Selected for a Viewpoint in Physics PHYSICAL REVIEW D 79, 105022 (2009) Astrophysical probes of unification

Asimina Arvanitaki,1,2 Savas Dimopoulos,3 Sergei Dubovsky,3,4 Peter W. Graham,3 Roni Harnik,3 and Surjeet Rajendran5,3 1Berkeley Center for Theoretical Physics, University of California, Berkeley, California 94720, USA 2Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 3Department of Physics, Stanford University, Stanford, California 94305, USA 4Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia 5SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA (Received 23 February 2009; published 26 May 2009) Traditional ideas for testing unification involve searching for the decay of the proton and its branching modes. We point out that several astrophysical experiments are now reaching sensitivities that allow them to explore supersymmetric unified theories. In these theories the electroweak-mass dark matter particle can decay, just like the proton, through dimension 6 operators with lifetime 1026 s. Interestingly, this time scale is now being investigated in several experiments including ATIC, PAMELA, HESS, and Fermi. Positive evidence for such decays may be opening our first direct window to physics at the super- 16 symmetric unification scale of MGUT 10 GeV, as well as the TeV scale. Moreover, in the same supersymmetric unified theories, dimension 5 operators can lead a weak-scale superparticle to decay with a lifetime of 100 s. Such decays are recorded by a change in the primordial light element abundances and may well explain the present discord between the measured Li abundances and standard big bang nucleosynthesis, opening another window to unification. These theories make concrete predictions for the spectrum and signatures at the LHC as well as Fermi.

DOI: 10.1103/PhysRevD.79.105022 PACS numbers: 12.10.Dm, 12.60.Jv, 95.35.+d, 98.80.Ft

M4 TeV 5 M 4 I. LONG LIFETIMES FROM THE UNIFICATION 8 GUT ¼ 3 1027 s GUT : SCALE AND ASTROPHYSICAL SIGNALS m5 m 2 1016 GeV (1) One of the most interesting lessons of our times is the evidence for a new fundamental scale in nature, the grand Similarly a long-lived particle decaying through dimen- 16 unification (GUT) scale near MGUT 10 GeV, at which, sion 5 GUT suppressed operators has a lifetime in the presence of superparticles, the gauge forces unify M2 TeV 3 M 2 [1,2]. This is a precise, quantitative (few percent) concord- 8 GUT ¼ 7s GUT : (2) 3 16 ance between theory and experiment and one of the com- m m 2 10 GeV pelling indications for physics beyond the standard model. Both of these time scales have potentially observable con- Together with neutrino masses [3,4], it provides indepen- sequences. The dimension 6 decays cause a small fraction dent evidence for new physics near 1016 GeV, significantly of the dark matter to decay today, producing potentially 19 below the Planck mass of Mpl 10 GeV. The LHC may observable high-energy cosmic rays. The dimension 5 de- considerably strengthen the evidence for grand unification cays happen during big bang nucleosynthesis (BBN) and if it discovers superparticles. Furthermore, future proton can leave their imprint on the light element abundances. decay experiments may provide direct evidence for physics There is, of course, uncertainty in these predictions for the at MGUT. In this paper we consider frameworks in which lifetimes because the physics at the GUT scale is not GUT scale physics is probed by cosmological and astro- known. physical observations. If the dark matter decays through dimension 6 GUT In grand unified theories the proton can decay because suppressed operators with a lifetime as in Eq. (1), it can the global baryon-number symmetry of the low-energy produce high-energy photons, electrons and positrons, standard model is broken by GUT scale physics. Indeed, antiprotons, or neutrinos. Interestingly, the lifetime of or- only local symmetries can guarantee that a particle remains der 1027 s leads to fluxes in the range that is being explored exactly stable since global symmetries are generically by a variety of current experiments such as HESS, MAGIC, broken in fundamental theories. Just as the proton is VERITAS, WHIPPLE, EGRET, WMAP, HEAT, long-lived but may ultimately decay, other particles, for PAMELA, ATIC, PPB-BETS, SuperK, AMANDA, example, the dark matter, may decay with long lifetimes. If Frejus, and upcoming experiments such as the Fermi a TeV mass dark matter particle decays via GUT sup- (GLAST) gamma-ray space telescope, the Planck satellite, pressed dimension 6 operators, its lifetime would be and IceCube, as shown in Table I. This is an intriguing

1550-7998=2009=79(10)=105022(35) 105022-1 Ó 2009 The American Physical Society ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009)

TABLE I. The lower limit on the lifetime of a dark matter particle with mass in the range 10 GeV & mc & 10 TeV, decaying to the products listed in the left column. The experiment and the observed particle being used to set the limit are listed in the top row. HESS limits only apply for mc > 400 GeV and are shown for two choices of halo profiles: the Kravtsov (K) and the NFW. PAMELA limits are most accurate in the range 100 GeV & mc & 1 TeV. All the limits are only approximate. Generally conservative assumptions were made and there are many details and caveats as described in Sec. II. Extragalactic rays Galactic ’s Antiprotons Positrons Neutrinos Decay SuperK, channel EGRET HESS PAMELA PAMELA AMANDA, Frejus qq 4 1025 s qffiffiffiffiffiffiffi 1027 s eþe 8 1022 s2 1022 s mc ðKÞ 1024 s2 1025 sðTeVÞ 3 1021 sð mc Þ qffiffiffiffiffiffiffiTeV mc TeV þ 8 1022 s2 1022 s mc ðKÞ 1024 s2 1025 sðTeVÞ 3 1024 sð mc Þ qffiffiffiffiffiffiffiTeV mc TeV þ 1025 s1022 s mc ðKÞ 1024 s1025 sðTeVÞ 3 1024 sð mc Þ TeV mc TeV 25 26 25 23 ð mc Þ WW 3 10 s qffiffiffiffiffiffiffi 3 10 s410 s810 s TeV 24 24 mc 25 23 TeV 9 10 sðmc ¼ 100 GeVÞ 2 10 s ðKÞ 2 10 s8 10 sð Þ TeV mc 22 2 10 sðmc ¼ 800 GeVÞ qffiffiffiffiffiffiffi 23 ð ¼ Þ 25 mc 4 10 s mc 3200 GeV 5 10 s TeV (NFW) 22 24 23 25 ð mc Þ 8 10 s 10 s10s10s TeV coincidence, presented in Sec. II, that may allow these these anomalies could be due to astrophysics and not new experiments to probe physics at the GUT scale, much as particle physics. Nevertheless, the Li problems are sugges- the decay of the proton and a study of its branching ratios tive of new physics because a new source of energy dep- would. Possible hints for excesses in some of these experi- osition during BBN naturally tends to destroy 7Li and ments may have already started us on such an exciting produce 6Li, a nontrivial qualitative condition that many path. single astrophysical solutions do not satisfy. Further, en- GUT scale physics can also manifest itself in astrophys- ergy deposition, for example, due to either decays or ical observations by leaving its imprint on the abundances annihilations, during BBN most significantly affects the of light elements created during BBN. For example, neu- Li abundances, not the other light element abundances, trons from the decay of a heavy particle create hot tracks in making the Li isotopes the most sensitive probes of new the surrounding plasma in which additional nucleosynthe- physics during BBN. Finally, a long-lived particle decay- sis occurs. In particular, these energetic neutrons impinge ing with a 1000 s lifetime can naturally destroy the on nuclei and energize them, causing a cascade of reac- correct amount of 7Li and produce the correct amount of tions. This most strongly affects the abundances of the rare 6Li without significantly altering the abundances of the elements produced during BBN, especially 6Li and 7Li and other light elements 2H, 3He, and 4He. possibly 9Be. In this paper we explore astrophysical signals of GUT In fact, measurements of both isotopes of Li suggest a scale physics in the framework of supersymmetric unified discrepancy from the predictions of standard BBN (sBBN). theories [often referred to as SUSY GUTs or supersym- 7 7Li ð Þ 10 metric standard models (SSMs) [2]], as manifested by The observed Li abundance of H 1–2 10 is a 7Li particle decays via dimension 5 and 6 GUT suppressed factor of several below the sBBN prediction of H ð5:2 0:7Þ1010 [5]. In contrast, observations indicate operators. In order to preserve the success of gauge cou- a primordial 6Li abundance over an order of magnitude pling unification, we work with the minimal particle con- above the sBBN prediction. The lithium abundances are tent of the minimal supersymmetric standard model measured in a sample of low-metallicity stars. The Li (MSSM) with additional singlets or complete SU(5) mul- isotopic ratio in all these stars is similar to that in the tiplets. The effects of GUT physics on a low-energy ex- 6 periment are generally suppressed. However, these effects lowest-metallicity star in the sample: Li ¼ 0:046 0:022 7Li can accumulate and lead to vastly different physics over 6 [6]. This implies a primordial Li abundance in the range long times depending on the details of the higher dimen- 6Li ð Þ 12 6Li 14 H 2–10 10 , while sBBN predicts H 10 sion operators generated by GUT physics. For example, [7,8]. The apparent presence of a Spite plateau in the particles that would have been stable in the absence of abundances of both 6Li and 7Li as a function of stellar GUT scale physics can decay with very different lifetimes temperature and metallicity is an indication that the mea- and decay modes depending on the particular GUT phys- sured abundances are indeed primordial. Of course, though ics. Conversely, such decays are sensitive diagnostics of there is no proven astrophysical solution, either or both of the physics at the GUT scale. The details of these decays

105022-2 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) depend upon both the physics at the GUT scale and the The first of these are SUSY theories that solve the strong low-energy MSSM spectrum of the theory. So, astrophys- CP problem with an axion. The other is the split SUSY ical observations of such decays, in conjunction with in- framework. Both these frameworks provide particles that dependent measurements of the low-energy MSSM can have lifetimes long enough to account for the primor- spectrum at the LHC, would open a window to the GUT dial lithium discrepancies without additional inputs, and scale—just as proton decay would. The role of the water are included in Sec. IV. and photomultipliers that register a proton decay event are now replaced by the Universe and either the modified Li II. ASTROPHYSICAL LIMITS ON DECAYING abundance or the excess cosmic rays that may be detected DARK MATTER in today’s plethora of experiments. To characterize the varieties of GUT physics that can In this section we describe the existing astrophysical give rise to decays of would-be-stable particles we enu- limits on decaying dark matter, as summarized in Table I. merate the possible dimension 5 and 6 operators, each one Note that the limits on dark matter decaying into many of which defines a separate general class of theories that different final states (e.g. photons, leptons, quarks, or breaks a selection rule or conservation law that would have neutrinos) are similar even though they arise from stabilized the particle in question. This approach has the different experiments. These different observations are advantage of being far more general than a concrete theory all sensitive to lifetimes in the range given by a and encompasses all that can be known from the limited dimension 6 decay operator, as in Eq. (1). This can be low-energy physics experiments available to us. In other understood, at least for the satellite and balloon experi- words, all measurable consequences depend on the form of ments, because these all generally have similar accep- the operator and not on the detailed microphysics at the tances of ð1m2Þð1yrÞð1srÞ3 1011 cm2 ssr.For unification scale (e.g. the GUT mass particles) that give comparison, the numberR of incident particles from decay- 10 kpc d3r GeV 28 1 rise to it. ing dark matter is 2 ð0:3 3Þð10 s Þ r mc cm The presence of supersymmetry, together with gauge 1010 cm2 s1 sr1, where these could be photons, posi- symmetries and Poincare´ invariance, and the simplicity trons or antiprotons, for example, depending on what is of the near-MSSM particle content greatly reduces the produced in the decay. This implies such experiments number of possible higher dimension operators of dimen- observe ð3 1011 cm2 ssrÞð1010 cm2 s1 sr1Þ sion 5 and 6 and allows for the methodic enumeration of 30 events which is in the right range to observe dark matter the operators and the decays they cause. This is what we do decaying with a dimension 6 decay lifetime. in Secs, III, IV, and V. We work in an SU(5) framework Not only are there limits from astrophysical observa- because any of the SU(5) invariant operators we consider tions, there may be indications of dark matter decaying or can be embedded into invariant operators of any larger annihilating from recent experiments. PAMELA [9] has GUT gauge group so long as it contains SU(5). Of course, observed a rise in the positron fraction of cosmic rays such operators may in general contain several SU(5) op- around 50 GeV. ATIC [10] and PPB-BETS [11] have erators so the detailed conclusions can be affected. As an observed a bump in the spectrum of electrons plus posi- example, we study a model that is made particularly simple trons with a peak around 500 GeV. Finally, there are claims in an SO(10) GUT in Sec. V. that WMAP has observed a ‘‘haze’’ which could be syn- The dimension 6 operators of Sec. III have many poten- chrotron radiation from high-energy electrons and posi- tially observable astrophysical signals at experiments trons near the Galactic center. This is consistent with dark searching for gamma rays, positrons, antiprotons or neu- matter annihilating [12] and possibly also with dark matter trinos. We separate them into R-conserving and R-breaking decaying [13]. classes and in each case we also build UV models which We will call the decaying dark matter particle c with give rise to these operators. The dimension 5 operators of mass mc . Sec. IV have potentially observable effects on BBN, may solve the lithium problems, and give dramatic out-of-time decays in the LHC detectors. Section V presents frame- A. Diffuse gamma-ray background from EGRET works and simple theories that have both dimension 5 and Observations of the diffuse gamma-ray background by 6 operators destabilizing particles to lifetimes of both 100 EGRET have been used to set limits on particles decaying and 1027 s to explain Li and lead to astrophysical signa- either into qq or [14], as reproduced in Table I.We tures today in PAMELA/ATIC and other observatories. adapted these limits for the other decay modes shown in the ¼ In Sec. VI we similarly look at the consequences for table. We took the age of the Universe to be t0 13:72 Fermi/GLAST and PAMELA/ATIC. In Sec. VII we outline 0:12 Gyr 4:3 1017 s and the abundance of dark matter 2 þ þ LHC-observable consequences of some of these scenarios to be DMh 0:11 [15]. For the e e , , and (operators) that could lead to their laboratory confirmation. decay modes the limit comes from assuming that these Finally, there are two more classes of theories that fit produce a hard W or Z from final state radiation 102 of into the elegant framework of supersymmetric unification. the time. The limit on the lifetime is given conservatively

105022-3 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) as 3 103 times the limit on the WþW decay mode, commonly used Navarro-Frenk-White (NFW) profile [21] since only one gauge boson is radiated and its energy is with ð; ; Þ¼ð1; 3; 1Þ, rs ¼ 20 kpc, and ð8:5 kpcÞ¼ slightly below mc . For the þ decay mode, the strongest GeV 2 0:3 cm3 . There is an even more sharply peaked profile, the limit comes from considering the hadronic branching frac- Moore profile [22], which is defined by Eq. (4) with tion of the . The decays into leptons ee and ð; ; Þ¼ð1:5; 3; 1:5Þ, rs ¼ 28 kpc, and ð8:5 kpcÞ¼ 30% of the time. The rest of the decay modes have several GeV 0:27 cm3 . There is also the very conservative Burkert hadrons and one which carries away at most one-half of profile [23–25] the energy [16]. Thus we estimate the hadronic fraction of the energy from the decay as 1 0:7 0:4. The limit on ðsÞ¼ 0 ; (5) 2 ð þ s Þð þ s2Þ 1 1 2 qq is relatively insensitive to the mass of the decaying rs rs particle in our range of interest 100 GeV & mc & where ¼ 0:839 GeV and r ¼ 11:7 kpc. We sometimes 10 TeV. We take this to imply that it depends only on 0 cm3 s the total energy produced in the decay and not as much on translate limits on the annihilation cross section v into the shape of the spectrum, giving a limit on the decay width limits on the decay rate using the flux from annihilations into ’s which is a factor of 0.4 of that into qq. To set a limit Z 2vN þ ¼ on decays into W W , the ratio between the photon yield annihilation 2 drd: (6) þ 2 8mc from W W and qq is approximated as 3 from [17]. A conservative limit on decays to is calculated using B. Galactic gamma rays from HESS the Kravtsov profile. If the NFWq profileffiffiffiffiffiffiffiffiffiffi is used instead, the 25 mc HESS observations of gamma rays above 200 GeV from limit is stronger: >5 10 s 1 TeV. If we had used the the Galactic ridge [18] can also be used to limit the partial Burkert profile,q theffiffiffiffiffiffiffiffiffiffi limit would have been much weaker: decay rates of dark matter with mass mc > 400 GeV. The >3 1022 s mc . In this case the central profile is so limit on the flux of gamma rays comes from this HESS 1 TeV analysis in which the flux from an area near the Galactic flat that there is essentially no difference between the center ( 0:8 lepton l. Ignoring the logarithmic Earth within a solid angle , r is the distance from the 2 dependence on mc we estimate this as giving 10 photons Earth, mc is the mass of the dark matter and is its decay per decay for the light leptons and 1 102 for ’s with rate, and N is the number of photons from the decay 2 energy high enough to count in the ‘‘edge’’ feature in the which we will set equal to 2 for our limits. The density final state radiation spectrum. We then scale the limits from of dark matter is taken as decay to by those factors because the edge is assumed ðsÞ¼ 0 ; (4) to be visible as the line from . Clearly, a more realistic ð s Þð1 þðs ÞÞðÞ=ðÞ analysis would include a better determination of the ob- rs rs servability of the edge feature. where s is the radial coordinate from the Galactic center. We do not place limits on decays to WW or because We use the Kravtsov profile [20] with ð; ; Þ¼ the spectrum of photons produced by final state radiation ð Þ ¼ ð Þ¼ 2; 3; 0:4 , rs 10 kpc, and 0 is fixed by 8:5 kpc does not have a large hard component. These can produce GeV 0:37 cm3 for our limits. This gives conservative limits since many softer photons but these are better limited by lower the flux from the Galactic center is much less than in the energy gamma-ray observations such as EGRET and are

105022-4 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) 1 counted in the first column. Although the qq decay mode is limited to 12 . Similarly the Z decays 20% of the time may have a large final state radiation (FSR) component, to [16] and since there are two neutrinos, each of which this will still give a bound worse than the HESS bound on carries away about half the energy, the limit on decays to 0 2 1 the mode. Additionally the qq mode produces ’s ZZ is slightly stronger: 5 4 . which decay to photons but these are at low energies so We do not limit decays to or qq because we expect HESS cannot place good limits on them. So the qq mode is these to be better limited by direct gamma-ray and anti- also better limited by the EGRET observations. proton observations.

