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one of the most promising `` smoking - gun '' signals for establishing the existence of the dark matter particle is the possible observation of a sharp cosmic @xmath0-ray line from dark matter annihilation or decay @xcite . the forthcoming cherenkov telescopes @xcite , the current fermi large area telescope @xcite and the hess instrument @xcite will allow to probe this possibility with further sensitivity . if such a signal is observed in the near future , the question of the identification of the dm particle that could have caused it will become crucial . such a signal could be induced through annihilation , coannihilation or decay . for all these scenarios , it is generally assumed that the photon is emitted through the loop of a charged particle . beside this general class of models , there exist other ways along which dm could emit monochromatic photons . one possibility consists in assuming that the @xmath0-ray line is due to a @xmath2 chern - simons interaction @xcite . another possibility , much less studied , would be to consider a photon directly emitted by the dm particle . this is a priori perfectly possible if dm is not exactly neutral , but is millicharged . for an annihilation such a possibility is not much of an option because the associated @xmath0-ray line would be in general suppressed with respect to the total cross section , by the square of the millicharge . given the constraints there are on the total cross section ( in particular from the relic density in the thermal freezeout scenario ) , this would lead to a signal sizeably smaller than present or near future sensitivities . instead for a decay , there is a priori more freedom because the decay lifetime is not so directly constrained by the relic density . in this work we consider such a decay possibility .    in the following we will first consider the two main frameworks that can in a simple way justify a millicharge for the dm particle , kinetic mixing and stueckelberg scenarios . in such scenarios , in order to justify that the dm particle would have a slow decay , we assume that its stability is due to an accidental symmetry that , being accidental , would be naturally broken by any uv physics . along these lines , the decay is naturally slow because suppressed by powers of the uv scale , just as expected for the proton . the appropriate language to consider in a model - independent way the possibility of a slow decay is therefore the one of the higher - dimensional operator effective theory . unlike for an annihilation , the use of an effective theory for a decay is fully justified since one expects a clear scale separation . consequently , such an effective theory allows for a systematic study of possibilities . we will determine all dimension - five and dimension - six operators that can lead to a two - body radiative decay from a millicharged fermion , scalar or vector dm particle . these operators come in addition to the effective operators which can lead to a @xmath0-ray line in the case where dm would be exactly neutral , given and studied in ref . the former operators involve a covariant derivative of the millicharged field , whereas the latter ones can involve a photon only from the presence of a hypercharge or @xmath3 field strength @xmath4 in the operator .    in the following , we will perform a detailed analysis of the constraints that hold on the various `` millicharged operators '' for the fermionic dm case . the scalar and vector cases will be discussed more briefly before concluding . a simple constraint that turns out to be relevant in some cases is that the dm particle lifetime should be larger than the age of the universe . another one concerns the emission of cosmic rays ( cr ) that could be associated to the one of the photon , either from the particle that accompanies the photon in the decay final state , or from other decays that the effective operator unavoidably predicts on top of the radiative one . gauge invariance in particular predicts decays where the photon is replaced by a @xmath5 . if the electromagnetic coupling to the @xmath5 is not millicharge suppressed , the flux of cosmic rays produced is much larger than the flux of monochromatic photons . in particular , if the particle accompanying the photon in the final state is a neutrino , which is the only standard model ( sm ) particle possibility ( a decay of special interest being `` poly - monochromatic '' , i.e.  monochromatic for both types of cosmic rays that are the less affected while propagating ) , we will see that an observable @xmath0-ray line is not an option , unless the dm mass is quite low . therefore , except for this case , the possibilities we will find point towards multi - component dm scenarios . other constraints are related to the fact that along the stueckelberg scenario the dm particle is charged under a new @xmath6 gauge group , which may be at the origin of the unsuppressed emission of the associated @xmath7 . a millicharge for a particle can either be postulated as just so ( from assuming an hypercharge such that @xmath8 is small ) or induced from a dynamical process , typically a small mixing parameter between the sm hypercharge gauge boson and a new @xmath6 gauge boson . the first option requires another particle to carry just so the same millicharge in such a way that the dm particle can decay into it . for the more appealing second option , one can point out two simple scenarios , depending on whether the @xmath6 gauge boson is massless or massive .      