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JID:PLB AID:30267 /SCO Doctopic: Astrophysics and Cosmology [m5Gv1.3; v 1.134; Prn:10/06/2014; 11:56] P.1(1-4) Physics Letters B ••• (••••) •••–•••

1 Contents lists available at ScienceDirect 66 2 67 3 68 4 Physics Letters B 69 5 70 6 71 7 www.elsevier.com/locate/physletb 72 8 73 9 74 10 75 11 76 12 X-ray line signal from decaying axino warm dark 77 13 78 a b 14 Ki-Young Choi , Osamu Seto 79 15 80 a Korea Astronomy and Space Science Institute, Daejon 305-348, Republic of Korea 16 81 b Department of Life Science and Technology, Hokkai-Gakuen University, Sapporo 062-8605, Japan 17 82 18 83 19 a r t i c l e i n f o a b s t r a c t 84 20 85 21 Article history: We consider axino warm in a supersymmetric model with R-parity violation. In this 86 Received 11 March 2014 22 scenario, axino with the mass ma˜ 7keVcan decay into and resulting in the X-ray line 87 23 Received in revised form 14 May 2014 signal at 3.5 keV, which might be the origin of unidentified X-ray emissions from galaxy clusters and 88 Accepted 3 June 2014 24 Andromeda galaxy detected by the XMM-Newton X-ray observatory. 89 Available online xxxx © 2014 Published by Elsevier B.V. This is an open access article under the CC BY license 25 Editor: A. Ringwald 90 3 26 (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP . 91 27 92 28 93 29 94 30 95 1. Introduction In Section 2 we introduce the model of axino dark matter and 31 96 in Section 3 we consider the R-parity violation and decay of axinos. 32 97 Various astrophysical and cosmological observations provide We summarize in Section 4. 33 98 convincing evidences for the existence of dark matter (DM). Dark 34 99 matter distribution spans in wide range of scales from galaxy to 2. Axino dark matter 35 100 clusters of galaxies and the large scale structure of the Universe. 36 101 Recently, anomalous X-ray line emissions have been observed The strong CP problem and the hierarchy problem in the Stan- 37 102 from galaxy clusters and also in the Andromeda galaxy [1,2]. While dard Model can be naturally solved in the supersymmeric axion 38 103 those might be a result of systematic effects, it would be interest- model [11,12]. If axino, the fermionic of axion, is the 39 104 ing if the line came from the new source of astrophysical phenom- lightest supersymmetric (LSP), then it is a good candidate 40 105 ena or from new physics. It was suggested that the signal might of dark matter [13–17]. The effective operator of the axino can be 41 106 come from decaying dark matter with the mass and lifetime, derived by the supersymmetric transformation of the axion inter- 42 107 actions and is given by 43 108 mDM 7keV,   44 αs 109 Leff = i a˜ μ, ν G˜ b Gb 45 × 27 × 28 a˜ γ5 γ γ μν 110 τDM 2 10 –2 10 sec, (1) 16π fa 46 111 α C   47 assuming the they are the dominant component of dark mat- Y aY Y ˜ μ ν ˜ 112 + i aγ5 γ , γ YYμν, (2) 48 ter. Some theoretically interesting particle models have been sug- 16π fa 113 49 gested such as [1–3], exciting dark matter [4], ˜ 114 where fa is the Peccei–Quinn breaking scale, and αs, G, Gμν and 50 millicharged dark matter [5,6], axion like particle [7–9], in the ef- 115 , Y˜ , Y are the gauge couplings, fields and the field 51 fective theory [10]. αY μν 116 strength for SU 3 and U 1 gauge groups respectively. The 52 In this paper, we study the axino in an ( )c ( )Y 117 mass of axino is expected to be of the order of mass, 53 R-parity violating supersymmetric model. With bilinear R-parity 118 but it can be much smaller [18–23], or much larger [24] than the 54 breakings, mix with and thus the axino can 119 typical supersymmetric particle mass scale, depending on the spe- 55 decay into photon and neutrino. We find that the axino mass with 120 cific models [25]. Here we take the light axino mass of the order 56 7keVcan have the proper lifetime and relic density for the X-ray 121 of keV as dark matter component. 