X-ray photons from late-decaying majoron dark matter
Federica Bazzocchi, Massimiliano Lattanzi, Signe Riemer-Sorensen, Jose W. F. Valle
aa r X i v : . [ a s t r o - ph ] J u l Submitted to:
JCAP
X-ray photons from late-decaying ma joron darkmatter
Federica Bazzocchi , Massimiliano Lattanzi , SigneRiemer-Sørensen and Jos´e W F Valle AHEP Group, Institut de F´ısica Corpuscular – C.S.I.C./Universitat de Val`enciaEdificio Institutos de Paterna, Apt 22085, E–46071 Valencia, Spain Oxford Astrophysics, Denis Wilkinson Building, Keble Road, OX1 3RH, Oxford,UK and Istituto Nazionale di Fisica Nucleare, Via Enrico Fermi 40, 00044 Frascati(Rome), Italy Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, JulianeMaries Vej 30, DK-2100 Copenhagen, DenmarkE-mail: [email protected]
E-mail: [email protected]
E-mail: [email protected]
E-mail: [email protected]
PACS numbers: 14.60.Pq, 12.60.Jv, 14.80.Cp
Abstract.
An attractive way to generate neutrino masses as required to account for currentneutrino oscillation data involves the spontaneous breaking of lepton number. Theresulting majoron may pick up a mass due to gravity. If its mass lies in the kilovoltscale, the majoron can play the role of late-decaying Dark Matter (LDDM), decayingmainly to neutrinos. In general the majoron has also a sub-dominant decay to twophotons leading to a mono-energetic emission line which can be used as a test of theLDDM scenario. We compare expected photon emission rates with observations inorder to obtain model independent restrictions on the relevant parameters. We alsoillustrate the resulting sensitivities within an explicit seesaw realisation, where themajoron couples to photons due to the presence of a Higgs triplet. -ray photons from late-decaying majoron dark matter
1. Introduction
While solar and atmospheric neutrino experiments [1, 2, 3] are confirmed by recent datafrom reactors [4] and accelerators [5] indicating unambiguously that neutrinos oscillateand have mass [6], current limits on the absolute neutrino mass scale, m ν < ∼ direct role as dark matter.However, the mechanism of neutrino mass generation may provide the clue to theorigin and nature of dark matter. The point is that it is not unlikely that neutrinos gettheir mass through spontaneous breaking of ungauged lepton number [10, 11]. In thiscase one expects that, due to non-perturbative quantum gravity effects that explicitlybreak global symmetries [12], the associated pseudoscalar Nambu-Goldstone boson -the majoron J - will pick up a mass, which we assume to be at the kilovolt scale [13].The gauge singlet majorons resulting from the associated spontaneous L–violation willdecay, with a very small decay rate Γ, mainly to neutrinos. However, the smallness ofneutrino masses (Eq. (1)) implies that its couplings to neutrinos g Jνν are rather tiny andhence its mean life is extremely long, typically longer than the age of the Universe. Asa result such majorons can provide a substantial fraction, possibly all, of the observedcosmological dark matter.Here we show how the late-decaying majoron dark matter (LDDM) scenario, andin particular the majoron couplings g Jνν and g Jγγ to neutrino and photons respectively,can be constrained by cosmological and astrophysical observations.The paper is organized as follows. In Sec. 2 we describe the basic cosmologicalconstraints on the LDDM scenario, in Sec. 3 we describe the “indirect detection” ofthe LDDM scenario and determine the restrictions on the relevant parameters thatfollow from the x-ray background and the emission from dark matter dominated regions.In Sec. 4 we compare the sensitivities of CMB and x-ray observations to the LDDMscenario, stressing the importance of the parameter R = Γ Jγγ / Γ Jνν . Finally in Sec. 5 wediscuss an explicit seesaw model realisation of the LDDM scenario, where the majoroncouples to photons due to the presence of a Higgs triplet.