in the massless case , a millicharge is induced for an originally neutral particle if the unbroken @xmath6 gauge boson kinetically mixes with the hypecharge gauge group @xcite , @xmath9 applying first a non - unitary transformation to get rid of this non - canonical kinetic term , one can always in a second step rotate both gauge boson fields with a unitary transformation because both gauge bosons are massless . there is therefore some arbitrariness in defining both fields . we make the convenient choice to go to the basis where the state which is essentially the hypercharge gauge boson couples to both @xmath10 and @xmath11 generators , whereas the other one , which is essentially the @xmath6 gauge boson , couples only to the @xmath11 generator . it allows to put the kinetic mixing suppression in the production decay process rather than in the detection , see e.g.  ref . @xcite . in this basis , and after electroweak symmetry breaking , the covariant derivative @xmath12 becomes    @xmath13    with @xmath14 . a field with charges @xmath15 , @xmath16 , and @xmath11 couples to the photon field @xmath17 with charge @xmath18 with @xmath19 . in particular , a field with @xmath20 acquires a millicharge @xmath21 . note that everywhere in the following we will make the approximation @xmath22 . existing constraints on the parameters apply in general on the millicharge @xmath23 , rather than on @xmath24 directly , see below . a value of @xmath25 is therefore not excluded . however , it is generally expected smaller than one . for instance , if we consider the minimal scenario where the only dm couplings are those of eq.([lagrangian_kin_mix ] ) , the thermal relic abundance of the dm is provided by the annihilation into dark photons . by requiring the right dark matter abundance , we get a value for @xmath26 as a function of @xmath27 this constraint together with eq . ( [ mc_bound ] ) below gives the bound @xmath28 , justifying our approximation . it is well known that if the @xmath6 symmetry is spontaneously broken , so that the corresponding gauge boson becomes massive , a kinetic mixing interaction does not induce any millicharge for an originally neutral field . in the massive case there exists nevertheless the stueckelberg option . the stueckelberg mechanism allows to have a massive gauge boson without breaking the corresponding gauge symmetry . we will here consider an extension of the sm by a @xmath6 as in @xcite . this model contains a scalar which has stueckelberg couplings to both @xmath29 and @xmath6 . as a consequence , the neutral gauge bosons mix , and in the mass eigenstates basis the covariant derivative reads @xmath30 where @xmath31 and @xmath32 stand for the sine and cosine of the various angles with @xmath33 , with @xmath34 the `` bare '' mass of the @xmath35 gauge boson , respectively @xcite . the expression of the electromagnetic charge is @xmath36 , with @xmath37 . in this way , an originally neutral field acquires a charge of @xmath38 . note that the stueckelberg scenario as origin of a millicharged dm ( like the `` just - so '' scenario ) might be questioned by considerations of quantum gravity / string theory @xcite . the list of possible radiative decays that could be generated by the millicharge of a particle is extremely reduced and in this sense points towards a rather precise kind of scenario . for the fermion dm case , there is only one decay possibility , @xmath39 with @xmath40 and @xmath41 necessarily carrying the same millicharge . in the following , when establishing the list of operators that could lead to a sizable monochromatic photon signal , we will not specify the exact nature of the fermionic partner of the dm in these operators . it could be either a dirac or a majorana fermion , and it could be either a particle beyond the sm or a neutrino . the former option points towards a multi - component fermion dm scenario . note that the results obtained below , in particular those of fig . [ fig : kin_mix ] , do not depend on how the abundancies of these components pile up to saturate the observed value of @xmath42 , except those depending on the direct detection constraints on a millicharge . up to dimension six , there is only a very limited number of operators that can induce a @xmath39 decay from the millicharge of @xmath40 and @xmath41 . first of all , we only find a single dimension - five operator @xmath43 for this operator and all operators below , the addition of its hermitian conjugate is implicit . do not give any radiative two - body decays because this would require that the scalar field has both a vev and a millicharge , which would give a mass to the photon . similarly , operators with a @xmath44 or @xmath45 do not give any radiative decays as can be seen from the use of the equations of motion . note also that operators with an additional @xmath46 are redundant since both fermions in the operator are different fields ( i.e.  it can always be reabsorbed in the definition of one of the fermion field ) . ] the presence of the @xmath47 implies that this operator can be rewritten as a sum of operators where both covariant derivatives have been replaced by a sum of field strengths of the gauge boson to which the particle couples ( each one multiplied by the corresponding gauge coupling ) . dipole operators ( as relevant for example for the @xmath48 decay ) , with the difference that the photon would here be radiated by a millicharged particle instead of a charged lepton or charged gauge boson . ]    as for the dimension - six operators we find only three possibilities , @xmath49    their structure are equivalent up to one operator that does not produce monochromatic photons but can give other decays ( including two - body decays ) , hence different amounts of cosmic rays . as for the operator of eq . ( [ ofdpsisig ] ) , the covariant derivative of the operators of eqs . ( [ o6fdpsisig ] , [ o6fddmsig ] ) can be traded for a sum of field strengths . in summary , up to dimension six , we are left with four operator structures only , as given in eq . ( [ ofdpsisig ] ) and eqs . ( [ o6fdpsisig])-([o6fd2sig ] ) . at the two - body decay level , the scalar field in the last three operators can intervene only through its vev . for the quantum numbers of these fields there is in principle an infinity of possibilities and we will see how , when considering the constraints on the various operators , a simple global picture can emerge despite of this fact . as for the non - millicharged operators in ref . @xcite , there are a priori essentially two main ways to constraint the operators and thus to possibly discriminate between them , from @xmath0-ray line spectral features and from the associated continuum of cosmic rays produced . the fact that the lifetime of the dm particle must be longer than the age of the universe provides an additional constraint which is relevant in special cases .    