 from invisible Higgs Constraints decay from width9 LHC mono- experiments and Planck survey 5.1 Constraints5.2 from CDMS II Constraints and5.3 from Planck CoGeNT data and Constraints Planck5.4 from data CRESST II Constraints and5.5 from Planck XENON data 100 Constraints and from Planck LUX data and Planck data 6.1 Explanation6.2 of excess gamma Explanation ray of emission gamma from ray galactic bump centre from Fermi bubble’s low galactic latitude 24 15 21 16 17 19 13 20 2.2 Lagrangian invariant under of the universe.of The dark particle matter naturethat deduced of most from DM of cosmological the candidate observations DM is mentioned could still above be unknown. tends made to of The weakly suggest relic interacting massive density particles (WIMPs) [6–9] 1 Introduction The overwhelming cosmologicalistence and of astrophysical an evidencesnamely unknown have non-luminous the now matter dark established(WMAP) present matter the], [1–3 in (DM). ex- BOSS the [4] or Experimentsto universe more consolidate like in recently the Planck Wilkinson enormous fact [ 5] that Microwave amount, measure this Anisotropy the non-baryonic baryonic Probe DM fraction constitutes precisely around Contents 1 Introduction1 2 Theoretical3 framework 3 Constraints on model parameters5 4 Calculation of relic abundance 5 Constraining the parameter space with Dark Matter direct detection 6 Confronting indirect Dark Matter detection experiments 7 Discussion and conclusion A Direct detection cross-section B Photon flux due to DMC20 annihilation DM11 halo profiles 28 30 31 33 JCAP03(2015)011 symmetry 2 Z symmetry, but the 10 GeV. Some ear- 2 Z ∼ symmetry. This ensures the two singlet 0 2 Z × 2 Z – 2 – etc. Fermi Gamma-ray Space Telescope (FGST), operated from mid ν , γ 10 GeV DM mass have been done [61, 62]. XENON 100 [63, 64], how- ∼ Direct detection DM experiments can detect DM by measuring the recoil energy of a The indirect detection of DM involves detecting the particles and their subsequent decay The regions in and around the GC are looked for detecting the dark matter annihilation Amongst the non-minimal extensions, a DM model where SM is extended by a complex If our visible sector is enriched with so many particles, the DM sector should, in princi- The minimal extension with a single gauge singlet real scalar stabilised by a symmetry protecting the other one spontaneously breaks. In all these non-minimally 2 target nucleon of detectingcleons. material in Experiments casepresent like a their CDMS DM results [54–56], particleplane. indicating DAMA happens allowed [57, to These zones scatter58], experiments off in CoGeNT seem such the [59] nu- to scattering orever, prefer cross-section CRESST did low — [60] not dark DMments observe matter and mass has any masses presented potential anDM upper DM masses. bound event on Recent DM-nucleon contradictingtion. findings scattering claims cross-section by for of LUX various [65] the have earlier fortified experi- claimsproducts, produced by due XENON to 100 DMcentre collabora- annihilations. of gravitating Huge bodies concentrationDM of such DM particles as are over the expected time. sun at or the the galactic centreproducts (GC) such as as they can capture scalars as two components ofreal dark scalars matter our in endeavourobservations. is this to framework. explain In both our direct present and model indirect with detection two DM experimental lier works on of ’08, has been looking for the gamma ray from the GC [66]. The low energy gamma singlet scalar has beenbeen considered discussed in in refs. refs.–45]. [43 [46, 47], A where DM model one with scalar two is real protected scalars by has ple, a be composed ofa more model than one with component.nent two We dark DM therefore matter candidates. intend has toDM discuss been In model in discussed some is this in that earlier paper spectacular the details. works signals DM [48–53] The in annihilation the advantage can theannihilation of be idea dark cross-sections such enhanced of matter in a so multicompo- detection thisnitude that multi-component experiments. model one compared can can, Hence to enjoy in thetwo-component that enhancement general, dark thermal of upto expect matter averaged a the modeltwo few where models real orders the gauge with of Standard singlet one mag- Model scalars real protected sector by is scalar. a extended by In adding this work, we consider a in the context ofextensively dark studied matter in was the proposedbeen literature discussed by [19]-[ with Silveira a and41]. global Zee U(1) In in symmetry. ref. ref. [42] [18] the and singlet then scalar it DM was model has Z extended models there is, however, only one DM candidate. and they are non-relativisticModel or (SM) cold of in particlein physics. nature. the Many This such framework calls extensionsKlein of for have [10, been supersymmetry, an11], suggested extension extra inert invery triplet of dimensions, the [12] massive the literature axion or DM Standard supersymmetry etc. whereasPhenomenology breaking Models models of models like such simpler like mAMSB extensions as SMSSMmodel [ 13] of14], [ Kaluza predict [17] SM axion has like [15]sector been fermionic is predict DM elaborately particularly DM model interesting studied. of because [16] lower of or Amongst mass. its inert all simplicity. doublet such options, extending the scalar JCAP03(2015)011 (2.1) 4 0 S 0 4 4 4 k S 4 4 + k 3 -ray from GC and 0 + γ S 3 0 3 3 S k ) 3 0 3 k + S 0 2 ) are added to the Stan- 0 0 + S S 2 , SS 0 2 b 3 S 2 ) k k 0 2 ’s denote the couplings between 2 k δ symmetry is confronted with the S + and 0 + 0 0 2 0 S + 0 S Z S S 2 × 2 SS λ SSS m c 4 2 2 λ 0 a 1 3 m k 2 δ 1 Z k ( δ + 1 3 + 0 + 2 0 + 2 0 – 3 – 2 HS HS ) SSSS † SS † b 4 00 2 H 2 H k k H † 0 2 2 2 δ + 2 H δ + 0 ( + S 4 S λ + 0 0 0 ’s are the couplings between these singlets themselves. + k HS HS HS SSS † H † † † a 4 H k H H H ( 00 0 1 2 1 2 2 2 2 1 δ δ 4 δ 2 m + + + + -ray flux from possible DM annihilation in the galactic halo may help γ ) = 0 H, S, S ( is the ordinary (SM) Higgs doublet. In the above V H The paper is organised as follows. In section2 we discuss the theoretical framework The general form of the renormalisable scalar potential is then given by, The emission of gamma rays from Fermi bubble may also be partially caused by DM As mentioned earlier, in this work, the proposed model of a two-component dark matter where the singlets and the Higgs and of our proposedunitarity, model. triviality and experimental TheHiggs constraints boson theoretical from have constraints been therelic from discussed invisible density vacuum in calculations. branching stability, section3. ratioPlanck The perturbative observations of in The model the section5. following is section Explanation confronted of contains with the the direct observed relevant detection excess of experiments and experimental findings of bothtion experimental direct results and we indirectparameter first DM put space experiments. constraints is on further Fromexperimental the constrained the observations. model by direct parameter We the then space. detec- reliceter choose The density benchmark space model results points to given fromconsideration by explain this different WMAP/Planck constrained results DM param- halo from profiles. indirect detection experiments annihilation taking into Fermi bubble by our model is studied in2 section6. We conclude in Theoretical section7. framework We propose adard model Model. where two real scalar singlets ( annihilations. The Fermiupward bubble and downward is from aLarge the lobular Area galactic Telescope plane structure [69]. and ofplane has and The gamma been emit lobes ray gamma discovered spread emission recently rayThe up with gamma by zone to energy emission Fermi’s both extending is a supposed fromof few a to kpc cosmic be few above GeV produced ray and to fromspectra electrons. about the below from inverse a the Compton the But hundred galactic scattering GeV. higheration more (ICS) galactic cosmic involved latitude electron study regionlower distribution, of latitudes. can it this be The cannot emission explained satisfactorily reveals by explain that ICS the taking while emission into the from consid- the with two real gauge singlet scalars protected by a ray from GCexplained shows by some known astrophysics. bumpy Ais structures plausible provided around explanation by of a DM such annihilations few a [67, non-power GeV68]. law which spectrum cannot be properly explain this apparent anomaly [70–72]. JCAP03(2015)011 (2.4) (2.9) (2.2) (2.7) (2.8) (2.5) (2.6) (2.3) onto the 2 Z 0 is given by 4 0 SS S 4 S . 00 2 4 2 S or not, we discuss 4 k k . 4 2 4 k 0 + and Z + 12 22 S , , 0 2 + S S 0 M M S 2 . 12 12 2 S 2 k ) 12 11 2 HS SSS 0 2 † k a 4 θM θM S M M + 0 k , H 2 + 1 4 S 00 2 0 sin sin 2 2 , δ θ θ + ≡ 0 = 0 , HS SS 4 + † . c 0 4 S b 3 HS 4 † k k S 0 H 2 2 cos 0 0 4 22 2 / S 2 H 4 + 2 S = k δ S 00 2 0 2 0 4 / 2 0 + 2 cos − M 4 2 2 Z k k δ − a 12 3 − −→− + + v k 0 22 11 − 0 2 M 2 2 + + 0 δ S ) 2 = 4 + 2 2 11 S 0 are odd under the same ) / 2 θM θM SSSS 0 + 3 H 0 2 2 0 2 2 0 Z b S 4 M † 2 2 2 k 0 2 , and the rest of the particles are even, k H v Z Z – 4 – 0 k 2 × S 2 † and k 2 00 2 2 H k = = δ ( Z Z + × × + −−−−→ H 0 1 0 θ 4 λ ( S 2 2 2 + 2 + sin + sin δ 0 and S 4 / λ Z Z 2 2 0 0 + 00 0 2 / 11 22 = S 2 S k + S 2 HS tan 2 3 are given by v H † Z −→− k HS 2 † θM θM 2 SSS H † δ H † a 2 2 4 4 + S S H = 0 2 k H / 2 + 2 δ H ( 2 1 0 2 2 2 2 2 δ v 4 δ 1 m + k 2 00 2 and m + + δ = cos = cos 1 1 2 S ) = 2 2 S S 0 ) = = 0 M M 0 = 0, so that the scalar potential (2.4) further reduces to SS c 4 are odd under the same H, S, S M k 0 ( H, S, S S ( V = V are stabilised by different discrete symmetries, b 4 k 0 and S = S 00 2 k After the spontaneous symmetry breaking the mass matrix for The stability of DM particles is achieved by imposing a discreet symmetry and denotes the vacuum expectation value of the Higgs. After diagonalisation the masses of = S 2 00 2 v √ If the physical eigenstates some parameters of the potential vanish: 2.2 Lagrangian invariant under δ Lagrangian. Depending on whether two scenarios for completeness. 