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Physical Review D 97, 055019 (2018) PHYSICAL REVIEW D 97, 055019 (2018) Colder freeze-in axinos decaying into photons Kyu Jung Bae,1,* Ayuki Kamada,1 Seng Pei Liew,2 and Keisuke Yanagi3 1Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon 34126, Korea 2Physik-Department, Technische Universität München, 85748 Garching, Germany 3Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan (Received 24 July 2017; revised manuscript received 2 November 2017; published 15 March 2018) We point out that 7 keV axino dark matter (DM) in the R-parity violating (RPV) supersymmetric (SUSY) Dine-Fischler-Srednicki-Zhitnitsky axion model can simultaneously reproduce the 3.5 keV x-ray line excess and evade stringent constraints from the Ly-α forest data. Peccei-Quinn symmetry breaking naturally generates both the TeV-scale μ term and the MeV-scale RPV term. The RPV term introduces a tiny axino- neutrino mixing and provides axino DM as a variant of the sterile neutrino DM explaining the 3.5 keV x-ray line excess. Axinos are produced by freeze-in processes via the μ term. The resultant phase space distribution tends to be colder than the Fermi-Dirac distribution. The inherent entropy production from late-time saxion decay makes axinos even colder than those without saxion decay. The resultant axino DM takes the correct relic density and is compatible even with the latest and strongest constraint from the Ly-α forest data. DOI: 10.1103/PhysRevD.97.055019 I. INTRODUCTION partner, axino (a˜), is a DM particle and can be regarded as sterile neutrino in phenomenology.1 The axino mass is of An anomalous 3.5 keV line excess in the XMM-Newton order of keV in some models [10], although it is naively of and Chandra x-ray spectra of the Andromeda galaxy and order of the gravitino mass since it is generated by the galaxy clusters was first reported by two independent SUSY breaking. groups [1]. Subsequent studies have shown that a similar In this model, the Peccei-Quinn (PQ) symmetry breaking excess is also found in the Galactic Center [2] and in the at v ∼ 1010 GeV simultaneously generates the TeV-scale Suzaku data [3]. While there are reports of null detection, PQ μ term via the Kim-Nilles mechanism [11] and MeV-scale e.g., in dwarf spheroidal galaxies [4], the decaying dark bilinear R-parity violating (bRPV) term [12]. The μ term matter (DM) explanation of the 3.5 keV line excess is yet to induces freeze-in production [13] of axino DM. The scalar be excluded (see Ref. [5] for a thorough review). SUSY partner of axion, saxion (s), decays via the same Sterile neutrino is a benchmark example of 7 keV interactions, leading to the late-time entropy production. decaying DM [6]. In the simple model, its mass and The resultant axinos take the correct relic abundance. mixing angle with active neutrino determine its phenom- The bRPV term generates the tiny axino-neutrino mixing enology. On the other hand, there are two unsatisfactory required for the 3.5 keV line. Furthermore, TeV-scale points. First, the tiny mixing angle required for the 3.5 keV 2 −10 SUSY resolves the hierarchy between the electroweak line, sin 2θ ∼ 10 , is yet to be theoretically motivated, scale and the grand unification scale [14], although the and also it does not provide the correct relic abundance via hierarchy between the electroweak scale and the soft the Dodelson-Widrow mechanism [7]. Second, even if breaking scale has been highlighted by the null detection other production mechanisms are introduced, the resultant of SUSY particles at the Large Hadron Collider sterile neutrino DM tends to be too hot to be compatible (LHC). TeV-scale SUSY also improves the grand unifica- with the up-to-date Ly-α forest data [8]. In this article,we tion of the standard model (SM) gauge couplings. propose the R-parity violating (RPV) supersymmetric Meanwhile, Peccei-Quinn (PQ) symmetry explains why (SUSY) Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion quantum chromodynamics preserves CP symmetry very model as a solution to these problems. The fermion SUSY accurately [15]. All the 7 keV DM models proposed to explain the *[email protected] 3.5 keV excess need to be revisited to examine whether their structure formation is compatible with the up-to-date Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to 1Different realizations of 7 keV axino DM decay were the author(s) and the published article’s title, journal citation, considered in Ref. [9]. Nevertheless, none of them discussed a and DOI. Funded by SCOAP3. phase space distribution of axino DM or Ly-α forest constraints. 