A theory of extra radiation in the Universe
aa r X i v : . [ h e p - ph ] N ov KEK-TH-1418IPMU-10-0189
A theory of extra radiation in the Universe
Kazunori Nakayama a , Fuminobu Takahashi b and Tsutomu T. Yanagida b,ca Theory Center, KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan b Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa 277-8568, Japan c Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
Abstract
Recent cosmological observations, such as the measurement of the primordial He abundance, CMB, and large scale structure, give preference to the existence ofextra radiation component, ∆ N ν >
0. The extra radiation may be accounted forby particles which were in thermal equilibrium and decoupled before the big bangnucleosynthesis. Broadly speaking, there are two possibilities: 1) there are about10 particles which have very weak couplings to the standard model particles anddecoupled much before the QCD phase transition; 2) there is one or a few lightparticles with a reasonably strong coupling to the plasma and it decouples after theQCD phase transition. Focusing on the latter case, we find that a light chiral fermionis a suitable candidate, which evades astrophysical constraints. Interestingly, sucha scenario may be confirmed at the LHC. As a concrete example, we show that sucha light fermion naturally appears in the E -inspired GUT. Introduction
One of the most important discoveries in cosmology is that the Universe is expanding.According to general relativity, the expansion rate is determined by the energy containedin the Universe. In fact, measuring the expansion rate has been one of the central issues incosmology, because it provides fundamental cosmic age and distance scales. For instance,a precise measurement of Type Ia supernovae (SNe) revealed that the present Universe isfilled with dark energy, which accelerates the cosmic expansion [1, 2]. It is even possibleto infer the particle content of the Universe in the past, by measuring the primordialabundance of He, the cosmic microwave background (CMB) anisotropies, and large scalestructure (LSS).The primordial abundance of He was the key observational evidence for the big bangtheory. The big bang nucleosynthesis (BBN) calculation agreed reasonably well with theobserved the He mass fraction Y p together with other light element abundances givenin terms of a function of the baryon-to-photon ratio, η . In the post-WMAP era, η wasdetermined to a very high accuracy [3], which allowed the internal consistency check ofthe BBN calculation based on the standard big bang cosmology.It is known that the Y p is sensitive to the expansion rate of the Universe during theBBN epoch , while it is a rather insensitive baryometer. In the post-WMAP era, it turnedout that the helium mass fraction determined by extragalactic HII regions was smallerthan the value of Y p predicted by the BBN calculation using the WMAP determined η . The apparent tension was partly due to the underestimated error associated withthe early determinations of Y p , and it was pointed out that the precise determinationof the helium abundance is limited by systematic uncertainties [10]. Since then, as thephysical processes as well as the associated systematic corrections have been studiedthoroughly, the estimated helium mass fraction has increased substantially. Recently, theauthors of Ref. [11] claimed an excess of Y p at the 2 σ level, Y p = 0 . ± . ± . N eff = 3 . +0 . − . (2 σ ). For comparison, the WMAP value is given by Y p =0 . ± . N eff = 3 . Y p is also sensitive to large lepton asymmetry, especially of the electron type, if any [4, 5, 6, 7, 8, 9]. Y p = 0 . ± . gives N eff = 4 . +0 . − . (68%CL) [3]. By combining the latest result of the AtacamaCosmology Telescope (ACT), the constraint is slightly improved and becomes N eff =4 . ± .
75 (68%CL) [17]. Thus, the CMB and LSS data suggests the presence of extraradiation at the 2 σ level.It is remarkable that, while the helium abundance, the CMB and LSS data are sensitiveto the expansion rate of the Universe at vastly different times, all the data mildly favoradditional relativistic species, ∆ N eff ∼
1. Although it may be still premature to drawa definite conclusion, we assume in the following, that there is indeed extra radiationsuggested by the current observations, and study its implications for particle physics.The extra radiation may be “dark” radiation composed of unknown light and relativis-tic particles, X i , where the subscript i = 1 · · · n labels different species. Among variouspossibilities of production mechanisms, we focus on a scenario that X i were in thermalequilibrium in the early Universe. This is because some amount of fine-tuning is necessaryto account for ∆ N eff ∼ X i is produced non-thermally by the decayof heavy particles [18]. If we assume that X i is in equilibrium, their total abundanceis determined by the number of species n and the decoupling time. In particular, theabundance of X i that has decoupled before the QCD phase transition is diluted by afactor of 5 ∼
10. Therefore, broadly speaking, there are two possibilities: (1) there are5 ∼
10 light particles in equilibrium and decoupled before the QCD phase transition, or(2) there is one or a few light particles in equilibrium which has decoupled after the QCDtransition before the BBN epoch. In the former case, X i has only suppressed couplings If X i has a renormalizable coupling with the SM particles, X i enters thermal equilibrium at a latetime. We will discuss this case in Sec. 2.1.