2.1 Lagrangian invariant under If only where so that the scalar potential (2.1) reduces to the following, JCAP03(2015)011 . 0 2 δ (3.4) (3.3) (3.1) (3.2) (2.10) (2.11) and 2 δ , 0 2 k are given by , , . , 0 0 0 2 0 S k > > 1 > 23 11 and 23 a a ¯ a S 13 √ 13 a ¯ a 23 12 a 12 a a + 2¯ √ 22 of order 3 to be copositive are a ) + 2 + , , , √ , 2 23 symmetry. The criteria for coposi- A 0 0 0 0 a 11 scattering processes can be avoided, 13 2 a . , 0 a > > > 11 Z > a √ S 2 2 0 + 22 33 33 33 v v 23 2 2 + S a a a 0 2 2 a 33 δ δ , a 11 11 22 a 22 0 ↔ + a a a a + + √ √ √ > √ 2 13 0 2 2 22 12 a k k SS a – 5 – a + + + 22 √ + = = + 12 13 23 , a 13 0 a a 0 a 2 33 S 2 a 33 S a a = = > = M + M 2 12 22 cases, if a 13 23 11 12 a 33 ( 0 2 ¯ ¯ ¯ a a a a a 11 Z − a √ × 33 √ 12 a 2 a ) with the squares of real fields as single entity. Lagrangian re- 2 b Z 22 + S a 2 a 33 11 S and a a ab 2 22 = λ a Z A 11 × a 2 √ det Z invariant Lagrangian. symmetry which ensures the stability of scalar dark matter has the terms which 0 2 2 Z Z × 2 In both After spontaneous symmetry breaking the respective masses of The necessary conditions for a symmetric matrix Z from which sufficient conditions for vacuum stability can be obtained. Derivation of the necessary and sufficient conditions for the model is much simpler with copositivity than 1 ab with the other used formalisms. and The last criterionand given (3.4)) in below eq. (3.2) is a simplified form of the two conditions (eqs. ( 3.3) The four beyond SM parameters determining the masses of the scalars are the model canfewer give number rise of to beyond athe SM two-component parameters, DM in scenario. the However, following as we the will restrict later ourselves case only has to tivity allow one toλ derive properly the analytic vacuum stability conditionsgiven for by such [73–76], matrix 3 Constraints on modelThe parameters extra scalars presentrevisit in constraints the emanating modelpotential. from modify Perturbative vacuum the unitarity stability can scalar also conditionsdecay potential. get width and affected of Hence by triviality Higgs these it from ofon scalars. is LHC these the Limit severely prudent constraints. on restricts Higgs to the such invisible models. In the3.1 following we elaborate Vacuum stabilityCalculating conditions the exact vacuumever, stability for conditions many for dark anyas matter model models quadratic is the form generally quartic ( difficult.specting part How- of the scalarcan potential be can expressed be like that.in expressed a The scalar similar potential form of as our above proposed because model of can also preservation be of expressed JCAP03(2015)011 [20]. (3.6) (3.7) (3.9) (3.5) (3.8) 0 and (3.10) λ . 0 4 > 0 k 2 S > p 2 M ) v 0 4 2 1 k 4 − k > q 0 2 + k λH a 4 3 k v and )( + 0 4 λ 2 4 λk k H q √ λ The conditions eq.) (3.1 impose 2 2 2 + v v 2 ) basis for the potential eq. (2.9) is 1 2 . 3 0 2 , , , , 2 0 δ 0 0 0 0 0 for the Higgs and also contributes to . − + , . )( 2 < > > > > ,S 4 3    > 2 2 2 2 0 0 0 0 4 0 4 4 4 4 2 a 4 v v 2 λv 2 δ 0 or 2 2 k δ λk k k 0 2 2 2 1 k ,S 4 δ δ λk λk , k 2 4 > vλH 2 a 4 k p 2 are copositive. 0 for k = h k q p 2 + + + q + δ 0 A 2 2 0 2 > 2 2 H λ δ + + 2 δ δ k k + 4 – 6 – H δ 0 2 2 M (    a 4 v δ δ λ = = 2 k , k 2 4 r 0 0 2 0 and S m 2 S = 0 to be a local minimum we should have + M > < k i + M > λ 4 Λ = 0 4 2 2 2 S λ √ δ h 0 4 H k λ, k 2 model is bounded from below if eq. (3.6) and eq. (3.7) are 4 m 0 2 = 0, + 2 particles Z i + 4 0 k S 4 × h S p H 2 0 is a part of well known Sylvester’s criterion for positive semidefiniteness. 0 2 4 λ Z δ > and + = A 2 principal submatrices of 2) and S 0 4 k H × √ 0 q the other inequality has to be satisfied [74]. SS 2 , v/ δ V or + 0 4 = (0 k 0. This is also a global minimum as long as i 4 The conditions of eqs. (3.6) and (3.7) simply determine the vacuum stability bounds on The matrix of quartic couplings Λ in the ( H > h λk The criterion, det 0 2 2 S q For M our model. We restrict the parameter space3.2 by these conditions for Perturbative later unitarity calculation. The bounds potential of the and simultaneously satisfied. Then, the masses of the The potential of thecan scalar be sector written after as, electroweak symmetry breaking in the unitary gauge where one that the three 2 given by Copositivity criteria of eqs. (3.1)conditions, and (3.2) yield the necessary and sufficient vacuum stability The Higgs mechanism generates a mass of JCAP03(2015)011 , , 0 S 0 HS S (3.20) (3.18) (3.19) (3.21) (3.13) (3.14) (3.16) (3.11) (3.12) (3.15) (3.17) → → HS , , , HH 2 0 , , 2 processes are S S 2 0 SS S → H , 2 2 denotes the matrix and the scattering 2 S S H 0 2 , 2 δ → . 0 2 → M M M 1 1 1 → . , 2 + 0 2 S − − − 0 0 4 SS T S 2 u u S S u 2 2 S S , S, HS , 4 0 S 2 2 is the centre of mass (CM) 0 0 H H M 2 + + 4 + M k 2 a θ , 4 δ 2 2 4 δ s 2 2 ,S k S S M M − v v 2 0 HH H − + 2 2 HS cos u S M M δ δ − − + u 2 0 1 1 M 1 d 4 → S u u 2 + 0 − − → + − 2 t t 0 2 S → ) for the above 2 t k 2 + + H 2 0 2 4 2 H 4 T k 2 2 + + λ → H H M 2 2 HH HS λ M 2 2 2 3 v v 2 1 3 + +1 , 2 0 v v 2 2 T M M − H − S − 0 2 2 δ δ 2 t δ δ 2 t Z − − M S SS 1 δ + + t t 2 0 2 + 2 + 2 − k v 0 2 2 CM i H H → + + s 2 2 HH, HS, SS, S S S p , – 7 – , 0 + + s M M 2 2 1 1 0 H H 2 [78]. In the above, M M S 2 2 2 0 0 δ 2 2 CM f δ 2 H − − M M 1 2 v v p S − − S 2 0 s s 2 2 2 H 2 4 2 H 0 2 M , s s HS δ δ − − v δ v 2 2 H H 2 2 0 M 2 0 2 2 M s s s being the incident angle between two incoming particles. δ δ | ≤ v 2 2 M M vδ π 2 ) 2 − HH − θ v v 1 δ 0 δ 1 + 3 0 2 2 t s + + a 32 δ δ 2 2 → 0 1 + 1 + 3 1 + 3 1 + = 0 2 + + S H 2 Re( + + 2 0 | S 4 4 0 v 0 HS M a a 4 4 k k 0 0 a 2 2 2 2 H 0 2 . The matrix elements ( S δ k δ δ δ k 0 2 2 , δ vδ S 0 = 6 = = = 6 = = = = = 3 + + S 0 0 S S 0 HH 0 SS SS HS S HH HH HH HS S → → → → → 0 → → → → → 0 2 processes with → 0 0 0 S S 0 0 SS S S S 0 0 SS HS 0 S S T → HH HS S T T S S are the initial and final momenta in CM system and T T SS T T T T , , 0 S CM i,f 0 SS p S The possible two particle states are → → After that, tree-level perturbative unitarityapplied [77] to in scalar this elastic model scattering processes (eq. has (3.11)). been The zeroth partial wave amplitude, must satisfy the condition energy, processes include many possible diagrams such as element for 2 HH SS calculated from the tree level Feynman diagrams for corresponding scattering and given by, JCAP03(2015)011 (3.31) (3.25) (3.26) (3.27) (3.28) (3.29) (3.30) (3.32) (3.22) (3.24) (3.23) , 2 0          2 δ H H H H H 0 H 0 0 0 0 0 S S S S S S + 2 → → → → → 2 2 0 → S δ H S v , 0 0 0 0 SS 0 SH 0 S HH 0 S 0 0 S π 3 a a a a a a 8 π , π , π , π . π , ) + 2 S S S 6 6 8 8 S S 8 8 r 8 4 0 S 2 0 0 0 0 0 g S S S S S S ≤ → → → → → 0 → | ≤ | ≤ | ≤ | ≤ | ≤ S + 3 H S H 0 0 a 4 4 0 4 2 2 0 0 0 SS 2 0 SH 2 δ δ 0 S k k 0 HH k S 0 0 S | | | | , | a M g a a , a a a ) 2 ) 1 . λ 0 0 0 g 0 0 λ 0 S S S S S : : : : : : 0 S 0 0 0 0         0 S 0 0 S S S S + 3 S 0 2 + 2 S + 3 0 S S δ → → 0 → 0 4 → → 0 0 4 0 → 1 4 SS SS S k S H g S HH k S S 0 0 0 ( 0 SS a 4 SH 0 0 S 0 HH 0 S 0 S 0 0 0 0 0 0 → → , 3 2 a k → a a a a 0 a → 2 → → + 6 + 6 δ 0 0 4 S h + – 8 – a 0 4 2 a 4 h 0 k are thus obtained at one-loop level as 0 0 0 SS S γ δ k 4 t k γ 0 SH SH HH S SH SH SH 0 SH 2 y HH HH (2 S δ → (2 2 → → + → → 0 2 0 → 2 for δ 0 0 0 6 , 24 S δ H 4 S 0 δ 0 2 0 and and k SS 0 SH 0 0 S δ for HH 0 S 0 for 0 S − + 2 and 4 a + a a a a a a , 4 2 k k h 0 a 4 a 4 a k 4 6 SS k k HS k 2 λγ SS SS 0 SS 2 SS SS 0 , 2 2 + 6 SS λ δ δ HS 0 0 2 0 00 0 0 0 0 0 0 2 δ 0 4 δ δ → 3 → → → 2 → → → 0 → k 0 + δ for each individual process above we obtain S + 4 H + S 0 → 0 , 2 0         S 2 SS 0 2 SH 0 0 S 0 2 0 4 1 2 2 2 0 HH 0 S 0 S 0 a δ δ λ m a π a k a HS a a S 1 , 16 0 2 HS | ≤ k 0 = 4 = 4 = 6 = 2 ) for for HH 2 HH HH S 0 HH HH HH , 0 2 2 2 a 2 → → → ) to infinite value up to the ultraviolet cut-off scale Λ of the model. This for → → 0 → ,M dt k dλ dt dt dt S λ 2 H S dδ dδ S dk 0 0 0 2 , SS 0 2 2 SH 0 2 S 0 Re( HH 0 S 0 S 0 π λ | ,M a a π π a a π a a −→ 2 H 16 16 16 16          M = s symmetry, we have to solve the renormalization group (RG) evolution equations M 0 2 Z Therefore to check the triviality in our model, namely the two scalar singlet model with Requiring Now using eq. (3.12), we have calculated the partial wave amplitude for each of the × 2 for all the runningdetermining parameters the of beta this model. functionsmodel, namely, for We have our chosen model. only one-loop The contribution RG in equations for the couplings in the requires that Landau pole of the Higgs bosonZ should be in higher scale than Λ. 3.3 Triviality bound The requirement for ‘trivialitythat bound’ the on renormalization any group modelsuch models evolution is (say, should guaranteed by not one push of the the quartic conditions coupling constant of scattering processes and the coupled amplitude can be written as a matrix form, JCAP03(2015)011 ) L is SM , λ 0 2 M (3.35) (3.36) (3.38) (3.33) (3.34) (3.37) , δ 2 , SU(2) , δ Y 0 2 , k 2 38% [80]. Γ , k [79] a 4 < t are U(1) , k 0 4 m t . y , k inv) = , 4 ! 2 k µ 0 g → 2 S 2 H , 1 M H M g 4 ( . Such invisible decay channels B 0 − , S 0 and 1 S 2 t s inv y 2 for running of top Yukawa coupling, 0 2 or δ inv , + Γ + 3 /v 0 2 + Γ 1 SS δ 2 1 2 − 2 S g SM 2 ) H δ ). Although we have solved the RG equation Γ denotes the renormalization scale and π M 4) 0 2 , M 3 4 / δ 2 is very small as we can see from eq. (3.31) that µ / is the invisible Higgs decay width, which in our δ , ) (3 – 9 – ) + 4 − a 4 t , λ 2 0 0 4 2 2 k 2 1 δ − inv and k m δ ( inv) = on 2 + 2 2 s s + g k 2 2 0 0 4 2 + 2 α + 2 4 δ → δ k 4) 2 k 0 2 2 a