by spectral features we mean the number of @xmath0-ray lines produced , their relative energies and relative intensities . however , for the millicharged operators there is no way to get more than one @xmath0-ray line from a unique given operator since in the final state , on top of the photon , one can only find the @xmath41 particle .    to determine what are the possibilities to distinguish among the various operators from a cosmic ray multi - channel analysis , we will proceed as for the case of non - millicharged operators in ref . the whole issue is that for a given operator , due to gauge invariance , there always is a continuum flux of cosmic rays associated to the production of a @xmath0-ray line , especially if its energy is larger than the @xmath5 boson mass . the decay rate of the dm particle into photons is proportional to its millicharge squared . therefore , to determine the upper bounds existing on the photon over cosmic rays ratios , we will need to know ( in some cases ) what are the bounds which hold on the millicharge of a metastable particle within the mass range we consider , @xmath50 gev . in this mass range , there are no relevant accelerator constraints @xcite . there are nevertheless stringent constraints from cosmology as well as from direct detection data . as well - known , in the usual @xmath51cdm model , which fits well both the cmb anisotropy and large scale structure data , it is assumed that there is no dm - baryon interaction other than gravitational . an additional dm - baryon interaction such as the one provided by a millicharge modifies this picture by rendering dm effectively `` baryonic '' . this affects the cmb power spectrum as well as the baryon acoustic oscillations , leading to the upper bound @xcite @xmath52 where @xmath53 is the dm - baryon momentum - transfer cross - section and @xmath54 is the dm - baryon relative velocity . in our case , the relevant cross - section is the rutherford one and @xmath55 eq . ( [ cmb_bound ] ) translates into the following bound on the dm millicharge @xmath56 where @xmath57 is the electromagnetic fine structure constant . the direct detection bounds are much more model - dependent than the cmb ones . they crucially depend on the mass of the particle exchanged between the nucleon and the dm particle . in the massless @xmath6 gauge boson case , the elastic nucleon - dm scattering is proportional to the inverse of the recoil energy squared , @xmath58 . this results in a huge enhancement of the scattering cross section with respect to the usual wimp case where the cross section is typically suppressed by the inverse of the square of the gev - tev mass of the particle exchanged . for @xmath59  few  gev this results in upper bounds on the millicharge of order of @xmath60-@xmath61 , see fig . 9 of ref . @xcite ( where the @xmath62 parameter is nothing but @xmath63 in our notation ) . for the stueckelberg case , these constraints remain also valid as long as the @xmath7 is lighter than @xmath64 mev , see for example fig.1 of ref . @xcite . beyond these values , the upper bound on the millicharge scales as @xmath65 , so that it quickly becomes weaker than the cmb bound ( this occurs for @xmath66 gev ) . in the following , when the bound on the millicharge is relevant to determine the upper bound on the @xmath0-ray line , we use the cmb bound . we will see that this bound already excludes an observable @xmath0-ray line for these cases ( hence a fortiori when the direct detection bounds are stronger , this is even more excluded ) . note also that all these direct detection constraints assume a standard local dm density , which might not apply depending on how large the dm particle millicharge is , because it can be shielded by galactic magnetic fields @xcite . for instance , when @xmath67 , the depletion of the local dm relic density from magnetic shielding begins to be sizeable , therefore weakening the direct detection bounds . the photon over cosmic rays ratio in both kinetic mixing and stueckelberg scenarios is given by @xmath68 @xmath69 here , the @xmath70 ratios hold for the number of cosmic rays ( of a given type and of a given energy ) produced per particle p , and @xmath71 are functions of the @xmath72 and @xmath73 masses . for @xmath74 , they always are equal to unity except for the operator of eq . ( [ o6fd2sig ] ) , see below . in these equations @xmath75 is the millicharge which , as said above , is equal to @xmath76 and @xmath77 in the kinetic mixing and stueckelberg cases , respectively . as for the coupling to the @xmath5 , @xmath78 , as eqs . ( [ lagrangian_kin_mix])-([lagrangian_stuck ] ) show , it takes the simple form @xmath79 respectively ( where @xmath80 indicates the tangent of @xmath81 ) . the coupling to the @xmath7 , which applies only in the stueckelberg case , is @xmath82 finally , the coupling to the @xmath83 , @xmath84 , can take very different values as a function of the multiplets considered in the various operators ( and the associated clebsch - gordan coefficients ) . in practice , we will consider the cases which , among all possible multiplet configurations up to @xmath3 quintuplets , minimize @xmath84 , hence maximize the @xmath85 ratio .    