C. Neutrino limits from SuperK, AMANDA, and Frejus D. Positrons and antiprotons from PAMELA To find the limits on dark matter decays from astrophys- We translate recently published limits from PAMELA ical neutrino observations we start by finding the limits on on the annihilation cross sections of dark matter into the decays directly into two neutrinos using [27]. The given various final states into limits on the decay rate. This can be limit on annihilation cross section into is almost inde- done because a dark matter particle of mass mc decaying pendent of the dark matter mass mc in the range into one of the given final states (e.g. qq) yields exactly the 10 GeV gauge boson is radiated and its energy is slightly less mc þ 26 cm3 than . The limits on come from the fact that mc 3 10 2 ¼ 4 1028 s s : (8) muons always decay as ! ee and the tends to TeV v carry away almost half the energy. Further all produced neutrinos will oscillate a large number of times over these It turns out that this is almost independent of halo profile Galactic distances before reaching the Earth so all neutri- and the size rmax of the local sphere used to define it. We nos count equally for detection (and [27] already assumed expect limits from ATIC to be similar to our limits from for their limit that all three neutrino species are produced PAMELA because roughly the same signal that fits ATIC will fit PAMELA (see, for example, Sec. VI). equally). So we ignore the soft e and give the limit as þ þ þ 1 The limits from positrons in the e e , , , 4 , where is the limit on the lifetime into . The 1 and WW channels are translated from the annihilation factor 4 comes from assuming the has half the energy of 2 cross-section limits from [28]. Really we use the largest the and the neutrino background scales as E . annihilation cross section which could explain the ob- Equivalently, the bound on scales with mc (because served PAMELA positron excess [9] given propagation the bound on annihilations from [27] is constant in mc )so uncertainties (model B of [28]) and translate this into a þ a decay to is like a decay to but with a decaying decay rate. This means that lifetimes around and up to an particle of half the mass and half the dark matter density. order of magnitude greater than those given in Table I are þ 1 Similarly, the limit on of 4 is set by assuming that the best fit lifetimes for explaining the PAMELA positron the , which is always produced in decay, generally excess. This is most true for the lepton channels, while carries away about half the energy of the . Most decays decays to WW do not seem to fit the shape of the positron are two- or three-body so we expect this to be a good spectrum very well (see e.g. [17,28]). Note that these life- approximation [16]. times are in qualitative agreement with those found in [29]. The W decays one-third of the time to l [16] and the Note that we do not place a limit on the qq channel because neutrino has about half the energy so the decay to WþW this is better limited by the PAMELA antiproton measure-

105022-5 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) ment. The limit on comes from assuming the usual 3 1. Explaining the electron/positron excess 3 10 factor times the WW limit from one of the neutrinos In the previous section we set limits on the decay rate of producing a W from final state radiation. It is possible that a dark matter particle using several experiments including a stronger limit could be set by considering soft W brems- PAMELA. The limits from positron observations were less strahlung from the neutrino, turning the neutrino into a stringent than they would have been had PAMELA not hard positron and the limit would then come from that seen an excess. In this section we consider what is neces- positron and not from the decay of the W. We do not sary to explain the PAMELA/ATIC positron excesses. A attempt to estimate this. more detailed analysis of individual models is presented in The limit from positrons on the decay channel arises Sec. VI. when positrons are produced through an off-shell photon. Because of the large positron signal and hard spectrum The relative branching ratio of this decay is well known 0 detected by PAMELA the best fit to the data is achieved from decay [30] with a decaying (or annihilating) particle with a direct channel to leptons. Further, the lack of a signal in anti- 2 protons disfavors channels with a large hadronic branching c ! þ mc f f ¼ 4Q 7 fraction such as qq or WW. Thus the PAMELA excess is fit ln ; (9) þ þ c ! 3 mf 4 well by a dark matter particle that decays to e e , , or þ with the lighter two leptons providing the best fit [17,28]. As in the previous section, we translate the cross where f is a fermion of charge Q, lighter than c . Counting sections given in [28] using Eq. (8) to find the range of the production of muons as well (since they always decay lifetimes which best fit the PAMELA positron data given to electrons), a conservative estimate for this branching the propagation uncertainties. We find the best fit for fraction is 4% in our range of masses 100 GeV & mc & masses in the range 100 GeV & mc & 1 TeV is 1 TeV. We assume the produced positron to have an en- mc þ 25 TeV 26 TeV ergy around 3 . The scaling of the limit on the e e 2 10 s & & 8 10 s : (10) channel with mc comes from the scaling of the number mc mc density of dark matter. Thus the energy of the produced The range comes from the uncertainties in the propagation positron is not very relevant in our range of mc so the limit þ of positrons in our galaxy and we estimate it by using the on the decay channel is just 4% of the limit on e e . maximum and minimum propagation models from [28] The limits from antiprotons on the qq and WW channels (models B and C). It is difficult to fit just the PAMELA come from comparing the antiproton fluxes computed in positron excess (not even considering antiprotons) with [17] with data from PAMELA [31,32], finding the limit this decays to WW unless the dark matter is light mc & gives on annihilation cross section, and converting this into 300 GeV or very heavy mc * 4 TeV [17]. We will not a limit on the decay rate using Eq. (8). These are almost consider these mass ranges because we also wish to fit the exactly the same limits as would be derived by translating ATIC spectrum which requires masses in the range the limits on the annihilation cross section from [33] into 1 TeV & mc & 2 TeV. Note that while this paper was in limits on the decay rate. The limits on the eþe, þ, preparation [35] appeared which generally agrees with the þ, and channels come from hard W bremsstrahlung results presented here. from the leptons producing antiprotons and we take this to So for explaining the PAMELA/ATIC excesses, we are be 3 103 of the limit on WW (the same factor as used most interested in a model in which dark matter decay above). Note that these antiproton limits are most appli- releases between 1 and 2 TeVof energy, dominantly decay- cable in the range 100 GeV & mc & 1 TeV and are es- ing to hard leptons with a lifetime given in Eq. (10). Such a sentially independent of mass in that range (equivalently model must also avoid the limits on other subdominant the annihilation cross-section limits scale linearly with decay modes to hadrons which are given in Table I.For mc ). example, a 1.6 TeV dark matter particle produces an end The limit from antiprotons on the decay channel point of the electron/positron spectrum around 800 GeV, in comes when one of the photons is off-shell and produces agreement with ATIC. Such a particle must have a lifetime a qq pair. Using Eq. (9) and summing the contributions to decay to leptons in the range 1025 s & & 5 1026 s from the four light quarks (using their current masses) with and a lifetime to decay to qq longer than * 1027 s. a factor of 3 for the number of colors, we estimate a branching ratio Bðc ! qqÞ4% at mc ¼ 100 GeV (rising to 6% at mc ¼ 1 TeV). Note that this is in rough III. DARK MATTER DECAYS BY DIMENSION 6 agreement with the one-photon rate found in [34]. If we OPERATORS conservatively assume that the quark pair has energy ¼ The decays of a particle with dark matter abundance into 1 2 mc , then we find that the limit is 0.02 of the limit on the the standard model are constrained by many astrophysical qq decay channel. observations. These limits (see Sec. II) on the decay life-

105022-6 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) TABLE II. A rough estimate of the scale M that suppresses the suppression from multibody phase space factors and yield dimension 6 operator mediating the decay of a TeV mass particle a lifetime 1026 s. In Table II, we present the scale M 26 in order to get a lifetime 10 s for decays with various required to yield this lifetime for scenarios with different numbers of particles in the final state. Phase space is accounted numbers of final state particles. The scale M varies from for approximately using [36]. Lifetimes scale as M4. Specific the putative scale where the gauge couplings meet 2 decays may have other suppression or enhancement factors as 16 discussed in the text. 10 GeV for a two-body decay to the right-handed neu- trino mass scale 1014 GeV for a five-body decay. We Number of final state particles Scale M (GeV) note that the scale 1014 GeV also emerges as the Kaluza- 2 1016 Klein scale in the Horava-Witten scenario. In the rest of the 3 3 1015 paper, we will loosely refer to these scales as MGUT. 4 5 1014 The observations of PAMELA/ATIC can be explained 5 1014 through the decays of a TeV mass particle with dark matter abundance if its lifetime 1026 s (see Sec. II). PAMELA, in particular, observes an excess in the lepton channel and times are in the range 1023–1026 s. Current experiments constrains the hadronic channels. In our operator analysis, like PAMELA, ATIC, Fermi, etc., probe even longer life- we highlight operators that can fit the PAMELA/ATIC times. These lifetimes are in the range expected for the data. However, we also include operators that dominantly decays of a TeV mass particle through dimension 6 GUT produce other final states like photons, neutrinos and had- suppressed operators. In this section, we present a general rons in our survey. While these operators will not explain operator analysis of such dimension 6 operators. the PAMELA data, they provide new signals for upcoming A dimension 6 operator generated by integrating out a experiments like Fermi. For concreteness, we consider particle of mass M scales as M4. This strong dependence SU(5) GUT models. We classify the dimension 6 operators on M implies a wide range of possible lifetimes from small into two categories: R-parity conserving operators and variations in M. The decay lifetime is also a strong function R-breaking ones. In the R-conserving case, we will add of the phase space available for the decay, with the lifetime singlet superfield(s) to the MSSM and consider decays scaling up rapidly with the number of final state particles from the MSSM to the singlet sector and vice versa. The produced in the decay. Since we wish to explore a wide singlets may be representatives of a more complicated class of possible operators, we will consider decays with sector (see Sec. V). In the R-breaking part we will consider different numbers of particles in their final state. Motivated the decay of the MSSM lightest supersymmetric particle by the decay lifetime 1026 s being probed by experi- (LSP) into standard model particles. As a preview of our ments, we exploit the strong dependence of the lifetime results, a partial list of operators and their associated final on the scale M to appropriately lower M to counter the states is summarized in Table III.

TABLE III. A partial list of dimension 6 GUT suppressed decay operators. For each operator, we list its most probable MSSM final state. The lifetime column gives the shortest lifetime that this operator can yield when the scale suppressing the operator is 1016 GeV. In the mass scale column, we list the highest possible scale that can suppress the operator in order for it to yield a lifetime 1026 s. Assumptions (see text) about the low-energy MSSM spectrum were made in order to derive these results. All the operators are in superfield notation except for the soft R violating operators.

Lifetime (s) Mass scale (GeV) 16 26 Operator in SU(5) Operator in MSSM Final state (MGUT 10 GeV) (lifetime 10 s) R-parity conserving SyS10y10 SySQyQ, SySUyU, SySEyE Leptons 1026 1016 y y y y 26 16 S SHuðdÞHuðdÞ S SHuðdÞHuðdÞ Quarks 10 10 y y y y y y y y 28 15 S 10f5f 10f S QL U, S UD E, S QD Q Quarks and leptons 5 10 10 y y y y y y 26 16 S 5fHu 10f S LHu E, S DHu Q Leptons 10 10 2 2 2 26 16 S W W S W EMW EM, S W ZW Z (line) 10 10 Hard R violating 37 13 5fð5fÞ5fð5fÞ5f DDDLL Quarks and Leptons 10 10 Soft R violating m4 m4 L 3 SUSY ~ SUSY ~ 30 14 2 Hu5f 2 Hu‘ Quarks 4 10 7 10 MGUT MGUT m3 m3 L 3 SUSY ~ SUSY ~ 32 14 2 Hu5f 2 Hu‘ Leptons 6 10 10 MGUT MGUT y L 3 mSUSY ~6 mSUSY ~6 y þ 32 14 2 HdW@5f 2 HdW@‘ 2 10 10 MGUT MGUT

105022-7 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) A. R-parity conserving operators respectively. It is conceivable that SUSY breaking soft 2 The lifetimes of the decays of MSSM particles to the masses may make ms~ negative leading to a TeV scale h i MSSM LSP are far shorter than the dimension 6 GUT VEV s~ for s~. In this case, additional interactions in the suppressed lifetime 1026 s currently probed by experi- singlet sector will be required to stabilize the VEV at the ments. In a R-parity conserving theory, the MSSM cannot TeV scale. A decay mode with a singlet VEV will typically lead to decays with such long lifetimes since the MSSM dominate over modes without a VEV since the former have LSP, being the lightest particle that carries R parity, is fewer particles in their final state leading to smaller phase stable [2]. These decays require the introduction of new, space suppression (see discussion in Sec. III A 1 a). TeV scale multiplets. Limits from dark matter direct de- Upon SUSY breaking, there are two distinct decay top- tection [37,38] and heavy element searches [39] greatly ologies: constrain the possible standard model representations of (1) A component of the singlet is heavier than the the new particle species. In this paper, we will add a new MSSM LSP and this component can then decay to singlet chiral superfield S in addition to the MSSM [40]. it. The relic abundance of the singlet can be gener- The singlet may emerge naturally as one of the light ated if the singlet is a part of a more complicated moduli of string theory or it could be a representative of sector, for example, through the decays of heavier another sector of the theory (see Sec. V). standard model multiplets (see Sec. V). Decays between the singlet sector and the MSSM can (2) Alternatively, the MSSM LSP is heavier than the happen through the dimension 6 GUT suppressed operators singlets. In this case, the MSSM LSP will decay to in Table III only if there are no other faster decay modes the singlets. between the two sectors. Such decay modes might be We now divide our discussion further based on the final allowed if there are lower dimensional operators between state particles produced in the decay. Motivated by the singlet sector and the MSSM. In Sec. III A 1, we con- PAMELA/ATIC and Fermi, we will be particularly inter- sider models where lower dimensional operators are for- ested in operators that produce leptons and photons. bidden by the imposition of a singlet parity under which S a. Leptonic decays.—The R- and singlet parity conserv- has parity 1. This parity could be softly broken if the ing operators in Table III that contain leptonic final states scalar component of the singlet s~ develops a TeV scale are vacuum expectation value (VEV) hs~i. In Sec. III A 2,we y y y y S S5 5 S S10 10f consider models without singlet parity that require addi- f f and f : (12) 2 M2 tional model building to ensure the absence of dangerous MGUT GUT lower dimensional operators between the singlets and the MSSM. These operators can be generated by integrating out a ð Þ For the rest of the paper, we will adopt the following GUT scale U 1 BL gauge boson under which both the SU(5) conventions: S will refer to a SU(5) singlet, ð5; 5Þ to MSSM and the S fields are charged. At low energies the a fundamental and an antifundamental of SU(5) and first of these operators will lead to couplings of the form ð10; 10Þ to the antisymmetric tensor of SU(5). The sub- s~ s~ l~sy6@l and d~sy6@d (13) script f identifies standard model fields, W denotes 2 2 MGUT MGUT standard model gauge fields and Hu and Hd are standard model Higgs fields. The subscript GUT refers to a field while the second operator will lead to similar operators with a GUT scale mass. l~, e~, ~, q~, u~ and d~ refer to sleptons involving u, q and e. Here we have suppressed all flavor and squarks. H~u and H~d refer to Higgsinos and W~ refers to indices. a wino. We first consider the case when the singlet scalar devel- ops a TeV scale VEV hs~i. In this case, the operators in (13) 1. Models with singlet parity mediate the decay of the singlets to the MSSM LSP or vice versa. With a VEV insertion, the operators in (13) yield The R-parity conserving operators in Table III that also conserve singlet parity are hs~i hs~i l~sy6@l and d~sy6@d: (14) M2 2 y y y y GUT MGUT S S5 5f S S10 10f f ; f ; 2 2 When the singlet fermion is heavier than the MSSM MGUT MGUT y (11) LSP, these interactions mediate its decay into MSSM y 2 S SH ð ÞHuðdÞ S W W states. In particular, when the singlet fermion is heavier u d ; and : 2 2 than a slepton, it can decay to a slepton-lepton pair. The MGUT MGUT component operators of (14) produce the two-body final The decay topologies of these operators are determined by state (see Fig. 1) the low-energy spectrum of the theory. SUSY breaking will s ! ll~ (15) split ms and ms~, the singlet fermion and scalar masses,