( / 4 a 4 (or k H a 4 k k ( (9 2 H k 2 1 and ) is strong coupling at the scale of 2 1 δ B ) with energy scale can be obtained from the plots as it is t (1 + 4 − + 6 0 2 2 t 26 which at present is allowed at 95% CL [81–85]. However as + δ 0 v 2 + S . m + 6 πM m = δ ( 2 0 0 2 4 4 2 s 2 and 2 32 a 4 k k h α ∼ 2 (or √ k m γ k = S = 18 = 4 = 2 = 18 ) starts growing. is deviated from the SM RG equation only by the almost smooth term inv) inv ) = 2 corresponding to the recent value of Higgs mass, 126 GeV. The other t ). In eqs.) (3.29)–(3.36 0 0 0 2 2 4 4 Γ a 4 λ δ m → dt dt dt dt dk dk dk dk init 2 2 2 2 = H + 2 λ µ/M π π π ( π 2 µ B 2 ( 16 16 16 , the influence of 16 δ t ). But the allowed region for ‘triviality bound’ for a given Higgs mass shrinks as 0 2 y 2 δ = 171 GeV and 0 2 δ = log( t t m and + 2 We have solved all the RG equations given above and checked the consistency of all 2 2 δ 2 δ where The benchmark pointresults, 4A gives in table we intend,5.4 to consistent interpretother the with dark low the matter mass direct XENON regions search of experiments 100 dark (CDMS direct II, matter CRESST, claimed detection CoGeNT to etc.) be along probed with by several model is given by [40], an arbitrary scale. Here where for the RG equation of (2 the term, (2 denotes the SM Higgs decay width and Γ 3.4 Constraints fromIf invisible kinematically Higgs allowed, Higgs decay boson width can decay to gauge couplings and top Yukawa coupling,for respectively. gauge In and our top calculation,condition, Yukawa the couplings RG are equations also taken into account. We have taken the initial with scale used in thisfor model assigning is initial shown. values in The theof benchmark evaluation mass point of the 4A of running of of eachdetermined table various5.4 by scalar couplings.has couplings The been variation chosen are severely restricted by the presentfraction data from Large Hadron Collider (LHC). The branching is bounded at 95% CLto to fermion be couplings less fixed thanparticles 19% to are by their allowed the SM global in fits values. the to loops If the Higgs the such data bound a keeping restriction get Higgs is relaxed lifted to and additional the quartic couplings withinwe the have suitably taken choseninitial scale values of of parameters the inparameter theory. our space. model For In should the have1 figure initialisation, beenthe chosen variation from of the different allowed parameters region of ( JCAP03(2015)011 Μ Μ Μ Μ M M M M ln ln ln ln 16 16 16 16 14 14 14 14 12 12 12 12 (f) (d) (h) (b) 10 10 10 10 8 8 8 8 6 6 6 6 4 4 4 4 ¢ 4 k 2 2 Λ ∆ k 0.4 0.3 0.2 0.1 0.5 0.1 0.2 2200 2100 2000 1900 1800 1700 - - 0.001030 0.001025 0.001020 0.001015 0.001010 0.001005 0.026 0.025 0.024 0.023 – 10 – Μ Μ Μ Μ M M M M ln ln ln ln 16 16 16 16 14 14 14 14 12 12 12 symmetry with different energy scales. 12 0 2 (c) (e) (g) (a) 10 10 Z 10 10 × 8 8 8 2 8 Z 6 6 6 6 4 4 4 4 4 a 4 ¢ 2 . Plot showing the variation of different couplings present in the framework of two scalar ¢ 2 k k ∆ k 2400 2300 2800 2700 2600 2500 0.0120 0.0115 0.0130 0.0125 0.00104 0.00102 0.00112 0.00110 0.00108 0.00106 0.00104 0.00102 0.00112 0.00110 0.00108 0.00106 Figure 1 singlet model with JCAP03(2015)011 ), X γ inv) (4.1) → ’ studies ) particle. H X ( X B etc.) require /Z ± are suppressed than W , with a 0 ), or mono-photons ( S 0 /Z searches are subleading. j S ± X W or , mono- γ , ) SS ) of the DM particles that escape eq T 2 S / n E − 2 S n (SM). The varieties of ‘mono- search for singlet dark matter is given in ( i ’ searches where the DM production at the h X σv X −h searches – 11 – searches uses the quarks or gluons self-interactions = denoting a dark matter particle) as a consequence X is the thermal averaged annihilation cross-section of S X i χ ( Hn σv h ¯ ). The experimental technique used by the proton-proton χ h χ + 3 -ray from Fermi bubble and galactic centre), in some cases S γ and dt dn S collider (or LHC) follow from two processes, whereby the single p − p are the number density and equilibrium number density respectively of eq 2 and the Higgs boson decays invisibly to S / , or mono-Higgs ( n H /Z channels precisely and may put stronger limits on them. Other constraints from ) in the M ± and X /Z ≤ W S ± 0 S n ) collider for studying the mono- p ,M − S p j/γ/W or mono- ( leading to some final channelsThe containing a signature pair of of the darkenergy matters pair and and of a can single dark SM be( matter ( measured has been from assumed the to data. be The in the emission missing channels transverse of the single particles For the present modelthe the case signatures with like mono-Higgsloop-induced mono-photon, since interactions. mono- the The former study signatures of (mono- mono- searches although the low massthe dark invisible matters decay are width of strongly Higgs.the constrained mono- from The the future LHC collider with datacollider much for data higher such luminosity can as probe effectssinglet on scalar electroweak precision model observablespresent in have been two ref. real discussed [21] singlet for real (Barger model. et al.)4 and the qualitative Calculation study of is relicThe similar relic abundance in abundance for our a darkgiven matter as, species is calculated by solving the Boltzmann equation particle emission canthis be can due be toof emitted effective initial along couplings state with ofmodel, radiation the DM masses from to of SM. lightexperiments the proposed are quarks In dark low or the matters and constrained alternatively present hence by case the different of dark constraint matter two from search singlet LHC scalar mono- dark matter refs. [86, 87]. In thediscussion present will scenario with be two real similarSince scalar the singlets to DM added that masses to are SM, given low, the in LHC qualitative is refs. still [86, insensitive to87] put except strong constrains now on this the mono- is for two singlets. which have been performed by the LHC include mono-hadronic jets ( the detector recoiling against some final state the dark matter candidate, where the dark matter. One of theof techniques dark chosen matter by paircollider Large production is Handron measured by from Collider the the ‘mono- (LHC) missing transverse to energy ( explore the signature indirect searches (low energy M disfavoured by the LHCwhere observations. DM annihilation This is issinglet mediated a scalars by well cannot the known perhapsexplaining SM problem evade the Higgs. with the low all The mass constraintthe zones. such present from 126 model models, the For GeV quantitative consisting Higgs SM estimations of Higgs invisible we as two width have a chosen data3.5 benchmark. the for Higgs to be Constraints from LHC mono- JCAP03(2015)011 (4.7) (4.3) (4.4) (4.5) (4.6) (4.2) K) and , , we can , o 0 ! Y 2 S ! ) is obtained 0 n 0 2 S 0 T eq eq n 2 S 2 S , the final value contribute to the 0 f eq eq = n n 2 S 2 S 0 x 1183. n n is the total entropy T . S − 0 0 . The Planck survey e 1 − 2 S at ) to < , − n 2 S 0 and 2 Y n