before coming to the constraints which hold for the various operators , note that in the following we will not consider in many details the amount of cosmic rays the @xmath7 could give . the limits on the intensity of the @xmath0-ray line we will give below hold for the case where the @xmath7 does not give any cosmic rays . this can be the case for example if the @xmath7 decays essentially to @xmath86 ( if @xmath87 ) . this situation gives the maximum upper bound that could be reached . when neglecting the contribution of the @xmath7 to the cosmic rays , both stueckelberg and kinetic mixing scenarios give rise to the same fig . [ fig : kin_mix ] bounds at the lowest order in @xmath88 and @xmath24 respectively . at the end of sec . [ constraints ] , we will discuss how our results might be affected if , instead , the @xmath7 mainly decays into sm particles . for the unique dimension - five operator , the quantum numbers of @xmath40 and @xmath41 are necessarily the same , and in particular @xmath90 . the simple crucial remark to be done at this stage , not only valid for this operator but for all operators , is that unless the fields to which the covariant derivative applies is a singlet of both @xmath3 and @xmath29 , there will always be a two - body decay production of a @xmath5 and/or a @xmath83 in a way which is not suppressed by the value of the millicharge . as a result in this case , the production of cosmic rays is boosted , by the inverse of the millicharge squared , with respect to the production of the @xmath0-ray . z bosons are produced in this way as soon as the @xmath15 of the particle to which the covariant derivative applies is different from zero , see eqs . ( [ czkm ] ) and ( [ czstu ] ) . as for the @xmath84 coupling , for the dimension - five operator one can write it as @xmath91 . for an @xmath3 multiplet of dimension @xmath92 , @xmath93 if @xmath94 and @xmath95 in all other cases . similarly , @xmath96 if @xmath97 and @xmath98 in all other cases . as a result , both @xmath99 and @xmath100 , hence @xmath84 , can be zero only if @xmath101 , that is to say if one considers a sm singlet .    from this discussion there are three general cases    * . in this case there is no @xmath83 production and the @xmath5 production involves two powers of the millicharge , as for the @xmath0 production . as a result we get an unsuppressed ratio @xmath102 at the lowest order in @xmath24 for the kinetic mixing case and in @xmath88 for the stueckelberg case . in the latter case , this is a good approximation if @xmath103 , which is what is expected if there is a big splitting between the sm gauge bosons and the @xmath7 masses . * . in this case , there is production of @xmath83 bosons and @xmath104 in eq . ( [ ratio_ddpsidpsi ] ) , meaning that @xmath105 at the lowest order in @xmath106 or @xmath88 . here , in order to obtain a conservative model - independent upper bound , we made the hypothesis that the charged @xmath41 components produced in two - body decays together with @xmath83 bosons do not yield an important contribution to cosmic rays production . * . in this case we have both unsuppressed production of @xmath5 and @xmath83 . here we will consider only the case with @xmath107 and @xmath108 , as it is the one which maximizes the @xmath109 ratio of eq . ( [ ratio_ddpsidpsi ] ) . it gives @xmath110 with @xmath111 at the lowest order in @xmath106 or @xmath88 .      in this case , the relevant quantum numbers are those of @xmath41 . the maximal ratios as a function of the value of @xmath113 follow the same pattern as for the previous operator . in the same way , one has three cases    * : prediction ( [ ratio_a ] ) . * : prediction ( [ ratio_b ] ) . * : prediction ( [ ratio_c ] ) . now , the relevant quantum numbers are those of the dm particle . here , the three cases are :    * : prediction of eq . ( [ ratio_a ] ) . * : the ratio is maximized with @xmath115 , which gives is obtained for a situation with @xmath40 a triplet , and @xmath41 and @xmath88 quintuplets . any combination of smaller multiplets gives a bigger value of @xmath84 . for example , taking @xmath40 as a hyperchargeless triplet , and both @xmath41 and @xmath88 as doublets of hypercharge 1 , gives @xmath116 . ] @xmath117 * : the ratio is maximized with @xmath118 and @xmath119 , which gives @xmath120      the phenomenology of this operator is more involved than the one of the operators above because it depends in a complicated way on the couplings of both @xmath41 and @xmath40 to the various bosons . nonetheless , maximizing the @xmath109 ratio requires @xmath41 and @xmath40 to have the same quantum numbers , which greatly reduces the complexity of the @xmath109 ratio .    in the case where both @xmath40 and @xmath41 are sm singlets , this ratio is given by @xmath122 at the lowest order in @xmath24 or @xmath123    in the case where @xmath40 and @xmath41 are not sm singlets , the predictions are quite lengthy and we only give them for the cases where @xmath124 and @xmath125 in the appendix . unlike all previous cases where the dependence on @xmath126 is negligible for @xmath127 , here , from the longitudinal @xmath83 contribution , there are terms in @xmath128 which imply a power law dependence on @xmath129 , see appendix . this is associated to the fact that , unlike the other operators , this one is not equivalent to a single operator involving a field strength . this will give rise to a different behaviour of the constraints below , as the bounds obtained for the @xmath121 operator get stronger when @xmath129 increases . [ fig : kin_mix ] shows the constraints obtained on the photon over cosmic rays ratios for the different operators involving a millicharged dm . for low masses , up to @xmath130 tev , the most stringent bounds are provided by pamela measurements of cosmic antiprotons @xcite , whereas for higher masses , the relevant constraints come from measurements of the diffuse gamma background from fermi - lat @xcite and hess @xcite . the methodology used to obtain these constraints is the same as in ref . @xcite . by comparing the constraints from cosmic rays on @xmath131 and the limits from direct searches for photon line spectral features , this plot shows which operator are compatible with a possible near future observation of a @xmath0-ray line . a clear pattern emerges from these results . except for the case in which the dm is a singlet of the sm gauge groups , none of the effective operators associated to a millicharged dm taken individually would be able to produce a @xmath0-ray line strong enough to meet the current experimental sensitivity without overproducing antiprotons and diffuse photons . actually , in all the cases in which the dm is not a sm singlet , the observation of a spectral photon line would be associated to an excess of cosmic rays from five to ten orders of magnitude higher than the present experimental bounds from pamela or fermi - lat and hess . this result is interesting because it singles out a unique possibility for the sm quantum numbers of the dm : a sm singlet . unfortunately , it does not allow to discriminate , neither among the mechanisms responsible for the millicharge of the dm , nor among the various operators . when the dm is a singlet , all operators lead to the prediction of eq . ( [ ratio_a ] ) , @xmath132 , except op.