105022-8 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) lepton scale where the gauge couplings meet) in order for the three-body decays mediated by this gauge sector to have lifetimes of interest to this paper. singlet fermion The decays discussed above can also produce quarks in slepton their final states. The decay rate is a strong function of the phase space available for the decay and is hence a strong function of the squark and slepton masses. As discussed in ~ s Sec. VII B, the hadronic branching fraction of these decays can be suppressed if the squarks are slightly heavier than FIG. 1. A singlet fermion decaying to a lepton-slepton pair the sleptons. Since squarks are generically heavier than with a singlet scalar VEV hs~i insertion. sleptons due to renormalization-group (RG) running, the suppressed hadronic branching fraction observed by with a lifetime of PAMELA is a generic feature of these operators. An inter- esting possibility emerges when the spectrum allows for 3 2 4 26 1 TeV 1 TeV MGUT the decay of the singlet fermion to an on-shell slepton- ! ~ 2 10 s s l l m hs~i 1016 GeV lepton pair. This decay produces a primary source of (16) monoenergetic hot leptons. However, the subsequent decay of the slepton to the MSSM LSP will also produce a lepton ¼ per lepton generation, where m ms ml~. whose energy is cut off by the slepton and LSP mass When the MSSM LSP is heavier than the singlet fer- difference. With two sources of injection, this decay could mion, it will decay to the singlet fermion and a lepton- explain the secondary ‘‘bump’’ seen by ATIC in addition to antilepton pair through the operators of Eq. (12). These the primary bump (see Secs. VII B and VI). decays (see Fig. 2) are of the form The scalar singlet s~ can decay when the singlet gets a LSP ! lþ þ l þ s: (17) VEV. In the presence of such a VEV, s~ can decay to a pair of scalars (i.e. sleptons and squarks) or fermions (i.e. The lifetime for this three-body decay is leptons and quarks). The decays of s~ to a pair of sleptons is also mediated by the operators in (12) which in compo- 3 2 4 4 1 TeV 1 TeV MGUT Rl þ 26 nents yield terms of the form LSP!sl l 10 15 s; m hs~i 10 GeV 0:5 hs~i hs~i (18) ~ ~ ~ ~ 2 s~ @l @l and 2 s~ @d @d (19) MGUT MGUT where Rl is the ratio of the LSP mass to the slepton mass and we assumed that m ms; if this is not the case, m as well as terms involving q~, u~, and e~. should be replaced by the available energy in the decay s~ will now decay directly to two sleptons (see Fig. 3)or two squarks, with a lifetime m ¼ m ms. Similarly, when the singlet fermion is heavier than the MSSM LSP but lighter than the slepton, 3 2 4 26 1 TeV 1 TeV MGUT the singlet fermion will decay to the MSSM LSP through a !~~ 2 10 s s~ l l m hs~i 1016 GeV three-body decay mediated by an off-shell slepton. Note s~ that the decay lifetime 1026 s when the mass scale sup- (20) 15 pressing the decay is M 10 GeV.InaUð1Þ UV GUT B L per generation (and per representation). The hadronic completion of these operators, this scale is the VEV of the branching fraction of this decay is generically suppressed broken B L gauge symmetry. The B L symmetry must since squarks are expected to be heavier than sleptons (see be broken slightly below the GUT scale (i.e. the putative Sec. VII B). s~ can also decay to a pair of fermions. These

slepton

~ s

slepton

~s FIG. 2. MSSM neutralino decaying to a singlet LSP and an eþe pair. The decay is dominantly into leptons because slep- FIG. 3. A singlet scalar s~ decaying to a slepton pair with a tons are typically lighter than squarks. singlet scalar VEV hs~i insertion.

105022-9 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) 5 4 4 decays are mediated by the operators 26 1 TeV MGUT Rl ! 10 s: s~ LSPsl l m 3 1014 GeV 0:5 hsi h i ~ y6 s~ y6 (24) 2 s~ l @l and 2 s~ d @d; (21) MGUT MGUT If the MSSM neutralino is heavier than the singlets, then which can also be extracted from (12). However, the its decays through the operators in (13) are also four-body decays of a scalar to a pair of fermions (of mass mf) are decays similar to the decay discussed above. The lifetime mf 2 26 14 helicity suppressed by ð Þ [41]. These decays will pre- from this decay is 10 s when MGUT 3 10 GeV, ms~ dominantly produce the most massive fermion pair that is which is roughly the scale of the right-handed neutrino in a allowed by phase space. seesaw scenario. In fact, if this decay is mediated by a ð Þ Owing to this helicity suppression, the hadronic branch- U 1 BL gauge boson, the scale MGUT that suppresses this ð Þ ing fraction from the decays of s~ can be smaller than 0.1 decay is the VEV that breaks the U 1 BL gauge symmetry and accommodate the PAMELA antiproton constraint if which is roughly the mass of the right-handed neutrino. one of the following conditions are satisfied by the scalar The decays discussed in this section involve decays between the singlet sector and the MSSM LSP. In order singlet mass m , the slepton mass m~ and the top quark s~ l for these dimension 6 GUT suppressed operators to be mass mt: involved in the decays between these sectors, it is essential (i) ms~ ml~, ms~ mt.—In this case, the spectrum allows both sleptons and the top quark to be pro- that there are no other faster decay modes available in the duced on shell. Hadrons are produced in this process model. One such mode can be provided by a light grav- from the decays of the top quark. The branching itino. If the gravitino is the MSSM LSP, then the super- fraction for top production is ðmt Þ2 which is smaller particles of the MSSM will rapidly decay to the gravitino ms~ TeV5 with lifetimes 2 . If one component of the singlet is than 0.1 if ms~ * 3mt. F heavier than the gravitino, then that component will decay (ii) ms~ > 2ml~ and ms~ < 2mt.—In this case, sleptons are m5 produced on shell. Hadrons can be produced in this to its superpartner and the gravitino with a lifetime F2 , process either through direct production of the b where m is the phase space available for this decay. Since quark or through off-shell tops. The branching frac- we are interested in the decays of TeV mass particles, this tions of these hadronic production channels are scenario is relevant only when the gravitino mass ð F Þ is Mpl smaller than 0.1 since the direct production of b is & ð 11 Þ2 & m less than a TeV, i.e. F 10 GeV . When F suppressed by ð bÞ2 and the decays mediated by off- ð 11 Þ2 ms~ 10 GeV , the above decays occur with lifetimes shell tops are suppressed by additional phase space 106 s which are far too rapid. factors. Another possibility is for the gravitino to be the MSSM When the scalar singlet does not get a VEV, S parity is LSP and be heavier than the singlets. In this case, the conserved. Decays between the singlets and the MSSM gravitino will decay to the singlet sector with a decay must involve either the decay of the heavier component of ð F3 Þ 6 ðð1011 GeVÞ2Þ3 rate M5 yielding a lifetime 10 s F which the singlet to its lighter partner and the MSSM or the decay pl of the MSSM to the two singlet components. We first is also far too rapid. The dimension 6 GUT suppressed consider the case when one of the singlet components is operators discussed in this section lead to astrophysically heavier than the MSSM LSP. Without loss of generality, we interesting decays only when the gravitino is not the assume this component to be the scalar singlet s~. s~ can MSSM LSP and has a mass larger than TeV. This forces * ð 11 Þ2 decay to its fermionic partner and a lepton-slepton pair the primordial SUSY breaking scale F 10 GeV , through a three-body decay mediated by the operators in making the gravitino heavier and forcing it off shell in (13) if the slepton is light enough to permit the decay. The the decays mediated by it. Integrating out the gravitino, m2 M ð s~Þ2ð plÞð ~ Þ lifetime for this decay mode is operators of the form F F s~ s5f5f are generated. The masses ms~ in this operator are the singlet and soft 5 4 26 1000 GeV MGUT SUSY breaking masses 1 TeV. The decays mediated by ! ~ 10 s: (22) s~ sl l m 1015 GeV this operator have lifetimes * 1037 s for F * ð1011 GeVÞ2 and will not compete with dimension 6 GUT operators The three-body decay of s~ to the singlet fermion and discussed in this section. slepton-lepton pair may be kinematically forbidden if the The constraints on the gravitino mass can be evaded if slepton is heavy. s~ then decays to the singlet fermion and there are more singlets in the theory. For example, if the the MSSM through a four-body decay: dark sector contains flavor, standard model particles may be emitted during ‘‘flavor-changing’’ decays in the dark s~ ! lþ þ l þ s þ LSP: (23) sector. Consider, for example, an SU(6) extension of the GUT group on an orbifold. The chiral matter fields and The lifetime in this case is their decomposition to SU(5) representations are

105022-10 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) ^ are lighter than the squarks and the Higgsinos, the decays 6 i ¼ 5i þ Si; 15i ¼ 10i þ 5i; (25) will predominantly proceed via the leptonic channels and where the index i represents flavor. We break the SU(6) hence these UV completions will also be compatible with symmetry by projecting out the light modes of the 5-plet 5^ the constraints on the hadronic channel imposed by by orbifold boundary conditions at the GUT scale. In the PAMELA. absence of the 5-plet, the singlet superfields S do not have c. Decays to gauge bosons.—The only operator in Yukawa couplings that connect them to the MSSM fields, Table III that contains gauge boson final states is eliminating direct decay modes between the singlets and W W 2 the MSSM. S 2 : (28) Once the heavy off-diagonal SU(6) gauge multiplets are MGUT integrated out, operators of the form This operator may be generated by integrating out a 1 y y 1 y y heavy axionlike or dilaton field that couples linearly to S S L L S S D D 2 2 i j j i or 2 i j j i (26) both W and S2. For example, at the GUT scale we may MGUT M GUT write a superpotential are generated. These operators may lead to dark-flavor- W ¼ M 10 10 þ M X X changing decays of si ! sj þ li þ lj or si ! sj þ di þ dj GUT GUT GUT GUT GUT GUT if there are mass splittings among the singlets. These þ þ 2 XGUT10GUT10GUT XGUTS ; (29) splittings can arise due to explicit SU(6) breaking terms (which may be present on the brane which breaks this where MGUT is a GUT scale mass. Integrating out the symmetry). Soft SUSY breaking will also contribute to heavy 10GUTs will lead to a one-loop coupling of the W W mass splittings in the singlet scalar sector. These splittings form XGUT =MGUT (see Sec. IV C). Using this can cause the decay of a scalar singlet s~i to a singlet effective operator and integrating out XGUT leads to the ~ fermion sj and a lepton li-slepton lj pair. In this case, the operator lepton and slepton emitted in this process will belong to 2W W different families. The hadronic branching fraction of these 2 S : (30) 4MGUT operators relative to the leptonic channel depends strongly on the masses of the various broken SU(6) gauge bosons. The decay topology of this operator is similar to the This branching fraction is suppressed if the SU(6) gauge topologies already discussed in Sec. III A 1 a but leads to boson that connects the singlets and the leptons is lighter new final states. For example, when the scalar singlet s~ than the boson that connects the singlets and the quarks. develops a TeV scale VEV, this operator can lead to decays The decays mediated by these operators are immune to between the MSSM LSP and the singlet fermion that result the effects of the gravitino since these decays explicitly in the direct production of a monochromatic photon. The require off-diagonal gauge bosons. A relic abundance of lifetime for this decay is the singlets can again be generated through nonthermal h i 2 3 15 4 29 s~ m 3 10 GeV processes as discussed in Sec. V. ! þ 3 10 s; s LSP 1 TeV 1 TeV M b. Decays to Higgses.—The R- and singlet parity con- GUT serving operators in Table III that contain Higgs final states (31) are ¼ with m ms mLSP. y SySHyH SySH H This signal is noteworthy since Fermi will have an u u ; d d : (27) M2 M2 enhanced sensitivity to a photon line up to a TeV. Direct GUT GUT decays to monochromatic photons is also a qualitatively These operators are very similar to the operators discussed different feature permitted for decaying dark matter. The in Sec. III A 1 a. They can also be generated by integrating production of monochromatic photons from dark matter out a GUT scale Uð1ÞBL gauge sector and the topologies annihilations is loop suppressed and hence annihilations of the decays mediated by these operators are also similar always lead to bigger signals in other standard model to the decay topologies of the operators discussed in that channels before yielding signals in the photon channel. subsection. However, since these operators involve final However, direct decays of dark matter to monochromatic state Higgses, they will always yield an Oð1Þ hadronic photons can happen independently of its decays to other branching fraction. channels. In any particular UV completion, the leptonic operators The operator discussed in this section will also induce discussed in Sec. III A 1 a and the Higgs operators pre- decays involving Z’s or decays to a chargino and a W sented in this section may be simultaneously present. The boson. The relative rates compared to the photon decay hadronic branching fraction of the decays between the will be set by the decay topology, the bino vs wino com- singlets and the MSSM is a strong function of the phase position of dark matter, as well as the relative size of the space available for the various decay modes. If the sleptons Uð1ÞY vs SUð2ÞL couplings. Hadronic decays to a gluino

105022-11 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) and a gluon are also possible if they are kinematically allowed.

2. S-number violating operators A different class of operators are Kahler terms that break the global S number, for example, y y y y y y S 10fHu 5f;S10fHd 10f;S10f5f 10f: (32) The first two operators involve an R-even S and allow the lightest neutralino of the MSSM to decay to the fermion component of S. If the neutralino has a significant Higgsino component, the decay proceeds just through the single y y dimension 6 vertex and so is three-body. In this case the FIG. 4. A way to generate the operator S 10fHd 10f. first operator produces both leptons and hadrons and the second produces only hadrons. In this case, it is possible to than the LSP, it will still decay just to a Higgs and two make the first operator produce mostly leptons if SU(5) leptons or just to two leptons if the channel where the breaking effects in the UV completion make the coefficient y y Higgs goes to its VEV dominates. The details of the decay of the S Hu LE component dominate over that of the y y depend on the mass spectrum of the MSSM particles. Such S Hu QD. If the neutralino is mostly gaugino, the decay a decay could yield an interesting electron/positron spec- proceeds through an off-shell Higgsino, squark, or slepton trum. Cosmic ray observations could then give important and is four-body. In this case, the first operator could evidence for the mass spectrum of the MSSM, as discussed produce both hadrons and leptons. Here, the lepton-only in Sec. VI. channel will dominate if a slepton is lighter than all the One example of a UV theory which can generate the y Higgsinos and squarks. Again, the second produces only operator Sy10 H 10 is shown in Fig. 4. We have added hadrons, as in Table III. f d f two new fields at the GUT scale 10GUT and 24GUT and their The third operator in Eq. (32) has an R-odd S, so the c neutralino will decay to the scalar component of S. This conjugate fields 10GUT and 24GUT, in order to give them generally produces both leptons and hadrons vectorlike GUT masses. The superpotential is taken to be ! þ þ W ¼ S þ þ H : N0 s~ l 2 jets; 24GUT24GUT 10f24GUT10GUT d10GUT10GUT (33) ! þ þ ! þ (34) N0 s~ 2 jets; or N0 s~ 3 jets: If the right-handed sleptons are the lightest sleptons, the This preserves a ‘‘heavy parity’’ under which the GUT channel with charged leptons can dominate. scale fields 10GUT and 24GUT and their conjugates are odd The decays from the MSSM to S mediated by the and everything else is even. This ensures no mixing hap- operators in Eq. (32) are either three- or four-body and pens between the new GUT scale fields and the MSSM their rates are as shown in Table III, probing scales as fields. Further this preserves a Peccei-Quinn (PQ) symme- ð Þ¼ ð Þ¼ ð Þ¼ shown in Table II. try with charges Q Hu Q Hd Q 24GUT 2, ð Þ¼ ð Þ¼ ð Þ¼ ð Þ¼ Of course, these operators also allow the S to decay to Q 10f Q 5f Q 10GUT 1 and Q S 4. MSSM particles, if S has a primordial abundance. A pri- These symmetries and R parity forbid all dangerous op- mordial abundance of S could be generated, for example, erators of dimension lower than 6 that would cause a faster by decays at around 1000 s by dimension 5 operators, as decay, except for SHuHd which is a superpotential term happens in the model in Sec. VB. The second and third and so will not be generated if it does not exist at tree level. operators in Eq. (32) will always produce hadrons in the Similar box diagram ways exist to generate the other decay of S, but the first operator could produce mostly S-number violating operators. A combination of PQ sym- leptons if, for example, the lepton component dominates metry and R parity forbids dangerous operators of dimen- due to SU(5) breaking effects as described above. In a sion 5 or lower for the three operators in Eq. (32) except for y y SH H in the case of the first two operators and S5 H for theory with this operator S 10fHu 5f, if the LSP of the u d f u MSSM has a large Higgsino component, then the decay of the third operator. These are in the superpotential and so the fermion S will be three-body to a Higgsino and two will not be generated if not there at tree level. leptons. In such a scenario, the scalar s~ could have two- Another possible UV model to generate these operators body decays to lepton or slepton pairs. Also possible are is to expand the GUT gauge group beyond SU(5) and three-body decays to a Higgs and two leptons or to a integrate out the heavy (GUT scale) gauge bosons. For y y Higgsino, a slepton, and a lepton with the slepton then example, the operator S 10f5f 10f may be generated by decaying to the LSP and a lepton. Even if the s~ is lighter integrating out an SO(10) gauge boson at the GUT scale. If

105022-12 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) this is the case, the field S is a right-handed neutrino and some model building would be required to assure the decay of the neutralino does not happen by dimension 5 operators mediated by Yukawa couplings. This may happen if the lightest right-handed sneutrino has no Yukawa coupling, suggesting one of the neutrinos would be completely mass- less. Generating one of the other operators involving a Higgs would require an even larger group than SO(10). We do not consider such models further. 1 FIG. 6. Gaugino loop generating LHu from 2 HuLWW MGUT B. R-parity breaking operators after SUSY breaking. The minimal extension of the SSM allowing the dark matter to decay without introducing any new light particles operators, the low-energy loops will never generate dimen- arises if R parity is broken. R parity is a symmetry imposed sion 5 terms because Lorentz symmetry leads to cancella- to forbid renormalizable superpotential operators tion of the linear divergencies. So the diagram in Fig. 5 by itself gives rise only to dimension 6 operators like D2 HyH UDD; QDL; LLE; and H L; (35) 10f u d, but not to dimension 5 terms. Still the ex- u istence of such a diagram is a signal that it will be chal- lenging to UV complete such a theory without generating that would otherwise cause very rapid proton decay. As a y the 10 H H term as well. by-product, it stabilizes the LSP which, if neutral, makes f u d an excellent dark matter candidate. Consequently, dark In fact, there are also examples of operators for which matter decay may indicate that R parity is broken. the problem arises directly at the effective field theory level. For example, consider the superpotential dimension 6 In this section, we will connect the smallness of R 1 operator 2 HuLWW . By closing the gaugino legs (see breaking to the hierarchy between the weak and the GUT MGUT scales. If R-parity violating effects are mediated through Fig. 6) it gives rise to the R-parity breaking HuL term. This GUT scale particles, their effects can be suppressed by the is a superpotential term, so one may think it is not gen- GUT scale. But the SUSY nonrenormalization theorem is erated. Indeed, this loop is zero in the SUSY limit. not enough to protect the theory from dimension 4 or However, in the presence of a SUSY breaking gaugino dimension 5 R-breaking operators, which would lead to mass m1=2 the loop is nonzero and quadratically divergent, too rapid LSP decay; for example, if R parity is broken and so it gives rise to the term m1=2HuL. The presence of such a there is no additional symmetry replacing it, kinetic mix- quadratic divergence does not contradict the lore that the y ings, such as Hd L, are allowed and are not suppressed by quadratic divergencies are cancelled in softly broken the high scale. SUSY, because at the end of the day we obtained a mass To illustrate this point consider a dimension 6 operator term of order the SUSY breaking scale m1=2. HuHd5f5f10f. In the presence of the MSSM Yukawa These problems lead us to two possible ways of consis- interactions, there is no symmetry that forbids the dimen- tently implementing R-parity breaking implying dimen- y sion 5 operator 10fHu Hd, and prevents it from being sion 6 dark matter decays. The first possibility is to generated in a UV completed theory, as can be seen from replace R parity by another discrete symmetry that forbids the existence of diagram 5. Note that in this example there the dimension 4 terms in (35) and also dimension 5 opera- is no problem at the effective field theory level because the tors that give rise to the dark matter decays, but allows y diagram in Fig. 5 cannot generate 10fHu Hd. If one starts dimension 6 decays. An alternative proposal is that the R with an effective field theory involving only dimension 6 parity is violated by a tiny amount, that is not put in by hand but related to the SUSY breaking scale. Let us illustrate each of these options in more detail.

