document: existence of dark matter  ( dm ) has been established , and its thermal relic abundance has been determined by the wmap experiment  @xcite . if the essence of dm is an elementary particle , the weakly interacting massive particle  ( wimp ) would be a promising candidate . 
   it is desired to have a viable candidate for the dark matter in models beyond the standard model  ( sm ) . 
   the wimp dark matter candidate can be accommodated economically by introducing only an inert scalar field  @xcite , where we use `` inert '' for the @xmath1-odd property . 
   the imposed @xmath1 parity ensures the stability of the dm candidate . 
   phenomenology in such models have been studied in , e.g. , refs . 
   @xcite .    on the other hand , it has been confirmed by neutrino oscillation measurements that neutrinos 
   have nonzero but tiny masses as compared to the electroweak scale  @xcite . 
   the different flavor structure of neutrinos from that of quarks and leptons may indicate that neutrino masses are of majorana type . in order to explain tiny neutrino masses , 
   many models have been proposed . 
   the seesaw mechanism is the simplest way to explain tiny neutrino masses , in which right - handed neutrinos are introduced with large majorana masses  @xcite . 
   another simple model for generating neutrino masses is the higgs triplet model  ( htm )  @xcite . 
   however , these scenarios do not contain dark matter candidate in themselves .    in a class of models where tiny neutrino masses are generated by higher orders of perturbation 
   , the dm candidate can be naturally contained  @xcite . in models in refs . 
   @xcite , the yukawa couplings of neutrinos with the sm higgs boson are forbidden at the tree level by imposing a @xmath1 parity . 
   the same @xmath1 parity also guarantees the stability of the lightest @xmath1-odd particle in the model which can be the candidate of the dm as long as it is electrically neutral .    in this paper 
   , we consider an extension of the htm in which by introducing the @xmath1 parity @xmath6 is generated at the one - loop level and the dm candidate appears . in the htm , majorana masses for neutrinos 
   are generated via the yukawa interaction @xmath7 with a nonzero vacuum expectation value  ( vev ) of an @xmath2 triplet scalar field @xmath8 with the hypercharge of @xmath9 . 
   the vev of @xmath8 is described by @xmath10 , where @xmath11 is the vev of the higgs doublet field @xmath12 and @xmath13 is the typical mass scale of the triplet field ; the dimensionful parameter @xmath14 breaks lepton number conservation at the trilinear term @xmath15 which we refer to as the @xmath14-term . as the simplest explanation for the smallness of neutrino masses , 
   the mass of the triplet field is assumed to be much larger than the electroweak scale . on the other hand 
   a characteristic feature of the htm is the fact that the structure of the neutrino mass matrix @xmath16 is given by that of the yukawa matrix , @xmath17 . 
   the direct information on @xmath16 would be extracted from the decay @xmath18 
   @xcite if @xmath19 is light enough to be produced at collider experiments , where @xmath19 is the doubly charged component of the triplet field @xmath8 . at hadron colliders , 
   the @xmath20 can be produced via @xmath21  @xcite and @xmath22  @xcite . 
   the @xmath20 searches at the lhc put lower bound on its mass as @xmath23  @xcite , assuming that the main decay mode is @xmath24 . 
   phenomenological analyses for @xmath20 in the htm at the lhc have also been performed in ref . 
   triplet scalars can contribute to lepton flavor violation  ( lfv ) in decays of charged leptons , e.g. , @xmath25 and @xmath26 at the tree level and @xmath27 at the one - loop level . 
   relation between these lfv decays and neutrino mass matrix constrained by oscillation data was discussed in refs .  @xcite . in order to explain the small @xmath0 with such a detectable light @xmath19 
   , the @xmath14 parameter has to be taken to be unnaturally much lower than the electroweak scale . 
   therefore , it would be interesting to extend the htm in order to include a natural suppression mechanism of the @xmath14 parameter ( therefore @xmath0 ) in addition to the dm candidate .    in our model , lepton number conservation 
   is imposed to the lagrangian in order to forbid the @xmath14-term in the htm at the tree level while the triplet yukawa term @xmath28 exists . 
   the vev of a @xmath1-even complex singlet scalar @xmath5 breaks the lepton number conservation by a unit . 
   an @xmath2 doublet @xmath3 and a real singlet @xmath4 are also introduced as @xmath1-odd scalars in order to accommodate the dm candidate . 
   then , the @xmath14-term is generated at the one - loop level by the diagram in which the @xmath1-odd scalars are in the loop . by this mechanism 
   , the smallness of @xmath29 is realized , and the tiny neutrino masses are naturally explained without assuming the triplet fields to be heavy . 
   the yukawa sector is then the same as the one in the htm , so that its predictions for the lfv processes are not changed . 
   see refs . 