([ratio_f ] ) which differs at dm masses close to @xmath133 , but only very slightly . as fig . 1 shows , this prediction gives the maximum @xmath0-ray line intensity allowed by cosmic rays constraints . this absolute bound turns out to be the same as in ref . @xcite for the neutral dm scenarios . as for a non - sm - singlet dm , in fig .  1 we have only considered the quantum numbers that maximize @xmath131 . the maximum ratios turn out to be identical for operators @xmath89 and @xmath134 . they differ by less than one order of magnitude for @xmath114 , which is within the uncertainty coming from the propagation models . the only operator providing very different bounds for non - singlet dm is the operator @xmath121 , due to the dependence of the @xmath131 ratios on the dm mass . not only are these bounds exhibiting a different behaviour for increasing @xmath129 , but they also differ by more than two orders of magnitude from all the previous bounds for @xmath135 tev . therefore , if a line were to be detected with a sensitivity of direct searches for monochromatic photons improved by several orders of magnitude , it would in principle be possible to discriminate this particular operator from the other ones where the dm is not a sm singlet . but , in practice , this does not appear at all to be a realistic option because this basically means a @xmath0-ray line with intensity smaller than the intensity of the photon continuum observed . putting together the results obtained for a millicharged dm and those derived for a neutral dm @xcite , we find that if a line were detected at the current experimental sensitivity without any excess of cosmic rays , it would not be possible to discriminate the millicharged sm - singlet scenario from the neutral dm case giving the same eq . [ ratio_a ] ratio ( prediction `` a '' in @xcite ) . however , if on the contrary a strong line were to be detected with a sizeable associated cosmic rays excess , only the more suppressed @xmath0-ray predictions `` b''-``e '' in ref . @xcite for neutral dm could explain it . as said above , all the bounds obtained have been computed under the hypothesis that the stueckelberg @xmath7 that could be present in two - body decay final states ( if kinematically allowed ) does not produce any cosmic rays by decaying subsequently . if this does not hold , the operators will give rise to more suppressed bounds . to estimate how important this contribution could be , we consider as an example , with @xmath136 , a @xmath7 boson which decays mainly to @xmath137 , a channel which is known to produce many cosmic rays . when the dm is not a singlet , we find bounds that are stronger by approximately two orders of magnitude . this stems from the fact that , in this case , a single @xmath7 produces a comparable amount of cosmic rays with respect to the sm gauge bosons , but , with @xmath138 , its coupling to the dm particle is stronger than those of the @xmath5 or @xmath139 bosons . if , instead , the dm particle is a sm singlet , the @xmath140 ratio does not depend anymore on the value of @xmath141 , but the coupling to the photon is suppressed by @xmath142 . instead of having a fixed bound on the ratio as given by eq . ( [ ratio_a ] ) , the following limit is obtained : @xmath143 the @xmath88 angle is constrained by the measurement of the @xmath5 width from lep , @xmath144 @xcite . this decreases the bound of eq . ( [ ratio_a ] ) by three to four orders of magnitude . interestingly , the observation of a @xmath0-ray line with intensity of order the present experimental sensitivity would therefore probe this possibility , see fig .  1 .    as mentioned above for the massless kinetic mixing case , the direct detection constraints on the millicharge are stronger than the `` universal '' cmb constraints we have used for fig .  [ fig : kin_mix ] . as a result , in this case , an observable @xmath0-ray line for the non - sm singlet scenario is even less of an option , not only because this would give even more cosmic rays , but also because it would give a dm lifetime smaller than the age of the universe . concerning possible rapid decays , note also that since the radiative decays are suppressed in all cases ( singlet case included ) by a factor of the millicharge squared , if there exist other ( non - radiative ) operators induced at the scale @xmath51 which destabilize the dm particle in a way which is not suppressed by this factor , they could easily induce decays much faster than the radiative ones . these decays could induce cosmic ray fluxes above the ones observed or even give a dm lifetime shorter than the age of the universe . the scenario is therefore viable if there is no such operator or if the associated decays do exist , but with a lifetime larger than the age of the universe and without an excessive associated production of cosmic rays . so far , we have discussed the constraints on the intensity of a @xmath0-ray line which hold from the bounds on the millicharge itself , as this is the parameter entering in the various rates . however , if one has some prejudice about the values of the parameters responsible for the millicharge , there are cases where stronger bounds on the @xmath0-ray line intensity apply . this is relevant in particular for the kinetic mixing case if , as for any gauge charge in the sm , one considers a value of the `` dark charge '' @xmath141 not far from unity . the issue here is that in the massless hidden gauge boson case , the dm particle does not only decay to @xmath145 but it also does to @xmath146 . as the @xmath147 does not produce any cosmic rays , the latter decay is not relevant for fig .  