) h S /T 2

eq Mpc S 0 SS Y 1 S DM 0 → , where M − 0 . − Ω S S from precision measurements of S 0 T 0 2 , → = , M 2 < S Y Y i h (value of 0 ( SS 0 i i = x . It follows that knowing 0 Y σv ( 0 DM Y 0 S 1227 x T σv 1093 σv cr , in the units of critical energy density, . e x . h ρ 0 − h M S S GeV S ) − h of < M and 0 ) M eq 2 0 2 2 2 S x 8 eq / x S h = n e 1 2 S ∗ n 10 g n S − DM 2 – 12 – 0 n × = − / cr Ω 2 S 1 S ρ 2 S n − Y are the present photon temperature (2.726 ( < n M 755 ( . f G = XX T XX = 2 π S → 1165 45 0 . → 2 Ω S 0 0 h and S SS S i i − 0 Ω T = σv σv −h −h dx dY = = 0 S S ). Here f Hn Hn , can be expressed as /T S ) is a singlet scalar. The total relic density is the sum of the relic densities of 0 + 3 πG + 3 M S 8 is the Hubble constant in the units of 100 km sec 0 S / S is the degrees of freedom. The relic density is the present entropy density evaluated at = 2 dt stands for a Standard Model particle. In both the eqs. (4.6) and (4.7) the first terms h or dt dn ∗ 0 f dn H g e X S x In the very early universe, both the scalars are in thermal and chemical equilibrium. The relic density of a dark matter candidate, Defining dimensionless quantities In the present work we consider a two component dark matter model with each compo- ( = 3 x cr on the right handsecond side terms are of for both thethe the contributions two equations of scalars in annihilation denote this to the two SM contribution component particles of dark whereas theBut matter the self-scattering as scenario. of the each universefrom of expands, the the universe plasma temperatureearlier and falls than contribute resulting the to someand lighter the species give relic one. rise to density. to be But a The decoupled total at heavier contribution scalar the in decouples relic present abundance epoch that both is probed components by are WMAP/Planck frozen or relics where freeze-out temperature respectively. ρ where compute the relic density of the dark matter candidate from the relation [88], In (4.4) provides the constraints onanisotropy the of dark cosmic matter microwave density background Ω radiation as consistent with the previous WMAP measurement 0 density, eq.) (4.1 can be written in the form, of relic density. Their individual contributionsBoltzmann can equations, be obtained by solving the following coupled nent ( where by integrating eq. (4.2) from an initial value each component. Thus in our model with two real scalars, both JCAP03(2015)011 . ) . 0 s or 2 S S ( ) in pro- σ M (4.9) (4.8) 4 (4.10) SS XX / ↔ ↔ ) 0 and Ω SM 2 S S 0 SS S + i S M i (4 σv h ˆ σv σ SM h → , or i ∼ ) can be expressed ) is the sum of the 0 ) s S σv 0 ( h DM S DM ˆ σ SM ↔ , 2 + S + 0 SS M i S 0 4 S DM σv SM − h ↔ are degenerate at some high scale and , s 0 ) for the annihilation channels of SS S → ) i i q s M ( ) pair annihilation into SM particles σv 0 σv σ . h s 0 S ) T and DM S 2 S √ h S or respectively. We therefore have, + M M 0 4 1 + Ω S S XX S − can be approximated as → s DM computer code [89, 90] to calculate Ω 0 is negligible from phase space considerations. In ds K ( i S – 13 – 0 0 s and 2 = Ω S S S 0 σv i ∞ M q S h S 4 DM Z σv ↔ of th order modified Bessel function of second kind. h Ω can interact with the nuclei of the active material (see ) i 0 , SS x 0 ) = 2 S i ( s S 2 2 . The requirement of producing the right relic abundance ( XX 0 σv ˆ σ micrOMEGAs S K h → x 5 S and M and Ω SS ) therefore the total relic abundance (Ω M i 0 S S S 16 σv and h ) denote the so that = 0 2 x 3 and ( i , δ i S S σv K h . ,M 2 /T δ S ) such that M close enough = XX 0 ↔ x S The thermally-averaged values of cross-section ( The Feynman diagrams for singlet scalar ( SS experiments and Planck survey A situation like this can be realised by assuming that i 3 and σv then at low scale the degeneracy is slightly lifted due to some hidden sector physics. the eqs.) (4.6 andh (4.7) are small compared to the annihilation cross-section ( then the coupled Boltzmannpled equations equations in the each eqs. oneindependently.) (4.6 of In and which the (4.7) describes present areS work the reduced we to evolution have two of ensured decou- such each a this of scenario condition the each byin component of taking eq. the scalars the). (4.1 eqs. masses We (4.6) of have then and used (4.7) is reduced to the Boltzmann equation given where other cosmological observations. Inare the present singlet two scalars component modelindividual (with contributions, the Ω components with is the normalized annihilation cross-section of dark matter for will further restrict the allowed parameter space. If the self-scattering cross-sections between the two scalars ( dark matter toas Standard, ([40 Model88]), particles ( cesses. For non-relativistic dark matter figure3) in the directnucleus. detection experiments These and experimentsof leave have DM their indicated vs. signature some inof DM-nucleon form preferred the cross-section of parameters or plane. a of excludedexperiments If recoiled our zones into we model, in can some we the express cancomprising preferred translate these of mass or the cross-sections excluded results in obtained region terms from in direct the detection parameter space of our model The dark matter particles in the unitary gaugecan are be shown found in in2. figure refs. The [20, corresponding40]. expressions for cross-sections 5 Constraining the parameter space with Dark Matter direct detection JCAP03(2015)011 (5.1) . ) 2 cm 42 . 0 − + − H H S W W 10 H H × and S (5 2 H H S S S S S S N (in GeV) 50 GeV S M H 4 – 14 – as well. f 0 ¯ Z f S S N Z S (in GeV) H 100 GeV as well. S 0 M S H H 2 ) 2 δ S H S H S S S S = ( SI nucleon σ and Higgs. Similar annihilation channels exist for both . Lowest order Feynman diagram for singlet scalar-nucleus elastic scattering via Higgs . Tree level Feynman diagrams of DM pair annihilation to a pair of fermion and anti-fermion, ZZ , − In this model with two scalars, although the total event rate in a direct detection As presented in appendixA, the expressions for singlet scalar-nucleon elastic scattering W + Similar expression works for experiment, which is thethe sum types total of dark ofdepends matter individual on particles, event the the rates, mass nuclear of carries recoil the no dark energy information matter spectrum about particle. for Hence the the signal measured events nuclear recoil energy Figure 3 mediation. A similar diagram exists for cross-section are rather involved.mated as But [20] for all practical purposes eq. (A.3) can be approxi- Figure 2 W JCAP03(2015)011 2 2 = δ δ for - 0 2 S − δ 2 δ S M 6 GeV, for the for the and fix . − M 0 2 25 GeV), 0 2 δ δ S S = 8 ∼ is restricted − M 0 − are chosen to S 0 S S 0 S M = 8.6 GeV, S M ,Ω M 0 45) in the . = 0.45) is initially S S 0 0 2 and M . This value of cross- δ 2 ' S 2 cm δ 82 from this light purple . to be 0 41 0 (say) by choosing the point − S ' 0 10 2 S 50 GeV) is consistent with these plane shown as the light purple δ = 8.6 GeV, 6 GeV, × . . We then complete choosing our 0 2 0 0 > 9 δ S S . - 0 = 8 which satisfies both CDMS II direct S M 0 S M 7 GeV, . S M for singlet (say), we now calculate the allowed region for the singlet = 6 0 2 S S 0 δ S 6 GeV. We first calculate the CDMS II region . contribute to the relic density and participate − = 0.45 (as claimed by CDMS II). We could have M 0 0 – 15 – S 2 S = 8 δ M ) as shown by olive zone in figure 4(a). S 0 S and M S for the singlet 6 GeV with cross-section 1 for the other singlet 45 for 2 . . = 8.6 GeV, δ 0 0 2 δ S ' from Planck constraints on relic abundance of dark matter. Only plane. Similarly the relic density of the singlet − M and 0 2 0 0 2 δ S parameter space shown by the olive colour in figure 4(a) for the other for the singlet δ S S - 0 2 0 0 2 δ M M δ S . It is obvious that this allowed region in light purple is a part of the − − M S 0 0 S S . We now choose the benchmark point in the parameter space 0 M (say) to be M S plane which satisfies the CDMS direct detection experimental bounds and this is S 2 (or , this allowed region of parameter space in light purple colour would be in 0 δ 10 GeV) mass DM. CRESST II data prefer a relatively higher mass zone ( S S 45) in the − . 0 However in our model both ∼ S by choosing the point corresponding to the maximum likelihood point ( 0 ' M S 0 2 0.45. Needless to mention thatWith this this point is choice within of of the allowed parameter parameter space space of figure 4(a). detection bound and Planckthe relic light density purple constraints. zone. Thischosen On region in the is the other shown hand, in if figure the4(b) pointby ( singlet chosen the point in the parameter space in shown in figure 4(a) alsoby the represents olive the zone. allowed It parametric is straightforward space to (CDMS realise II that the allowed same region), contour section corresponds to other scalar the singlet plane for singlet abovementioned total allowed parametricsinglet space (CDMS II allowed region) can, in principle,component be one [53, used91]. tobe In nearly differentiate our degenerate. model, a Due thedistinguish to multi-component masses such the of mass dark degeneracy, the components it matter twoenergies may of singlets from not of be dark a the possible matter detectorin to single- experimentally in nuclei. terms of our Empowering modelspace model ourselves from parameters, with simply direct we the detection by willsurvey. experimental expression measuring We now results of have the go and broadly cross-section relic ahead explored recoil low density three ( in requirements DM constraining from mass Planck the ranges.in model CDMS addition parameter II to andobservation the CoGeNT of vouch any low interesting for zone. event.two Only experiments high XENON and mass DM Planck 100 ( data. and We LUX will now provide elaborate exclusion more regions5.1 on from them in non- the Constraints following. from CDMSCDMS II collaboration and has Planck recentlya data reported preferred observation contour of in threelikelihood the WIMP point mass at events of a and DM-SI mass provided scattering of cross-section 8 plane, with the maximum in direct detectioncorresponding experiments. to the So maximum we likelihood fix point Ω ( shaded region in figure benchmark4(b), point can (see now table accountregion. for5.1) This such by point Ω taking inobservations. the The parameter space same is prescription thus is consistent valid with if bothδ we CDMS first II consider and the Planck from other Planck singlet data allowing only a small region (light purple shaded region in figure 4(b)) plane. This restrictsa Ω small part of the previously allowed region in the Ω JCAP03(2015)011 - – 0 S 41 − M ) 8 GeV, 10 0 . or 10 GeV. plane by S 2 ∼ 0 2 ∼ δ δ = 7 - (or S − S plane choosing 0 S M 0 S 2 M δ M 7% 8% 81% 12% 77% 15% − 0 S plane. 82 in the light purple 0 2 . M δ 0 (b) − ' 0 Fraction for S Annihilation Branching 2 δ M /s) ) ) ) ) 3 ) ) plane. In panel (b) the light purple ¯ ¯ c c b b ¯ ¯ l l ¯ ¯ b c l b c l 2 i cm δ 7 GeV, 6 ( 4 ( 2 ( 3 ( 2 ( 2 ( ...... − σv 26 2 0 0 6 1 7 h − S           = 6 M 10 2 3 . . S × , we find the olive zone in the 3 8 ( 0 M ) S 2 45 are chosen from . – 16 – or cm = 0 S 9 9 SI . . 0 2 41 δ plane. The same is true for the allowed parameter space in 1 9 σ − 2 δ 10 × − ( S 6 GeV, . ) 0 M 2 δ = 8 0 S (or 0.82 0.45 plane is chosen to complete the benchmark point. 2 M 2 δ (a) δ 45 in the - . ) 0 S S . Benchmark point consistent with CDMS II contour and Planck data. M = 0 M 2 δ 6.7 8.6 (or plane when 7–11 GeV and elastic scattering cross-section with nucleon which is (GeV) S 2 . The other direct detection experiments like DAMA/LIBRA or CRESST II have plane. The point corresponding to Table 1 δ 2 . In panel (a) the olive region is the parameter space allowed in the ∼ M 2

6 GeV, − δ .

- cm S 1 point Benchmark With CoGeNT preferred zone we can do similar analysis as we did with CDMS II and S = 8 40 M plane respectively (see figure 5(a)). We now choose a benchmark point ( M − S 0 2 shaded region of δ 5.2 Constraints fromCoGeNT CoGeNT dark and matter Planck direct data roughly detection experiment predicts dark matter particle with a mass the allowed parameter zones forto explain CoGeNT CoGeNT are findings shown with in either figure 5(a) and figure 5(b). If we are in 10 also reported signals nearlysources. in that Also the zone spectra which ofare is the consistent not events with reported consistent by each with experiments other the like [92] known CRESST II background and and possibly CoGeNT attribute to dark matter of mass CDMS II 90%CL data.shaded region The is same the is only true parameter if space drawn allowed in by Planck data in the Figure 4 M the JCAP03(2015)011 2 δ 56) . − 0 plane S region 8 GeV, ) . 0 2 ' M plane by S σ δ 0 2 - 0 2 δ = 7 S δ (or S , which then M − 0 M 0 S S S 5% 5% . . M 8 GeV, 7% . 80% 81% 12% 7 12 25 GeV. CRESST II = 7 0 S ∼ (b) M contour has crossover with Fraction for Annihilation Branching plane choosing σ 0 2 δ /s) ) ) ) ) 3 plane. ) ) − ¯ ¯ c c b b ¯ ¯ l l ¯ ¯ 0 b c l b c l 0 2 S δ 61 from this light purple region of i cm . 7 ( 6 ( 4 ( 6 ( 7 ( 4 ( 0 M − ...... σv 26 0 3 0 0 4 0 0 h − S '           M 0 2 10 plane (shown as light purple shaded region 6 7 δ . . × 0 2 plane. In panel (b) the light purple shaded region 4 5 ( δ 2 - . Planck results then restrict Ω ) 0 δ S 2 S − – 17 – S M cm 2 GeV, . M 0 8 SI . . 41 and repeat the similar procedure mentioned above to 9 9 σ − 0 = 8 S 10 0 S × ( 56 are chosen from . M ) 0 2 δ = 0 0 2 δ contour of the CRESST II data. We could have chosen 2 plane. This fixes Ω (or 0.61 0.56 plane. The same is true for the allowed parameter space in the σ 2 2 2 δ δ δ (a) - . Benchmark point consistent with CoGeNT and Planck data. ) S − 0 8 GeV, . S M S M M = 7 plane for the singlet 0 Table 2 8.2 7.8 S 0 2 (or contour can similarly be translated to the hatched region in the δ (GeV) M - S 0 σ . In panel (a) the olive region is the parameter space allowed in the S M

56) in the M

56 in the . . ecmr on 2 point Benchmark 0 ' = 0 2 2 in figure 5(b)). We then take δ plane when δ is the only parameter space allowed by Planck data in the CoGeNT data. The same is true if drawn in can be reproduced by a tiny region in the figure 5(b) to completevalid for the the CoGeNT other benchmark case point where presented we in initially choose table the5.2. point to The be same ( is Figure 5 obtain the CoGeNT benchmark point (table 5.2 ). 5.3 Constraints fromWe CRESST have II analysed and the Planck 1 data in the of CRESST II dataCDMS as II well. and Butexperiments. CoGeNT as low the We low mass rather massdata regions, part prefer of the of to 1 outcome the work 2 is with expected DM to of be higher similar mass to these JCAP03(2015)011 ) 2 cm plane ) 0 0 2 δ 42 S plane by − − 0 2 0 δ 10 (or S plane. plane to the − 0 2 M S × 0 0 2 δ δ S 6 - . − 0 7% 7% M 0 81% 12% 81% 12% S S plane for the other M = 1 M plane for the singlet 0 2 δ plane. In panel (b) the 2 - SI 0 δ 2 - σ S (b) δ S Fraction for M Annihilation Branching − M S contour and Planck data. (see figure 6(a)). The best fit /s) M ) ) ) ) σ 3 GeV, 3 ) ) 0 ¯ ¯ c c b b . ¯ ¯ l l ¯ ¯ b c l b c l S i cm 4 ( 4 ( 2 ( 9 ( 6 ( 3 ( ...... σv 26 36) in the 2 0 0 3 0 0 h 36 are chosen from . . 36) in the − . 0           0 10 0 8 = 0 ' . . × ' 0 2 3 4 ( 0 2 δ plane. The same is true for the allowed parameter δ 2 ) 2 δ 2 δ – 18 – − cm S 3 GeV, 6 2 . SI . . 41 3 GeV, M 1 3 σ . − 3 GeV, . plane for the singlet 10 = 25 0 0 2 × = 25 S δ 47 from this light purple region to complete the CoGeNT ( . The relic abundance constraint from Planck survey then . - = 25 0 0 S 0 M ) contour (mass of DM = 25 S S 36 in the 0 2 . S δ ' σ M M M 0 2 = 0 δ (or 0.47 0.36 2 δ 2 contour. The same is true if drawn in δ (a) ) σ plane when 0 S 2 or in the 3 GeV, δ . 3 GeV, . M contour is ( S − . Benchmark Point consistent with CRESST II 1 σ S 23.3 25.3 (or , which in turn limits the allowed parameter space in the = 23 = 25 (GeV) 0 M 0 S S S and we repeat the similar procedure stated aboved. S . In panel (a) the olive region is the parameter space allowed in the 0