2. Cosmological constraints
The LDDM hypothesis can be probed through the study of the CMB anisotropyspectrum. In fact, current observations, mainly of the Wilkinson Microwave AnisotropyProbe (WMAP) lead to important restrictions. Indeed, the LDDM scenario has beenexplored in detail within a modified ΛCDM cosmological model; in particular, it hasbeen shown that the CMB anisotropies can be used to constrain the lifetime τ J ≃ Γ − Jνν and the present density Ω J = ρ J /ρ c of the majoron [15]. -ray photons from late-decaying majoron dark matter Jνν < . × − sec − , (2)at 95% CL [15].This result is independent of the exact value of the decaying dark matter particlemass, and is quite general, in the sense that a similar bound applies to all invisibledecays of cold or warm dark matter particles [16, 17, 18].The CMB spectrum can also be used to constrain the majoron energy density. Thiscan be translated to a limit on the majoron mass in a model-dependent way. Given themajoron mass m J and lifetime τ J , the present majoron density parameter Ω J can bewritten as: Ω J h = β m J .
25 keV e − t /τ J , (3)where h is the dimensionless Hubble constant, t is the present age of the Universe, andthe parameter β encodes our ignorance about the number density of majorons. Thenormalization in Eq. 3 is chosen such that β = 1 if (i) the majoron was in thermalequilibrium in the early Universe; and (ii), it decoupled sufficiently early, when all thequantum degrees of freedom in the standard model of fundamental interactions wereexcited.This simple picture can be changed if: (i) The majoron could not thermalize beforeit decoupled from the other species, or (ii) The entropy generated by the annihilationof some particle beyond the standard model diluted the majoron abundance after itsdecoupling.In any case it is reasonable to assume that the majoron decoupled at T &
170 GeVsince its couplings to all the other particles in the standard model (SM) are tiny. Usingthe WMAP third year data, the following constraint on Ω J h can be obtained (95%C.L.) assuming the dark matter to consist only of majorons [15]:0 . ≤ Ω J h ≤ .
13 (4)Since Eq. (2) implies τ J ≫ t , the above constraint together with Eq. (3) gives:0 .
12 keV < βm J < .
17 keV (5)Our ignorance of the details of the majoron production mechanism, namely thevalue of β , can always be used in order to accommodate additional restrictions to themajoron mass m J coming from observations of the large scale structures.The limits quoted above apply to the invisible decay J → νν . There exist alsothe very interesting possibility to use the CMB polarization to directly constrain theradiative decay J → γγ . This is because photons produced by dark matter decaycan inject energy into the baryonic gas and thus affect its ionization history. Thiswill ultimately lead to modifications of the CMB temperature-polarization (TE) cross-correlation and polarization auto-correlation (EE) power spectra. In Ref. [19], WMAP -ray photons from late-decaying majoron dark matter rad of long lived dark matter particles like the majoron: ζ Γ rad < . × − sec − , (6)where ζ is an “efficiency” factor describing the fraction of the decay energy actuallydeposited in the baryon gas. This depends, among other things, on the energy of theemitted photon. As a rule of thumb, consider that for redshifts 10 < z < . ζ ∼
1. On the other hand, the Universe istransparent with respect to the propagation of photons with E ≫ ζ ∼ rad canbe obtained from CMB polarization.
3. X-ray analysis
In a variety of neutrino mass generation models with spontaneous violation of leptonnumber, majorons have an effective interaction term with photons g Jγγ
J ǫ νµρσ F νµ F ρσ . (7)Majorons in the keV range are therefore expected also to decay radiatively into twophotons of energy E γ ≃ m J /
2, since the decay can be considered to a very goodapproximation as happening in the dark matter rest frame. This leads to a mono-energetic emission line as a characteristic signal of our decaying dark matter model.Such an emission line could be possibly be detected both in the diffuse x-raybackground and in the emission from dark matter dominated regions. We now considerthe constraints coming from both kinds of observations.In the following, when necessary, we will consider a LDDM scenario within a ΛCDMcosmology with Ω Λ = 0 .
75, Ω DM h = 0 .
11, Ω b h = 0 . h = 0 .