3o the standard model (SM) sector, and it is in general difficult to study the propertiesof dark radiation by experiments. Also a mild fine-tuning is necessary to account for∆ N eff ∼ We focus on the latter case because it can naturally explains the deviationfrom the standard value, ∆ N eff ∼
1, and because, as we shall see, it leads to interestingimplications for the LHC. For simplicity we assume n = 1 unless otherwise stated.In order to account for the excess ∆ N eff ∼ X must be lighter than 0 . Such a light mass is a puzzle and clearlycalls for some explanation. The light mass could be a result of an underlying symmetrysuch as gauge symmetry, shift symmetry, or chiral symmetry. In the following sectionwe consider each case and discuss possible astrophysical constraints. As we shall see, achiral fermion, coupled to the standard model with interactions suppressed by the TeVscale, is a viable candidate for dark radiation. Interestingly enough, such a scenario maybe within the reach of the LHC.
In this section we discuss various possibilities for generating the extra radiation, ∆ N eff ≃ X . In order for X to be regarded as radiation both at the BBNand CMB epochs, its mass must be smaller than ∼ . We consider the followingthree symmetries: gauge symmetry, shift symmetry, and chiral symmetry. First, a gaugesymmetry forbids a bare mass of the gauge boson. While a scalar mass is not protectedby symmetries in general, there is an important exception, that is, a Nambu-Goldstone For instance, there might be a hidden SU(N) gauge symmetry and a massive matter field in thebifundamental representation of the SU(N) and SM gauge groups. Assuming that the mass is heavierthan the weak scale, the SU(N) gauge bosons can account for ∆ N eff ∼ N = 3 ∼
4. If the mass of the matter happens to be at the weak scale, it may bewithin the reach of the LHC. Note that the temperature of X is in general lower than the CMB photon temperature by at most ∼
4. The bound on the mass is still valid, taking account of this factor. FT thanks J. Redondo forpointing out this issue. We do not consider sterile (right-handed) neutrinos [19] here because there is no symmetry to keeptheir mass light, especially in the context of the seesaw mechanism and the leptogenesis scenario. Supersymmetry (SUSY) helps to obtain a light scalar boson, since it relates a scalar boson to itsfermionic superpartner. However SUSY must be spontaneously broken, and this generically induces ascalar boson mass heavier than 0 . X is related to theeffective number of neutrino species as∆ N eff = ρ X ρ ν = ǫ (cid:18) g ∗ ν g ∗ X (cid:19) / , (1)where ǫ = / / . (2)Here ρ ν ( ρ X ) and g ∗ ν ( g ∗ X ) are the energy density of one neutrino species( X ) and rela-tivistic degrees of freedom g ∗ evaluated at the time of decoupling of neutrinos ( X ) fromthermal plasma. The relativistic degrees of freedom drops sharply from about 50 to 20 at T ∼
200 MeV during the QCD phase transition. In the standard cosmology, the neutrinosdecouple at a temperature about a few MeV, and g ∗ ν is equal to 10 .
75. The helium abun-dance is sensitive the expansion rate at the decoupling of neutrinos. After the neutrinodecoupling, g ∗ becomes 3 .