M M

M S Table 3 ecmr on 3 point Benchmark . Choice of this point fixes Ω for the singlet space in the CRESST II datalight of purple shaded 1 regionchoosing is the only parameter space allowed by Planck data in the point for the CRESST II 1 singlet Figure 6 benchmark point presented in(table3) table3. if We our wouldCRESST have initial obtained II choice the 1 of same the benchmark point point which corresponds to the best fit point for the S tip (shown as thechoose light purple zone in figure 6(b)) of the CRESST II allowed zone. We then restricts Ω corresponds to the point ( JCAP03(2015)011 0 2 SI S δ σ and − S S 05) and M . 0 ) keeping 0 2 ' δ 2 , δ 2 δ , 0 S M = 90 GeV, (b) . S 0 . This in turn restricts Ω S M S for the two components | 55 GeV and a continuous region 0 022 ( . S 0 ∼ M 2 GeV. We thus get the zone (shown 0 ' S − ≤ 2 δ M 0 S S window, we perform a parameter scan in M 0 | M S − ) plane, indicated as the olive region in fig- 022). This fixes Ω S 05) and proceeding similarly as above, leads to 0 . 2 . ) participates to have a conservative estimate. δ 0 – 19 – 0 0 M = 54 GeV, S − ' ' S 0 2 2 S δ δ M (or M S = 0.050 = 0.022 2 2 (or 022 etc. which would have fixed Ω 2 . δ 0 . We investigated this parameter space ( 100 0 2 = 90 GeV, δ = 54 GeV, δ = 54 GeV, = 90 GeV, S S δ − ' S (GeV) S ' 0 2 S S δ M M M (a) M and 2 = 2 GeV. Choosing δ 0 Allowed parameter space for XENON 100 S ), 0 Allowed zone taking M Allowed zone taking M S M = 2 GeV and compute the allowed region in this parameter space which is plane imposing the constrain = 54 GeV, ) plane by XENON 100. Panel (b) shows the parameter space allowed by XENON 100 M 0 − | 2 0 0 2 0 10 δ δ S S S . In panel (a) the solid olive region represents the parameter space allowed in the 85 GeV onwards. From each of these two regions we will now choose benchmark − − M (or M M 0 0 1 S ∼ S

S 0.1 Again choosing ( First we choose ( We ﬁrst constrain the diﬀerence of masses

−

0.01 2

δ M

M ' M in our present two component dark matter model. The parameter space is thus reduced S 0 M as blue dots inis figure 7(a)) how consistent the with benchmark both point XENON 4A 100 as and given Planck in observations. table This 5.4, is obtained. | consistent with XENON 100density. bound The for results scattering aresmall cross-section plotted island and in of Planck figure allowed results7(b). parameter for From space relic figure at,7(b) around it reveals that there are a from Planck data. Inthe order to reproduce this Ω the benchmark point 4Bchosen shown in table 5.4 . Needless to mention that we could have as well Figure 7 (or from points. keeping keeping the DMconsistent mass with difference both less XENON than 100 2 and GeV, Planck we observations. now denote in5.4 panel (a) the Constraints parameter from space XENONXENON 100 100 and collaboration Planck data observation did they not have observe set any an prospective upper signal bound of on DM. spin independent From scattering this cross-section non- S to ure7(a). HereWe we need assume to find only ible the with parameter Planck spaceother observations. suitable dark Our for matter producing strategyzone experimental here DM in results relic is the considered abundance plane somewhattours. earlier compat- of different in scattering from this cross-section the and work cases dark where of matter the mass allowed is given by closed con- for various darklowed matter region masses. in In the the context of our model this translates into an al- JCAP03(2015)011 ∼ ) 0 S S M (or S 8% 7% 3% 6% 2% 2% 8% 2% 1% ...... 55% 10% 05% 43% 08% 05% ...... 8 8 78 78 99 86 13 13 0 0 0 12 0 0 0 Fraction for Annihilation Branching ) ) − − /s) W W ) 3 ) ) ) ) ) ) + + ¯ ¯ c c b b ¯ ¯ ) ) ) ) l l ¯ ¯ ) ) b c b l c l ¯ ¯ c c b b ¯ ¯ l l ¯ ¯ cm b c l b c l W W ZZ i 26 − 83 ( 29 ( 82 ( 11 ( 52 ( 32 ( 29 ( 28 ( 024 ( 48 ( 004 ( 016 ( 002 ( 003 ( 002 ( σv ...... h 7 1 0 3 0 0 4 3 0 0 0 0 0 0 0 10                                     × ( 94 95 32 78 . . . . 9 3 4 3 – 20 – ) 2 cm 0 4 8 6 SI . . . . 45 2 1 0 2 σ − 10 × ( ) 0 2 δ 57 GeV. But the continuum starts around 135 GeV. For the (or 0.045 0.022 0.011 0.050 2 . Benchmark Points consistent with XENON 100 and Planck data. ∼ δ ) S 0 S M M Table 4 92.0 54.0 56.0 90.0 (or (GeV) S To compare with the literature which attempts explaining the experimental observations M

135 GeV cannot reproduce the morphological features of indirect detection observations. ecmr on 4B point Benchmark ecmr on 4A point Benchmark 5.5 Constraints from LUXLUX collaboration and has Planck recently published data theirAs results we which have confirm done to for XENON XENONin 100 100, findings. figure8. we show We the see allowed zonesspace that by LUX similar around and to Planck XENON observations 100, here also we get an island in the parameter assuming certain branching fractions of5.4 Higgsthe to relevant SM branching particlesbenchmark ratios we points for have is denoted the that in chosen in tables cisely benchmark whereas our5.1– points. the case previous the The analysis braching hasStill main been ratios the feature performed are experimental assuming of determined certain data our from branching can fractions. the be model confronted pre- remarkably well. 6 Confronting indirect Dark MatterThe region detection surrounding experiments thedensity Milky of Way dark is matter. rich in Thisdark astrophysics region matter, and is as is promising no for assumed other better to astrophysical understanding have source of a or the high properties region of is as accessible as the galactic centre 57 GeV point the phenomenology∼ will be similarSo to we XENON will 100. not However discuss high the DM LUX masses allowed parameter space any further in this work. JCAP03(2015)011 2 δ − S M -ray flux γ 07) and keeping the . 0 ' 2 δ (b) is the position vector from the 100 GeV. surrounding the galactic centre ~r ∼ o = 132 GeV, S M ), with ~r ( ρ 022 ( . 50 MeV to -ray emission from GC and low latitude of 0 γ ∼ ' 2 – 21 – δ -ray flux from the singlet scalars in this model constrained = 54 GeV, γ = 0.070 = 0.022 2 2 S 100 M -ray data from galactic centre region observed by Fermi telescope γ (GeV) ' = 54 GeV, δ S S = 132 GeV, δ S M (a) Allowed parameter space for LUX ) plane by LUX. Panel (b) shows the parameter space allowed by XENON 100 keeping 10 0 2 Allowed zone keeping M = 2 GeV. Choosing δ Allowed zone keeping M . In panel (a) the solid olive region represents the parameter space allowed in the 0 − S 0 M S

0.1

Detailed studies on spectral and morphological features of the gamma rays from the DM distribution follows a density function, We now discuss observations of excess