72, correspondingto the best fit values of the CMB analysis in Ref. [15].
Photons produced in late majoron decays will show up in the diffuse x-ray background,if the Universe is transparent with respect to their propagation. This is indeed thecase after the Universe has been completely reionized ( z . F ( E ) of decay radiation at the present time ( z = 0) is given by [20]: F ( E ) = c π (cid:18) EE γ (cid:19) N γ Γ Jγγ n J ( z ) H ( z ) (cid:12)(cid:12)(cid:12)(cid:12) z = E γ /E (8)where N γ = 2 is the number of photons produced in each decay, n J ( z ) is the numberdensity of majorons at redshift z , H ( z ) is the Hubble parameter, and E γ = m J / -ray photons from late-decaying majoron dark matter E at which we are observing due to the cosmological redshift of photons. In other words,when looking today at an energy E < m J / E γ = m J / E = E γ and a flux given by: F ( E γ ) = c π N γ Γ Jγγ n ,J H , (9)where the subscript 0 denotes quantities evaluated at the present time.This should be compared with the observed diffuse x-ray flux from ASCA [21] andHEAO-1 [22], operating in the 0.4-7 keV and 3-500 keV ranges respectively. The fluxcan be modeled as [23] (units are sec − cm − sr − ): F obs ( E ) = (cid:18) E keV (cid:19) − . , < E <
25 keV , (cid:18) E keV (cid:19) − . ,
25 keV < E <
350 keV , (cid:18) E keV (cid:19) − . ,
350 keV < E <
500 keV , (10)Below 1 keV, the strong galactic emission must be carefully removed in order tofind the extragalactic signal [24], and consequently we do not extrapolate the aboveapproximation to lower energy for the purpose of the present analysis.Then, requiring F ( E γ ) ≤ F obs yields an upper limit for the majoron decay widthto two photons Γ Jγγ . In particular, in the range, 1 keV ≤ E γ ≤
25 keV we have:Γ
Jγγ sec − . . × − (cid:18) h . (cid:19) (cid:18) Ω J h . (cid:19) − (cid:16) m J keV (cid:17) . . (11)This limit, together with the constraints at higher energies, is shown in Fig. 1.This simple analysis, and the resulting constraint, can be improved in two ways.First of all, one can look for small distortions in the smooth diffuse flux produced by aDM emission line that is possibly lying well below the background signal. In addition,one can take into account the contribution to the signal coming from the Milky Way.This was applied to the HEAO-1 data in Refs. [25, 26]; in this way, the above constraintscan be improved by as much as three orders of magnitude (see below). Finally, we notethat bounds in the soft x-ray region can be obtained from the observations of a high-resolution spectrometer [27]. Observations of the x-ray emission from dark matter dominated regions can be used torestrict the decay rate into photons and the mass of any dark matter candidate with -ray photons from late-decaying majoron dark matter γ [keV]10 −34 −32 −30 −28 −26 −24 −22 −20 Γ J γγ [ s − ] Diffuse x−ray
Figure 1.
Upper limit from the diffuse x-ray argument. The filled region is excluded.Data from [21, 22]. a radiative two-body decay. This follows from the consideration that the detected fluxfrom a dark matter dominated object gives a very conservative upper limit on the fluxgenerated by dark matter decays in that object.Since the dark matter in cosmological structures is practically at rest (v/c ≈ − ),the line broadening due to motion of the dark matter is negligible compared to theinstrumental resolution of current day x-ray detectors. Hence, a good instrumentalspectral resolution increases the sensitivity to a mono-energetic emission line.For majorons the 0.1-0.3 keV x-ray interval is very interesting. Unfortunately thisrange is not accessible with any of the standard CCD instruments on board the presentx-ray observatories Chandra and
XMM-Newton . However,
Chandra carries the HighResolution Camera (HRC) which combined with the Low Energy Transmission Grating(LETG) makes it possible to obtain spectra in the 0.07-10.0 keV range. The resolutionof grating spectra is very high ( E F W HM ≈ -ray photons from late-decaying majoron dark matter Chandra
HRC/LETG observation of the Seyfert 1 galaxy NGC3227 (observation id 1591), shown in Fig. 2. NGC3227 has a redshift of z = 0 . . Figure 2.