1 . however , it is naturally faster than the former decay by a factor of @xmath148 . one has therefore to make sure that the resulting lifetime is not shorter than the age of the universe . imposing that @xmath149 , and imposing that the millicharge satisfies the cmb bound of eq . ( [ mc_bound ] ) , we show in fig . 2 the upper limits which hold on the intensity of the @xmath0-ray line for various values of the dark charge @xmath141 . clearly , for large values of @xmath141 one gets competitive bounds with respect to those derived from @xmath0-ray line direct searches , whereas smaller values give irrelevant bounds . 2 also shows the constraints we get assuming the direct detection bounds mentioned above ( i.e.  fig . 9 of ref . @xcite , disregarding possible weakening of these bounds from magnetic shielding ) . these constraints are quite stringent , leading to unobservable @xmath0-ray lines , unless the dark charge is small enough . in fact , @xmath150 is necessary in order to get @xmath151 . these constraints are obtained assuming that the relic density of @xmath40 is the observed one . for smaller relic density values one gets weaker constraints . in the stueckelberg case , all these considerations become obviously irrelevant as soon as the @xmath7 gauge boson mass is above @xmath129 ( or above @xmath152  gev for what concerns the direct detection bounds ) . from the above results it is clear that , since the neutrino is not a sm singlet , it is not an option within the @xmath154  gev range considered above . moreover in this case , since the millicharge of both fermions in the various operators must be equal , and since the millicharge of the neutrinos is extremely well bounded , the millicharge of the dm particle is also extremely well constrained . the most stringent constraint applies on the electronic neutrino . assuming charge conservation in @xmath155 decay , and using the experimental results from @xcite and @xcite : @xmath156 and @xmath157 , the constraint @xmath158 is obtained . independent , less stringent upper bounds also hold from neutrino magnetic dipole moment searches , see _ e.g. _ @xcite . in the case of @xmath159 and @xmath160 , the most stringent constraints come from stellar evolution @xcite . if neutrinos acquire a millicharge , their electromagnetic interactions would provoke extra energy losses in the core of red giants . this would delay the time of helium ignition , and as a consequence , the core of red giants would be heavier than in the standard case when helium lights up . but the mass of the red giant core at helium ignition is constrained by measurements from globular clusters . these constraints turn into the following bound on the charge of neutrinos : @xmath161 . this bound holds as long as @xmath162 kev , implying that it applies to all flavours . to get a lifetime allowing for an observable @xmath0-ray line , the huge suppression due to this millicharge could in principle be compensated by considering smaller @xmath51 scales , taking typically @xmath163 gev for dimension - five operators , and @xmath164 gev for dimension - six operators . however , since the @xmath5 emission rate is enhanced with respect to the @xmath0 emission by a factor of @xmath165 , this would clearly imply a decay rate to @xmath166 leading to a lifetime much shorter than the lifetime of the universe . similarly this would have given a huge amount of cosmic rays . in fig . [ fig : kin_mix ] and rescale them by a factor of @xmath167 where @xmath168 refers to the bound of eq . ( [ mc_bound ] ) . ] therefore , due to several reasons , a line observed at the present sensitivities with energies above the @xmath5 mass could not be attributed at all to a millicharged dm decaying in neutrino and photon through one of the operators under study . more generally , one could ask whether this possibility is also excluded for lower dm masses . here , there are a priori two directly connected constraints which must be fulfilled , giving an upper and a lower bound on @xmath129 . the upper bound comes from the fact that , even if for @xmath169 the @xmath5 can not be produced on its mass shell , it can be produced off - shell and subsequently decay to a pair of fermions . this could result in a lifetime shorter than the age of the universe and/or to too many cosmic rays . for instance , supposing that a @xmath0 line , to be observable , must result from a two - body decay typically giving a lifetime @xmath170  sec , it is easy to see that the three - body decay lifetime ( from @xmath171 ) is shorter than the age of the universe , unless @xmath172 the limit coming from the single neutrino channel gives therefore a strong enough limit on @xmath129 to render irrelevant the limits one could get from all other possible @xmath5 decay channel , except from the @xmath173 channel . it is easy to see that the latter channel gives up to a very good approximation the stronger constraint , @xmath174 which holds in order to avoid overproduction of galactic center @xmath175  kev photon from overproduction of positrons . the limit on the lifetime of a dm particle with mass below @xmath176  mev is given by @xmath177 @xcite . as for the lower bound , it comes from the fact that , if one decreases too much @xmath129 , one gets a decay into a photon and a neutrino which is too slow to account for any observable photon line that could be detected in the future . for instance , let us consider the x - ray line recently reported with energy @xmath1  kev and flux @xmath178 @xcite . assuming a standard dm density along the line of sight , such a line , if better confirmed experimentally , could be understood from a