   @xcite for some discussions about two - loop realization of the @xmath14-term - term in ref . 
   @xcite is given with softly - broken @xmath30 symmetry , but the tree level @xmath14-term would be also accepted as a soft breaking term . 
   the two - loop @xmath14-term in ref . 
   @xcite is given with @xmath31 symmetry which is broken by a vev of a scalar @xmath32 , but the tree level @xmath33 seems allowed by the @xmath31 . ] . 
   this paper is organized as follows . in sec . 
   [ sec : htm ] , we give a quick review for the htm to define notation . in sec . 
   [ sec:1-loop ] , the model for radiatively generating the @xmath14 parameter with the dark matter candidate is presented . 
   some phenomenological implications are discussed in sec . 
   [ sec : pheno ] , and the conclusion is given in sec . 
   [ sec : concl ] . 
   the full expressions of the higgs potential and mass formulae for scalar bosons in our model are given in appendix . 
   in the htm , an @xmath34 triplet of complex scalar fields with hyperchage @xmath9 is introduced to the sm . 
   the triplet @xmath8 can be expressed as @xmath35 where @xmath36 . 
   the triplet has a new yukawa interaction term with leptons as @xmath37 where @xmath38  ( @xmath39 ) are the new yukawa coupling constants , @xmath40  [ @xmath41 are lepton doublet fields , a superscript @xmath42 means the charge conjugation , and @xmath43  ( @xmath44 ) denote the pauli matrices . 
   lepton number  ( @xmath45 ) of @xmath8 is assigned to be @xmath46 as a convention such that the yukawa term does not break the conservation . 
   a vacuum expectation value @xmath47  [ @xmath48 breaks lepton number conservation by two units . 
   the new yukawa interaction then yields the majorana neutrino mass term @xmath49 where @xmath50 . 
   the scalar potential in the htm can be written as @xmath51 ^ 2   + \lambda_3\ , { { \text{tr}}}[(\delta^\dagger \delta)^2 ] \nonumber\\ & & { }   + \lambda_4\ , ( \phi^\dagger \phi ) { { \text{tr}}}(\delta^\dagger \delta )   + \lambda_5\ , \phi^\dagger \delta \delta^\dagger \phi , \end{aligned}\ ] ] where @xmath52  [ @xmath53 is the higgs doublet field in the sm . 
   the @xmath14 parameter can be real by using rephasing of @xmath8 . because we take @xmath54 
   , there is no nambu - goldstone boson for spontaneous breaking of lepton number conservation . 
   the small triplet vev @xmath47 is generated by an explicit breaking parameter @xmath14 of the lepton number conservation as @xmath55 where @xmath11  ( @xmath56 ) is the doublet vev defined by @xmath57 .    in order to obtain small neutrino masses in the htm , at least one of @xmath58 , @xmath38 
   , @xmath59 should be tiny . 
   a small @xmath14 is an attractive option because @xmath60 can be small ( @xmath61 ) so that triplet scalars can be produced at the lhc . 
   furthermore , large @xmath38 can be taken , which have direct information on the flavor structure of @xmath16 . 
   there is , however , no reason why the @xmath14 parameter is tiny in the htm . in our model presented below , the @xmath14 parameter is naturally small because it arises at the one - loop level . 
   since we try to generate the @xmath14-term in the htm radiatively , the term must be forbidden at the tree level . 
   the simplest way would be to impose lepton number conservation to the lagrangian . 
   the conservation is assumed to be broken by the vev of a new scalar field @xmath5 which is singlet under the sm gauge symmetry . 
   notice that @xmath5  [ @xmath62 is a complex ( `` charged '' ) field with non - zero lepton number although it is electrically neutral . 
   one might think that the vev of @xmath5 could be generated by using soft breaking terms of @xmath45 . 
   however , the @xmath14-term is also a soft breaking term . therefore lepton number must be broken spontaneously in our scenario . 
   one may worry about nambu - goldstone boson corresponds to the spontaneous breaking of the lepton number conservation ( the so - called majoron , @xmath63 ) . 
   however the majoron which comes from gauge singlet field can evade experimental searches ( constraints ) because it interacts very weakly with matter fields  @xcite . 
   it is also possible to make it absorbed by a gauge boson by introducing the @xmath64 gauge symmetry to the model ( see , e.g. , ref . 