2470-0010=2018=97(5)=055019(6) 055019-1 Published by the American Physical Society BAE, KAMADA, LIEW, and YANAGI PHYS. REV. D 97, 055019 (2018) α 5 3 2 constraint from the Lyman- forest data, mWDM > . keV 2 A ¼ μ A=vPQ ≃ μ 1 þ ð Þ WDFSZ e HuHd HuHd; 3 [16]. Weaker constraints are also worth mentioning since vPQ the uncertainty in the reported constraint from the baryon complexity like the temperature evolution of intergalactic μ ¼ 2 ð2 Þ where y0vPQ= Mà . The approximate equality is valid medium is in debate: m > 2.0 [17], 3.3 [18], and 16 WDM when considering the axino interaction. If Mà ∼ 10 GeV, 4.09 keV [19]. The constraints are reported in the conven- 10 y0 ∼ 0.1, and v ∼ 10 GeV, one finds μ ∼ 500 GeV. tional warm dark matter (WDM) model, but they can be PQ This is a well-known solution to μ-term generation by converted to those on the other 7 keV DM models once the the Kim-Nilles mechanism [11]. From this interaction, phase space distribution function of DM particles is given, freeze-in production of axinos occurs dominantly when as demonstrated in the followings. The conventional WDM the cosmic temperature (T) is of order of the mass of the model assumes that WDM particles follow the Fermi-Dirac other SUSY particle involved in the process [21–23]. The distribution with two spin degrees of freedom, and they contributions from dimension-five anomaly operators (e.g., reproduce the observed DM mass density by tuning the axino-gluino-gluon) are suppressed [22]. present temperature (T 0) for a given mass (m ), WDM; WDM The bRPV term is also generated as [12] 3 m T 0 0 3 Ω 2 ¼ WDM WDM; ð Þ yi 3 0 A WDMh ; 1 W ¼ X L H ≃ μ 1 þ L H : ð4Þ 94 Tν 0 bRPV 2 i u i i u eV ; Mà vPQ ∼ 1016 0 ∼ 1 ∼ 1010 where Tν;0 is the present neutrino temperature. It If Mà GeV, yi , and vPQ GeV, one finds ¼ 0 1 ¼ 5 3 μ0 ∼ follows that TWDM;0 . Tν;0 for mWDM . keV. i MeV. This term generates an axino mixing with active Meanwhile, the present temperature is given by T0 ¼ neutrino. The mixing angle is given by ð10 75 106 75Þ1=3 ≃ 0 5 . = . Tν;0 . Tν;0 for 7 keV DM decoupled μ0 μ0 7 1010 jθj ≃ vu ≃ 10−5 keV GeV when the effective massless degrees of freedom count all 4 ; ¼ ¼ 106 75 ma˜ vPQ MeV ma˜ vPQ the SM particles, gà gSM . The comparison of ð Þ their naive warmness, T0=m, reads as ð0.1Tν;0=5.3 keVÞ < 5 ð0.5Tν;0=7 keVÞ. 7 keV DM is hotter than the conventional WDM disfavored by the latest Ly-α forest data and results where vu is the VEV of Hu and ma˜ is the axino mass. in a too smooth matter distribution of the Universe. For a more robust analysis, we need to compare the III. FREEZE-IN PRODUCTION linear matter power spectra by taking account of the phase The axino production is governed by the following space distribution of DM particles. We obtain the phase Boltzmann equation: space distribution by integrating the Boltzmann equation and find that it is typically colder than the Fermi-Dirac one. df ˜ ðt;pÞ ∂f ˜ ðt;pÞ 1 dRðtÞ ∂f ˜ ðt;pÞ 1 The saxion also makes axino DM colder, since its late-time a ¼ a − p a ¼ Cðt;pÞ; s ≲ Oð100Þ dt ∂t RðtÞ dt ∂p E decay at TD GeV injects a certain amount of entropy to the thermal bath after axino decoupling. We ð6Þ show that freeze-in 7 keV axino DM is concordant with the α current constraints from the Ly- forest data. where fa˜ ðt; pÞ is the axino phase space distribution as a function of the cosmic time (t) and the axino momentum II. MODEL (p), RðtÞ is the cosmic scale factor, and Cðt; pÞ=E is the collision term. Due to feeble interactions of the axino, one The DFSZ solution to the strong CP problem invokes a can safely neglect f ˜ in the collision term. Then by coupling between a PQ symmetry breaking field (X) and a integrating both sides from ti to tf, one finds the up- and down-type Higgs doublets (Hu;d) [20]. Its Z SUSY realization is given by the following superpotential, tf 1 RðtfÞ fa˜ ðtf;pÞ¼ dt C t; p : ð7Þ t E RðtÞ ¼ y0 2 ð Þ i WDFSZ X HuHd; 2 Mà Once one collects all the relevant contributions to the collision term, it is easy to obtain the axino phase space where y0 is a dimensionless constant and Mà is a cutoff distribution. We do not provide details here, but refer scale.
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