Cosmic-ray Electron and Positron Excesses from Hidden Gaugino Dark Matter
aa r X i v : . [ h e p - ph ] M a y UT-09-15IPMU 09-0065
Cosmic-ray Electron and Positron Excesses from HiddenGaugino Dark Matter
Satoshi Shirai , , Fuminobu Takahashi and T. T. Yanagida , Department of Physics, University of Tokyo,Tokyo 113-0033, Japan Institute for the Physics and Mathematics of the Universe, University of Tokyo,Chiba 277-8568, Japan
Abstract
We study a scenario that a hidden gaugino dark matter decays into the standard-model particles (and their supersymmetric partners) through a kinetic mixing withthe gaugino of a U(1) B − L broken at a scale close to the grand unification scale.We show that decay of the hidden gaugino can explain excesses in the cosmic-rayelectrons and positrons observed by PAMELA and Fermi. Introduction
The cosmic-ray electrons and positrons have attracted much attention since the PAMELAcollaboration [1] released the data showing rapid growth in the positron fraction fromseveral tens GeV up to about 100 GeV. Recently, the cosmic-ray electron plus positronflux was measured with the Fermi satellite [2] with significantly improved statistics. TheFermi data shows that the ( e − + e + ) spectrum falls as E − . over energies between 20 GeVand 1 TeV without prominent spectral features. The H.E.S.S. collaboration also measuredthe cosmic-ray ( e − + e + ) spectrum from 340 GeV up to several TeV [3], suggesting thatthe spectrum steepens above 1 TeV. The Fermi and H.E.S.S. results are in agreementwith each other where the energy of the two data overlaps. Combining the PAMELA,Fermi and H.E.S.S. results, therefore, it is likely that there is an excess in the electronand positron flux above several tens GeV up to 1 TeV.We have recently presented a scenario that thermal relic Wino dark matter (DM)of mass about 3 TeV, decaying through an R-parity violating operator ¯ eLL , naturallyaccounts for the PAMELA and Fermi excesses simultaneously [4]. In the model, themagnitude of the R-parity breaking as well as the Wino mass are closely tied to thegravitino mass, m / , of O (10 ) TeV. Interestingly enough, the lifetime of the Wino DMnaturally becomes of O (10 ) seconds, which is suggested by observation to account forthe electron/positron excess. The only drawback of this scenario might be that all su-persymmetric (SUSY) particles must have masses heavier than several TeV and thereforebeyond the reach of LHC.In this paper, we consider a hidden gaugino of an unbroken U(1) gauge symmetry asa candidate for DM [5, 6]. Since the longevity of DM originates from its extremely weakinteractions with the standard model (SM) particles, the SUSY particles in the SM sectorcan have masses well below the DM mass, possibly within the reach of LHC. As pointedout in Ref. [5], the decay of the hidden gaugino proceeds through a kinetic mixing with aU(1) B − L gaugino living in the bulk (see also Ref. [7]). The decay rate suppressed by theU(1) B − L breaking scale provides the desired magnitude of the lifetime. In addition, thehidden gaugino DM will mainly decay into a lepton and slepton pair, if the squarks aresubstantially heavier than the sleptons. Therefore the decay process can be lepto-philic2n concordance with the absence of the excess in the antiproton fraction [8]. In Ref. [5],we considered a case that the hidden gaugino decays universally into a lepton and sleptonpair in the three generations. In this paper, we study more generic decay processes suchas that into the third generation as well as three-body decays with a virtual sleptonexchange. We will show the decays of the hidden gauginos can explain the anomalousexcesses observed by PAMELA and Fermi.This paper is organized as follows. In Sec. 2 we briefly describe our hidden gauginoDM model. The predicted positron fraction and the electron spectrum will be shown inSec. 