dm decay into a photon and a neutrino , if the lifetime is @xmath179 s @xcite . it is interesting to stress that such kind of lines could in principle be accounted for by any model leading to one of the fermion radiative operator reported in ref . @xcite ( for the non - millicharged case ) or by any of the millicharged operators considered here , provided the operator can match the constraint that @xmath41 must be a lepton doublet and @xmath40 must be a singlet ( as its mass must lie in the kev range ) . mass , also holds for lower mass . to explain this recently reported line , one would not need necessarily to assume a fermion dm candidate . the scalar or vector operators given in this reference , or in section [ scalarvector ] below , could also account for it , provided there exists another lighter scalar or vector particle to accompany the photon in the decay final state . to distinguish among these operators appears to be hopeless , given the fact that the associated neutrino flux is basically unobservable at these energies . for various other possible explanations of this line , see refs . @xcite . ] for the millicharge option this latter requirement excludes the dimension - five operator but not the three dimension - six operators of eqs . ( [ o6fdpsisig])-([o6fd2sig ] ) with @xmath88 the scalar sm doublet . for these operators one has nevertheless to check that for such low masses , and given the stringent constraints on the millicharge of neutrinos , one can get a lifetime of order the one needed . the radiative lifetime one gets for any of these three operators is the same @xmath180 which , for the parameter values indicated , is about the one needed . given the uncertainties on the experimental flux needed , on the dm lifetime needed , and on the bounds on the neutrino millicharge from red giants , at the effective theory approach level one concludes that a small millicharge for the neutrino could be at the origin of this @xmath0-ray line , or more generally of observable kev - mev low energy lines , provided there is new physics around the corner at colliders and provided that the millicharge of the @xmath159 or @xmath160 is close to its upper bound . in other words , despite of the very stringent bounds which exist on them , neutrino millicharges could consequently have an observable effect in the form of a x - ray line . note also that within the kev - mev mass range discussed here , for @xmath181 kev , the generation of the relic density for a fermionic sm singlet dm can nevertheless be challenging @xcite . finally , remark that in the kinetic mixing scenario , imposing as above that @xmath182 , gives the constraint @xmath183 , which means @xmath184 . after studying the possibility for a millicharged dm of the fermionic type to emit an observable @xmath0-ray line through its decay , we now turn to the scalar and vector dm cases . if the dm particle is of the scalar or vector type , there also exist operators that could a priori lead to such a line . for what concerns the emission of cosmic rays , the phenomenology of these operators turns out to be similar to the fermion case . therefore , in the following , we will limit ourselves to the determination of the operators and to a few additional general comments which slightly distinguish these scenarios from the fermion case . due to angular momentum conservation considerations , a scalar dm particle can not decay to a scalar and a massless gauge boson . therefore , it can only decay to a photon and another massive spin - one particle , which necessarily carries the same millicharge . as a result , the scalar case is similar to the vector case . the operators that can allow a decay of a scalar dm particle into a vector particle and a photon , could also hold for a vector dm particle decaying into a scalar and a photon . in principle , a vector dm particle could nevertheless also decay in a different way , into a photon and another vector particle . note that a necessary condition for the vector dm to acquire a millicharge is to be a complex field , therefore associated to a non - abelian gauge group .    for the scalar - vector - photon case we found only one dimension - five operator @xmath185 and two dimension - six operators @xmath186 as said above , in these operators the dm particle can be either one of the scalar particle or a vector particle , the latter in one of the covariant derivative of eq . ( [ osv6fdd ] ) or in one of the non - abelian hidden sector @xmath187 field strengths of eqs  ( [ osv5])-([osv6ff ] ) . the photon can show up from one of the @xmath187 field strengths , through gauge boson mixing . this occurs for instance if , on top of a kinetic mixing between the hypercharge gauge boson and a @xmath6 gauge boson , there is , through symmetry breaking , a mixing between this @xmath6 gauge boson and gauge boson(s ) of the new non - abelian symmetry ( whose field strength is @xmath187 ) . in this way the @xmath187 field strength provides a photon field proportionally to the millicharge of the complex gauge boson in this field strength . ) and a @xmath188 @xmath187 field strengths , both field strengths must be taken in their quintuplet combination , which means that the scalar field is a quintuplet . ] note that no operator containing only covariant derivatives remains . this can be shown using equations of motion and rotating away non - canonical kinetic terms . operator ( [ osv6fdd ] ) is equivalent to op . ( [ osv6ff ] ) up to operators that do not produce monochromatic photons .    