   @xcite ) . in this paper 
   we just accept the majoron without assuming the @xmath64 gauge symmetry for simplicity . 
   if @xmath5 has @xmath65 , we can have a dimension-4 operator @xmath66 . 
   this gives a trivial result @xmath67 at the tree level . 
   although the dim.-4 operator could be forbidden by some extra global symmetries with extra scalars to break them , we do not take such a possibility in this paper . 
   we just assume the @xmath5 has @xmath68 . 
   then the lepton number conserving operator which results in the @xmath14-term is of dimension-5 as @xmath69 we consider below how to obtain the dim.-5 operator at the loop level by using renormalizable interactions of @xmath70 . ] . 
   we restrict ourselves to extend only the @xmath71-singlet scalar sector in the htm because it seems a kind of beauty that the htm does not extend the fermion sector and colored sector in the sm . 
   an unbroken @xmath1 symmetry is introduced in order to obtain dark matter candidates , and new scalars which appear in the loop diagram for the @xmath14-term are aligned to be @xmath1-odd particles . 
   we emphasize that the unbroken @xmath72 symmetry is not for a single purpose to introduce dark matter candidates but utilized also for our radiative mechanism for the @xmath14-term .    . 
   list of particle contents of our one - loop model . [ cols="^,^,^,^,^,^,^",options="header " , ]     we present the minimal model where the dim.-5 operator in eq . 
   ( [ eq : dim5op ] ) is generated by a one - loop diagram with dark matter candidates . 
   table  [ tab:1-loop ] shows the particle contents . a real singlet scalar field @xmath4 and the second doublet scalar field @xmath3  [ @xmath73 
   are introduced to the htm in addition to @xmath5 . 
   lepton numbers of @xmath4 and @xmath3 are 0 and @xmath74 , respectively . 
   then @xmath75 conserves lepton number . in order to forbid the vev of @xmath3 
   , we introduce an unbroken @xmath1 symmetry for which @xmath4 and @xmath3 are odd . 
   other fields are even under the @xmath1 . 
   the yukawa interactions are the same as those in the htm . 
   the higgs potential is given as @xmath76 here we show only relevant parts for radiative generation of the @xmath14-term 
   . see appendix for the other terms . 
   vacuum expectation values @xmath11 and @xmath77  [ @xmath78 are given by @xmath79 the @xmath1-odd scalars in this model are two cp - even neutral ones ( @xmath80 and @xmath81 ) , a cp - odd neutral one ( @xmath82 ) , and a charged pair ( @xmath83 ) . 
   the cp - even scalars are defined as @xmath84 where @xmath85 and @xmath86 . squared masses of these scalars 
   are given by @xmath87 notice that @xmath88 . 
   we assume @xmath89 and then @xmath80 becomes the dark matter candidate . 
   hereafter it is assumed that the mixing @xmath90 is small . 
   the @xmath14-term is generated by the one - loop diagram . 
   figure  [ fig:1-loop ] is the dominant one in the case of small @xmath90 . 
   then , the parameter @xmath14 is calculated as @xmath91 the one - loop induced @xmath14 parameter can be expected to be much smaller than @xmath92 . 
   the suppression factor @xmath93 is estimated in sec . 
   [ subsec : dm ] . 
   we call it `` a.  oryzae diagram ''  @xcite . , 
   title="fig : " ] -term . 
   we call it `` a.  oryzae diagram ''  @xcite . 
   , title="fig : " ] 
   if @xmath94 , the dark matter candidate @xmath80 is given by @xmath95 approximately because we assume small mixing . 
   see , e.g. , ref . 
   @xcite for studies about the inert doublet scalar . 
   let us assume @xmath96 and @xmath97 . as shown in ref . 