1. Hard R-parity breaking R parity is not the only discrete symmetry that forbids the dangerous lepton and baryon-number violating opera- tors (35). Alternative discrete symmetries may arise from broken gauge symmetries and ensure the longevity of the proton. Heavy fields may have couplings that preserve these symmetries but not R parity [42,43]. As a result, 2 y FIG. 5. D10fHu Hd generated by HuHd5f5f10f and the these symmetries allow for the LSP to decay at the non- MSSM Yukawas. renormalizable level. One such operator,

105022-13 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) TABLE IV. The charges of the SM fields and the GUT scale where we took into account the five-body phase space and fields under a Z3 discrete that substitutes R parity. loop suppression. This example illustrates two generic features of LSP Particle Z3 charge decays in the presence of Z symmetries replacing R ið4=3Þ N 10f e parity. Typically the allowed operators have a large number 5f 1 ið4=3Þ of legs, such that the decay rates are significantly sup- Hu e pressed by final state phase space. Such operators also H eið2=3Þ d tend to involve quarks, resulting in order one hadronic 10 1 GUT branching fractions.

DDDLL 2. Soft R-parity breaking 2 ; (36) Even if R parity is violated only through GUT fields, in MGUT the absence of a symmetry, kinetic mixings can still gen- arises when there is GUT scale antisymmetric representa- erate order one R-parity violating effects. This problem tion of SU(5), while the fundamental theory obeys a Z3 could be avoided if R parity is broken only through SUSY symmetry (see Table IV). This operator is generated by the breaking effects involving GUT fields. These effects will combination of the couplings be communicated to the MSSM through the GUT fields mSUSY 2 þ þ resulting in suppressions ð Þ . Take, for example, two W 10GUT5f5f 10GUT10GUT5f 10GUT10GUT; MGUT pairs of heavy 5 5 and two heavy singlets S and S . The (37) 1 2 interactions between the GUT and MSSM fields are that violates R parity. is the adjoint that breaks SU(5) W S 5 H þ S 5 5 þ M S2 þ M S2 down to the SM gauge group. It is essential that it splits the 1 GUT1 u 2 GUT2 f GUT 1 GUT 2 þ þ colored and the electroweak parts of 10GUT; otherwise, MGUT5GUT 5GUT MGUT5GUT 5GUT : (40) 5 1 1 2 2 R-parity violation would come through ð5fÞ which is zero. The Z3 symmetry also ensures that there are no kinetic The important point is that the R parities of these heavy mixings between light and heavy fields that introduce rapid fields are not fully defined with this superpotential—S1, dark matter (DM) decay. The LSP decays to 5 SM fermions 5GUT1 have equal R parity and S2, 5GUT2 have opposite R through a sparticle loop (see Fig. 7) parity. To break R parity one needs two soft terms for heavy fields, for instance, ! 3 jets þ 2‘: (38) m2 S~ S~ and m2 5~ 5~ : (41) The rate of decay is of order SUSY 1 2 SUSY GUT1 GUT2 5 mc mc 5 m 4 Consequently, the R-parity breaking coefficients in the 14 ð 26 Þ1 GUT c 10 4 3 10 s 13 ; MSSM sector are proportional to the product of the two MGUT 1 TeV 10 GeV 2 soft masses and are always suppressed by at least MGUT . (39) Indeed, the loop of heavy fields generates the R-breaking B term

4 mSUSY ~ 2 hu5f; MGUT which is effectively dimension 6. Even though this scenario works at the spurion level, it is hard to implement in a full theory of SUSY breaking. First, we need to sequester the source of R-parity violation from the MSSM fields but not from the GUT fields. In a toy model with one extra dimension, the MSSM and R-breaking fields are located on different branes, while the GUT fields are free to propagate in the bulk. Then R-parity breaking is communicated to the MSSM fields only through loops of GUT particles. Care has to be taken in order to suppress the effects of gravity that propagates everywhere and may communicate unsuppressed R viola- tion to the MSSM. This is ensured if the soft terms for the

FIG. 7. LSP decay in a theory with a Z3 symmetry substituting heavy fields are generated by a gauge mediation mecha- R parity. nism. However, as discussed in Sec. III A 1, the MSSM

105022-14 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) LSP can decay through these dimension 6 GUT suppressed can solve the primordial lithium abundance problem. For operators only if the LSP is not the gravitino. This require- concreteness, we consider SU(5) grand unification. A so- ment forces the F term responsible for the MSSM soft lution to the primordial lithium problem involving dimen- masses to be much larger than the one responsible for R sion 5 GUT suppressed operators requires the introduction breaking. Consequently, we need two very different scales of a new TeV scale particle species . We restrict ourselves of SUSY breaking, one for the MSSM sector and another to models that involve the addition of complete, vectorlike for the GUT sector. It is not clear if such a SUSY breaking SU(5) multiplets in order to retain the success of gauge mechanism can be successfully embedded into a UV coupling unification in the MSSM. We will only consider completion. operators that preserve R parity, automatically ensuring the existence of a stable dark matter candidate. The operators IV. THE PRIMORDIAL LITHIUM PROBLEMS AND are classified on the basis of the SU(5) representation of . DIMENSION 5 DECAYS In each case, we discuss the relic abundance and hadronic branching fraction of the decaying species that solves the Recent observations [44,45] of the 7Li=H and 6Li=H primordial lithium problem and the corresponding LHC ratio in metal-poor halo stars suggest a discrepancy be- signatures. tween the standard BBN and observationally inferred pri- mordial light element abundances. As pointed out in [46,47], the decay of a particle with a lifetime A. Operator classification 100–1000 s could explain this anomaly if the energy den- We illustrate the possible dimension 5 GUT suppressed 2 sity h of and the hadronic branching fraction BrðHÞ operators in Table V. The operators are classified on the 2 4 are such that h BrðHÞ10 . The required density of basis of the SU(5) representation of . The R parity of is at the time of its decay is similar to the expected relic indicated by subscripts e (R-even) and o (R-odd) and density of a particle of mass M 100 GeV with electro- chosen to make the operators in Table V R-invariant. We weak interactions. The decay of such a particle can explain restrict ourselves to the cases when is a singlet, a the 7Li and 6Li abundances if its lifetime 100–1000 s. fundamental ð5; 5Þ or an antisymmetric tensor ð10; 10Þ of Previous work [48] has concentrated on obtaining this the SU(5) group. As illustrated in the second and third lifetime within the context of the MSSM through either columns of Table V, it is straightforward to construct a the decays of the gravitino to the LSP or the decays of the number of dimension 5 operators inducing the decay of next to lightest supersymmetric particle (NLSP) to the or LSP decay, depending on which one is lighter, in all gravitino depending upon the low-energy SUSY spectrum. these cases. The hadronic branching fraction for the corre- Because of the small production cross section of the grav- sponding decays is typically quite significant, as the op- itino, the former scenario is difficult to test at collider erators involve either Higgs fields or quarks. experiments and either requires nonthermal mechanisms Note that fundamental or antisymmetric representations or tuning of the reheat temperature of the Universe to of SU(5) are not good dark matter candidates; a stable furnish the relic abundance of the gravitino. The latter fundamental would imply Dirac DM, which is excluded scenario involving the decay of the NLSP to the gravitino by direct detection searches [37,38], while an SU(5) anti- has been discussed extensively in the literature [49]. The symmetric does not have a neutral component. Only when desire to generate a dark matter abundance of gravitinos is a singlet is the LSP phenomenologically allowed to be from the decay of the NLSP while simultaneously allowing heavier than and decay to it. In this case, naturally for the required hadronic branching fraction forces the inherits the LSP thermal relic abundance. If this singlet is NLSP to be the stau with a mass 1:5 TeV in the generic heavier than the LSP, one needs to introduce TeV scale parameter space of the theory. The LHC reach for such interactions that would give a thermal calculable abun- long-lived charged staus is 500 GeV [50] making it dance, or rely on nonthermal production mechanisms such difficult to test this scenario at the LHC. Other previous as tuning of the reheat temperature, in order to yield the work has suggested that late decays can affect nucleosyn- required abundance. Because of this difference between thesis [51,52]. ’s that do and do not carry SM charges, we have only In this paper, we point out that supersymmetric GUT included the quadratic in operator in the of a singlet . theories provide a natural home to another wide class of This operator allows for the LSP decay into ’s, but does models that could explain the lithium anomalies. not make the lightest component of unstable. Dimension 5 operators suppressed by the GUT scale are A small subtlety in all the cases is that we can also a generic feature of supersymmetric GUT theories. If construct relevant and marginal gauge-invariant operators decays through such an operator, then its decay rate involving and the MSSM fields. If present, they would 3 mediate the decay of without GUT scale suppression. ð M Þ ð Þ1 2 is naturally 100 s . MGUT These dangerous operators are collected in the last column In the following, we perform a general operator analysis of Table V. In particular, the kinetic mixing terms such as y of the possible dimension 5 GUT suppressed operators that o 5f (here o is an R-odd antifundamental GUT multiplet;

105022-15 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) TABLE V. The possible dimension 5 GUT suppressed operators classified on the basis of their generation in the superpotential or through soft breaking of PQ symmetry or through kinetic mixing in the Kahler potential. The subscript f denotes standard model families, W are gauge fields and Hu and Hd are the Higgs fields of the MSSM. The R parity of is denoted by its subscripts e and o for even and odd parities, respectively.

SUð5Þ rep. Superpotential terms Kahler terms Soft PQ breaking y y Singlet e10f10fHu, e10f5fHd, e10 10f, eHu Hu, ð ÞeHuHd f y MGUT 2 H H , 10 5 5 , 5 H e;o u d o f f f o f d ð ÞoHu5f MGUT eW W ð Þ y ð Þð y y y Þ 5; 5 eHu5f5f, eHuHuHd, e 10f10f, e Hu; e Hd; o 5f y MGUT o10f10f10f, o5fHuHd o10f Hu ð Þ 5 MGUT o f y y y y ð10; 10Þ 10 10 H , 10 5 H , e 10 5 , e 5 5 ð Þðo 10 ; 5 5 Þ e f f d e f f u f f f f MGUT f e f f y o5f5f5f, e5f5fHd oHu5f ð Þ 10 MGUT o f the effect of this term is equivalent to the mixing between continuous PQ symmetry with the following charge assign- o and 5f in the MSSM Yukawa interactions) are not ments for the MSSM fields: protected by SUSY nonrenormalization theorems and Q ¼ 1;Q¼Q ¼ 2;Q ¼3: will be inevitably generated unless forbidden by some 10f Hd Hu 5f additional symmetries. However, it is relatively straight- forward to impose Peccei-Quinn symmetries that either The charges are chosen in such a way that the MSSM superpotential is invariant. If the charge of is equal to forbid these operators or make them GUT suppressed as Q ¼ 8, the dimension 5 operator H 5 5 is allowed, well. e u f f Let us illustrate how this works in several concrete while all other operators mediating decay are forbidden. examples. If is an R-even singlet, the only dangerous In fact, one can check that this is the only possible charge operator is H H . We can forbid it by imposing a dis- assignment that avoids kinetic mixing and allows to e u d decay without requiring soft breaking of the PQ symmetry. crete Z symmetry !. With this symmetry, the only 2 There are more possibilities if the Higgs charges are not allowed dimension 5 operator is 2H H . As a result, is e u d opposite so that the PQ symmetry is softly broken by the the dark matter, and the lithium problem is solved by the term. Finally, let us use this example to illustrate that there decay of the LSP into pairs of particles. is no problem to go beyond the effective theory analysis Other superpotential dimension 5 terms for an R-even and construct renormalizable models generating the re- singlet are of the form W , where W are Yukawa terms i i quired operators at the GUT scale. Namely, let us consider present in the MSSM Lagrangian. In this case, we need to the following renormalizable superpotential: use a symmetry other than Z2 under which is neutral. The Higgs fields carry charges Q and Q such that Q þ Q ¼ þ þ u d u d W 10GUT5f5f 10GUTHue MGUT10GUT10GUT: 0, and the charges of the MSSM matter fields are deter- ð Þ mined by requiring that the MSSM Yukawa terms do not Here 10GUT; 10GUT is a pair of R-even GUT scale fields ¼ violate the symmetry. Then the MSSM term is forbidden with the PQ charge Q10 6. By integrating out the heavy by this symmetry; however, it can be generated if the fields one obtains the dimension 5 operator eHu5f5f at symmetry is spontaneously broken by the TeV VEV of low energies. the field S with charge ( Qu Qd) coupled to Higgses In addition to decays involving the chiral supermultip- through the term SHuHd. The new massless Goldstone lets of the MSSM, singlet ’s can also have decays involv- boson will not appear if the actual symmetry of the action ing the gauge supermultiplets W through operators of the is just a discrete subgroup of this continuous symmetry, so form WW . These operators can be generated through that one can make all components of S massive. The lowest an axionlike mechanism where is the Goldstone boson of dimension operator involving , S and MSSM Higgses is some global symmetry broken at the GUT scale. SHuHd. When S develops a VEV it gives rise to the marginal operator HuHd mediating decay, whose co- B. Relic abundance efficient is naturally suppressed by the ratio of the soft PQ 2 ð Þ breaking scale to the scale where the dimension 5 op- The energy density h Br H that must be injected into hadrons is plotted against the lifetime of the decay- erator is generated, MGUT. 7 It is straightforward to generalize these arguments to ing particle in Fig. 8. The Li problem can be solved when 0:1 1=3 the lifetime 100 sð 2 Þ . The operators de- other cases as well. For instance, for the fundamental to h BrðHÞ avoid the kinetic mixings with Higgses or matter fields one scribed in Sec. IVA can cause decays between the can impose a discrete symmetry which is a subgroup of the MSSM and the sector with these lifetimes.