3. The last section is devoted to discussion and conclusions. In this section we will briefly describe the model proposed in Ref. [5]. The reader isreferred to the original reference for more details.Suppose that a hidden U(1) gauge multiplet ( λ H , A H , D H ) is confined on a brane,which is geometrically separated from the brane on which the SUSY SM (SSM) particlesreside, in a set up with an extra dimension. We introduce a U(1) B − L gauge multiplet inthe bulk so that those two sectors are in contact only through a kinetic mixing of theU(1) B − L and hidden U(1) multiplets. The mixing is written as L K = 14 Z d θ ( W H W H + W B − L W B − L + 2 κW H W B − L ) + h . c ., ⊃ − i (cid:16) ¯ λ H ¯ σ µ ∂ µ λ H + ¯ λ B − L ¯ σ µ ∂ µ λ B − L + κ ¯ λ H ¯ σ µ ∂ µ λ B − L + κ ¯ λ B − L ¯ σ µ ∂ µ λ H (cid:17) , (1)where κ is a kinetic mixing parameter of O (0 . λ H for thehidden gaugino in the mass eigenstate, its interaction with the SSM particles can beexpressed as [5] L int ≃ −√ g B − L Y ψ κ (cid:18) mM (cid:19) λ H φ ∗ SSM ψ SSM + h . c ., (2)where g B − L denotes the U(1) B − L gauge coupling, Y ψ is the (B − L) number of φ and ψ , m represents a soft SUSY breaking Majorana mass of λ H , and M ( ≡ g B − L v B − L ) is the massof λ B − L arising from the spontaneous breaking of U(1) B − L at a scale v B − L . If the masses3f φ and ψ are much smaller than m , the lifetime of λ H is estimated to beΓ − ( λ H → ψ + φ ) ∼ sec g − − L Y − ψ κ − (cid:18) m (cid:19) − (cid:18) M GeV (cid:19) C ψ , (3)where C ψ is a color factor of ψ , i.e., 3 for quarks and 1 for leptons. On the other hand, ifthe mass of φ is larger than m , the decay proceeds with a virtual exchange of φ , leadingtoΓ − ( λ H → ψ + ψ ′∗ + ˜ χ ) ∼ sec g − − L Y − ψ κ − (cid:18) m φ m (cid:19) (cid:18) m (cid:19) − (cid:18) M GeV (cid:19) C ψ , (4)where we have assumed that the main decay of φ is into ψ ′∗ and a SM gaugino ˜ χ .It is quite remarkable that the hierarchy between the B − L breaking scale ∼ GeV and the SUSY breaking mass of the hidden gaugino of O (1) TeV naturally leads to thelifetime of O (10 ) seconds that is needed to account for the electron/positron excess.Note also that the longevity of the λ H DM arises from the geometrical separation and thehierarchy between M and m , not from conservation of some discrete symmetry such asthe R parity.Throughout this paper we assume that the R parity is preserved, and that the lightestsupersymmetric particle (LSP) is the lightest neutralino in the SSM which also contributesto the DM density. For the moment we assume that λ H is the dominant component ofDM, while the abundance of the neutralino LSP is negligible. Even if this is not the case,the prediction on the cosmic-ray fluxes given in the next section can remain unchanged,since the fraction of λ H in the total DM density can be traded off with the lifetime, aslong as the fraction is larger than about 10 − . We will come back to this issue in Sec. 4. As we have seen in the last section, λ H has a very long lifetime and decays into theSSM particles through a small mixing with the λ B − L . The decay of λ H causes the SUSY The seesaw mechanism [9] for neutrino mass generation suggests the Majorana mass of the (heaviest)right-handed neutrino at about the GUT scale. Such a large Majorana mass can be naturally providedif the U(1) B − L symmetry is spontaneously broken at a scale around 10 GeV. λ H ,the hadronic decay can be suppressed, which results in a small amount of antiprotons andphotons [10]. We assume that it is the case.We fix in the present analysis the masses of the λ H and the neutralino LSP to be 3TeV and 200 GeV, respectively. In general, SUSY cascade decays are very complicated.To simplify the analysis, we focus on the following three extreme cases. Case I [ Universal decay into a lepton and slepton pair ]: The λ H decays into thethree lepton and slepton pairs at the same rate, and the sleptons subsequently decayinto LSP + charged lepton. We set that the lifetime of λ H is 9 × sec., and m ˜ e R = m ˜ µ R = m ˜ τ = 2 . λ H . Case II [ Decay into a tau and stau pair ]: The λ H decays into a tau and stau pair,and the stau decays into LSP + tau. The lifetime of λ H is 6 × sec., and m ˜ τ = 2 . λ H . Case III [ Three-body decay into the lepton, anti-lepton and neutralino ]: The λ H decays into the e + + e − + LSP, µ + + µ − + LSP, τ + + τ − + LSP at the same rate.The lifetime of λ H is 1 . × sec. All sfermion particles are heavier than λ H . Asfor the matrix element of the DM decay, we approximate that the sleptons are muchheavier than λ h , i.e., m ˜ ℓ ≫ m .The electron and positron energy spectrum is estimated with the program PYTHIA [11].For the propagation of the cosmic ray in the Galaxy, we adopt the same set-up in Ref. [5]based on Refs. [12, 13], namely the MED diffusion model [14] and the NFW dark matterprofile [15]. As for the electron and positron background, we have used the estimationgiven in Refs. [16, 17], with a normalization factor k bg = 0 .