   @xcite , these values satisfy constraints from the lep experiments  @xcite and the wmap experiment  @xcite . the mass splitting ( @xmath98 ) suppresses quasi - elastic scattering on nuclei ( @xmath99 mediated by the @xmath100 boson ) enough to satisfy constraints from direct search experiments of the dm  @xcite . by using eqs .   and 
   , we obtain @xmath101 in order to be consistent with our assumption of small @xmath90 ( e.g. , @xmath102 ) , @xmath103 is required . the value in eq . 
   results in @xmath104 for the greater value of @xmath105 , the larger @xmath106 is predicted . 
   in particular , by taking @xmath105 to be the tev scale , we obtain @xmath107 , which yields @xmath108 for @xmath109 and @xmath60 to be at the electroweak scale . 
   such a value for @xmath47 is suggested in the recent study of radiative corrections to the electroweak parameters  @xcite .    on the contrary , if we take @xmath110 which is allowed in a tiny region  @xcite , values in eqs .   and become 10 times smaller . 
   we mention that the wmap constraint might be changed by a characteristic annihilation process @xmath111 where @xmath112 interaction is governed by @xmath109 ( not by a tiny @xmath14 ) . 
   this additional process could sift allowed value of @xmath113 to lower one while @xmath114 due to the lep constraint . 
   then , @xmath106 might become larger than the value in eq .   because of larger @xmath115 . 
   this undesired effect would be easily avoided if @xmath116 is away enough from @xmath117 .    on the other hand , @xmath80 comes dominantly from @xmath4 if @xmath118 . 
   see , e.g. , ref . 
   @xcite for studies about the real inert singlet scalar . 
   coupling @xmath119 of the @xmath120 interaction ( @xmath121 is the sm higgs boson ) determines annihilation cross section of @xmath80 and scattering cross section on nuclei . 
   if we introduce the @xmath64 gauge symmetry , the scattering of @xmath4 on nuclei can be mediated also by the gauge boson @xmath122 . 
   notice that the parameter @xmath123 ( and also the @xmath64 gauge coupling constant ) does not affect on @xmath14 parameter in eq .  . 
   let us estimate the magnitude of @xmath106 . 
   in the usual htm , @xmath38 is expected to be @xmath124 for @xmath125 in order to suppress lfv processes . 
   thus , we may accept @xmath126 as a value which is not too small . 
   assuming @xmath127 for example gauge symmetry in order to eliminate the majoron , @xmath77 should be a little bit larger ( e.g. , @xmath128 ) due to constraint on the mass of @xmath122 . 
   ] , we have a suppression factor as @xmath129 thus , even if the value of @xmath92 is in the tev scale , we can obtain @xmath130 although we need further suppression with @xmath131 to have @xmath132 . 
   if we use @xmath133 , we obtain @xmath134 which can connect the tev scale @xmath92 to the ev scale @xmath6 .      . 
   the bosonic decay of @xmath135 contains information of @xmath92 indicated by a red blob . ] 
   the characteristic feature of our model is that @xmath92 is much larger than @xmath14 . 
   let us consider possibility to probe the large @xmath92 in collider experiments . 
   a favorable process is shown in fig . 
   [ fig : lhc ] for @xmath136 . for simplicity 
   , we take @xmath137 which results in @xmath138 . 
   recently , it was found in ref . 
   @xcite that the electroweak precision test prefers @xmath139 in the htm where the electroweak sector is described by four input parameters . 
   however , results in ref . 
   @xcite might not be applied directly to our model is generated at the 1-loop level . ] because the scalar sector is extended . 
   since @xmath140 is the most interesting decay in the htm , we assume @xmath141 in order to forbid @xmath142 . even in this case , the dm @xmath80 can be light enough ( @xmath143 ) so that @xmath1-even charged scalar @xmath144 ( @xmath145 ) can decay into @xmath146 via @xmath92-term which is indicated by a red blob in fig .  [ 
   fig : lhc ] . 
   the partial decay width of @xmath147 is determined by @xmath148 while the width of @xmath149 is proportional to @xmath150 . 
   taking @xmath151 , @xmath152 , @xmath153 , and @xmath154 for example , we have @xmath155 and @xmath156 . 
   then , @xmath144 dominantly decays into @xmath146 . 
   finally , @xmath157 decays into @xmath158 . 
   therefore , from a production mechanism @xmath159 , we would have @xmath160 as a final state in fig . 