36 for T ≪ MeV. Thus, if the decoupling temperature of X isbetween a few MeV and 100 MeV, g ∗ X is comparable to g ∗ ν , and one can naturally ex-plain the extra radiation ∆ N eff ∼
1. In the following we focus on this case, since otherwise∆ N eff becomes either smaller or bigger than 1, which would necessitate multiple speciesof X or non-thermal production to achieve ∆ N eff ∼ We consider a U(1) gauge symmetry (see footnote 3 for the case of non-Abelian gaugegroup). The general Lagrangian for a hidden photon γ ′ with a mass of m γ ′ is given by L = − F µν F µν − B µν B µν + χ F µν B µν + 12 m γ ′ B µ B µ , (3)where B µ and B µν denote the hidden photon field and its field strength. The third termrepresents a kinetic mixing between γ and γ ′ , and χ is a numerical coefficient. In this5xample, since the hidden photon has a renormalizable coupling to the usual photon, itenters thermal equilibrium at a late time, which should be contrasted to the other twocases considered in the following, where the abundance of extra radiation is fixed afterthe decoupling.By redefining A µ and B µ as A ′ µ = (1 − χ ) / A µ and B ′ µ = B µ − χA µ , we can remove thekinetic mixing term and obtain canonical kinetic terms. Then, there appears a photon-hidden photon mixing in the mass matrix as M = m γ ′ (cid:18) χ / (1 − χ ) χ/ p − χ χ/ p − χ (cid:19) , (4)where χ satisfies | χ | <
1. Note that det M = 0 and hence there is a massless eigenstate,which can be regarded as a photon. In this setup we can calculate the probability for aphoton to be converted into a hidden photon in thermal plasma. If the effective rate Γ forproducing a hidden photon by the process like γe → γ ′ e exceeds the Hubble parameter H ,hidden photons are considered to be thermalized. Here the rate Γ is estimated as [20, 21],Γ ≃ χ (cid:18) m γ ′ m γ (cid:19) Γ C for m γ ′ ≪ m γ χ Γ C for m γ ′ ≫ m γ , (5)where m γ is the effective photon mass in the medium, and Γ C ∼ α e T is the Comptonscattering rate, and χ ≪ T & m γ ∼ T , while the hidden photon mass must be smaller than ∼ . m γ ′ . . | χ | <
1. Thus, thisscenario cannot explain ∆ N eff ∼ In the situation m γ ′ ∼ m γ , there is a resonant enhancement of the conversion rate, which is analogousto the MSW resonance in neutrino oscillations. It is possible to obtain ∆ N eff ∼ χ ∼ − , using the resonant enhancementof the conversion for a certain choice of m γ ′ ∼ N eff ∼ both at the BBN and CMB epochs. Also, the helium abundance is decreased because of the enhancement of η after the BBN, which will make the agreement with the observation worse. .2 Spin 0 - NG bosons Next, let us consider a NG boson a , which is associated with the spontaneous breakdownof some global symmetry at a scale of f a . We assume that the explicit breaking of thesymmetry is so small that the a remains practically massless. The value of N eff is at most4 / L = α e π af a F µν ˜ F µν . (6)The freeze-out temperature is determined by the balance between the Hubble expansionrate, H ∼ T /M P , and the rate of processes such as γe ↔ ae , where M P ≃ . × GeVis the reduced Planck mass. The latter rate is evaluated asΓ( γe ↔ ae ) ∼ h σv i n e ∼ α e T f a , (7)for T & h σv i is the cross section of the corresponding process and n e denotes the electron number density. We then find that the freeze-out temperature of a is T f ∼ f a / GeV) . Thus we need f a ∼ GeV to account for the extraradiation. However, it is excluded by the constraints from the cooling of stars and whitedwarfs. For example, the constraint from the observation of horizontal branch (HB) starsgives f a & GeV [22].Next let us consider a case that a interacts with hadrons, as in the case of QCD axion[23]. The interaction Lagrangian is given by L = α e C aγγ π af a F µν ˜ F µν + α s π af a F aµν ˜ F µνa + af a im q ¯ qγ q. (8)It is possible that the axion-photon-photon coupling C aγγ is small due to an accidentalcancellation in the hadronic axion model [24, 25]. In this case constraints from HBstars can be avoided, while the freeze-out temperature is comparable to or higher than O (10) MeV due to the axion-hadron coupling for f a . GeV [26, 27]. On the otherhand, the observation of SN1987A constrains f a as 10 GeV . f a . GeV due to theaxion-hadron interaction term [25], which translates into the axion mass of 1 −
10 eV, theso-called “hadronic axion window”. Therefore the axion mass is too heavy for the axion7o be regarded as an extra radiation at the CMB epoch; such axions should be ratherregarded as a hot dark matter component. Including the hot dark matter componentdoes not improve a fit to observational data. In fact, it was recently shown in Ref. [28]that the axion mass is constrained as m a < N eff ∼ Let us consider a chiral fermion ψ , which is assumed to have a non-vanishing charge ofa new U(1) gauge symmetry and hence its mass term is forbidden. It is coupled to thegauge boson A µH , as L int = ig Aψψ A µH ¯ ψγ µ ψ . We also assume that SM fermions, which wecollectively denote by f , have interactions with A µH , as L int = ig Aff A µH ¯ f γ µ f . We assumethat the U(1) gauge symmetry is spontaneously broken and therefore the A H acquiresa heavy mass, m A . Integrating out the heavy gauge boson, we obtain an effective fourfermion interaction as L eff = 1Λ ( ¯ f γ µ f )( ¯ ψγ µ ψ ) , (9)where Λ = m A g − Aψψ g − Aff is the cutoff scale.The freeze-out temperature of ψ is determined again by the balance between theHubble expansion rate, H ∼ T /M P , and the rate of the interaction such as e + e − ↔ ψψ .The latter is evaluated as Γ( e + e − ↔ ψψ ) ∼ h σv i n e ∼ T Λ , (10)for T & h σv i is the cross section of the corresponding process. The freeze-out temperature of ψ is then evaluated roughly as T f ∼ / TeV) / . Thus thelight chiral fermion with a cutoff scale of O (1)TeV is a prime candidate for the extraradiation.Let us discuss astrophysical constraints on such ψ . Clearly, if Λ & ψ with electrons is weaker than the usual weak interactions, and hence the coolingof stars through the emission of ψ is not efficient. The energy loss rate of stars due toemissions of ψ is suppressed by the factor G − F / Λ ∼ .