57 line emission. In this scenario, as an interesting consequence, the 122 The primordial axinos are generated from the thermal plasma 58 upper bound on the neutrino mass imposes that the Bino mass is 123 during reheating after the primordial inflation. If the reheating 59 lighter than about 10 GeV. 124 60 temperature is lower than the decoupling temperature [13] 125     61 2 3 126 E-mail addresses: [email protected] (K.-Y. Choi), [email protected] fa 0.1 62 T = 1011 GeV , (3) 127 (O. Seto). dec 12 63 10 GeV αs 128 64 http://dx.doi.org/10.1016/j.physletb.2014.06.008 129 65 0370-2693/© 2014 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3. 130 JID:PLB AID:30267 /SCO Doctopic: Astrophysics and Cosmology [m5Gv1.3; v 1.134; Prn:10/06/2014; 11:56] P.2(1-4) 2 K.-Y. Choi, O. Seto / Physics Letters B ••• (••••) •••–•••

1 the axinos cannot reach the thermal equilibrium. Then axinos are 66 2 generated through scatterings and decay of heavy in the 67 3 thermal plasma, and the amount could be abundant enough for 68 4 axino to be the dominant dark matter component [14–16]. The 69 5 abundance of thermally produced axinos depends on the reheating 70 6 temperature for the KSVZ axion model [26].1 The axino number 71 7 density to entropy density ratio is estimated as [15,16,27,28] 72 8      73 11 2 9 −5 6 1.108 10 GeV TR 74 Y ˜ = 2.0 × 10 g log . (4) 10 a s 6 75 gs fa 10 GeV 11 76 With this, the relic density of non-relativistic axino at present is −5 −4 −3 12 Fig. 1. The reheating temperature TR versus fa for given ξi = 10 , 10 , 10 77 given by 13 (Blue, Red, Green) respectively to explain X-ray line emission. The small value of 78    f < 5 × 108 GeV (cyan) is disallowed by the SN1987A. On the curved black line 14 a 79 2 ma˜ Ya˜ the thermally produced axino and non-thermally produced axion (misalignment) Ω˜h = 0.28 . (5) 15 a 10 keV 10−4 can give correct relic density for dark matter. The upper region of the black line is 80 16 disallowed due to the overabundance of axino and axion dark matter. (For interpre- 81 17 We can find that O(1–10 keV) axino can be a natural candidate tation of the references to color in this figure legend, the reader is referred to the 82 web version of this article.) 18 for warm dark matter when the reheating temperature is around 83 6 7 11 19 10 –10 GeV and Peccei–Quinn scale fa = 10 GeV. Such ther- 84 2 20 mally produced keV axino is a warm dark matter candidate and be erased in the early Universe by the B–L violating interac- 85 21 may solve various problems at the small scale in cold dark mat- tions [51–53]. However if one of the flavors of the R-parity 86 22 ter model [34,35]. This range of reheating temperature is free from violating couplings is preserved and the slepton mixing is small 87 23 the gravitino problem [36,37]. enough, the problem can be avoided [46]. 