0.01 2

δ − M ' S galactic centre region havegamma been ray studied emission in from refs. the [67, region92]. that encompasses In 5 ref. [92], the spectrum of the has been done. is studied afterCatalog subtracting [93] the and known sources disc from emission the template. data The of the main Fermi reason Second of Source the disc template emission DM mass difference lessboth than 2 LUX GeV, and we Planck now observations. denote in panel (a) the parameter(GC). space consistent The with Fermi Gammahigh luminous Ray gamma Space ray Telescope emission (FGST) between has been employed to survey the Fermi bubble, which doesthe not light appear of to DM have annihilation.observations “standard” can In be origins, particular explained but we byDM can show our direct be that proposed the detection understood model morphological experiments in withWe features will and parameter of point spaces DM these out consistent relic in with the abundance subsequent significance discussions constraints that of from thewe Planck such uncertainties do survey. involved astrophysical in not observations understanding intendfeatures are to of quite fit the the substantial. observations data, in terms but So of rather at DM6.1 limit this annihilation ourselves by point to our reproduce Explanation model. the ofThe morphological excess low gamma energy (few ray GeV) emissiongive a from hint galactic of centre aof low gamma mass dark rayformalism. matter. from In We the have this computed section annihilationby we CDMS of have II discussed dark and the CoGeNT matter phenomenology experiments from and finally galactic comparison centre with the in observed this present Figure 8 (or centre of the galaxy. Severalsome such representative DM cuspy halo to profiles flatin are profiles the available for appendixC. in our For the a numericalDM literature. estimations. particular annihilation We DM These using choose halo are eq. profile presented (B.2) one for can the calculate the present photon model flux framework due in to appendixB. M JCAP03(2015)011 (6.1) [94, ]95 kpc as these 2 , , kpc) 7 kpc 7 kpc R/ ( × R > R < . The spectra from the millisecond for for 00208 . , sc galactic longitude containing huge amount of o 1 + 0 . R/R 40 – 22 – − e , ± ) ) R R ( ( -energy range from 300 MeV to 10 GeV and drops by ) = 0 Millisecond pulsars sc γ sc R /z /z ( | | z z sc z can also accelerate both electrons and cosmic ray protons. −| −| e e ∝ ∝ gas gas -ray in TeV-scale [99] which may in principle explain the high energy ρ ρ γ galactic latitude and 15 kpc and . o = 3 sc ) denotes the location relative to the GC in cylindrical coordinates. The chosen R R , z However there are some astrophysical propositions that can morphologically explain the Super-massive black holes The other astrophysical objects, the gamma rays from which may yield spectra similar where ( values of gamma-ray flux structure frompulsar the population inner [98], part centralspatially of supermassive extended galactic gamma black centre. ray hole distribution These [67, feature include97] from millisecond etc. GC. which can explain this order of magnitude beyondgamma 10 ray GeV. emission from From the thebelow central morphological 300 MeV region characteristics the of of residual ourenergies gamma this galaxy, it ray it residual could has could originate been originate from showndark from a in matter. point-like spatially [68, source extended92], but Also, that componentsfrom at or higher the if may galactic the be centre very isgamma from analysed, emission high annihilating the from energetic galactic spectral ridge. portion shapeup The is to of galactic found a ridge the to width is match residualwhite an of fairly inner dwarfs gamma 5 well region [96]. with ray of the galaxy The emission with extending standard molecular convention cloud is in that thedecay the ridge to and high high pions energy are energy cosmic producedbe gamma. nucleons in interact assumed Therefore, huge amount the to which residual subsequently containresidual emission low spectrum from energy is GC tail considered supposeddominance here of to at can ridge above be GeV emission. dominated scale. by Also the very point low source energy [68, part97] of which the loses its These accelerated electrons thencan produce be gamma accounted ray forthese from electrons any inverse produce unresolved Compton gamma scattering ray and emission from galactic centre region. But to that observed by FGST data are values are best suitable toconventional tool fit used for to probe the thepion observational density data decay of of is neutral 21-cm hydrogen. estimated Hto by The line be flux integrating of surveys in this gamma which good distribution rays isgamma from agreement over the ray with the the spectrum line-of-sight observed and is morphology it brighter of is for the found diffuse emission. The residual gamma ray from galactic centrethis observed type by of different mechanism experimentsBut cannot like HESS, fully the HAWC. account Hence cosmic forinteraction the ray FGST with protons data interstellar accelerated forThis gas. low by energy scenario the gamma Decay may rays. black of partiallylot hole of explain these can astrophysical the pions parameters produce FGST likeproton yield pions ISM residual propagation gamma gas through through emission rays distribution ISM the feature or of gas as unknown etc. lower diffusion there which energy. coefficient are appear for not a fully understood. pulsars are hardfew in GeV. nature beyond Thismillisecond a tends pulsars to few in considerable indicate GeV, numbers that i.e., which are surrounding it still the to falls galactic be off probed centre, with experimentally. there But much may rapidity be after other a is the gammainteraction ray with produced gas. fromAssuming the the Though neutral gas inverse distribution pion to Compton decay be and which of Bremsstrahlung the is following can outcome form, also of contribute. cosmic ray JCAP03(2015)011 annihilation 0 S 0 S and channel with NFW halo SS b ¯ b 80%, but for higher masses, when ∼ – 23 – ) which falls off very rapidly with radial distance from r -ray emission due to DM annihilation. We work with ( 2 γ ρ channel has a branching ratio b ¯ b channel opens up, it drastically changes. However such a DM candidate ZZ or − 55 GeV DM the W + − In ref. [100] it has been argued that by considering few annihilating dark matter scenarios In this section we extend the above discussion for the multi-component DM scenario A potentially strong proposition about the nature of this bumpy feature of the residual We see that for low mass DM, the plots in figure9 and figure 10 corresponding to W 55 GeV and for all DM profiles other than the cuspy Moore profile, the DM annihilation profile have been shown tofits fit in data such [100]. discussionfor In of different order DM generic to annihilation models, get channelsfor an in for 10 idea tables different of benchmark5.1–5.4 where points.we our We have specific see quoted model that branching although ratios benchmark points chosendetection from experiments the and Planck modelthe survey. parameter For observed each space spectra suchpoint already benchmark from points sources constrained the we and by try theoretically galactic to direct calculated match ridge ones. from ref. We [100]. plot the Then emission we from add with some standard darkwith matter good halo statistics. profiles,leptonic low channels Few mass [103] benchmark dark or cases, matter 30 GeV such can dark fit as matter the 10 GeV annihilating spectrum dark to matter annihilating to as discussed incandidate our model. helps enhance As the mentioned total in the abstract, presence of more than one DM GC explaining the “bump”. It also resolves the problem posed from pulsar explanation. is also compatible with data. gamma emission from GC isAs dark in matter dark annihilation matter as indicated scenario,factor by the for Hooper angular flux et width calculation al. of contains [100–102]. the spectra is narrow since the astrophysical benchmark points 1 andprofile 2 offers respectively, a indicate betterIsothermal that agreement with profile a the flat is data. DM stillThe For halo XENON the benchmark 100 profile promising point benchmark like 3, one, point∼ figure Isothermal 4A whereas11 is Moore usedshows for that profilecontribution figure overestimates is12 , the rather where small we data. see comparedNFW that to profile for contributions works DM from masses better point sources for and XENON galactic 100 ridge. benchmark point 4B, used for figure 13 . there are discrepancies whichpulsar immediately catalog, contradict the thisharder scenario. spectral spectrum index for From the the ofAlthough average FGST’s a gamma pulsar first very is from few required pulsarsfor pulsars to have the match certainly is residual the a emission centred observed veryshape [98] hard gamma at below spectral one spectrum. 1.38 10 index needs GeV that but butFermi to can pulsar to a be have catalog. fit accounted much larger the The number gammameasure globular the clusters, flux of spectral rich of these index in the but gamma typesorder bumpy here pulsars spectral to of too, have comply the also pulsars data been the whichdecrease do studied angular not very are to distribution favour rapidly not very pattern along hard presenthas of the spectral not in outward nature. the been radial found emission, In distance from the astrophysicalthe but data. pulsar fact the From density significance all that should the of some abovethe such discussions, different residual rapidity one mechanism may emission conclude is from required galactic to centre observed explain by this FGST. bumpy spectral shape of the spectra to getincreasing theoretically order predicted of “cuspiness”: residual(4) Moore flux (1) [107–109]. Isothermal for [104], four (2) DM NFW halo [105], (3) profiles Einesto arranged [106] in and JCAP03(2015)011 = = 0 S = 2 S M α M 100 100 few GeV of GC of GC =0.45 =0.45 = 0.82 = 0.82 o o 2 2 ' 2 ' 2 δ δ ∼ δ δ =8.6, =8.6, S S = 6.7, = 6.7, ' ' S S 10 10 Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission E (GeV) E (GeV) annihilation we use rays between 0 with spectral index, 1 1 Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M 10 kpc) up and down from S (b) NFW Gamma Spectrum for M Gamma Spectrum for M γ (d) Moore 0 α ± S − = E Total Computed Residual Emission from GC (NFW) Total Computed Residual Emission r Total Computed Residual Emission from GC (Moore) -annihilation is calculated for ( o SS 0.1 0.1 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual Observed Residual Gamma Ray Emission from inner 5 50

∼

0.001

1e-05 1e-06 1e-07 1e-08 1e-05 1e-06 1e-07 1e-08

) s cm (GeV dN/dE E 0.0001

) s cm (GeV dN/dE E

-1 -2 2

-1 -2 2 of galactic centre. The red data points represent o – 24 – 100 100 =0.45 of GC of GC =0.45 2 = 0.82 = 0.82 o o 2 δ ' 2 ' 2 δ δ δ =8.6, = 8.6, S S = 6.7, = 6.7, ' ' S S 10 10 Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission E (GeV) E (GeV) -ray ﬂux from the inner 5 1 1 Gamma Spectrum for M Gamma Spectrum for M Gamma Spectrum γ 82 and is represented by the dash-dotted cyan line. Total calculated residual Gamma Spectrum for M Gamma Spectrum for M . (c) Einasto 45 and is denoted by the dotted violet line. For . (a) Isothermal = 0 = 0 0 2 Total Computed Residual Emission from GC (Einasto) 2 δ δ Total Computed Residual Emission from GC (Isothermal) Total Computed Residual Emission 0.1 0.1 Observed Residual Gamma Ray Emission from inner 5 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual . Residual

1e-08 1e-05 1e-06 1e-07 1e-08 1e-07 1e-06 100 GeV range and they are extended almost -ray bubbles and the haze can have a strong correlation that attribute to the fact that

dN/dE (GeV cm (GeV dN/dE E ) s 0.0001

dN/dE (GeV cm (GeV dN/dE E ) s

2 -1

-2 γ

2 -1 -2 ∼ 7 GeV and 6 GeV and -ray flux is denoted by the solid black curve. Each sub-figure is calculated for different DM halo . . to the galactic plane.WMAP In haze [111] ref. which [110],galaxy is confirmed the the from non-thermal, bubble data microwave emissionand of emission different ROSAT has from ongoing [113] the been experiments X-ray innerthe worldwide studied emission part such as data. of as the an Planck Evidences [112] they extension [112] might of have show been that aFermi near common bubble origin. the the galactic gamma When we ray plane, move spectrum far follows from a the power galactic law, plane along the 6 γ profiles, as indicated in their respective captions. 6.2 Explanation of gammaFrom ray the bump Fermi Gamma-Ray from Space Fermitures Telescope bubble’s that (FGST) contain low data large galactic a amountof latitude of pair gamma-ray galactic of had bilateral centre. been lobular found These in struc- the lobes, upper known and lower as regions Fermi bubbles, emit 8 the observed flux. Pointand source and blue galactic dotted ridge lines1 emissions respectively. are consistent represented with DM by CDMS annihilation the II light in green and our dashed Planck model data is (see calculated table for5.1). benchmark point Figure 9 JCAP03(2015)011 100 100 2 GeV and of GC of GC =0.56 =0.56 . = 0.61 = 0.61 o o 2 2 ' 2 ' 2 δ δ δ δ -annihilation = 8 =7.8, =7.8, SS S S = 8.2, = 8.2, ' ' 0 S S S 10 10 Point Source Emission Point Source Emission M Galactic Ridge Emission Galactic Ridge Emission E (GeV) E (GeV) 1 1 Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M (b) NFW Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M (d) Moore Total Computed Residual Emission from GC (NFW) Total Computed Residual Emission Total Computed Residual Emission from GC (Moore) 0.1 0.1 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual Observed Residual Gamma Ray Emission from inner 5 annihilation we use 0

0.001 1e-05 1e-06 1e-07 1e-08 1e-05 1e-06 1e-07 1e-08

) s cm (GeV dN/dE E 0.0001

) s cm (GeV dN/dE

E S -1 -2 2

-1 -2 2 of galactic centre. DM annihilation is calculated o – 25 – 56. For -spectrum has a peak at a few GeV energy range. . γ 100 100 = 0 =0.56 of GC of GC =0.56 2 = 0.61 = 0.61 o o 2 δ ' 2 ' 2 2 δ δ δ δ =7.8, = 7.8, S S = 8.2, = 8.2, ' ' S S 10 10 Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission 8 GeV and . E (GeV) E (GeV) -ray ﬂux from the inner 5 γ 1 1 Gamma Spectrum for M = 7 Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M Gamma Spectrum for M (c) Einasto S (a) Isothermal where the inverse Compton scattering (ICS) is the mechanism of production M 3 − Total Computed Residual Emission from GC (Einasto) E Total Computed Residual Emission from GC (Isothermal) Total Computed Residual Emission -ray spectrum from bubble very near the galactic plane have been proposed. Pop- . Residual 0.1 0.1 γ Observed Residual Gamma Ray Emission from inner 5 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual

61. Notations are same as in ﬁgure9.

1e-08 1e-05 1e-06 1e-07 1e-08 1e-07 1e-06 The picture of the gamma ray emission from Fermi bubble from the low galactic latitude

dN/dE (GeV cm (GeV dN/dE E ) s 0.0001

dN/dE (GeV cm (GeV dN/dE E ) s

2 -1 -2

2 -1 -2 = 0 0 2 Figure 10 This cannot be explained bying the of known light astrophysical source processeshas like by inverse cosmic generated Compton electrons some scatter- in interestnature steady-state. in of This astrophysics non-ICS community and nature of different the origins spectrum for this bumpy is somewhat different. In this case the for benchmark point 2 consistent with CoGeNT and Planck data (see table 5.2). of these types ofgalaxy gamma [110, rays.114] due Also,galactic to similar magnetic the field. distribution synchrotron can radiation produce effect radio with emission the in interaction the of microgauss ulation of millisecondannihilating pulsars dark [115, matter],116 scenariodetailed cosmic [67, study ray on100, the interaction119, et morphology120] with al. and have gas spectral [72]. been signature [ 117, studied of]118 Fermi in bubble or great is an details. given in A Hooper is calculated for δ over all the energywell range explained observed by by approximate the powerdex, FGST. law 3, spectrum This i.e., of type electron of distribution gamma with ray spectral spectrum in- can be JCAP03(2015)011 100 100 3 GeV and of GC of GC =0.36 =0.36 . = 0.47 = 0.47 o o 2 2 ' 2 ' 2 δ δ δ δ -annihilation annihilating diffuse emis- SS = 23 =25.3, =25.3, =23.3, =23.3, ' ' S S S S 0 10 10 S Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission M E (GeV) E (GeV) 1 1 Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M (b) NFW Gamma Spectrum for M Gamma Spectrum for M (d) Moore -ray emission with very high γ -ray spectrum generated by such Total Computed Residual Emission from GC (NFW) Total Computed Residual Emission Total Computed Residual Emission from GC (Moore) γ 0.1 0.1 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual Observed Residual Gamma Ray Emission from inner 5 annihilation we use 0