01 (Λ / TeV) − compared with that Following discussions do not much depend on whether a new gauge boson is associated with anAbelian or non-Abelian gauge group. Here we consider the case of U(1) gauge boson for simplicity.
8y the neutrino emission, where G F is the Fermi constant. Therefore constraints fromstars can be easily evaded. On the other hand, the supernova cooling argument placesa much tighter constraint. This is because the neutrinos are trapped inside a supernovabecause of its extremely high density and temperature, and such ψ may carry a significantamount of energy from the supernova. The constraint on Λ from the supernova coolingargument reads G − F / Λ . × − , namely, Λ & ∼ g ∗ X ≃
20. Thus, in order to explain ∆ N eff ∼
1, a couple of such ψ ’s are needed.We may simply assume the presence of such a new U(1), but it may be a part of alarge gauge group of the grand unified theory (GUT). In the next section we give oneexample inspired by the E GUT, which fulfills the required property. In particular, thereare three light chiral fermions in this model. E -inspired GUT We have seen that a chiral fermion is a suitable candidate for the extra radiation of theUniverse. Now we discuss a possible origin of the new U(1) gauge symmetry and the extrafermion.We need an additional gauge symmetry to forbid a bare mass for a chiral fermion, andthe simplest one is a U(1) gauge symmetry. The U(1) symmetry must be spontaneouslybroken at TeV scale to produce the right abundance of extra radiation. An importantconstraint on such U(1) is that it must be free from the quantum anomaly. One ofthe anomaly-free U(1)s is U(1) B − L , which naturally appears in the SO(10) GUT. Actu-ally, however, the U(1) B − L symmetry should be spontaneously broken at a scale muchhigher than the weak scale, in order to explain tiny neutrino masses through the seesawmechanism [30]. Then, we need to enlarge the gauge group, and in fact, an additionalanomaly-free U(1) often appears in the breaking pattern of a GUT gauge group with ahigher rank.Here we consider a gauge group of two additional anomaly-free U(1)’s, SU (5) × U (1) ψ × U (1) χ , where SU(5) includes the SM gauge groups. This is inspired by the E modelof the GUT [31], since it has a symmetry breaking pattern, E → SO (10) × U (1) ψ O (10) × U (1) ψ SU (5) × U (1) ψ × U (1) χ ψ (SM) (1 , (1) ψ (SM) ¯5 (1 , − ψ (SM) (1 ,
5) = ν R Ψ ( − ψ ( ) ( − , − ψ ( ) ¯5 ( − , (4) ψ (4 , φ ( ) (1 , (1) φ ( ) ¯5 (1 , − φ ( ) (1 , ( − φ ( − , − ⊃ SM Higgs φ ¯5 ( − , ⊃ SM HiggsΦ (4) φ (4 ,
0) = φ X Table 1: Notation and charge assignments on the fields in the model.and SO (10) → SU (5) × U (1) χ . Although our result does not depend on the details ofunderlying higher rank GUT theory, we use the E notation in the following analyses forconcreteness.The E group has a representation, which can be decomposed as = + − + in terms of the SO(10) representation, where the subscript denotes the U(1) ψ charge. Letus take a fermion Ψ in a representation, which contains Ψ , Ψ and Ψ . Then,Ψ contains all the SM fermions in one generation as well as a SM singlet fermion whichis identified with a right-handed neutrino. Note that is decomposed as = + ¯5 + in terms of the SU(5) representation. See Table 1 for notation and charge assignments.We also introduce a scalar Φ in a representation, which contains Φ , Φ and Φ .The Φ is the Higgs field in the H (= H + ¯5 H in terms of SU(5) representation), whichcontains the SM Higgs boson. All the SM Yukawa couplings arise from Φ Ψ Ψ . Forinstance the Yukawa couplings associated with the SM fermions Ψ can be written asΦ Ψ Ψ . On the other hand, the right-handed neutrino, ψ = ν R , which is a SU(5)singlet of Ψ , obtains a mass from an interaction, Φ Ψ Ψ , where Φ is a SO(10) representation Higgs, a part of the representation of E [32]. If the singlet partof Φ develops a large vacuum expectation value (VEV), the right-handed neutrino ac-10uires a Majorana mass of ∼ h Φ i . Note that the VEV leaves 5 U (1) ψ − U (1) χ unbroken,which we call U (1) X in the following.The singlet fermion Ψ = ψ remains massless as long as U (1) X is unbroken. Let usassume that the U (1) X is spontaneously broken only by the non-vanishing VEV of φ X , h φ X i = ξ , where φ X is the SO(10) singlet Higgs scalar. The U(1) X gauge boson thenacquires a mass of the order of ξ . In order to have a cutoff scale Λ of O (1)TeV in the fourfermion interaction (9), hereafter we will set ξ = O (1)TeV. The ψ obtains a mass onlythrough the following higher dimensional operator, L ∼ φ ∗ X φ ∗ X ψ ψ M + h . c ., (11)where the form of the interaction is determined by the U(1) ψ charge conservation. Thus, ψ obtains a mass m ∼ ξ /M ∼ − eV, where we have substituted ξ = 1 TeV and M = M P . If there is such a singlet fermion ψ in each generation, we would have∆ N eff ∼ & ψ in the E -inspired GUT is a suitable candidate for the extra radiation.Let us comment on the fate of Ψ , which acquires a mass m f of order of ξ througha coupling to the singlet Higgs, Φ Ψ Ψ . The Ψ decays into the Higgs and the singletfermion through the interaction Φ Ψ Ψ . Since the SM Higgs has a mass of O (100)GeV,the non-colored part of Ψ decays quickly into the SM Higgs and Ψ . However, thecolored Higgs must have a huge mass of order of the GUT scale in order to suppress theproton decay, and hence the colored part of the Ψ can decay only through the exchangeof virtual colored Higgs boson. The decay rate is suppressed asΓ(Ψ color ) ∼ − m f M ≃ (10 sec) − (cid:16) m f (cid:17) (cid:18) GeV M GUT (cid:19) . (12)Thus its lifetime is much longer than the present age of the Universe, and is regarded as astable particle. The relic abundance of colored particles was estimated in Ref. [33], whereit was pointed out that they annihilate efficiently after the QCD phase transition and theabundance is significantly reduced. However, even such a small amount of stable coloredparticles may have dangerous effects on BBN [34].The cosmological problem of the stable colored particles can be avoided if the re-heating temperature of the Universe after inflation is lower than the mass m f ∼ TeV,11hich however is difficult to reconcile with the leptogenesis scenario. Alternatively, wemay introduce a small mixing between Ψ and the SM fermions. Note that there is aninteraction, L = yφ ( ) ψ (SM) ¯5 ψ ( ) + h . c ., (13)where y is a coupling constant taken to be real, φ ( ) is a part of Φ , ψ (SM) ¯5 and ψ ( ) are a part of Ψ and Ψ , respectively. If φ ( ) develops a tiny VEV of h φ i , the coloredpart of Ψ will be mixed with the SM quarks, and therefore it will decay into the SMparticles via the mixing. The decay rate is estimated to beΓ(Ψ color ) ∼ − θ m f ≃ (10 − sec) − (cid:18) θ − (cid:19) (cid:16) m f (cid:17) , (14)where θ ≃ y h φ i /ξ denotes the effective mixing angle. Note that the VEV of φ ( ) breaks Z B − L ) , and therefore, it cannot be arbitrarily large, since otherwise the baryonasymmetry would be erased before the electroweak phase transition. Requiring that ψ (SM) ¯5 - ψ ( ) conversion process, whose rate is given by Γ ∼ α s θ T , does not reach equilibriumbefore the electroweak transition, we find θ . − [35, 36]. The Ψ color decays much beforethe BBN for such a small value of θ . Interestingly, the decay of Ψ color may be observedinside the detector at the LHC.Another solution is to extend the above framework to a SUSY version. Then Ψ willdecay into a SM fermion and SUSY particles via an exchange of a fermionic superpartnerof Φ . The decay rate of this process is now given byΓ(Ψ color ) ∼ − m f M ≃ (10 sec) − (cid:16) m f (cid:17) (cid:18) GeV M GUT (cid:19) . (15)and hence is much faster than that induced by the dimension six operator, as long as theΨ color is heavier than the SM particles and their superpartners. Thus it can decay beforeBBN begins, and become cosmologically harmless. Although this decay process producesSUSY SM particles, their abundance is negligibly small because the Ψ color annihilatesefficiently during the QCD phase transition, as mentioned above [33].12 Discussion and Conclusions