88 24 Due to the R-parity violation, the stability of LSP is not guar- 89 25 3. R-parity violation and axino decay anteed anymore [40–42]. For bilinear R-parity breakings, the light 90 26 axino decays dominantly into photon and neutrino and the decay 91 27 We consider the bilinear type R-parity violation with the usual rate is given by [48–50] 92 28 μ-term superpotential in the minimal supersymmetric standard √  93  2 2 m3  ˜  2 model CaY Y αem a˜ 2 2 νi 29 Γ˜ = Γ˜→ = |U ˜ | , (11) 94 a a γνi 3 2 γ˜ Z 30 128π f v 95 W = L H (6) i a i 31 R/ p iμ i u, 96 32 where the –Zino mixing is given by 97 where Li and Hu are chiral super fields of the lepton doublet 33 ∗ 98 and up-type Higgs doublet and i parameterizes the size of the  S Z˜ α Sγα˜ 34 R-parity violation. By redefining the L and H , we can eliminate = 99 i d Uγ˜ Z˜ M Z , (12) m ˜ 35 the R-parity violating term in Eq. (6), then R-parity violating effect α χα 100 36 101 appears only in the scalar potential [38,39], 37 with the mixing matrix S. In the case of M1 M2, μ, 102 2 ˜ ∗ ˜ it is simplified to be 38 V = m L H + B L H + h.c., (7) 103 R/ p Li Hd i d i i u 39 2 2 3  104 − 2 2 − 2 C α m˜ 40 where the coefficients are Bi Bi and mL H (m˜ mH )i . aY Y em a 2 105 i d Li d Γa˜ ξ . (13) 128π 3 f 2 i 41 From this scalar potential, the sneutrinos obtain non-zero vacuum a i 106 42 expectation values (VEVs) 107 Although axino can also decay to three neutrinos mediated by Z- 43 108 2 + mL H cos β Bi sin β , this mode is highly suppressed and negligible. 44 ν˜ =− i d v, (8) 109 i 2 The X-ray emission line observed by the XMM-Newton can be 45 m ˜ 110 νi explained with an appropriate lifetime and the relic abundance of 46  √ 111 axinos, if those satisfy the relation 47 where tan β ≡H /H  and v ≡ H 2 +H 2/ 2 174 GeV 112 u d u d   48 and mν˜ is the sneutrino mass. Since the non-zero VEVs of sneutri- 2 113 i Ωa˜h 49 nos induce mixings between and , the neutrinos τ˜ = τDM , (14) 114 a 0.1 50 mix with neutralinos and can obtain mass at the tree level as 115 51 [39,47] where τDM is given in Eq. (1). We note here that, even though 116 52  117 2 2 2  2  2 2 the axinos are not the dominant component of dark matter, the μ M (M1 g + M2 g )/g ξ 53 m 1 i i , (9) enhanced decay rate can compensate to adjust the observed flux 118 ν 2  2 2 2 54 (g M1 + g M2)v μ sin β cos β − 2M1 M2μ of X-ray line. 119 55 In Fig. 1, we show the parameter space of TR versus fa to 120 where ξi parameterizes the R-parity breaking given by 56 explain the X-ray line emission for given R-parity violating param- 121  ˜ −5 −4 −3 57 g νi eters ξ = 10 , 10 , 10 (Blue, Red, Green) respectively. Here 122 ξ = √ . (10) i 58 i the small value of f < 5 × 108 GeV (cyan) is disallowed by the 123 2M1 a 59 SN1987A and the upper gray region is ruled out by the overabun- 124 The upper bound of the neutrino mass m  1 eV constrains 60 ν dance of the thermally produced axino and produced by 125 the R-parity breaking parameters. The asymmetry can 61 the misalignment mechanism with an order unity misalignment 126 62 angle [43]. 127 63 128 1 For the DFSZ axion model [29] the axino abundance is almost independent of In the white region and on the black strip, the axino de- 64 the reheating temperature in the wide range [30–32]. cay can explain the X-ray line emission with proper values of 129 65 2 −5 130 For non-thermally produced warm axino dark matter, see, e.g., Ref. [33]. ξi  10 . On the black strip, axino constitutes whole dark matter JID:PLB AID:30267 /SCO Doctopic: Astrophysics and Cosmology [m5Gv1.3; v 1.134; Prn:10/06/2014; 11:56] P.3(1-4) K.-Y. Choi, O. Seto / Physics Letters B ••• (••••) •••–••• 3

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