The observed
Chandra
HRC/LETG spectrum of NGC3227 (folded withthe instrumental response).
In general, the instrumental response cannot be unfolded from the spectrum in amodel independent way. Instead a model is folded with the instrumental response andfitted to the data using χ statistics (here we have used the spectral fitting package Sherpa distributed with CIAO).The model is used to determine an upper limit on the received flux. Since nophysical quantities are derived from the empirical model, it is chosen to fit the data(and as such do not necessarily represent a physical model of the emission). The datawere split into two intervals: 0.072-0.276 keV and 0.276-4.14 keV and fitted separatelyto models composed of a power law and four Gaussians for the lower interval and twopower laws and two Gaussians for the higher interval. In order to ensure that no emissionlines are sticking above the model, the fitted model was re-normalised so there were nobins in the spectrum at more than 2 σ above the model.As mentioned above, any emission line is smeared out because of the instrumentalresolution. Towards lower energies the smearing has the shape of a Gaussian withthe width given by the instrumental resolution. Towards higher energies, where theextension of the source plays a role, the smearing depends on the overall distribution -ray photons from late-decaying majoron dark matter E γ + F W HM instrumental > E > E γ − F W HM smearing instead of the exact shape of the smeared lines (the difference between the two methodsis negligible [29]).The mass of NGC3227 has been taken to be 10 solar masses which is conservativelylow based on the luminosity of the galaxy [34]. The observational field of view is ≈
25 kpcat the distance of NGC3227, reducing the observed mass to about a tenth of the totalmass. This is probably an underestimate of the observed mass, but a larger observedmass will only improve the constraints.Assuming only one kind of dark matter, the observed flux, F obs , at a given photonenergy yields an upper limit on the decay rate from two-body radiatively decaying darkmatter: Γ Jγγ ≤ πF obs D L M fov . (12)The determined flux is dominated by the baryonic emission of the galaxy, which varieswith energy, introducing an apparent energy dependence on the constraint.The resulting constraint on the decay rate is shown in Fig. 3 together with earlierpublished constraints.
4. X-ray versus CMB
In the previous sections we have shown how the CMB can be used to constrain theinvisible decay J → νν , while x-ray observations can constrain the radiative decay J → γγ ‡ . From a theoretical point of view, a very important quantity is the branchingratio of the decay into photons BR ( J → γγ ) that, as long as the decay to neutrinos isby far the dominant channel, is given by the ratio of the decay widths: BR ( J → γγ ) ≃ R = Γ Jγγ Γ Jνν . (13)Note that the decay J → νν arises at the tree-level, while the radiative J → γγ mode proceeds only through a calculable loop diagram. Beyond this, theory can notpredict the expected value of R , which is strongly model-dependent. Here we use R as a ‡ We do not consider the CMB polarization limit in the following because (i) it depends on the efficiencyof the energy transfer to the baryonic gas and (ii) it turns out to be less constraining than x-rays inthe regions of interest. -ray photons from late-decaying majoron dark matter γ [keV]10 -34 -32 -30 -28 -26 -24 -22 -20 Γ J γγ [ s - ] SPI INTEGRAL Milky WayHEAO XRBBullet Cluster and M31XMM Milky WayPrototype cryogenic spectrometerNGC3227 Chandra LETG
Figure 3.