105022-16 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) Bailly, Jedamzik, Moultaka 2008 and cannot cause a dimension 5 decay of the electroweak Y >0.258 10-1 p . For example, with a ð10; 10Þ, the only gauge-invariant operator that can be extracted from 5f5fHd in Table V is T T 10-2 EDDHd , where Hd is the color triplet Higgs. This op- erator cannot cause a dimension 5 decay of the E and is h -3 not listed in Table VI. There are also operators in Table V B 10 2 from which standard model operators that belong to more h

X D/H>4x10-5 than one category in Table VI can be extracted. For ex- Ω -4 10 ample, the operator 10f5fHu generates an operator con- taining quarks EQfDfHd and an operator containing -5 10 leptons and Higgses EEfLfHd. We include this operator in both categories in Table VI. A UV completion of this 10-6 operator involves integrating out GUT scale SU(5) multip- 102 103 104 105 lets. Oð1Þ SU(5) breaking effects at the GUT scale (like τ (sec) doublet-triplet splitting) can result in one of the operators (say, EQfDfHd) being suppressed relative to the other FIG. 8 (color online). This figure from [47] plots the energy (EEfLfHd). 2 density that must be injected into hadrons versus the decay The relic energy density h of these electroweak lifetime in order to solve the primordial lithium problems. multiplets is 0:1ð M Þ2. The decays mediated by the 7 TeV Decays in the red region solve the Li problem and decays in operators in Table VI that involve quarks or only contain 6 the green region solve the Li problem. Higgses have Oð1Þ hadronic branching fractions. These operators can solve the 7Li problem if the lifetime is 1. Electroweak relics 100 sðTeVÞ2=3 (Fig. 8). However, these decays cannot M Let us first consider how the lithium problems can be solve the 6Li problem. A solution to the 6Li problem 2 solved by the colorless components of fundamental or requires a hadronic energy density injection h BrðHÞ & antisymmetric representations of SU(5). Standard model 104 around 1000 s. Collider bounds on charged particles gauge interactions generate a thermal abundance of the imply that M > 100 GeV. Consequently, the relic energy 2 3 electroweak multiplets in ð5; 5Þ and ð10; 10Þ. We focus on density h is greater than 10 . Because of the Oð1Þ the standard model operators that are extracted from the hadronic branching fraction, the hadronic energy density SU(5) invariant operators in Table V and contain the elec- injected is also greater than 103. This injection is too large troweak multiplets [the lepton doublet L in ð5; 5Þ and the and overproduces 6Li (Fig. 8). right-handed positron E in ð10; 10Þ] from the . These The MSSM products of the decays mediated by the operators can be classified into three categories: operators purely leptonic operators in Table VI may or may not that involve quarks or only contain Higgses, operators that contain sleptons. For example, in the decay of the fermi- y are purely leptonic and operators that involve leptons and onic component ino of the , the operator 5f5f yields y Higgs doublets. This classification is presented in Table VI. a lepton-slepton pair while the operator 5f does not Operators in Table V that contain Higgs triplets when produce any sleptons. The hadronic branching fraction of the ’s are electroweak multiplets have not been included decays that involve sleptons depends upon the MSSM in Table VI since the Higgs triplets are at the GUT scale spectrum. An Oð1Þ hadronic branching fraction will be

TABLE VI. The classifications of dimension 5 operators based on the standard model operators that can be extracted from them. These operators are generated using the electroweak multiplets in . Operators that require the Higgs triplet fields are ignored. The subscript f denotes standard model families and Hu and Hd are the Higgs fields of the MSSM. The R parity of is chosen in order to make these operators R-invariant.

SUð5Þ rep. Quark and Higgs operators Purely leptonic operators Leptonic operators with Higgs doublets ð¼ Þ ð¼ Þ ð Þ y Singlet 10f5fHd QfDfHd , 10f5fHd EfLfHd , M Hu5f, 5f Hd 2 y GUT 10f10fHu, HuHd, 10f5f5f, 10f5f5f, 10f 10f y y 10f 10f, WW , Hu Hu y y y y ð5; 5Þ 10 10 ð¼ lQ U Þ, H H H , ð Þ 5 , 5 H H , 10 H , f f f f u u d MGUT f f u d f u y y 10f10f10f ð Þ5 ð Þð Hu; HdÞ MGUT f MGUT y ð10; 10Þ 10f5fHuð¼ EQfDfHdÞ, 5f5f, 10f5fHuð¼ EEfLfHdÞ, y y y 10 10 H , 5 5 5 , y10 5 ð Þ10 ð Þð 10 ;5 5 Þ, H 5 f f d f f f f f MGUT f MGUT f f f u f

105022-17 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009)

LSP lepton slepton

slepton lepton

FIG. 9. The decay of a slepton to a lepton and the LSP. Higgs produced from the decay of the sleptons if the SUSY FIG. 11. decay to a slepton, lepton and Higgs. spectrum contains charginos or other neutralinos between the slepton and the LSP. These decays can solve the 7Li through final state radiation of Z and W bosons with a problem but not the 6Li problem. When this is not the case, branching fraction 102 as discussed above. The had- the slepton predominantly decays to its leptonic partner ronic branching fraction of operators with both leptons and and the LSP (Fig. 9). The slepton decay can directly Higgses is the ratio of the decay rate to processes involving produce hadrons through off-shell charginos (Fig. 10). the Higgs and the rate to processes where the Higgs is But these decays are suppressed by phase space factors replaced by hhi. For example, the operator Hu5f5f can and additional gauge couplings. The branching fraction for cause the to decay to a Higgs, slepton and lepton 4 3 these processes is 10 . The leptons produced in these ð M Þ (Fig. 11) with a rate h 1923M2 . When the Higgs is decays could be ’s. However, even though the has an GUT h i Oð1Þ branching fraction into hadrons, the hadrons pro- replaced by h , this operator causes the to decay to a ð hhi2 Þ duced in this process are pions. A solution to the primordial lepton-slepton pair (Fig. 12) with a rate l 2 M. 8MGUT lithium problem requires the injection of neutrons [46,47] The decay to a Higgs directly produces hadrons and the and hadronic energy injected in the form of pions is h 1 branching fraction for this decay mode is ¼ð 2Þ ineffective in achieving this goal. The dominant hadronic l 24 ðMÞ2 2ð M Þ2 branching fraction in these leptonic decays is provided by hhi 10 500 GeV . With M 500 GeV, this had- final state radiation of Z and W bosons off the produced ronic branching fraction is sufficiently small to allow this lepton doublets. These bosons decay to hadrons with an decay to solve both the 7Li and 6Li problems. However, we Oð1Þ branching fraction. Using the branching fraction for cannot replace the Higgs field by hhi in every such operator final state radiation of Z and W bosons from [53], we in Table VI that has leptons and Higgses. After electroweak estimate that the relic abundance and hadronic branching symmetry breaking, the masses of the electrically charged þ 0 ð Þ fraction from the decays of a 600 GeV–1 TeV satisfy the l and neutral l components of the lepton doublet in 5; 5 2 ð Þ 4 fþ constraint h Br H 10 . These decays can solve the are split. The charged fermion l is heavier than the 7Li and 6Li problems if the lifetime 1000 s. f0 neutral fermion l by MZ [54,55] while the masses The hadronic branching fraction of the decays mediated of the corresponding scalar components are additionally by the operators involving both leptons and Higgses in ð Þ 2 split by cos 2 MW [56]. When the fermion components Table VI is model-dependent. Naively, these operators are lighter than the scalars, all the components of l rapidly Oð Þ should have an 1 hadronic branching fraction since f0 the Higgs decays predominantly to b quarks. However, decay to l . In this case, the lithium problems can be f0 the Higgs operators in these fields can be replaced with solved with ð5; 5Þ’s only through the decays of l . the Higgs VEV hhi, resulting in an effective purely leptonic f0 y With l , the operator 10f Hu does not lead to any decay mode. These leptonic decay modes produce hadrons ð Þ ð Þ SU 3 U 1 EM invariant operators when Hu is replaced

lepton LSP

slepton W, Z slepton

lepton h

FIG. 10. The decay of a slepton to a lepton, gauge boson and FIG. 12. decay to a slepton and lepton with a Higgs VEV hhi the LSP through an off-shell chargino. insertion.

105022-18 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009)

f0 by hhi. The only decay mode for the l that is permitted by particles is that we are adding new fields in the complete this operator is a decay to the right-handed positron and a GUT multiplets that contain also colored components. Let charged Higgs, resulting in an Oð1Þ hadronic branching us now discuss their story. fraction. As discussed earlier, the decays mediated by this operator cannot solve the 6Li problem but can address the 2. Colored relics 7 Li problem. For the fundamental we have at least one pair of long- The relic abundance of a singlet is model-dependent. lived quarks d;d, where d has quantum numbers of the A thermal abundance of can be generated if the is right-handed MSSM d quarks (and, as before, if the mass coupled to new, low-energy gauge interactions like a R R ð Þ splitting between -even and -odds quarks is small U 1 BL. It could also be produced through the decays of enough, we have another pair of long-lived colored parti- new TeV scale standard model multiplets or through a cles). For antisymmetric we have long-lived vectorlike tuning of the reheat temperature of the Universe. The quarks with quantum numbers of both the right-handed hadronic branching fraction of the singlet operators in MSSM u-quark and left-handed u and d quarks . Table V is also model-dependent. Operators like u;u Q;Q The evolution history in the early Universe is signifi- 10 10 H have an Oð1Þ hadronic branching fraction f f u cantly more involved for colored particles [57] and the since QfUfHu, the only standard model operator that corresponding relic abundances are borderline to be incal- can be extracted from it, contains quark fields. However, culable. The point is that, in general, heavy long-lived an operator like 10f5fHd yields both QfDfHd and colored particles experience two epochs of annihilation EfLfHd. A UV completion of this operator involves as the Universe expands. First, they suffer from the con- integrating out GUT scale SU(5) multiplets. Oð1Þ SU(5) ventional perturbative annihilations at high temperatures breaking effects at the GUT scale (like doublet-triplet before the QCD phase transition. The resulting relic abun- splitting) can result in the operator QfDfHd being sup- 2 dance of the colored particles is at the level h pressed relative to E L H . Because of these tunable M f f d 103ð Þ2. This is a very interesting number—as follows model dependences, the decays of singlet ’s can solve TeV from Fig. 8, if correct it would imply that a long-lived both 7Li and 6Li problems as long as their relic abundance colored particle with a mass in the sub-TeV range solves h2 * 10 4. both lithium problems. Yet another possibility available in the singlet case is However, colored particles experience a second stage of that the MSSM LSP is heavier than the R-odd component annihilations after the QCD phase transition that can sig- of . Then the LSP will decay to and the abundance nificantly reduce the abundance. Indeed, after the QCD will be close to the dark matter abundance today. In fact, if phase transition they hadronize—get dressed by a soft no other stable particles are added, then itself will be a QCD cloud of the size of order 1 . It is plausible dark matter particle. This scenario shares many similarities QCD with the scenario where the gravitino is the lightest R-odd that when two slowly moving hadrons involving heavy particle, so that the LSP can decay. If there is no additional colored particles collide, a bound state containing two mechanism for generating [such as the coupling to new heavy particles forms with geometric cross section 30 mb. This conclusion is somewhat counterintuitive— low-energy gauge interactions like Uð1ÞBL], the decaying MSSM LSP should have rather high relic abundance naively, one may think that the soft QCD cloud cannot 2 * prevent two heavy particles from simply passing by each LSPh 0:1 depending on the mass ratio between the LSP and . This makes it somewhat challenging to solve other without forming a bound object. The argument, the 6Li problem. This is achievable though if the LSP is a however, is that the reaction goes into the excited level of 1 slepton coupled to the singlet through purely leptonic the two system of the size of order QCD.Atlow operators. enough temperatures the angular momentum of such a It is worth stressing that a generic property of all our state is close to the typical angular momentum of two ð Þ1=2 1 models is the presence of several long-living particles with colliding hadrons Li mT QCD so that one may somewhat different lifetimes and masses. There are two satisfy the angular momentum conservation law by emis- sources for proliferation of different long-living species. sion of a few pions. Assuming that the reaction to such an The first is related to R parity. Indeed, as the parity ! excited level is exothermic the geometrical cross section is broken only by dimension 5 operators, the lightest appears to be a reasonable estimate. After the excited state particle in the multiplet is always long-lived. However, if with two ’s forms it decays to the ground level and ’s SUSY breaking mass splitting between the lightest R-odd annihilate. As a result the relic abundance can be reduced 2 6 and R-even particles is smaller than the mass of the MSSM to the values below h 10 for a TeV mass particles, LSP, both of these particles are metastable and will decay where they do not affect the lithium abundance. only through -parity violating dimension 5 operators. Definitely, many of the details of this story are rather Their presence does not change much in our discussion. uncertain at the quantitative level and this conclusion has Another reason for the existence of several long-lived to be taken with a grain of salt. We discuss some of the

105022-19 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) involved uncertainties in more detail in Sec. IV D. where Ci are model-dependent coefficients of order one. Interestingly, in the models we are discussing here, one These interactions are often generated at the one-loop may avoid going into the detailed discussion of this com- level, for instance, by integrating out vectorlike fields plicated process and be rather confident that the residual acquiring the mass from the VEV of S due to interactions abundance of the colored particles is close to that given by like SQQ (Kim-Shifman-Vainshtein-Zakharov model the perturbative calculation. The reason is that in order for [58,59]). As a result, as compared to the general model- the above mechanism to operate the two particles in the independent analysis above these dimension 5 operators bound state should be able to annihilate with each other. contain extra one-loop suppression factors. Consequently, This is the case for some candidate long-lived colored to be relevant for the lithium problem the high-energy scale particles, such as a gluino in the split SUSY scenario or a fa entering here has to be somewhat lower than the GUT 14 stop NLSP decaying into a gravitino, but not always true. scale fa 10 GeV. Still, this scale is intriguingly close For instance, for antisymmetric annihilation is pos- to the GUT scale. sible in some of the bound states (e.g. uu ) but not in the The relevance of the axino for the lithium problems others (e.g. uQ ). Once formed, these bound states go to crucially depends on its mass. We will focus our attention the Coulombic ground state, which is compact and does on the gravity mediated SUSY breaking, so that there is no not get converted into other mesons any longer. Through light gravitino. Then the saxion receives a mass of the same weak decays such a meson decays to the energetically order as other soft masses, Fsusy=MPl. On the other hand, preferred neutral ground state that survives until individual the mass of the axino is a hard SUSY breaking term and its particles decay. In fact, it is likely that an original value is highly model-dependent. If it is generated at the hadron is a baryon, given that the reaction converting a loop level, it is suppressed by at least one extra loop factor, meson and ordinary proton into a baryon and pion is and varies between GeV down to the keV range. It may exothermic. This does not change the story much; after two also be generated at the tree level after SUSY is broken, if transitions one obtains in this case baryons containing SUSY breaking triggers some singlet fields to develop three ’s, such as uQQ. Again, such a baryon will VEVs giving rise to the axino mass. In this way the axino decay to the stable state and will survive until individual acquires mass of the same order as other soft masses. particles decay. Similarly, for fundamental an order In all other respects, the axino is a particular example of one fraction of them ends up being in the compact baryonic adding an MSSM singlet. If the axino is lighter than the state ddd which is safe with respect to annihilations. LSP, and the MSSM LSP is binolike, it will decay to axino We do not attempt here to analyze the above processes at and photon. The corresponding lifetime is the precision level, but this discussion implies that the resulting abundance of colored ’s while being somewhat f 2 1 TeV 3 reduced from its perturbative value is still high enough to 103 s a ; 1014 GeV m solve 6Li problem, or even both lithium problems. a

C. Supersymmetric axion where ma is the axino-LSP mass difference. The had- We already mentioned dimension 5 decays involving the ronic branching fraction in this case is due to decays with gravitino as one solution of the lithium problems that does virtual photon producing quarks and is at the few percent not involve new particles beyond those present in the level; see Eq. (9). If the resulting axino is the only cold dark 7 MSSM. There is another well-motivated particle in the matter component now these decays may solve the Li 6 MSSM that may have similar effects—the axino (see problem, but not the Li problem. If the dominant compo- [34] for a detailed discussion of axino properties and nent of the cold dark matter is the axion, and the LSP is cosmology). light, so that its thermal abundance is low, the LSP decay to The axion is a well-motivated new pseudoscalar particle. the axino may solve both lithium problems. It solves the strong CP problem and may constitute a fraction, or all, of the dark matter. Axionlike particles are D. Split SUSY also generic in string models. In supersymmetric models, In the split SUSY framework [60], the SUSY breaking the axion is a part of a chiral supermultiplet S, so it comes scale is not the TeV but an intermediate scale up to together with the scalar (saxino) and the fermionic (axino, 1012 GeV. All the scalars are at that scale except one a~) superpartners. Being a (pseudo)Goldstone boson, the Higgs that is tuned to be light. The gauginos and axion supermultiplet couples to the MSSM fields sup- Higgsinos are protected by chiral symmetries and they pressed by the PQ breaking scale fa. The leading inter- are at the TeV scale, giving thermal dark matter and actions are with the gauge fields allowing for the gauge couplings to still unify at the Z S X3 C GUT scale. The gluino of split SUSY can only decay L ¼ d2 i i W2 þ H:c:; (42) through an off-shell squark (see Fig. 13) and its lifetime f 4 ðiÞ a i¼1 is set by the SUSY breaking scale:

105022-20 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) hadrons and there is no significant reduction in the gluino abundance. These uncertainties render the final gluino abundance incalculable. However, the case where there is no second round of annihilations after the QCD phase transition provides an interesting scenario for the LHC. The gluino mass range that gives the measured 7Li abundance is 300–7000 GeV [61]. If the gluino is lighter than 2 TeV, it will be produced at the LHC, stop inside the detector and then decay, allowing its discovery, the measurement of its life- time, and the determination of the SUSY breaking scale [62]. As the gluino is the heaviest of the gauginos, this also suggests that all low scale split particles have a good chance of being discovered at the LHC. For a 300 GeV gluino of a 1000 s lifetime, its decay can solve both the 7Li FIG. 13. Gluino decay through an off-shell squark. and 6Li problems (see Fig. 8) and it will be abundantly produced at the LHC. The potential discovery of a gluino with a lifetime 100–1000 s at the LHC will solidify the 1 m5 m 5 2 109 GeV 4 gluino ð Þ1 gluino primordial origin of the discrepancy between the measured g~ 3 4 100 s : 128 mSUSY 1 TeV mSUSY Li abundances and sBBN. (43)

9 10 V. MODELS FOR LITHIUM AND DECAYING DARK When the SUSY breaking scale is 10 –10 GeV, and the MATTER gluino lifetime is 100–1000 s, it becomes an excellent candidate for solving the lithium problem (see Fig. 8), if The primordial lithium abundance discrepancies and the 2 4 1 its abundance is between g~h 10 –10 . observations of PAMELA/ATIC can be explained by the Even though the gluino lifetime is well determined by decays of a TeV mass particle through dimension 5 and 6 the squark masses, its abundance is difficult to know GUT suppressed decays (see Secs. III and IV). The dimen- because it involves strong dynamics [57,61]. At a tempera- sion 6 operators mgluino ture of 20 the gluino will thermally freeze out. Its cross section is calculable, since QCD is still perturbative at y y y y SmSm10f 10f SmSm5f 5f 2 those times, and its abundance is roughly given by h 2 ; 2 ; MGUT MGUT 3ðmgluino Þ2 10 1 TeV . After the QCD phase transition, the gluino y y (46) 2 W W gets dressed into colored singlet states, R hadrons, which SmSmHuðdÞHuðdÞ Sm ; and 1 2 2 have a radius of QCD. The question is if these extended MGUT MGUT states can bind to form gluinonium states g~ g~ with a geometric cross section 2 30 mb that will lead to a QCD in Sec. III allow decays between a singlet sector Sm and the second round of gluino annihilation and suppress its abun- MSSM with lifetimes long enough to explain the signals of dance by several orders of magnitude. PAMELA/ATIC. A large class of dimension 5 operators Whether this second round of annihilations happens were discussed in Sec. IV. In particular, operators of the depends on the details of R-hadron spectroscopy. form For example, even if the lightest state is an R-, the reaction W W 10mSm5f5f Sm R þ baryon ! R baryon þ (44) and (47) MGUT MGUT may well be exothermic due to the lightness of and, if it has a geometric cross section, most of the gluinos will end allow for the population of the singlet Sm sector through up in R-baryon states. Gluino annihilation now depends on dimension 5 decays from the MSSM or a new TeV scale the reaction: SU(5) vectorlike sector, for example, 10m. In this section, we will show that both of these decays can be naturally R baryon þ R baryon ! g~ g~ þ 2 baryons: (45) embedded into SUSY GUT models. These models can If this reaction is exothermic, it may suppress the gluino naturally solve both the primordial lithium abundance abundance by many orders of magnitude. If this reaction is problem and the observations of PAMELA/ATIC. We endothermic for high angular momentum gluinonium also consider models yielding monoenergetic photons states, it may leave a significant number of gluinos in R that give qualitatively new signals for Fermi.