1e-06 1e-07 1e-08 1e-05 1e-06 1e-07 1e-08 1e-05

) s cm (GeV dN/dE E 0.0001

) s cm (GeV dN/dE

E -ray emission as given by the

-1 -2

2 S

-1 -2 2 γ of galactic centre. DM annihilation is calculated o – 26 – 36. For . 100 100 = 0 of GC of GC =0.36 =0.36 = 0.47 = 0.47 o o 2 2 2 ' 2 ' 2 δ δ δ δ δ -ray excess can be attributed to the excess population γ =25.3, =25.3, =23.3, =23.3, ' ' S S S S 10 10 Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission 3 GeV and . E (GeV) E (GeV) which have the advantage of producing -ray ﬂux from the inner 5 γ 1 1 Gamma Spectrum for M Gamma Spectrum for M Gamma Spectrum = 25 Gamma Spectrum for M Gamma Spectrum for M (c) Einasto 25 GeV or so to provide a good description of the observed emission. But S (a) Isothermal is due to the fact that the cosmic ray protons are scattered with the gas M ∼ Total Computed Residual Emission from GC (Einasto) scenario at the galactic halo region. Total Computed Residual Emission from GC (Isothermal) Total Computed Residual Emission . Residual 0.1 0.1 Observed Residual Gamma Ray Emission from inner 5 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual -emission and also the spectrum of the cosmic ray protons should follow a bumpy γ

47. Notations are same as in ﬁgure9.

1e-08 1e-05 1e-06 1e-07 1e-08 1e-07 1e-06 On the other hand the spectral nature of excess gamma emission from the lower latitude Another possibility of this The explanation of this low latitude excess dN/dE (GeV cm (GeV dN/dE E ) s dN/dE (GeV cm (GeV dN/dE E ) s

2 -1 -2 2 -1 -2 millisecond pulsars = 0 0 2 of Fermi bubble may be consistent with the gamma spectrum calculated from the Figure 11 objects is not veryAlso well the understood distribution as ofconstrained a from very such various few objects astrophysical pulsars observations. outside of the this galactic type have plane been as discovered. proposeddark is matter much more for benchmark point 3 consistent with CRESST II and Planck data (see table3). is calculated for δ sion mechanism present in thephenomenology Milky as Way the region. gas distributionof is But the merely the correlated with explanationnature the around cannot morphological fully structure this provide type the of peak observed inastrophysical the observation. cosmic proton spectral feature is not fully understood fromof the known luminosity over another types of pulsars. But the nature of JCAP03(2015)011 100 100 of GC of GC o o =0.022 =0.022 = 0.011 = 0.011 2 2 -annihilation ' 2 ' 2 -ray excess. δ δ δ δ γ = 56 GeV and SS 0 =54.0, =54.0, =56.0, =56.0, ' ' S S S S S 10 10 Point Source Emission Point Source Emission M Galactic Ridge Emission Galactic Ridge Emission 25 GeV, as preferred ∼ E (GeV) E (GeV) 1 1 (b) NFW (d) Moore Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M Gamma Spectrum for M Gamma Spectrum for M Total Computed Residual Emission from GC (NFW) Total Computed Residual Emission Total Computed Residual Emission from GC (Moore) zone of Fermi bubble. Like we did annihilation we use Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual Observed Residual Gamma Ray Emission from inner 5 0.1 0.1 0 o S

1e-05 1e-06 1e-07 1e-08 1e-09 1e-10 1e-07 1e-08 1e-06

) s cm (GeV dN/dE ) s cm (GeV dN/dE E

E S

– 10 -1 -2 2 -1 -2 2 o of galactic centre. DM annihilation is calculated for = 1 o – 27 – | b 022. For . | 100 100 = 0 of GC of GC o o =0.022 =0.022 = 0.011 = 0.011 2 2 2 ' 2 ' 2 δ δ δ δ δ =54.0, =54.0, =56.0, =56.0, ' ' S S S S 10 10 Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission E (GeV) E (GeV) 55 GeV, as allowed by XENON 100 works better. For very high DM -ray ﬂux from the inner 5 = 54 GeV and γ 1 1 ∼ Gamma Spectrum for M Gamma Spectrum for M Gamma Spectrum (c) Einasto Gamma Spectrum for M Gamma Spectrum for M S (a) Isothermal 7–11 GeV, as preferred by CDMS II or CoGeNT, the spectrum peaks at a M ∼ Total Computed Residual Emission from GC (Einasto) Total Computed Residual Emission from GC (Isothermal) Total Computed Residual Emission . Residual 90 GeV allowed by XENON 100, the calculated spectra tend to peak at a bit higher Observed Residual Gamma Ray Emission from inner 5 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual 0.1 0.1 ∼

011. Notations are same as in ﬁgure9.

1e-09 1e-07 1e-08 1e-06 1e-10 1e-11 1e-07 1e-08 1e-09 1e-05 1e-06 As the DM density is expected to be high for regions close to the GC, we concentrate dN/dE (GeV cm (GeV dN/dE E ) s dN/dE (GeV cm (GeV dN/dE E ) s

2 -1 -2 2 -1 -2 = 0 0 2 masses for GC, we workPlanck survey. with However, benchmark rather pointsfor than consistent that exploring with DM for profile all directin for DM detection figure which halo experiments the14. profiles, and GC wecontribution data present Here of was the best-fit the better plot steady observedlow explained. state flux DM These electron mass is plots spectrum shownlower are of energy after presented than the deducting that bubble. obtained inverseby from Compton We the CRESST see data. scattering II that The or higher for mass very zone energy than the observedpromise spectrum. to But explain overall the we morphological can conclude feature that of the the model Fermi bubble holds low some latitude on DM annihilation from low latitude Figure 12 δ benchmark point 4A consistent with XENON 100 and Planck data (see table 5.4). is calculated for JCAP03(2015)011 100 100 of GC of GC o o =0.050 =0.050 -annihilation = 0.045 = 0.045 2 2 ' 2 ' 2 δ δ δ δ = 92 GeV and SS 0 =90.0, =90.0, =92.0, =92.0, S ' ' S S S S 10 10 M Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission E (GeV) E (GeV) 1 1 (b) NFW (d) Moore Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M Gamma Spectrum for M Gamma Spectrum Gamma Spectrum for M are almost degenerate in mass. Total Computed Residual Emission from GC (NFW) Total Computed Residual 0 Total Computed Residual Emission from GC (Moore) S annihilation we use Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual Observed Residual Gamma Ray Emission from inner 5 0.1 0.1 0 and S

1e-05 1e-06 1e-07 1e-08 1e-09 1e-10 1e-05 1e-06 1e-07 1e-08

S ) s cm (GeV dN/dE E 0.0001

) s cm (GeV dN/dE E

-1 -2 2

-1 -2 2 of galactic centre. DM annihilation is calculated for o – 28 – 05. For . 100 100 = 0 of GC of GC o o =0.050 =0.050 = 0.045 = 0.045 2 2 2 ' 2 ' 2 δ δ δ δ δ =90.0, =90.0, =92.0, =92.0, ' ' S S S S 10 10 Point Source Emission Point Source Emission Galactic Ridge Emission Galactic Ridge Emission symmetry. We keep the symmetry unbroken to get a two component E (GeV) E (GeV) 0 2 -ray ﬂux from the inner 5 Z = 90 GeV and 1 1 γ Gamma Spectrum for M Gamma Spectrum for M Gamma Spectrum (c) Einasto Gamma Spectrum for M Gamma Spectrum for M Gamma Spectrum × S (a) Isothermal 2 M Z Total Computed Residual Emission from GC (Einasto) Total Computed Residual Emission from GC (Isothermal) Total Computed Residual . Residual Observed Residual Gamma Ray Emission from inner 5 Observed Residual Gamma Ray Emission from inner 5 Gamma Ray Emission from inner Observed Residual 0.1 0.1

045. Notations are same as in ﬁgure9.

1e-08 1e-09 1e-05 1e-06 1e-07 1e-09 1e-10 1e-05 1e-06 1e-07 1e-08 . dN/dE (GeV cm (GeV dN/dE E ) s dN/dE (GeV cm (GeV dN/dE E )

s Detailed calculations for the vacuum stability, perturbative unitarity and triviality con- 2 -1 -2 2 -1 -2 = 0 0 2 Figure 13 benchmark point 4B consistent with XENON 100 and Planck data (see table 5.4). straints on the modelparameter has spaces been used presented,model to which however explain forms brings an forth experimentalthe the integral results model traits part do of predicts of respectlighter any the unacceptably degrees Higgs-portal these paper. high of DM freedom constraints. invisible model. The toas Higgs the we The For model. decay feel low In width, DM that theor masses, till which present LUX work the observations calls we are conﬂict did for settleddo of not adding there take exist. CDMS is up II So that no or exercise pressingto we CoGeNT argument reproduce considered to observations indirect 126 GeV believe with DM that Higgs the experimental 7–11 mediated XENON results. GeV DM DM 100 annihilation processes throughout is calculated for δ 7 Discussion and conclusion We have explored a DMis model ensured adding by two real a scalarDM gauge singlets scenario. to theconsidering SM. The a The annihilation stability scenario of whereSuch the a the DM two heavier candidates indirect component DM DM real to experiments scalar compared the to DM lighter the model DM ones is models is containing better a suppressed suited single by to real scalar. explain both direct and JCAP03(2015)011 o o 100 100 -10 -10 o o = 0.56 = 0.45 = 0.61 =0.050 2 ' 2 ' 2 2 δ δ δ δ ) region. The -ray bump the o γ -10 = 7.8 GeV, o S = 8.2 GeV, =90.0 GeV, ' S = 92.0 GeV, S ' S =1 10 10 | b | E (GeV) E (GeV) Total Computed Flux in NFW Profile Total Computed Flux in Isothermal Profile Total Computed Flux in Isothermal Gamma Ray Flux for M Gamma Ray Flux for M Fermi bubble Gamma-ray Data for |b|=1 Fermi bubble Gamma-ray Data for |b|=1 Fermi bubble Gamma-ray Gamma Ray Flux for M o 100 Gamma Ray Flux for M -10 1 1 o = 0.47 (b) Benchmark point 2 = 0.36 ' 2 (e) Benchmark point 4B 2 δ δ

= 23.3 GeV,

= 25.3 GeV, S

S 1e-05 1e-06 1e-07 1e-08 1e-05 1e-06 1e-07 1e-08

) sr s cm (GeV dN/dE E ) sr s cm (GeV dN/dE

E 10 -1 -1 -2 2 -1 -1 -2 2 E (GeV) – 29 – Total Computed Flux in Isothermal Profile Fermi bubble Gamma-ray Data for |b|=1 Gamma Ray Flux for M Gamma Ray Flux for M o o 100 100 annihilation is represented by the blue dotted line. The -10 -10 0 1 o o = 0.82 (c) Benchmark point 3 = 0.45 =0.022 S 2 ' 2 2 = 0.011 0 δ δ δ ' 2 δ S = 6.7 GeV, S

= 8.6 GeV, =54.0 GeV,

' S

1e-07 1e-08 1e-05 1e-06 = 56.0 GeV,

dN/dE (GeV cm (GeV dN/dE E ) sr

s '

S 10 10 2 -1 -1 -2 E (GeV) E (GeV) annihilation. Total Computed Flux in Moore’s Profile Total Computed Flux in Isothermal Profile Total Computed Flux in Isothermal Gamma Ray Flux for M SS Gamma Ray Flux for M Fermi bubble Gamma-ray Data for |b|=1 Fermi bubble Gamma-ray Data for |b|=1 Fermi bubble Gamma-ray Gamma Ray Flux for M Gamma Ray Flux for M 1 1 (a) Benchmark point 1 -ray emission spectrum from the Fermi bubble’s low-latitude ( (d) Benchmark point 4A γ .

