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Gamma Ray Spectrum from Gravitino Dark Matter Decay

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Gamma Ray Spectrum from Gravitino Dark Matter Decay DESY 07-158 Gamma Ray Spectrum from Gravitino Dark Matter Decay Alejandro Ibarra* and David Tran^ Gravitiuos arc very promising candidates for the cold dark matter of the Universe. Interestingly, to achieve a sufficiently long gravitino lifetime, A-parity conservation is not required, thus preventing any dangerous cosmological influence of the ncxt-to-lightcst supersymmetric particle. When Im­ parity is violated, gravitiuos decay into photons and other particles with a lifetime much longer than the age of the Universe, producing a diffuse gamma ray flux with a characteristic spectrum that could be measured in future experiments, like GLAST, AMS-02 or Cherenkov telescopes. In this letter we compute the energy spectrum of photons from gravitino decay and discuss its main qualitative features. 1'ACS numbers: 95.35.+R, 11.30.1'b, 93.T0.Rz 2007 There is mounting evidence that dark matter is ubiq­ of the standard nucleosynthesis scenario. In nrost supcr­ uitous in our Universe [1]. Since the necessity of dark synmrctric scenarios, the NLSP is either- a ncutralino or matter was realized, many different particle physics can ­ a stair. On one hand, if the NLSP is a ncutralino, its Sep didates have been proposed. Among the most interesting late decay into hadrons can dissociate the primordial el­ candidates stands the gravitino [2], the supersymmetric ements [G]. On the other hand, if the NLSP is a stau, 28 counterpart of the gr aviton, which arises when global su­ it can form a borrnd state with ^He, catalyzing the pro­ persymmetry is promoted to a local symmetry. If the duction of ^Li [7]. As a result, the abrrndanec of ^Li gravitino is the lightest supcrsynmrctric particle, it con ­ is increased by a factor 300 GOO, in stark conflict with stitutes an excellent candidate for the cold dark matter of observations [8]. the Universe. The interactions of the gravitino arc com­ Several scenarios have been proposed that circumvent pletely fixed by the synmrctrics, and the thermal relic the above-mentioned difficulties [9]. The simplest, albeit density is calculable in ternrs of very few parameters, the the nrost radical one, is based on the assrrnrption that result being [3] [astro-ph] A-parity is not exactly conserved [10]. In fact, althorrgh experiments set very stringent borrnds on A-parity vio­ /100 GeV \ / mg lation, there is no deep theoretical reason why it should ^ ms/2 j llTcVV ' be exactly conserved. If A-parity is nrildly violated, the (1) NLSP decays into Standard Model particles well before while the relic density inferred by WMAP for the AGDM the first nucleosynthesis reactions take place, thus not model is = 0.1277l^%g [4]. In this formula, posing a jeopardy for the Standard Model predictions. T# is the reheating temperature of the Universe, mg/g Remarkably, even though the gravitino is no longer sta- is the gravitino nrass and m^ is the ghrino nrass. It is ble when A-parity is violated, it still constitutes a viable indeed remarkable that the correct relic density can be dark matter candidate [11]. The reason is that the gr av­ obtained for typical supcrsynmrctric parameters, m.g/g ^ itino decay rate is doubly suppressed by the Planck nrass 100 GeV, mg ^ 1 TcV, and a high reheating temperature, and by the smallness of the A-parity violation, which T# ^ 10^ GeV, as required by baryogcncsis through the translates into lifetimes much longer- than the age of the mechanism of thermal Icptogcncsis [5]. Universe. Nevertheless, gravitino decays could be hap­ Whereas the gravitino as the lightest supersymmetric pening at a sufficiently high rate for the decay products arXiv:0709.4593vl particle leads to a cosmology consistent with observa­ to be detectable in future experiments. tions, the cosmology of the Next-to-Lightest Supersym- In this letter we will concentrate on the photons pro- nrctric Particle (NLSP) is much more problematic. In duccd in gravitino decays, althorrgh in general other sta­ supcrsynmrctric nrodcl building, in order to prevent too ble particles arc also produced, such as electrons, protons, rapid proton decay, it is eonrnron to invoke a discrete neutrinos and their antiparticlcs. Denranding a high re­ synmretry called A-parity. When A-parity is exactly heating temperature for the Universe as srrggested by conserved, the NLSP can only decay into gravitiuos and thermal Icptogcncsis, T# 10^ GeV [12], it follows hour Standard Model particles with a decay rate strongly sup­ Eq. (1) that the gravitino nrass has to be mg/g 5 GeV pressed by the Planck nrass. As a result, the NLSP is for a ghrino nrass n?g 500 GeV. Consequently, we ex­ typically present in the Univer se at the tinre of Dig Dang pect the