105022-21 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) 0 A. SO(10) model W ¼ 110mSm10GUT þ 210GUT5f5f In SO(10), the MSSM superpotential is þ þ þ MGUT10GUT10GUT m10m10m msSmSm: ¼ þ WMSSM f16f16f10h 10h10h; (48) (52) where 16 and 10 are family and Higgs multiplets, re- f h The mass terms m and ms are at the TeV scale and MGUT is spectively. We add TeV scale multiplets ð16m; 16mÞ and a at the GUT scale. These interactions allow R-parity assign- þ GUT scale 10GUT along with the following interactions: ments 1 for 10m, Sm and 10GUT. The superpotential also 0 conserves a m parity under which S and ð10 ; 10 Þ have W ¼ 16 16 10 þ m16 16 þ M 10 10 : m m m m f GUT m m GUT GUT GUT parities 1. Soft SUSY breaking will contribute to the (49) scalar masses and lead to mass splittings between the These interaction terms allow for R-parity assignments fermion and scalar components. In particular, the singlet þ f 1 for 10GUT and 1 for 16m and preserve a m parity fermion mass ms will be different from the singlet scalar under which 16m and 10GUT have odd parity. Integrating mass ms~. Integrating out the GUT scale field 10GUT and the ð Þ out the 10GUT field and the SO(10) gauge bosons, we broken U 1 BL gauge sector, we get the dimension 5 and 6 generate the dimension 5 and 6 operators: operators: Z Z 16m16m16f16f 10 S 5 5 d2 ; d2 m m f f ; MGUT M GUT Z y Z y y 1 16m16m10h S S Y Y d4 ; and (50) d4 m m ; and 162 M 2 (53) GUT MBL y y Z Z y y 16m16m16f 16f 1 S S Y Y d4 ; d4 m m : M2 2 2 BL 16 MGUT where MBL is the VEV that breaks the SO(10) Uð1ÞBL Here the Y represents the other chiral multiplets 10m, 10f, gauge symmetry. The R- and m-parity assignments forbid 5 , H and H in the model. The gauge symmetries of the dangerous, lower dimensional Kahler operators like f u d y y standard model, supersymmetry and R and m parities 10GUT10h and 16m16f. The dimension 5 operators in (50) ensure that the operators in (53) are the lowest dimension connect the components of the 16 multiplet that are m operators that connect particles carrying m parity (i.e. Sm charged under the standard model to the singlet component and 10m) and the MSSM. Sm of the 16m and the MSSM. However, the only operator Consider the phenomenology of this theory when the in (50) that allows for two singlet fields Sm to be extracted y y mass m of the 10m particles is greater than the singlet 16 16 16 16 m m f f masses m and m . The 10 are produced with a thermal from 16m is the dimension 6 operator ( 2 ) which s s~ m MBL y y abundance due to standard model gauge interactions. They SmSm16f 16f yields ( 2 ). The phenomenology of this model is will decay to the singlets Sm and the MSSM particles M B L through the dimension 5 operator in (53) with lifetime identical to that of the SUð5ÞUð1ÞBL model discussed ð1 TeVÞ3ð MH Þ2 below. The decays of the standard model multiplets in 16m 1000 s m 1016 GeV , where m is the mass difference to the singlets Sm and the MSSM fields at 1000 s can between the 10m and the singlet (see Fig. 14). Following solve the primordial lithium abundance problems while the the discussion in Sec. IV, the decays of the electroweak and 26 7 decays between the singlets and the MSSM at 10 s can colored multiplets in the 10m can solve the primordial Li 6 reproduce the observations of PAMELA/ATIC. and Li abundance problems. The decays of the 10m gen- erate a relic abundance of the singlets sm and s~m. Since R B. SUð5ÞUð1ÞBL model and m parities are conserved in this model, decays between the singlets and the MSSM have to involve the dimension 6 We consider a SUð5ÞUð1ÞBL model, with Uð1ÞBL broken at the scale MBL near the GUT scale. The MSSM is represented in this model by the superpotential: Sm ¼ u þ d þ WMSSM 10f10fHu 10f5fHd HuHd; (51) 5 f f 10m f u where 10f and 5f are the standard model generations, f d and f are the Yukawa matrices and Hu and Hd are the ð Þ 5 Higgs fields. We add a GUT scale 10GUT; 10GUT ,aTeV f scale ð10m; 10mÞ and a singlet Sm to this theory with the 0 following additional terms W in the superpotential: FIG. 14. 10m decaying to Sm and sleptons.

105022-22 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) operators in (53) when the 10m fields are heavier than the singlets. These operators are identical to the R-parity con- serving operators discussed in Sec. III. Following the dis- cussion in that section, the decays mediated by these operators can explain the observations of PAMELA/ATIC. A decaying particle can explain the observations of ATIC if its mass is 1:2 TeV (see Sec. VI and [10]). We FIG. 15. Axino decay to the lighter axino and two photons. first analyze the case where one component of the singlet has a mass 1:2 TeV and this component decays to its superpartner and the MSSM. Without loss of generality, we sponding to different PQ symmetries, so that they are coupled to MSSM through different combinations of op- assume that the scalar singlet s~m is the decaying particle erators as in (42) (in other words, coefficients C are differ- with mass ms~ 1:2 TeV. The singlet fermion sm with a i ent in the two cases). mass ms and the MSSM LSP with mass MLSP are light. A In this case there are two axinos and after the LSP relic abundance of s~m is generated in the early Universe decays the dark matter will be a mixture of the two. The from the decays of the thermally produced 10m. The relic m 2 heavier of the axinos is unstable, but its decays involve energy density of the 10m is 0:2ð Þ . 10m decays to 1:5 TeV insertion of two dimension 5 operators, so effectively it has both sm and s~m. However, since sm is lighter than s~m, the dimension 6 suppression. Typically, the fastest decay chan- branching fraction for decays to sm is higher due to the nel is a~ ! a~ þ 2 (see Fig. 15), giving larger phase space available for the decay. When ms ms~, 1 2 ð ms~Þ3 the branching fraction for decays to s~m is 1 m . The f 4 m 2 TeV 7 relic energy density h2 of s~ is 0:2ð m Þ2ðms~Þ 33 a ; s~m m 1:5 TeV m 10 s 14 ð ms~Þ3 10 GeV TeV m12 1 m .Form 1:5 TeV and ms~ 1:2 TeV, we get h2 103. The decays of s~ can explain the observa- s~m m where m is the axino mass difference. The decays in- 24 12 tions of PAMELA/ATIC if the lifetime 10 s. This life- volving other gauge bosons are suppressed by the higher time can be obtained from the dimension 6 GUT mass of the intermediate gaugino in the diagram in Fig. 15. ð Þ suppressed operators in (53) if the U 1 BL symmetry is As discussed in Sec. IV C, axino masses are highly model- broken slightly below the GUT scale with a VEV MBL dependent and may be as high as of order m . If that is 15 SUSY 3 10 GeV. the case for one of the axinos, its decays will produce The other possible decay topology is for the MSSM LSP monoenergetic photons potentially observable by Fermi. to decay to the singlets, with the LSP mass MLSP Note that at the one-loop level the two axions (and 1:2 TeV. Stringent limits from dark matter direct detection axinos) are mixed by the gauge loops (see Fig. 16). This experiments [37] and heavy element searches [39] require mixing is generated at the high scale, so there is no reason the thermally generated 10m abundance to decay to the for it to be small. However, this does not change the MSSM and the singlets. The 10m can decay to the MSSM conclusion that the decay of one axino to the other is and the singlets sm through the dimension 5 operator in effectively dimension 6. Indeed, after one diagonalizes (53) if the spectrum permits the decay. Since the 10m has R axino kinetic terms and mass matrices, at the dimension 5 þ parity 1, its fermionic components 10m can decay only if level the resulting eigenstates have only couplings of the their mass is greater than the LSP mass 1:2 TeV. The form (42). An intuitive way to understand this is to note f scalars 10m can decay to the standard model and the that an axion is a (pseudo)Goldstone boson, so each axion 1 singlets as long as the scalars are heavier than the singlets. (and axino) carries a factor of fa with it. Consequently f processes involving two of them have dimension 6 However, if the scalars 10m and the singlets are too light, suppression. the MSSM LSP will decay to 10f and the singlet fermion m In principle, one may generalize this story to the broader through the dimension 5 operator in (53). This decay class of models explaining lithium problems by dimen- occurs with a lifetime 1000 s and will not explain the sion 5 decays. Namely, one may consider two singlet fields PAMELA observations. This decay mode must be shut off in order for the MSSM LSP to decay through the dimen- sion 6 operator in (53). This is achieved if the sum of the f 10m and singlet masses is larger than the LSP mass.

C. Supersymmetric axions The interesting example of the setup that provides both dimension 5 and dimension 6 mediated decays is a mild generalization of the axino model for lithium. Namely, let FIG. 16. Mixing between two axinos induced by the gauge us assume that there are two axionlike particles corre- loop.

105022-23 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) (not necessarily axinos), that do not couple directly to each periments will add new data. The PAMELA experiment is other and decay through the dimension 5 operators listed in expected to release positron data up to 270 GeV as well Table V. However, generically, there is a danger that the as measure the combined electron-positron flux up to dimension 5 operator involving two singlets can be gen- 2 TeV. The Fermi satellite, though optimized for gamma erated and as a result the transition of one singlet to another rays, has a large acceptance and is also capable of measur- will be rapid. One can avoid this problem for some choices ing the combined flux. HESS is also capable of measuring of operators by imposing additional symmetries, and for the combined flux and may be able to add to their already other choices of operators one may check that there are UV published data by measuring the flux at energies down to divergent diagrams already at the level of the effective 200 GeV, checking the ATIC bump. As has been shown theory that makes this proposal invalid. The advantage of for annihilations [65], assuming a new smooth component the axino scenario is that the absence of the dangerous of positrons that would explain the PAMELA rise accom- dimension 5 operators is built in automatically. panied by an equal spectrum of new electrons and extrap- olating to higher energies gives rough qualitative VI. ASTROPHYSICAL SIGNALS agreement with the height and slope of the ATIC feature. Here we would like to stress that analysis of the precise In this section we consider the astrophysical signals of shape of electron-plus-positron flux, particularly as data dark matter decaying through dimension 6 operators at improve, may allow for surprising discoveries. This may current and upcoming experiments including PAMELA, already be demonstrated by examining ATIC data closely ATIC, and Fermi. The main astrophysical signals of long- and considering models that fit its shape. lived particles decaying at around 1000 s from dimension 5 In what follows, we will take the published ATIC data operators are changes to the light element abundances as with only statistical errors as an example, and assume for produced during BBN. As well as solving the lithium now that there are no large systematics. Thus, we will problems, such a decay could make a prediction for the 9 discuss in detail how the spectrum may be fit, including abundance of Be [47]. These decays may also generate a its various features. Such an assumption may well be significant component of the current dark matter abun- wrong. ATIC may have many systematic effects in the dance of the Universe (see Sec. V), resulting in the pro- data, rendering small features meaningless. We will take duction of naturally warm dark matter that may contribute it seriously merely to give an example of all the informa- to observed erasure of small structure [63]. tion that may be extracted from a full spectrum, including small features on top of the overall bump. From this we A. Electrons and positrons and signals of SUSY learn an interesting new qualitative feature, that dark mat- The PAMELA satellite has reported [9] a rise in the ter decays can generically produce several features in the observed positron ratio above the expected background spectrum and not merely a smooth rise and fall around the starting at about 10 GeV and continuing to 100 GeV where dark matter mass. However, we do not believe that the the reported data end. The ATIC balloon [10] experiment ATIC data are conclusive yet. Future data with better has observed an interesting feature in the combined flux of systematics, including from the Fermi satellite, are neces- electrons and positrons which begins to deviate from a sary before we can definitively conclude anything from the simple power law around 100 GeV, peaks at around details of the electron spectrum. 650 GeV, and descends steeply thereafter. The HESS ex- The ATIC spectrum, shown in Fig. 18, may in fact periment [64] has added new data above 700 GeV, clearly contain two features—a soft feature around 100– observing the steep decline of the spectrum. It is attractive 300 GeV and a hard feature at 300–800 GeV. The hard to explain both the PAMELA and the ATIC signals as feature may extend to yet higher energies if HESS data are coming from a new population of electrons and positrons considered. The collaboration itself and the following lit- which are the products of dimension 6 decay of dark matter erature have generally highlighted the hard and more pro- suppressed by the GUT scale. As we have noted in nounced feature; however, it should be noted that the Sec. II D 1, such a GUT suppressed decay agrees with the statistical errors in the 100–300 GeV range are quite small, ATIC and PAMELA rates, both of order 1026 s. In this and when compared with a power law background extrapo- section we will show that the spectral shape observed by lated from low energies, the soft feature may well be more both experiments can be explained as well. We will find significant statistically. The soft feature also has a peculiar that decays of dark matter allow for a much better fit to shape: a sharp rise just below 100 GeV, followed by a ATIC data, as compared with models considered thus far, nearly flat or slightly descending spectrum up to when dark matter is allowed to decay to both standard 300 GeV. The shape of the hard feature is less clear, and model particles and superpartners. may be interpreted as either ending sharply at 800 GeV or Beyond the rough agreement in rates, additional impor- ending more smoothly around 2 TeV if HESS data are tant information may be gained by studying the spectral added. It is tempting to fit the two ATIC features by two shape of the ATIC feature as well as the PAMELA rise. different products of the same decay which would give These shapes will become even clearer as upcoming ex- these shapes.