Upper limit on the decay rate from NGC3227 (red), the Milky Way haloobserved with a prototype cryogenic spectrometer (salmon) [27],
XMM observations ofthe Milky Way (sand) [35],
Chandra observations of the Bullet Cluster [30] and M31[36, 37] (orange), HEAO-1 observations of the diffuse x-ray background (aquamarine)[25, 26], INTEGRAL SPI line search in the Milky Way halo (blue) [38, 39]. Filledregions are excluded. phenomenological parameter varying over the wide range 10 − − − (see, for instance,Fig. 6 below). It should be clear that the observations described in Secs. 2 and 3 restrictΓ Jνν and Γ
Jγγ , leaving the branching ratio unconstrained.However, we are also interested in knowing for which models the x-ray observationscan probe the decaying majoron dark matter hypothesis with higher sensitivity than theCMB. In particular, we expect that models with large branching ratios will be betterconstrained by the x-ray observations, since they will predict a larger production ofphotons.The x-ray limits presented in Sec. 3 have a mass dependence, which we need totake into account in our assessment of the relative constraining power of the two typesof observations. We know, however, from the CMB (see Eq. 5) that:0 .
12 keV β ≤ m J ≤ .
17 keV β , (14)at 95% C.L. Fixing the value of β is then equivalent to fixing the majoron mass, apartfrom a small uncertainty (which we take into account, see below). We express our resultin terms of β instead than m J .In order to compare the CMB and the x-ray constraints, we fix the value of β anddetermine the corresponding observational ratio of Γ Jγγ / Γ Jνν . According to the CMB -ray photons from late-decaying majoron dark matter −5 −4 −3 −2 −1 β −14 −12 −10 −8 −6 −4 Γ J γγ / Γ J νν White: CMB constraints strongestHatched: X−ray constraints strongest
Figure 4.
Sensitivity of CMB and x-ray observations to the LDDM majoron scenarioas a function of β and R = Γ Jγγ / Γ Jνν . The black lines are the loci of points where R = R ∗ , i.e., where the CMB and x-ray constraints (from a given object) are equivalent.In the hatched regions above the lines, X-ray constraints are stronger; below, CMBconstraints are stronger. The color codes are the same as in Fig. 3. See Sec. 4 fordiscussion. constraints, we take the mass of the majoron to be equal to m J = 0 .
145 keV /β , with anassociated 1 σ error of σ J = 0 .
01 keV /β . Then, we find the maximum Γ Jγγ allowed bythe x-ray emission for this value of the mass (as explained in Sec. 3.2). The uncertaintyin the exact value of the mass is taken into account by convolving the upper limitsshown in Fig. 3 with a Gaussian of mean m J and variance equal to σ J . Let us call thisvalue Γ max Jγγ .We also denote with Γ max
Jνν = 1 . × − sec − the CMB upper limit on thedecay width to neutrinos. Then for the following value of the branching ratio: R ∗ = Γ max Jγγ Γ max Jνν (15)the two sets of observations yield exactly the same constraining power. In other words,for this particular value of the branching ratio, it would be the same to constrain thedecay rate to photons using the x-rays and then obtain the decay rate to neutrinosusing Γ
Jνν = Γ
Jγγ /R , or to do the contrary, i.e. to use the CMB to constrain theinvisible neutrino decay channel and from that obtain a bound on the photon decay.Larger branching ratios ( R > R ∗ ) will be better constrained by observations of the x-ray emission, while smaller branching ratios ( R < R ∗ ) will be better constrained by theCMB.We repeated above procedure for β ranging from 10 − to 1, comparing the x-rayconstraints of Fig. 3, one at time, with the CMB constraint. We did not include the -ray photons from late-decaying majoron dark matter XMM observations of the Milky Way because they are discontinous and this makesthe mass-averaging procedure problematic. The results are illustrated in Fig. 4. Wecan roughly say that for small majoron masses ( β ∼ R & − , while we should use the CMB for R . − .For large neutrino masses, x-ray observations are better when R & − , while CMB ismore informative for R . − .