So far we have focused on a case that a light particle X was in equilibrium and decoupledafter the QCD transition. Let us here briefly mention the other possibility, namely, the X decoupled before the QCD phase transition. In this case, the number of species n mustbe about 5 ∼
10 in order to account for ∆ N eff ∼
1. We need some explanation for alight mass of these particles. As noted in the footnote 3, one possibility is a non-Abeliangauge symmetry. Another one is the supersymmetry. In the SUSY limit, the gravitinobecomes massless, and there might be several gravitinos in a supergravity theory withe.g. N = 8 [38]. If some of the gravitinos are extremely light, they may reach thermalequilibrium and decouples before the QCD phase transition [39, 40] and they may accountfor the extra radiation.In this paper we have investigated various possibilities to account for the extra ra-diation ∆ N eff ∼ N eff fromthe helium abundance determination, the forthcoming Planck result will tell us about∆ N eff with an accuracy of ∼ . X which was once in thermal equilibrium, we have found that a chiral fermion coupled tothe SM fermions through an interaction (9) is a viable candidate. Such a chiral fermionalso satisfies the current experimental and astrophysical constraints.Interestingly, our model of the chiral fermion has implications for the collider experi-ments. Let us comment on possible signatures at the LHC. In the model, there exists anew heavy gauge boson A H of mass of O (1) TeV which couples the light chiral fermionand and the SM fermions. The search strategy for such a gauge boson is same as the Z ′ boson search. The Tevatron experiment put the most stringent constraint on the A H bo-son mass, which depends on the coupling g Aff [41]. According to the ATLAS study [42],the A H boson mass of 3 TeV is within the reach of 5 σ discovery with integrated luminosityof 10 fb − .As a concrete realization of such a chiral fermion model, we have constructed a E -13nspired model. In this model, the above fermion X is identified with a SU(5) singletfermion Ψ in the representation of E and there also exist long-lived colored particlesΨ color with mass of O (1)TeV. The production cross section of such a particle at the LHC isaround 10 fb for the 1 TeV colored particle, and 10 − fb for the 3 TeV colored particle [43].Once produced, it leaves characteristic signatures on detectors depending on whether ahadronized particle has an electric charge or not [44], as well as on whether the particledecays inside the detector or not. Hence such a long-lived colored particle with mass of afew TeV may be within the reach of LHC.Thus, if the existence of the extra radiation is confirmed by the Planck satellite, theLHC may be able to discover signatures of a new gauge boson or a long-lived coloredparticle with mass of a few TeV. Acknowledgment
FT thanks Javier Redondo and Georg Raffelt for pointing out the relevance of the super-nova cooling argument. TTY thanks K. Izawa for a useful discussion on broken higherN SUSY theories. FT thanks Alejandro Ibarra, Mathias Garny and the theory group ofTechnical University Munich for the warm hospitality while the present work was final-ized. This work was supported by the Grant-in-Aid for Scientific Research on InnovativeAreas (No. 21111006) [KN and FT], Scientific Research (A) (No. 22244030 [FT] and22244021 [TTY]), and JSPS Grant-in-Aid for Young Scientists (B) (No. 21740160) [FT].This work was also supported by World Premier International Center Initiative (WPIProgram), MEXT, Japan.
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