1e-08 1e-06 1e-07 1e-05 1e-08 1e-05 1e-06 1e-07

dN/dE (GeV cm (GeV dN/dE E sr s 0.0001 )

dN/dE (GeV cm (GeV dN/dE E sr s )

2 -1 -2 -1

2 -1 -2 -1 Figure 14 total DM annihilationa contribution different is benchmark shown point by with the a solid DM black halo line. profile which Each explains sub-figure GC is low plotted energy for red points denote observed datacontribution after from subtracting the ICS contribution. The green dashed line denote best. JCAP03(2015)011 (A.1) represents N A ) can be taken. 0 2 δ (or 2 δ when we choose different 0 S ), it is quite sensitive to the respectively. , 2 2 0 δ N ) and 0 and 4 S M H (or S M 2 r 2 2 M δ µ 2 and S (or S M S M M 2 50 GeV. The advantage of dealing with this | N > π – 30 – |A 25 GeV. As XENON 100 and LUX seem to rule 4 2 v ∼ 2 2 ) denotes the reduced mass for the system of singlet δ S = M + N SI nucleus M σ ( / S M 100 GeV predicts a photon flux from DM annihilations peaked at higher N M > ). For this reason we choose to show the allowed zones in the plots, so 0 2 δ ) = (or 2 N,S δ ( r µ There is some advantage of addressing both direct and indirect detection experiments. In conclusion, with the proposed model we do not intend to show that it can explain Guided by the direct detection experiments we considered three DM mass zones. The We have chosen some representative “benchmark points” from the parameter space where scalar and target nucleus with individual masses choice of that the reader canthe roughly individual estimate photon the flux for changes each in of the the DM singlet annihilation scalars, cross-section and The allowed model parameterments space and relic is density rather constraintspredictions restricted as quite imposed by sensitive by the Planck. to directthat the This DM once makes assumed some detection indirect agreement DM experi- DM in halo the detection the profiles. direct indirect DM detection We sector experiments would are is better establishedin like and understood to the the to make background framework delineate effects a DM of in promise annihilation point a effects, to given identify model, theDM the right model. experiments DM with halo the profile. existing precision We have showall illustrated some the this experimental withframework results, our of which proposed the sometimes model, areDM model we contradictory satisfying wanted in both to nature. directon exploit and the the indirect Rather, viability advantage DM in experiments, ofdetailed to and the having calculations choose in for a this the theoretical multi-component process right constraints comment on DM this halo model profile. asAcknowledgments mentioned earlier. For completeness we also presented SR acknowledges support of seed grant from IIT Indore. A Direct detection cross-section The spin-independent singlet scalar-nucleusvistic elastic scattering limit cross-section can in be the written non-relati- as [20] Since DM annihilation cross-section is proportional to benchmark points within the allowed parameter space. “low” zone of 7–11CRESST GeV II is also indicated favours by a CDMS “mid” II, zone CoGeNT and CRESST II experiments. out these zones, theobservations only belong DM masses to consistent a with “high” both mass XENON zone 100 or LUX and Planck allowed by thecomes direct regarding detection the experiments robustnessannihilation and of cross-sections Planck the which chosen data. do benchmark depend points. Now on To the address obvious the question issue, DM zone is that theytoo do high not DM give mass riseenergies to than unacceptable what invisible has branchingmass been ratio zone observed for will in Higgs. be the probed But indirect by a detection future experiments. XENON 1T This [121] high and DM LUX measurements. JCAP03(2015)011 J to α (B.1) (B.2) (A.4) (A.5) (A.6) (A.2) (A.3) . , 062 062 . . 0 0 , ) ± ± n q ( p is the energy spectrum is the effective coupling m m 118 118 . . f γ γ Sq Sq G dE , dN , G . = 0 = 0 , J, SI 2 n p n i T s T s c,b,t 2 σ ∆Ω ) X ¯ ρ = , are proportional to the matrix stated as, n J ) q . ( ≈

SI ) nucleon ) 2 p ) r , f , f σ n ρ p,n f ( can be expressed as, f g ( γ SI γ p p,n ) T q p,n h

p ( T ( T q T q f ) σ r 2 f f f 005 008 ,S dE . . f dN γ γ ) ,S 2 0 0 0 27 f n 2 S ( i dE dN u,d,s ± ± SI p nucleon 2 and S,S + X 0 = M σ f σv ) m q ) ) i h M n n 2 q S,S ( 026 036 ( p,n + − (nucleus . . 2 p p σv ( – 31 – T g 2 r f m h (nucleon M S f X m µ m 2 r = 2 when this is not the case. Here we consider 2 4 = 0 = 0 µ M = 1 f Sq A α ) X 1 πα Ω is given by [124] G p n T d T d π 8 ) d p,n = n ( 1 ( T g q πα = = p T f 8 ) f , f , f γ n ( = 83]. [123 In fact, here γ SI p . 004 003 dE SI nucleus Φ 0 γ γ σ . . u,d,s d σ X Ω 0 0 Φ ray due to dark matter annihilation in galactic halo in angular = ≈ d q d dE − ± ± γ = n TG ) -flux over a solid angle ∆Ω can be expressed in terms of averaged f n 020 014 γ ( . . p denote proton and neutron respectively and f n = 0 = 0 84 and . p n T u T u and , of quarks in a nucleon and are given by 0 f f i p ≈ ¯ qq as is the atomic number of the nucleus. h . ¯ ¯ f J p TG A f f The integrated = 1 for self-conjugated WIMP while with suffix between dark matter and nucleon [122], α be unity as the singletchosen scalars from in the the two present scalar work) singlet model are (the self-conjugated. dark matter In candidate eq. (B.1) factor, of photons produced instate, a single annihilation channel of dark matter with some specific final the relevant matrixscattering element. cross-sections for The the singlet non-relativistic limit scalar-nucleus are and related singlet as [20] scalar-nucleon elastic where we have used the relation between Thus B Photon flux dueThe to differential DM flux annihilation of direction that produce a solid angle where where the expressionelement, for hadronic matrix element, JCAP03(2015)011 is C 0 and S (B.7) (B.4) (B.3) (B.5) (B.6) S or S 2 ) ) of each singlet 0 ) 0 S DM S . , can be given by, Ω with particular final s / , which is the photon , 0 0 f + Ω γ γ ). Now from eq. (B.1) S S (or Ω 0 is the total dark matter S S dE dN . S (Ω i or DM × σv = Ω S ρ h 0 S coordinate) coordinate) Ω DM -factor of eq. (B.4) contains the 1 (or 2 coordinate) J coordinate) (Ω S M l, b r, θ i ( ( 2 coordinate) coordinate) ), where l, b r, θ + σv S h 2 ) ) in this model. Likewise the density for S ) 0 Ω 2 DM r

l, b r, θ / Ω ( S ( ( ρ Ω 1 )( ρ − DM / − b 2 DM S Ω 2 l, b / . Also the spectrum b / from the galactic centre and the line connecting ( and Ω DM 2 DM 0 1

from GC and line of sight (Ω S DM ds r cos S r Ω S – 32 – l θ θ r )( Ω b J , cos . Since in our case the masses of the singlets (Ω M θ + Ω DM 0 ( ). Thus the total ﬂux which is the sum total of the ρ S + l.o.s sin S × cos cos ≈ db cos Z Ω

S DM -wave) respectively and hence inversely proportional to θ J S S R s 2 DM = dθ Ω Ω or Ω sr sr db Ω DM 1 M 2 dl / 2 2 Ω R sin J 0 S Ω R C S R 2 2 π M − − (for dl dθ 4 2 C 2 0 2 2

(Ω M M represents the angle between the line of sight of an observer S R R ( C r r i M C θ π DM 4 + + 2 ∆Ω ∆Ω σv ρ = = = = 2 2 h s s ( ∆Ω = tot or (say) as, = ( S can be written as, ¯ i J γ = M J γ r σv ) denote the DM halo profile. dE Φ h = r d Ω ( 0 is given by d ρ S denote galactic longitude and latitude respectively. 0 S b M the density can be written as ≈ , would be similar in nature as both the singlet masses are chosen to be nearly equal ) in this model is generated by thermal freeze-out. Hence each of them is inversely 0 ¯ S f and S S f l The relation between radial distance One can make a rough estimate of the enhancement of flux for the case of two component M are nearly similar, we can take (or 0 In the above the observer at earth to the galactic centre. dark matter as in the present framework. The relic abundance Ω In eqs. (B.3),located (B.5), atB.6) ( earth while looking at some point S proportional to theone thermal can averaged find cross-section thatproportional the to differential flux from the annihilation of each of the singlets spectrum produced instate a single annihilation channeland of hence singlet the branchingthe fractions singlets of are theinformation almost final of states equal the produced to density of insinglet that each the of of annihilation the the of particular other. one annihilating dark of matter The species. For the density (sum total densitiesthe of singlet the singlets and flux produced by each of the singlets can be approximately written with a constant factor with and where the factor, S their corresponding abundance, Ω JCAP03(2015)011 in 0 S (B.8) (C.2) (C.1) is the and DM S Ω C 2 )) taken to be M

8.5 kpc). r ( ∼ ρ (the mass diﬀerence 20 28 (kpc) 3.5 0 , c S r . is chosen to be 0.17. /α ) , and α γ 1 0 γ − 1.5 0 S β 0 2 ( S S ] !# γ Ω 3 3 2 β M 1 ) c − + 0 ˜ α 2 r/r 1 2 α S ρ S 1.5 Ω M

r r ) are nearly equal. Hence from eq. (B.7), 0 [1 + ( γ S )

c or 2 2 DM C ˜ α Ω − – 33 – r/r S ( " = ) = r ( tot ) = exp r halo γ ( F γ 0 dE Φ ρ Ein halo d Ω Halo Model F d Isothermal [104] ) = Moore [107–109] r ) for each singlet ( 0 ( are the parameters that represent some particular halo proﬁle listed . Parameters used for widely used dark matter halo models. is the distance between sun to the galactic centre ( S ρ c

r r or Ω is the local dark matter halo density at solar location ( and S Navarro, Frenk, White (NFW) [105] Table 5 with 0 γ is the DM abundance as measured by Planck. In the above ρ 3 , β is a parameter of the halo profile. In our work value of ˜ DM , α α Another halo profile, namely Einasto profile has also been involved for our study. A where ˜ different kind of parametric form is adopted in this halo profile [106] which can be written as, 0.4 GeV/cm in tableC. where where Ω corresponding flux in theabundances one scalar (Ω singlet model. Now in our case, the contributions to the lies within a fewthis model GeV to in be ourweight-factors for effectively case). the non-degenarate, two then Ifmulticomponet contributing these one dark terms matter different chooses in model masses the the wouldobtained would come total masses from out serve flux. a of to as single be Hence the the componentin different the singlets than dark general total that matter form would flux case. as, have for been The this total photon flux is then expressed From eq. (B.8), wethe can total conclude flux that is forEven then the if dependent one case on considers of both the non-degenarateof the relic masses densities relic masses of of densities of individual and two singlets theobserved singlets, masses to singlets photon of be flux can individual nearly produced equal, even singlets. theto in yield hierarchy two considerable that scalar amount singlet of ofcomponents model one total considered will in here. gamma singlet principle ray scalar be flux. nearly model The similar for effectivelyC degenerate masses DM of halo the profiles darkThe dark matter matter distribution is usually parametrised as a spherically symmetric profile, the flux is founddue to to be the equal choice to of the almost case degenerate when masses only of one the scalar singlets singlet is considered. This is JCAP03(2015)011 , B 267 , 89 D 83 (2003) 1 ]. (2013) (2013) 19 (2009) 148 ]. (2000) 167 Measuring the 11 208 SPIRE G 40 Nucl. Phys. ]. Phys. Rept. , , IN 333 Phys. 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