5. Particle physics
We now turn to the particle physics of our decaying dark matter scenario. Althoughmany attractive options are open [40] possibly the most popular scheme for generatingneutrino masses is the seesaw. The simplest type I seesaw model has no induced majoronradiative decays. For this reason we consider the full seesaw model, which contains aHiggs boson triplet coupling to the lepton doublets [41].In addition to the SM fields one has three electroweak gauge singlet right-handedneutrinos, ν cL i , a complex SU (2) L scalar triplet ∆, with hypercharge 1 and lepton number − σ , with lepton number 2. We will denote the scalar SU (2)doublet as φ . The Yukawa Lagrangian is given by L Y = Y u Q TL φu cL + Y d Q TL φ ∗ d cL + Y e L TL φ ∗ e cL + Y ν L TL φν cL + Y L L TL ∆ L L + Y R ν cL ν cL σ + H.c. (16)In order to extract the relevant couplings of the majoron that are responsible for thedecays in Eq. (2), we review here the main steps of the procedure developed in [11],using the basic two-component Weyl description of neutrinos as in [41].Using the invariance of the scalar potential under the hypercharge U (1) Y and leptonnumber U (1) L symmetries and assuming that these are broken spontaneously by thevacuum configuration, one finds, from Noether’s theorem, the full structure of the massmatrix of the imaginary neutral component of the scalars given in terms of their vacuumexpectation values (vevs) as [11] M I = C v v − v v v v v − v v v v v − v v v v − v v , (17)with C = ∂ V /∂ σ I and v , v , v are the vevs of the singlet, the doublet, and the triplet,respectively. One sees that M I has a non zero eigenvalue, m A = Tr M I and two nulleigenvalues. These correspond to the Goldstone bosons eaten by the Z gauge bosonand, as expected, to the physical Nambu-Goldstone boson associated with the breakingof U (1) L , the majoron J . The parameters of the scalar potential of the model can bechosen so that the pattern of vevs obtained by minimization respects the so–called (typeII) seesaw form, namely [11] v ≪ v ≪ v -ray photons from late-decaying majoron dark matter J , following from Eq. (17) takes a very simpleform in this seesaw approximation, namely [11] J ≃ − v v v φ I + v v ∆ I + σ I . (18)In the presence of the gravitationally induced terms that give mass to the majoron,the mass matrix of Eq. (17) is slightly modified, but these effects are sub-leading andnegligible.We are now ready to determine the coupling of the majoron with the light neutrinos.From Eq. (16) one obtains the full neutrino Majorana mass matrix as M ν = 12 Y L v Y ν v Y ν v Y R v ! . (19)so that the effective light neutrino Majorana mass matrix is given by [11]: M νLL = 12 (cid:18) Y L v − Y Tν Y − R Y ν v v (cid:19) . (20)The coupling g Jνν of the majoron to the neutrinos can also be obtained using Noether’stheorem according to the procedure described in Ref. [11]. In this way one finds thatthe majoron couples to the mass eigenstate neutrinos proportionally to their masses, g νJrs = − m νr δ rs v . (21)where v describes the scale at which the global lepton number symmetry breaks,typically 10 − GeV (see below).The decay width Γ
Jνν is given byΓ
Jνν = m J π Σ r ( m νr ) v , (22)Let’s now turn to g Jγγ . From the Yukawa Lagrangian of Eq. (16) and from Eq. (18)we have that the majoron interacts with the charged fermions through − v v v Y f ( − T f ) ¯ f γ f J = − v v v m f ( − T f ) ¯ f γ f J , (23)where T f is the weak isospin and we have assumed that the charged fermion massmatrices are diagonal. The interaction term of Eq. (23) gives rise to the interactionterm with photons given in Eq. (7), with an effective coupling given by g Jγγ = α π Σ f N f ( − T f ) Q f m J m f ! v v v . (24)where one notices the cancellation of the “anomalous-like” contribution Σ f N f ( − T f ) Q f .As a result we haveΓ Jγγ = α π m J ˜Λ γ , (25) -ray photons from late-decaying majoron dark matter γ = 1Σ f N f ( − T f ) Q f m J m f v v v , where Q f and N f are the electric charge of f and its colour factor, respectively.Fig. 5 shows how the currently allowed range of neutrino masses selects an allowedstrip in the plane v − m J consistent with neutrino oscillation data [6] and with thecosmological bounds on neutrino mass [42], assuming that the CMB bound (2) on the J → νν decay rate is saturated. J H keV L v H T e V L Β = Β = . Ú m Ν = D m a t m Ú m Ν = D m a t m Ú m Ν = e V Figure 5.