photons hour gr avitino dark matter decay in the nucleosynthesis, jeopardizing the successful predictions ener gy range of a few GeV, :.c. in the ganrnra ray energy range. The Energetic Ganrnra Ray Experiment Telescope (EGRET) aboard the Gonrpton Ganrnra Ray Obser­ * Bloc Ironic address: [email protected] vatory measured ganrnra rays in the energy range be­ t Elec Ironic address: [email protected] tween 30 MeV to 100 GeV. After- subtracting the galae- 2 tic foreground emission, the residual dux was found to could resemble an isotropic extragalactic dux (for a more be roughly isotropic and thus attributed to extragalac- detailed discussion, see [15]). In this expression phaio tic sources. The first analysis of the EGRET data by stands for the dark matter distribution in the Milky Way Sreekumar et of. [13] gave an extragalactic dux with an halo. For our numerical analysis we will adopt a Navarro- energy spectrum described by the power law Frenk-White density prodle [16] E2-^ = 1.37 x 10 6 f ^ 1 (cm2str s) ^GeV ^°^-r/rc(l + r/rc)2' ^ dE \1 GeV y (2) where r k the dkt^^ to the Galactic center, rc ^ 20 kpc in the energy range 50 MeV-10 GeV. The improved anal ­ is the critical radius and ph ^ 0.33 GeV cm-3. ysis of the galactic foreground by Strong et a! [14], opti­ mized in order to reproduce the galactic emission, shows In Eqs. (3,5) the only undetermined quantity is the a power law behavior between 50 MeV-2 GeV, but a clear energy spectrum of photons produced in the gravitino excess between 2-10 GeV, roughly the same energy range decay, dNY/dE, which depends crucially on the gravitino where one would expect a signal from gravitino decay. mass. If the gravitino is lighter than the W± bosons, it Although it is very tempting to look for explanations for decays mainly into a photon and a neutrino by means of this excess in terms of gravitino decays, in view of all the the photino-neutrino mixing that arises when R-parity is systematic uncertainties involved in the extraction of the violated [11]. Therefore, the spectrum is simply signal from the galactic foreground, we will not attempt to dt our predicted dux to the EGRET data. Nonethe­ (8) less, we will show later the EGRET data superimposed with our predicted dux for comparison. For this case, it was found in [10, 15] that the total The total gamma ray dux received from gravitino dark gamma ray dux received is dominated by the monochro­ matter decay receives two main contributions. The drst matic line coming from the decay of gravitinos in our one stems from the decay of gravitinos at cosmological Milky Way halo, while the redshifted line from the de­ distances, giving rise to a perfectly isotropic extragalactic cay of gravitinos at cosmological distances is somewhat diffuse gamma ray background. Dedning dN^/dE as the fainter. gamma ray spectrum produced in the gravitino decay, On the other hand, if the gravitino is heavier than the the dux received at the Earth with extragalactic origin W± or Z0 bosons, new decay modes are open. In ad­ has the following expression: dition to the decay mode into a photon and a neutrino that follows from the photino-neutrino mixing, Uy V, the 2E2 c r°°d dN7 y-°E2 gravitino can also decay into a W± boson and a charged £2S m3/2 7 Ji d(Ey) y2! + Qa/QmV eg lepton, through the mixing charged wino-charged lepton, (3) Uyf , or mto a Z0 boson and a neutrino, through the mix­ where y = 1 + z, z being the redshift, and ing zino-neutrino, Ug^The decay rates can be straight­ forwardly computed from the interaction Lagrangian of C7 =-------3^2/?c 1/9 ~ 10 7 (cm2s str) r3/2 \ 1 10^8 g j a gravitino with a gauge boson and a fermion [17] . The 8nT3/2Ho result for each decay mode reads: (4 Here, G3/2, mid G* are the gravitino, matter and 2™3/2 F(^3/2 ^32^"' cosmological constant density parameters, respectively, M^ Pc k the ^itical density, T3/2 the gravitino lifetime, and f Mw A Ho the present value of the Hubble parameter. r(^3/2 -» W=LfF) - |2™3/2 , In addition to the cosmological contribution, the to­ ' My 1^3/2/ tal gamma ray dux also receives a contribution from the |2 ^3/2 „ Mz A decay of gravitinos in the Milky Way halo. This contri­ F(^3/2 ^ ^-32^" (9) bution reads: M2 ™3/2/ 2 E2 dNy where (5) _ halo TU3/2 ^ dE ' f (x) ‘-k (10) where E^ ^ defined as E-y = %------- / Aialo(f)d/. (6) The fragmentation of the W± ^d the Z0 gauge bosons 8nT3/2 ./log will eventually produce photons, mainly from the decay of neutral pions. We have simulated the fragmentation The integration extends over the line of sight, so E^ of the gauge bosons with the event generator PYTHIA has an angular dependence on the direction of observa­ 6.4 [18] and calculated the spectra of photons in the tion, yielding a slightly anisotropic gamma ray flux that W ± mid Z0 ^^nds, whidi we de note by dNW/dE and 3 dN"Z/dE, respectively.
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