68. In Figs. 1 and 2, we showthe positron fraction, the electron plus positron total flux and the diffuse gamma ray flux.We can see from Fig. 1, the above three cases nicely explain the PAMELA result,while the case III seems to give a slightly better fit to the Fermi and H.E.S.S. data withrespect to the other two cases. Note however that the fit to the data has an ambiguitydue to the relatively large uncertainties in the background estimation, as well as possible If the LSP is the Wino, the slepton may also decay into neutrino and charged Wino with a largebranching fraction. τ decay in the case II tends to give more contribution. In all the three caseswe might be able to see some signatures from the λ H decay in the diffuse gamma-rays inthe future observation with the Fermi satellite. So far we have assumed that the hidden gaugino λ H is the main DM component. However,as long as the R parity is conserved, the neutralino LSP in the SSM also contributes tothe DM density. To avoid the overproduction of the neutralino LSP, we assume eitherneutralino-stau coannihilation or the Wino-like LSP. In the former case the stau massmust be close to the neutralino mass of O (100) GeV, and the cosmic-ray spectra for sucha mass spectrum were studied in Ref. [5]. In the latter case, the thermal relic abundanceof the Wino LSP of mass O (100) GeV is smaller than the observed DM density , and weeasily avoid the overproduction of the LSP.Let us discuss the production mechanism of the hidden gaugino, λ H , in the earlyuniverse. Since the λ H has only extremely suppressed interactions with the SSM particles,very high reheating temperatures would be needed to generate a right amount of λ H fromthermal particle scatterings. This will be in conflict with the big bang nucleosynthesis(BBN) constraint on the gravitino abundance [31]. As pointed out in Ref. [5], one possibleway to produce λ H is to make use of the gravitino decay. In fact, the gravitino must beheavier than λ H , since otherwise the λ H would promptly decay into the massless hiddengauge boson and the gravitino. Therefore, the gravitino produced at the reheating willdecay into the hidden gaugino and gauge boson as well as the SSM particles.Let us estimate the λ H abundance from the gravitino decay. To be concrete we con-sider two cases: m / = 10 TeV and 100 TeV, since the BBN constraint on the gravitinoabundance depends on the gravitino mass. In the former case, the gravitino abundance The Wino-like neutralino LSP can be realized in anomaly mediation [29], which is feasible withmore than two extra dimensions. In this scheme, hidden matter multiplets charged under the hiddenU(1) gauge symmetry must be introduced so that the hidden gaugino acquires a SUSY breaking mass. Another possibility is non-thermal production from the inflaton decay. However, as shown in Ref. [30],an equal or even greater amount of the gravitino will be also generated in a similar process, and thesituation will not be improved much. Y / ∼ − without spoiling the BBN result [31]. The correspond-ing reheating temperature is about 10 GeV, assuming the thermal gravitino production.The expected branching ratio of producing λ H is O (1)%, and the λ H abundance will beΩ λ h ∼ − . Note that the abundance of the neutralino LSP produced through thegravitino decay does not have enough abundance to explain the total DM density, andtherefore the dominant contribution must come from the thermal relic neutralino. Thismay be realized in the neutralino-stau coannihilation region. On the other hand, in thecase of m / = 100 TeV, the gravitino abundance can be as large as Y / ∼ − for areheating temperature T R ∼ GeV. The resultant λ H abundance will be Ω λ h ∼ − .Interestingly, the neutralino abundance from the gravitino decay is just a right amount toexplain the observed DM density Ω λ h ≃ . Thus, even if the λ H may not be the dom-inant component of DM, its fraction can be naturally in the range of 1 −
10% dependingon the gravitino mass and the reheating temperature. The predictions on the cosmic-rayspectra remain unchanged if we make the lifetime shorter correspondingly by adopting aslightly smaller value of the B − L breaking scale v B − L .In this paper we have studied representative decay processes in a scenario that a hiddenU(1) gaugino DM decays mainly through a mixing with a U(1) B − L , producing energeticleptons. We have shown that those energetic leptons from the DM decay can account forthe PAMELA and Fermi excesses in the cosmic-ray electrons/positrons. The predictedexcess in the diffuse gamma-ray flux around several hundred GeV can be tested by theFermi satellite, and will provide us with information on the decay processes. One of themerits of the current scenario is that the gaugino in the SSM can be within the reachof LHC, since at least one of the SSM neutralino lighter than the hidden gaugino DM isnecessary for the DM to decay. Acknowledgement
This work was supported by World Premier International Center Initiative (WPI Pro-gram), MEXT, Japan. The work of SS is supported in part by JSPS Research Fellowships The non-thermally produced neutralino will not annihilate efficiently even in the case of the WinoLSP, unless the gravitino mass is extremely large.
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