The strip indicates the region in the v − m J plane allowed by currentneutrino oscillation [6] and cosmological data [42], assuming the maximal J → νν decayrate. The vertical lines delimit the mass values required by the CMB observations, fordifferent values of β . The lower lines correspond to the cases of normal and inverse hierarchical neutrinomasses, while the top line holds when the three neutrinos are (quasi)-degenerate. Thevertical bands in the figure indicate the mass region of Eq. 5 singled out by the CMBobservations, for two different values of β .We also note from Eq. (25) that, for a fixed value of the majoron mass and thelepton number symmetry breaking scale v , the two-photon decay rate only depends onthe vev of the triplet and on the sum of the squared masses of the neutrinos, namelyon the two possible scenarios in the neutrino sector, hierarchical or degenerate. For agiven scenario the decay is then fixed only by v , as it can been seen in Fig. 6, wherethe top panel corresponds to the hierarchical case while the bottom one holds for thequasi-degenerate spectrum. The diagonal lines in Fig. 6 give the dependence of Γ Jγγ on m J , for different values of v . As it can also be seen from Eq. (25), the largest valuesof v correspond to the largest radiative decay rates. -ray photons from late-decaying majoron dark matter Β = Β = . v = G e V v = G e V v = . G e V v = . G e V Hier.Exp bound10 - - - - - - - m J H keV L G J ® ΓΓ H s - L Β = Β = . v = G e V v = G e V v = . G e V v = . G e V Deg.Exp bound10 - - - - - - - m J H keV L G J ® ΓΓ H s - L Figure 6.
Majoron decay rate to photons as a function of the majoron mass m J ,for different values of the triplet vev, v . We assume the invisible decay boundto be saturated. The top and bottom panels refer to hierarchical and degenerateneutrino mass spectra, respectively. The shaded regions are excluded by observationsas described in Sec. 3. The vertical lines are the same as in Fig. 5. One sees that in both scenarios small m J and v values lead to decay rates wellbelow the observational bounds. However, for large values of v , say, v = 5 GeV,roughly corresponding to the maximum compatible with precision measurements ofelectroweak parameters [43], the radiative rates fall within the sensitivities of the MilkyWay observations displayed in Fig. 3, and would be thereby observationally excluded.For lower masses the observational sensitivities would need to be improved by about 20orders of magnitude requiring completely new techniques from what is available today.The small radiative majoron decay rates would be avoided in models where the anomalydoes not cancel due to the presence of extra fermions. We mention also in this case thepossibility of further enhancement due to cumulative effects as those that might arise,for example, in higher dimensions.
6. Summary
We have investigated the production of x-ray photons in the late-decaying dark matterscenario, and quantified the sensitivity of current observations to such a mono-energeticemission line. In particular, we have studied the constraints from the diffuse x-rayobservations, as well as by considering the fluxes generated by dark matter dominatedobjects. These observations provide a probe of radiative dark matter decays and can beused as an “indirect detection” of the LDDM majoron scenario.We have illustrated this explicitly for the case where neutrinos get mass a la seesaw ,where the majoron couples to photons through its Higgs triplet admixture. Alternativeparticle physics realizations of the LDDM scenario can be envisaged, an issue which willbe taken up elsewhere. Let us also mention that Majoron dark matter decays can bepossibly probed in the future through 21-cm observations (see Ref. [44] for an applicationto other DM candidates). -ray photons from late-decaying majoron dark matter Acknowledgements
We thank Antonio Palazzo and Alexei Boyarsky for discussions.This work was supported by MEC grant FPA2005-01269, by EC Contracts RTN networkMRTN-CT-2004-503369 and ILIAS/N6 RII3-CT-2004-506222. The Dark CosmologyCentre is funded by the Danish National Research Foundation. ML is currentlysupported by INFN.
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