105022-24 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) If dark matter is a singlet which is heavier than the one for decays. In order to reproduce the ATIC shape, MSSM LSP, the products of its decay may be superpart- including its sharp rises in flux, we used a propagation ners. If this is the case, the decay of dark matter may model with a relatively thin diffusion region, ‘‘model B’’ of potentially allow us to discover supersymmetry and mea- [28](L ¼ 1 kpc), which was found to agree with cosmic sure its spectrum. Consider, for example, the simple di- ray data. In addition to the propagation model, the ATIC mension 6 operator of Eq. (12), which allows the singlet flux depends on the electron background spectrum which is fermion to decay to an electron and a selectron with a still highly uncertain [67] (a slope of 3:15 0:35), lifetime given by because it can only be constrained by the electron data 3 2 4 themselves as well as by photons to some extent [68]. This 26 1 TeV 1 TeV MGUT ! 2 10 s: is in contrast with the positron background which may be s ee~ h i 16 m s~ 10 GeV indirectly linked to spectra of nuclei. In this case we have (54) taken a background electron flux with a slope of 3:3 at This is a two-body decay and both particles are monoen- 20 GeV. ergetic. In particular, the electron (or positron) energy will Considering ATIC data alone (we will discuss HESS be later), the spectrum that gave a good fit (by eye) was ðEe;E;EþÞ¼ð700; 100; 200Þ GeV which may be in- 2 2 ms me~ verted to produce a heavy spectrum of Ee ¼ : (55) 2ms ms 2800 GeV;me~ 2000 GeV; The selectron, being a scalar, will then decay isotropically (57) m 1800 GeV: in its rest frame. Assuming the decay is directly to an LSP electron and a neutralino LSP the isotropic decay will It is remarkable that such a good fit to both ATIC features give a flat energy distribution in the ‘‘lab’’ frame between may be achieved by assuming the same rate of injection for two edges both the hard electron and the selectron, strengthening the ð 2 2 Þ 2 2 case for them to come from the same decay. Assuming the ms me~ mLSP me~ mLSP Eþ ¼ ;E ¼ : (56) singlet s makes up all of dark matter we can deduce its 2m2 2m e~ s lifetime from the rate that fits the ATIC spectrum to be The combined spectrum of the electron-positron pair emit- 1:5 1026 s. Using Eq. (54), this decay is probing a scale ted in the decay is shown schematically in Fig. 17. Note of 0:8 1016, remarkably close to the GUT scale. that if one were to measure the three energies Ee, E and The heavy selectron is required so that the selectron will Eþ, the mass of the dark matter, the selectron and the LSP be mildly boosted producing the feature at relatively low may be solved for without ambiguity. We further notice energies. The superpartner spectrum is quite sensitive to that the flat spectrum that the selectron produces is remi- the values of ðEe;E;EþÞ and thus to the shape of the niscent of the plateau above 100 GeV in the ATIC flux. The combined electron-positron flux. The uncertainties on hard monochromatic electron may produce the hard ATIC these masses are thus large, being affected by propagation feature. uncertainties as well as the statistical and systematic errors In the top left panel of Fig. 18 we show that such a decay of ATIC, HESS and future data. It will be interesting to can indeed fit the ATIC data remarkably well. We have perform a more systematic analysis as data improve. used GALPROP (v5.01) [66] to generate electron and posi- It is also interesting to consider other ways to get a tron background and also to inject and propagate the similar spectrum. For example, if dark matter is a scalar þ signal, modifying the dark matter annihilation package to singlet, it may be decaying both to an e e pair and to a e~þe~ pair. This would be given, for example, by the y y electron operator S 10fHu 5f from Sec. III A 2 where the Higgs gets a VEV. This operator does not have a helicity sup- dN pression because the scalar s~ decays to two left-handed spinors. In order to reproduce the hard ATIC feature at 700 GeVand the soft feature between 100 and 200 GeV, the selectron spectrum is lighter:

ms~ 1400 GeV;me~ 660 GeV; (58) E − E + Ee Energy mLSP 500 GeV:

FIG. 17 (color online). A schematic plot of a spectrum of the However, if the operators that lead to decays to electrons electron-positron pair emitted when a singlet dark matter particle and to selectrons are suppressed by the same high scale, as decays to an electron and a selectron. Such a spectrum provides would be expected in a supersymmetric theory, one would an explanation of the two features in the ATIC flux. expect that the decay to electrons would be more rapid due

105022-25 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) 500 s ee s ee ATIC 08 PAMELA 08 HESS 08 0.200 200 0.150 1 sr 1 s

2 100 m

2 0.100 GeV 50 Positron Fraction 0.070 dN dE 3 E

0.050 20

10 0.030 50 100 500 1000 5000 10 20 50 100 200 Energy GeV Energy GeV

FIG. 18 (color online). Left: The combined electron-positron flux for a heavy dark matter candidate decaying to an electron and a selectron. The selectron subsequently decays to a neutralino and a positron giving two features in the observed flux. The dotted curves are the various components of the flux—electron, selectron and background. ATIC (red circles) and HESS (blue squares) data are shown. The darker gray band is the HESS systematic error and the lighter gray is the area covered by this error after including the uncertainty in the energy scale shift in both directions. Right: The positron fraction for the same decay and PAMELA data. The dotted line is the expected background. to phase space. The ATIC spectrum, on the other hand, between the two data sets, regardless of whether the signal requires the two rates to be equal, which would imply the originates from annihilation or decays. two rates must be tuned independently somehow. An alternative approach is to begin with a smoother In the top right panel of Fig. 18 we show the positron signal that reproduces the PAMELA shape very well, but fraction this decay, s ! e~e, produces. Qualitatively the to give up on the various ATIC features and treat ATIC as a positron fraction agrees with that seen by PAMELA, a single smoother bump. This is shown in Fig. 19 in which monotonic rise. However, the positron fraction in this both the combined flux and the positron fraction are shown case stays flat until roughly 40 GeV before climbing rather for dark matter with a mass of 1.4 TeV that is decaying to abruptly whereas the PAMELA data go up more smoothly. an electron-positron pair. The lifetime of dark matter in this Though the fit is not perfect, the quantitative disagreement case is 3 1026 s which may result in a dimension 6 is not very significant. At yet higher energies, beyond the operator suppressed by a scale of 1:5 1016 GeV. This range of current data, the positron fraction undergoes a spectrum does not require sharp features and a more stan- wiggle, transitioning from the soft to the hard components dard propagation model was used (the diffusive convective of the spectrum. This feature is an interesting prediction for model of [69]). future PAMELA data or other experiments such as AMS2. Though the hard ATIC peak by itself fits a sharp The mild disagreement between the PAMELA data and electron-positron peak at around 700 GeV, when combined the spectrum that fits ATIC exemplifies that there is a mild with recent HESS data the hard feature may be interpreted tension between the detailed shape of the spectra observed as a broader bump, extending to a couple of TeV. The by the two experiments. This tension may be phrased ambiguity in interpretation arises from the uncertainty of model independently by noticing that given a smooth whether HESS is seeing the background beyond the ATIC power law for the electron background, say, the dotted bump, or the decline of the bump itself to a lower and background line in the right panel of Fig. 18, the difference steeper background. Though the HESS statistical errors are between it and the ATIC spectrum may be interpreted as small, these should be added to a larger systematic error signal, half of which is electrons and half of which is (shown as a gray band in the figures), and to an overall positrons. This new component of positrons can be com- energy scale uncertainty (whose effect is roughly shown in bined with the positron background and the total flux to the figure as a wider and lighter gray band). Nonetheless, give a positron fraction which has the peculiar shape seen the HESS decline motivates fitting the harder ATIC feature in the right panel of Fig. 18. The mild tension is thus with a smoother spectrum. This may be done without

105022-26 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) 500 s ee s ee ATIC 08 PAMELA 08 HESS 08 0.200 200 0.150 1 sr 1 s

2 100 m

2 0.100 GeV 50 Positron Fraction 0.070 dN dE 3 E

0.050 20

10 0.030 50 100 500 1000 5000 10 20 50 100 200 Energy GeV Energy GeV

FIG. 19 (color online). Left: The combined electron-positron flux for a heavy dark matter candidate decaying to an electron-positron pair. The dotted curves are the various components of the flux—signal and background. ATIC (red circles) and HESS (blue squares) data are shown. The darker gray band is the HESS systematic error and the lighter gray is the area covered by this error after including the uncertainty in the energy scale shift in both directions. Right: The positron fraction for the same decay and PAMELA data. The dotted line is the expected background. In this decay channel the fit to ATIC data is inferior to that in the previous case, but the fit to PAMELA data is slightly improved.

500 s e se ATIC 08 PAMELA 08 HESS 08 0.200 200 0.150 1 sr 1 s

2 100 m

2 0.100 GeV 50 Positron Fraction 0.070 dN dE 3 E

0.050 20

10 0.030 50 100 500 1000 5000 10 20 50 100 200 Energy GeV Energy GeV

FIG. 20 (color online). Left: The combined electron-positron flux for a heavy dark matter candidate decaying to a hard muon (2 TeV) and a selectron. The selectron subsequently decays to a neutralino and a positron giving two features in the observed flux. The dotted curves are the various components of the flux—muon, selectron and background. The more rounded spectrum of the hard muon is in qualitative agreement with HESS data. ATIC (red circles) and HESS (blue squares) data are shown. The darker gray band is the HESS systematic error and the lighter gray is the area covered by this error after including the uncertainty in the energy scale shift in both directions. Right: The positron fraction for the same decay and PAMELA data. The dotted line is the expected background.

105022-27 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) losing the good fit to the soft feature given by a monoen- 10 10 ergetic selectron. In Fig. 20 we show the combined flux and positron fraction from a heavy dark matter singlet decaying to a monoenergetic muon, with an energy of 2 TeV, and a 1 slow slepton, that produces a boxlike spectrum as in GeV 1 1 Fig. 17. The shape of the hard ATIC peak including the

HESS decline is qualitatively reproduced, within the dN dE propagation uncertainties. This particular spectrum may be achieved if a very heavy dark matter candidate (of order 8 TeV) is decaying to a heavy slepton (at 5.6 TeV) which 10 1 10 1 decays to a slightly lighter neutralino (5.5 TeV). Though 300 400 500 600 700 800 900 1000 this spectrum is very heavy, it is remarkable that a good fit E GeV to both features may be gotten from a single decay. FIG. 21. The spectrum of final state radiation from a mc ¼ 1600 GeV dark matter particle decaying in the Galaxy with B. Gamma rays lifetime ¼ 1026 s as would be seen at Fermi with a field of view ¼ 1srnear the Galactic center. The black curve is for the Gamma rays can provide the best evidence that dark c ! þ matter is the explanation for the observed electron/positron decay channel e e , and the dashed curve is for decays to þ. Gray is the expected background. excesses. Gamma rays produced in our Galaxy at energies of hundreds of GeVare not bent or scattered and so provide clean directional and spectral information. Such high- rays through FSR with a spectrum given in Eq. (7). Such energy gamma rays have been searched for with atmos- decays could come, for example, from the operators from pheric Cherenkov telescopes (ACTs) such as HESS and Sec. III. Figure 21 shows the spectrum of final state radia- will be searched for in the upcoming Fermi telescope tion expected from decays of dark matter in the Galaxy to (GLAST). Gamma rays from dark matter decays or anni- eþe and þ as would be seen by Fermi. We take the hilations will appear as a diffuse background with greater effective area ¼ 8000 cm2, the field of view ¼ 1srannu- intensity in directions closer to the Galactic center. There is lus around the Galactic center but at least than 10 away also an expected astrophysical diffuse background and so from it, and the observing time ¼ 3yr. This spectrum to distinguish the dark matter signal may require spectral exhibits an ‘‘edge’’ at half the dark matter mass which information as well. The classic signals of dark matter are could allow these gamma rays to be distinguished spectro- lines, edges, or bumps in the gamma-ray spectrum. scopically from the diffuse astrophysical background. Dark matter annihilations do not generically produce The third general mechanism which produces photons gamma rays as a primary annihilation mode. By contrast, from dark matter decays (or annihilations) is hadronic dark matter decays may directly produce photons as a decay (e.g. to qq) producing 0’s which then decay to primary decay mode, as discussed in Sec. III. Operators photons. These generally yield a soft spectrum, similar to y 2W W mSUSY 6 c ! such as S or 2 HdW@5f cause decays of the expected diffuse astrophysical backgrounds. Thus, we MGUT or c ! which produce monoenergetic photons and will not consider these signals, as a definitive detection neutrinos. This will appear as a line in the gamma-ray could be challenging. However, it is worth noting that these spectrum, easily distinguishable from backgrounds if the signals can be quite large because they are not suppressed rate is fast enough. This would also be a line in the diffuse by the factor of 10 2 that suppresses final state radiation. neutrino spectrum, perhaps detectable at upcoming experi- Figure 22 shows an estimate for the sensitivity of the ments such as IceCube, but it would likely be seen first in Fermi telescope to dark matter that decays to either or þ þ gamma rays. The exact reach of upcoming experiments e e . The sensitivity to decays to e e comes observing depends on the energy of the line as well as the halo profile the edge in the gamma-ray spectrum from final state ra- of the dark matter. However, it is clear from the conserva- diation, as in Fig. 21. Note though, the plot shows the reach þ tive limits in Table I that HESS observations are already in of Fermi in the lifetime of the primary decay c ! e e þ the range to detect such decays. Fermi and future ACT and not the FSR decay c ! e e . Roughly we see that þ observations will significantly extend this reach, probing the reach for e e is a factor of 102 worse than for , GUT scale suppressed dimension 6 operators. which is the expected probability to emit final state radia- Even if the primary decay mode does not include pho- tion. The sensitivity to the gamma-ray line signal (c ! tons, they will necessarily be produced by FSR, i.e. internal ) was found by demanding that the signal (which is bremsstrahlung, from charged particles that are directly entirely within one energy bin) be larger than 3 times the produced. In particular, if dark matter decay explains the square root of the expected diffuse astrophysical back- electron/positron excesses, then the decay must produce a ground in that bin. The signals were calculated from large number of high-energy electrons and positrons. Eqs. (3) and (7). The expected background was estimated These decays will then also produce high-energy gamma as [26,70,71]

105022-28 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) 30 30 10 10 sources of gamma rays, further reducing the astrophysical diffuse background. 29 29 10 10 From Fig. 22 we see that the most of the range of lifetimes which could explain the PAMELA and ATIC 10 28 10 28 þ

s excesses as a decay to e e should be observable at

τ 27 27 Fermi from the final state radiation produced. The same 10 e e 10 conclusion would hold for decays to þ. However,

26 26 decays to three-body final states would soften the produced 10 10 electron and positron spectrum, thus softening the spec- 25 trum of FSR gamma rays. This signal could be more 10 25 10 0 500 1000 1500 2000 difficult to observe with Fermi, though the injected elec- m GeV trons and positrons must always be rather high energy in order to explain ATIC so there is a limit to how soft the FIG. 22. A guess for the sensitivity of Fermi. The solid lines gamma-ray spectrum could be for any model which ex- are the expected reach of the Fermi telescope in the lifetime to c ! c ! þ plains ATIC. decay into the modes and e e as a function of It may be possible to distinguish dark matter decays the mass of the decaying dark matter. The signal from the second mode comes from internal bremsstrahlung gamma rays from the from annihilations, so long as the dark matter-produced electrons (but the plotted reach is for the primary decay mode component of the total diffuse gamma-ray background can into just eþe). The sensitivities are conservatively estimated be distinguished from the spectrum. The intensity of dark using the Burkert (isothermal) profile, though the NFW profile matter-produced gamma rays can then be measured as a gives essentially the same result. The gray band is the region of function of the observing angle. Because the decay rate lifetimes to decay to eþe that would explain the PAMELA scales as n while the annihilation rate scales as n2, the positron excess from Eq. (10). The ATIC excess would be dependence of the gamma-ray intensity on the angle from explained in this same band for masses near mc 1500 GeV. the Galactic center is different for decays and annihilations for a given halo profile. Of course, uncertainty in the halo profile could make it difficult to distinguish between the d2 two. In Fig. 23 we have plotted the Galactic gamma-ray ¼ 3:6 dEd flux as a function of the angle from the Galactic center at which observations are made (these halo profiles are 100 GeV 2:7 10 10 cm 2 s 1 sr 1 GeV 1: spherically symmetric around the Galactic center so only E the angle from the center matters). The intensity is shown (59)

10 8 10 8 The energy resolution of Fermi was estimated from [72]as the given function below 300 GeV and 30% between 1 300 GeV and 1 TeV. The sensitivity to the edge feature 9 9

sr 10 10 was estimated (similarly to [26]) by requiring that the 1 s

number of signal photons within 50% of the energy of 2 the edge be larger than 5 times the square root of the 10 10 10 10 number of background photons within that same energy

band. This sensitivity increases as the size of the energy bin Flux cm used is increased and does not depend on the actual energy 10 11 10 11 resolution of the detector (except for the assumption that it 0 πππ 3π is smaller than the energy bin used). This is clearly only a 424 crude approximation of the actual statistical techniques Angle which would be used to search for an edge. We exclude a 10 half-angle cone around the Galactic FIG. 23 (color online). The flux of Galactic gamma rays versus the angle from the Galactic center for dark matter decay to center from our analysis because the diffuse gamma-ray 28 2 photons with mc ¼ 1 TeV and ¼ 4 10 s versus dark background is expected to be much lower off the Galactic matter annihilation to 2 photons with mc ¼ 500 GeV and v ¼ plane. The annulus we consider, though it overlaps the 26 cm3 3 10 s . Note that the spike at 0 angle is cut off by a finite Galactic plane, is a good approximation to the dark matter angular resolution taken to be 3 10 6 sr. Solid lines are the signal from off the Galactic plane. Ignoring the Galactic fluxes from decays, and dashed lines are from annihilations. center reduces the signal. To be conservative we use Listed in order from top to bottom on the left edge of the plot: Eq. (59) for the background everywhere, though it is Moore profile (red curve), NFW profile (blue curve), Kravtsov probably an overestimate for the background off the profile (black curve), and Burkert or isothermal profile (green Galactic plane. Fermi may also be able to resolve point curve).