for the two operators of eqs . ( [ osv5])-([osv6ff ] ) , the emission of a @xmath5 is always suppressed by the millicharge squared , even if the scalars are non - sm singlet . this stems from the fact that the @xmath5 as the @xmath0 can come only from the field strength in these operators , not from a covariant derivative as for the fermion operators . this means that one gets the eq . ( [ ratio_a ] ) prediction even if the scalars are not sm singlets ( up to corrections in @xmath189 for @xmath190 ) . of course , as for the fermion case , one can saturate the ratio of eq . ( [ ratio_a ] ) only if there is no cosmic ray production from @xmath7 decay ( in the stueckelberg case ) . the latter could arise from the decay where the photon is replaced by a @xmath7 if this decay ( which is not suppressed by the value of the millicharge squared ) is not kinematically forbidden and if the @xmath7 subsequently decays into sm particles . as for the operator of eq . ( [ osv6fdd ] ) , it can lead to a non - millicharge suppressed production of @xmath5 and @xmath83 from the covariant derivatives , if the scalars are non - sm singlets . its phenomenology is therefore very similar to the one of the fermion operators . finally , about the possibility that a vector dm particle could decay into a photon and another vector particle , one could think about operators with only @xmath187 field strengths , for instance @xmath191 , through a similar mechanism where a @xmath187 could give a photon through gauge boson mixing . we did not find any simple realization of such a possibility . in summary , there are very few ways of probing the dm hypothesis that can really be considered in a systematic and model - independent way . however , for the decay of an absolutely neutral dm particle into a @xmath0-ray line , this turns out to be feasible @xcite . this stems from the facts that , on the one hand , the use of an effective theory is fully justified , slow enough decay can naturally be explained from a much higher scale physics , and , on the other hand , it turns out that there are very few operator structures of this kind . @xcite considered the usual scenario where the dm particle is absolutely neutral so that the photon appears in the operator through a field strength ( i.e. typically from a charged particle in a loop ) . here we show that , for the same reasons , such a study can also be systematically carried out in the less considered scenario where the dm is millicharged , having therefore a tree - level coupling to the photon through a covariant derivative , either from an ad - hoc millicharge , or through mixing of the @xmath29 gauge boson with another @xmath6 gauge boson .    to the emission of a @xmath0-ray line from such operators is associated the emission of a continuum of cosmic rays . the monochromatic photon to cosmic ray flux ratio is determined by the sm quantum numbers of the field on which the covariant derivative applies ( and in one case also crucially on the dm mass ) , and if this particle is not a sm singlet on the value of its millicharge . this leads to upper bounds on the intensity of the @xmath0-ray line produced , given in fig . [ fig : kin_mix ] . this figure shows that if the dm is only charged under the dark sector , it can lead to a line matching the present experimental sensitivities without overshooting the bound on the flux of antiprotons and diffuse photons . on the contrary , when the particle emitting the photon from its millicharge is also charged under the sm , the cosmic rays constraints are much stronger than direct searches for spectral lines . therefore , in this case , if a line were to be detected with energy above the @xmath5 mass and with about the present experimental sensitivity , it could not be explained in such a way . such a conclusion can also hold for @xmath129 far below the @xmath5 mass .    for the massless hidden gauge boson case ( and the massive case where @xmath192 is both below the gev scale and smaller than @xmath129 ) relevant additional constraints show up imposing that the two - body decay width to a @xmath147 ( z ) leads to a lifetime longer than the age of the universe . combining this constraint with the direct detection bounds on a millicharge , an observable @xmath0-ray line requires small values of the dark charge @xmath141 .    as for a decay into a neutrino and a photon , given the stringent constraints that exist on the millicharge of a neutrino , the @xmath5 mediated decay into three neutrinos , or into a neutrino and a electron - positron pair , this possibility is forbidden unless @xmath129 is below the mev scale . for lower masses , and down to the kev scale , an observable line induced in this way is not excluded by these considerations . such a neutrino millicharge scenario could even be at the origin of the recently reported , yet to be confirmed , 3.5 kev x - ray line . we acknowledge stimulating discussions with m.  gustafsson and m.  tytgat . this work is supported by the fnrs - frs , the iisn , the fria and the belgian science policy , iap vi-11 . thanks the ifae - uabarcelona theory group for its hospitality . in the case in which @xmath193 but is not a singlet , the denominator of eq . 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if a @xmath0-ray line is observed in the near future , it will be important to determine what kind of dark matter ( dm ) particle could be at its origin . 
 we investigate the possibility that the @xmath0-ray line would be induced by a slow dm particle decay associated to the fact that the dm particle would not be absolutely neutral . 
 a `` millicharge '' for the dm particle can be induced in various ways , in particular from a kinetic mixing interaction or through the stueckelberg mechanism . 
 we show that such a scenario could lead in specific cases to an observable @xmath0-ray line . 
 this possibility can be considered in a systematic model - independent way , by writing down the corresponding effective theory . 
 this allows for a multi - channel analysis , giving in particular upper bounds on the intensity of the associated @xmath0-ray line from cosmic rays emission . 
 our analysis includes the possibility that in the two - body decay the photon is accompanied with a neutrino . 
 we show that , given the stringent constraints which hold on the millicharge of the neutrinos , this is not an option , except if the dm particle mass lies in the very light kev - mev range , allowing for a possibility of explanation of the recently claimed , yet to be confirmed , @xmath1  kev x - ray line .