105022-29 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) for both decays and annihilations to 2 photons from a VII. LHC SIGNALS variety of halo profiles. We have chosen to scale the rates ¼ In this section, we study the LHC signals of the dimen- to the standard annihilation cross section (v sion 5 and 6 GUT suppressed operators considered in this 26 cm3 3 10 s ) and the decay rate that corresponds to paper. The dimension 5 operators lead to particle decays this from Eq. (8)( ¼ 4 1028 s). The shape of these with lifetimes 100–1000 s and these can have striking curves is independent of the overall normalization. The LHC signatures, particularly when the decaying particle is decay curves in Fig. 23 exhibit a universal behavior for colored or has electric charge. The dimension 6 operators * 26 large angles 8 , independent of the halo profile. This lead to particle decays with lifetimes 10 s and these stems from the fact that the integral of n is essentially just decays will not be visible at the LHC. However, the re- the total amount of dark matter and is relatively insensitive quirement that these operators explain the observations of to the distribution. Note that this universal shape of the PAMELA/ATIC leads to constraints on the low-energy decay curve is significantly different from the shape of the SUSY spectrum and these constraints can be probed at annihilation curves. With enough statistics, this difference the LHC. In the following subsections, we analyze the would be readily apparent. The annihilation curve from the signals of these two kinds of operators. Burkert profile is most similar to the decay curve and so would be the most difficult to distinguish. A. Signals of dimension 5 operators A telescope such as Fermi is ideally suited to the task of The dimension 5 operators introduced in Sec. IV medi- measuring the angular distribution of the gamma rays ate decays between the MSSM and a new TeV scale . The because of its large, Oð1srÞ, field of view and coverage is in a vectorlike representation of SU(5). In the follow- of the entire sky. Further, astrophysical backgrounds are ing subsections, we analyze the cases when is a ð10; 10Þ, significantly lessened away from the Galactic ridge, giving a ð5; 5Þ or a singlet of SU(5) and summarize our results in an advantage to Fermi over the existing HESS observations Table VII. which are mostly dominated by backgrounds. Fermi has an acceptance of 3 1011 cm2 ssr. Thus we can see from the scale in Fig. 23 that at least with a relatively strong 1. Decouplet relic decay mode into photons, Fermi could have enough statis- The most striking collider signals arise in the case when tics to differentiate the decay signal from an annihilation is a ð10; 10Þ. In this case, all the particles in the multiplet signal. either are colored or carry electric charge. When these If the WMAP haze is due to dark matter decays produc- particles are produced at a collider, they will leave charged ing electrons and positrons in the Galactic center, it may be tracks as they barrel out of the detector. This signal should possible to detect inverse Compton scattered photons with be easily visible over backgrounds at the LHC [50]. A Fermi. A study has been done for annihilating dark matter significant fraction of these particles will stop in the calo- [73]. It may be interesting to check both the possibility of rimeters and their late time ( 100–1000 s) decays will explaining the original WMAP haze and of observing the lead to energy deposition in the calorimeters with no corresponding inverse Compton gamma rays at Fermi, for activity in either the tracker or the muon chamber further decaying dark matter as well. enhancing the visibility of this signal [62]. The LHC reach

TABLE VII. Prominent signals of the dimension 5 decay operators considered in Sec. IV. The signals are classified on the basis of the SU(5) representation of the new particle and its mass M. When M >MLSP, the primordial lithium problem is solved by the decays of to the MSSM and vice versa when MLSP >M. Bounds on dark matter direct detection [37] force to decay to the MSSM LSP when [e.g. ð5; 5Þ, ð10; 10Þ] has Dirac couplings to the Z.

SUð5Þ rep. Spectrum Prominent signals and features

ð10; 10Þ M >MLSP Charged tracks from colored and electrically charged particles Measurement of mass, lifetime from stopped colored and charged particles Potentially visible displaced vertex from colored doublet decays Infer dimensionality and scale of decay from mass, lifetime measurements ð5; 5Þ M >MLSP Charged tracks from colored particles Measurement of mass, lifetime from stopped colored particles Charged track from scalar lepton doublet Potentially visible displaced vertex from lepton doublet decays Singlet MLSP >M Possibility of charged or colored LSP giving rise to charged tracks Charged LSP detection enables better measurement of SUSY spectrum ð Þ M >MLSP Discover new particles e.g. TeV scale U 1 BL] for thermally produced

105022-30 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) for such colored or electrically charged stable particles was Upon establishing this, a measurement of the scale analyzed in [50] and found to be 1 TeV for a right- mediating the decay can be inferred from the relation handed positron and at least 2 TeV for colored particles. M3 2 . As discussed in Sec. IV B 1, the primordial 6Li problem can be solved through the decays of a electroweak multi- 2. 5-plet relic plet only if its mass M & 1 TeV. In this scenario, the E ð Þ colored multiplets in the could also be light enough to be The colored particles in 5; 5 will give rise to charged produced at the LHC. tracks and late time decays similar to the decays of the ð Þ The production of these colored multiplets allows for colored multiplets in 10; 10 as discussed earlier in more dramatic signatures at the LHC. Let us first consider Sec. VII A 1. Electroweak symmetry breaking causes the case when the fermionic components of the colored mass splittings between the electrically charged compo- þ 0 SU(2) doublets ðU; DÞ in ð10; 10Þ are lighter than the scalar nent l and the neutral l. The collider phenomenology of components, so that the scalar components, if produced, the lepton doublet l depends upon the spectrum of the decay rapidly to the fermionic components. The masses of theory. We first consider the case when the scalar compo- ~ f the components of the colored SU(2) doublet fermions nents l are lighter than their fermionic partners l, so that ð f fÞ ð Þ f ~ U ;D in 10; 10 are split by MZ 350 MeV due the l, if produced, decay rapidly to the l. Upon electro- to electroweak symmetry breaking [54,55]. When the weak symmetry breaking, the masses of the scalar compo- heavier component of the doublet is produced at the ~þ ~0 ð Þ 2 nents l and l are split by cos 2 MW [56]. Depending LHC, it will decay to the lighter one with a lifetime upon the value of cosð2Þ, the l~þ can be lighter than l~0 .In 1 11 ¼ G2 ð350 MeVÞ5 4 10 s 1:2cm, producing a dis- þ F this case, the l~ will produce charged tracks as it traverses placed vertex that releases an energy 350 MeV resulting through the detector. Some of the l~þ’s will stop in the in the production of soft pions, muons and electrons. The l~þ lighter component will barrel through the detector where it detector and result in late time decays. The will rapidly ~0 ~0 ~þ will leave a charged track and may eventually stop and decay to the l when the l is lighter than the l . This decay after 100–1000 s. While it is difficult to trigger on decay produces hard jets and leptons along with missing ~0 the soft particles produced from the displaced vertex energy from the l that leave the detector and decay outside [54,55], the detector will trigger on the charged track it. produced from the decay and this track could potentially We now consider the case when the fermionic compo- f ~ be used to identify the displaced vertex and the soft parti- nents l are lighter than their scalar partners l. In this case, cles produced with it. The observation of the displaced ~ the scalars l, if produced, will rapidly decay to their vertex, while experimentally difficult, will unveil the pres- f fermionic partners l. Electroweak symmetry breaking ence of the SU(2) colored multiplet. fþ It is also possible that the scalar components of the makes the electrically charged fermionic component l f0 colored doublets are lighter than their fermionic partners. heavier than the neutral component l by MZ fþ f0 In this case, the fermionic components will decay rapidly 350 MeV [54,55]. The l decays to the l with a lifetime to the scalar components. The contribution from electro- 1 11 ¼ G2 ð350 MeVÞ5 4 10 s 1:2cm yielding a dis- weak symmetry breaking to the mass splitting between the F placed vertex. This displaced vertex produces soft pions, components of the colored SU(2) scalar doublets is ð Þ 2 muons and electrons with energies 350 MeV. The soft- cos 2 MW [56]. The decays of the heavier scalar com- ponent to the lighter component will be rapid, producing ness of these particles makes it difficult to trigger on them the lighter component and hard jets or leptons. The lighter unless the production of these particles is accompanied by component will again barrel through the detector produc- other hard signals like initial or final state radiation of ing a charged track and a late decay. This will also be a photons [55]. One possible source for this hard signal is ~ ~ striking signal at the LHC. the decay of the scalars l. If the l are produced, they will Since the are always pair produced and decay at rapidly decay to their fermionic counterparts. The LSP will similar times, it may be possible to determine their lifetime also be produced in this process resulting in the activation by correlated measurements of double decay events in the of missing energy triggers. calorimeter [62]. If all the particles in the multiplet are Another possible source for this hard signal is the col- light enough to be produced at the LHC, a measurement of ored particles in the multiplet. In the model discussed in their mass and lifetime will be a direct probe of the GUT Sec. VB, the colored particles in the SO(10) multiplet 16 scale. The decay rate of a particle of mass M through a can decay to the lepton doublets in the multiplet through dimension 5 operator scales as M3. A measurement of dimension 5 operators. In this case, the late time decays of fþ the masses and decay rates of the colored and electrically the colored multiplet can produce l . This decay will be charged multiplets can then be used to determine if and accompanied by a release of hadronic energy at the loca- M scale as expected for a dimension 5 decay operator. tion of the colored particle and a charged track that follows

105022-31 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) fþ the trajectory of the produced l . This track ends in a decay. Similarly, the number of singlet S’s that can be þ displaced vertex when the lf decays to the lf0. The late produced either through a new low-energy gauge symme- ð Þ time decay followed by the charged track can be used to try [e.g. U 1 BL] or through the decays of other particles trigger on this event. The discovery of soft particles at the that carry standard model quantum numbers is also too location of the displaced vertex, while difficult experimen- small to allow for the observation of the decay of the S. tally, will unveil the presence of the lepton doublet. The most promising signatures of these dimension 6 GUT suppressed operators are the astrophysical signatures of their decay. In Sec. III, we show that these dimension 6 3. Singlet relic GUT suppressed decays can explain the observations of The LHC signals for decays involving operators with PAMELA/ATIC. PAMELA has observed an excess in the singlet ’s is dependent on the MSSM spectrum. If the positron channel while it does not see an excess in the MSSM LSP is heavier than , then the MSSM LSP will antiproton channel. The hadronic branching fraction of decay to at 1000 s. Cosmologically, this decay could these decays must be smaller than 10% in order to account solve the lithium abundance problems and give rise to a for the PAMELA signal (see Sec. III). The need to suppress dark matter abundance of . In this scenario, since the the hadronic branching fraction of these decays can be used MSSM LSP is no longer the dark matter, the MSSM LSP to arrive at constraints on the superpartner spectrum. could be charged. The SUSY particles produced at the For concreteness, we consider the model in Sec. III A LHC will rapidly decay to the MSSM LSP and if this where the scalar component s~ of the S gets a TeV scale MSSM LSP is charged or colored, it will give rise to h i hs~isll~ hs~isqq~ VEV s~ . This leads to the operators M2 and M2 , where s charged tracks and late decays in the detector. The signals GUT GUT of SUSY in this scenario are significantly altered since the denotes the fermionic component of S, ðl;~ lÞ represent decays of SUSY particles are no longer associated with slepton and lepton fields and ðq;~ qÞ represent squark and missing energy signals as the charged MSSM LSP can be quark fields. This operator will mediate the decay of s to detected. However, if the MSSM LSP is neutral, it will the MSSM LSP if the mass Ms of s is greater than the LSP decay to the outside the detector and the LHC signals of mass MLSP. The hadronic branching fraction of this decay this scenario will be identical to that of conventional depends upon the mass splittings Msq~ and Msl~ between MSSM models. s and the squarks and sleptons, respectively. The following The cosmological lithium problem could also be solved options emerge: by decays of singlet ’s to the MSSM if the is heavier (i) Ms >Ml~ and Ms >Mq~.—This decay produces on- than the MSSM LSP. In this case, an abundance of must shell sleptons and squarks. The hadronic branching be generated through nonstandard model processes. This ðMsq~Þ3 fraction is M and this fraction is smaller than abundance can be generated thermally through new inter- sl~ 10% if Msq~ < 0:45Msl~. actions like a low-energy Uð1ÞBL or through the decays of heavier, thermally produced standard model multiplets to (ii) Ms Ml~ and Ms W and Z bosons yielding a 2 MSSM when the operators conserve R parity or cause branching fraction 10 for Ms > 1 TeV. The decays of the LSP to the standard model when the opera- hadronic branching fraction produced as a result tors violate R parity (see Sec. III). The decay rate for these of decays through off-shell squarks is smaller than processes is 1027 s1. The largest production chan- 102 since it is suppressed by additional phase nel for these particles at the LHC would be through the space factors and couplings. decays of colored particles. For example, the LSP would be The cases where the slepton is light enough to be pro- produced in the decays of gluinos. The production cross duced on shell (e.g. Ms >Ml~) allow for the possibility of section for a 200 GeV gluino at the LHC is 107 fb [62]. another correlated measurement at the LHC and astrophys- With an integrated luminosity of 100 fb1, the LHC will ical experiments like PAMELA/ATIC. The decay of the s produce 109 LSPs through the decays of the gluino. This to an on-shell lepton and slepton will generate a primary number is far too small to allow for the observation of the source of hot electrons from the leptons produced in this

105022-32 ASTROPHYSICAL PROBES OF UNIFICATION PHYSICAL REVIEW D 79, 105022 (2009) primary decay. These electrons will produce a bump in the This leads to interesting differences between the ex- Ms pected signals from dark matter decays and annihilations spectrum that will be cut off at roughly 2 . The sleptons produced in this process are also unstable and will rapidly [54,74]. Decaying dark matter can directly produce pho- decay to a lepton and the LSP. This process produces a tons with an Oð1Þ branching ratio, as seen in Sec. III. It can secondary lepton production channel that will also lead to a also produce light leptons without helicity or p-wave suppression and give signals in the range necessary to spectral feature cut off at Ml~ MLSP. This astrophysical measurement can be correlated with measurements of this explain the PAMELA/ATIC excess without boost factors mass difference at the LHC and these independent mea- [35,75–78]. Additionally, in our framework the hadronic surements can serve as a cross-check for this scenario. branching fractions can be naturally suppressed since slep- The other possible decay in this model is the decay of the tons tend to be lighter than squarks, perhaps explaining the LSP to the s which will happen if MLSP >Ms. In this case, lack of an antiproton signal at PAMELA. We have also leptons and quarks are produced through off-shell sleptons found that the signals produced by decays may show many and squarks, respectively (see Fig. 2). The hadronic interesting features beyond just a bump in the spectrum of M branching fraction of this decay is given by ð l~Þ4. This electrons and positrons. For example, the spectrum from Mq~ decays may accommodate the secondary feature visible in branching fraction is smaller than 10% if M < 1:8M .We l~ q~ the ATIC data at energies between 100–300 GeV. The note that the model discussed in this section naturally SUSY spectrum can allow for the direct production of a allows for small hadronic branching fractions. The had- slepton-lepton pair from the decaying dark matter. In this ronic branching fraction is determined by slepton and case, the subsequent decay of the slepton provides a sec- squark masses and since squarks are generically expected ondary hot lepton that can give rise to the observed sec- to be heavier than sleptons due to RG running, the hadronic ondary ATIC feature. It is also common in our framework branching fraction of these models is generically small. to have two dark matter particles, scalar and fermion These decays have a hadronic branching fraction that is at superpartners, that both decay at late times producing 2 least 10 for Ms 1 TeV due to final state radiation of interesting features in the observed spectra of electrons Z and W bosons. A measurement of antiprotons at or photons. PAMELA that indicates a hadronic branching fraction Such models will be tested at several upcoming experi- smaller than 102 will rule out this model. A hadronic 2 ments. The spectrum of electrons and positrons will be branching fraction that is larger than 10 will, however, measured to increasing accuracy by Fermi, HESS, and constrain the squark and slepton masses as discussed ear- PAMELA, testing the observed excesses. These measure- lier in this section. ments could potentially reveal not just the nature of dark VIII. CONCLUSIONS matter, but also the mass spectrum of supersymmetry and GUT scale physics. Excitingly, Fermi and ground-based In broad classes of theories, global symmetries that telescopes such as HESS or MAGIC will be providing appear in nature, such as the baryon number, are accidents measurements of the gamma-ray spectrum in the near of the low-energy theory and are violated by GUT scale future. These measurements have the potential to test physics. If the symmetry stabilizing a particle, such as the many of our models and, in particular, may be able to proton, is broken by short-distance physics, then it will observe final state radiation from models that explain the decay with a long lifetime. In a sense, a particle is con- electron/positron excess. Further, they could distinguish tinually probing the physics that allows it to decay. Thus, decaying and annihilating dark matter scenarios by the though the effects of GUT scale physics are suppressed at different angular dependence of the gamma-ray signals. low energies, this suppression is compensated for by the The supersymmetric GUT theories in which the dark long time scales involved. Intriguingly, short-distance matter decays through dimension 6 operators often have physics can be unveiled by experiments sensitive to long TeV mass particles that decay via dimension 5 operators lifetimes. with a lifetime of 1000 s. This results in relic decays Astrophysics and cosmology provide natural probes of during BBN which could explain the observed primordial long lifetimes. The dark matter particle appears stable, but lithium abundances. This TeV mass particle can be pro- dimension 6 GUT suppressed operators can cause it to duced at the LHC and if charged or colored will stop and 26 decay with a long lifetime 10 s. This can lead to decay inside the detector within 1000 s. This will allow observable signals in a variety of current experiments the measurement of its properties and directly make the including PAMELA, ATIC, HESS, and Fermi. Such obser- connection with primordial nucleosynthesis. vations can also probe the TeV scale physics associated with dark matter annihilations. However, annihilations ACKNOWLEDGMENTS cannot proceed through GUT scale particles since such a cross section would be far too small. Thus, the observation We would like to thank Nima Arkani-Hamed, Douglas of annihilations can probe TeV physics but does not probe Finkbeiner, Raphael Flauger, Stefan Funk, Lawrence Hall, GUT physics directly. David Jackson, Karsten Jedamzik, Graham Kribs, John

105022-33 ASIMINA ARVANITAKI et al. PHYSICAL REVIEW D 79, 105022 (2009) March-Russell, Igor Moskalenko, Peter Michelson, valuable discussions. P. W. G. acknowledges the hospitality Hitoshi Murayama, Michele Papucci, Stuart Raby, of the Institute for Advanced Study and was partially Graham Ross, Martin Schmaltz, Philip Schuster, Natalia supported by NSF Grant No. PHY-0503584. Toro, Jay Wacker, Robert Wagoner, and Neal Weiner for

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