   [ fig : lhc ] can be replaced with @xmath161 which decays into @xmath162 for @xmath136 . ] for which @xmath163 has the invariant mass @xmath164 at @xmath165 assuming that the value of @xmath165 has been known already .    if @xmath166 , then @xmath144 decays via @xmath92-term into @xmath167 or @xmath168 followed by @xmath169 where a sizable @xmath170 is assumed is small , @xmath81  ( @xmath171 ) decays into @xmath172 . ] . because of @xmath173 through @xmath174 , we have again @xmath160 with @xmath175 from @xmath159 . 
   in the usual htm in contrast , the final state with such @xmath163 is likely to include additional charged leptons ( @xmath176 from @xmath177 , @xmath178 from @xmath179 , etc . ) 
   if @xmath20 decay dominantly into @xmath180 . therefore , our model would be supported if experiments observe final states which include jets and only two @xmath181 whose invariant mass gives @xmath175 . 
   this potential signature might be disturbed by hadronic decays of @xmath182 because @xmath183 can result in @xmath160 with @xmath175 . 
   realistic simulation is necessary to see the feasibility . 
   we have presented the simple extension of the htm by introducing a @xmath1-even neutral scalar @xmath5 of @xmath68 , a @xmath1-odd neutral real scalar @xmath4 of @xmath184 , and a @xmath1-odd doublet scalar field @xmath3 of @xmath68 . the dm candidate @xmath185 in our model is made from @xmath4 and @xmath186 . the @xmath187 interaction which is the origin of @xmath0 ( and neutrino masses ) 
   is induced at the one - loop level while the @xmath188 interaction exists at the tree level . because of the loop suppression for @xmath14 parameter , the model gives small neutrino masses naturally without using very heavy particles .    for @xmath189 , the suppression factor @xmath190 is constrained by the dm relic abundance measured by the wmap experiment . 
   we have shown that @xmath191 is possible . 
   on the other hand , for @xmath192 , the suppression factor is somewhat free from experimental constraints on the dm . in our estimate , @xmath193 can be obtained as an example with @xmath126 . 
   the characteristic feature of the model is that @xmath92 is not small while @xmath14 can be small . 
   a possible collider signature which depends on @xmath92 would be @xmath160 with the invariant mass @xmath175 because more charged leptons are likely to exist in such final states in the usual htm . 
   the work of s.k .  was supported by grant - in - aid for scientific research nos . 
   22244031 and 23104006 . the work of h.s . 
   was supported by the sasakawa scientific research grant from the japan science society and grant - in - aid for young scientists ( b ) no . 
   the higgs potential of our model is given by @xmath194 where @xmath195 @xmath196 @xmath197 ^ 2   + \lambda_3\ , { { \text{tr}}}[(\delta^\dagger \delta)^2 ] \nonumber\\ & & { }   + \lambda_{4\phi}\ ,     ( \phi^\dagger \phi)\ , { { \text{tr}}}(\delta^\dagger \delta )   + \lambda_{4\eta}\ ,     ( \eta^\dagger \eta)\ , { { \text{tr}}}(\delta^\dagger \delta ) \nonumber\\ & & { }   + \lambda_{5\phi}\ ,     ( \phi^\dagger \delta \delta^\dagger \phi )   + \lambda_{5\eta}\ ,     ( \eta^\dagger \delta \delta^\dagger \eta ) \nonumber\\ & & { }   + \lambda_{s1}\ , |s_1 ^ 0|^4   + \lambda_{s2}\ , ( s_2 ^ 0)^4   + \lambda_{s3}\ , |s_1 ^ 0|^2 ( s_2 ^ 0)^2 \nonumber\\ & & { }   + \lambda_{s\phi 1}\ , |s_1 ^ 0|^2\ , ( \phi^\dagger \phi )   + \lambda_{s\phi 2}\ , ( s_2 ^ 0)^2\ , ( \phi^\dagger \phi ) \nonumber\\ & & { }   + \lambda_{s\eta 1}\ , |s_1 ^ 0|^2\ , ( \eta^\dagger \eta )   + \lambda_{s\eta 2}\ , ( s_2 ^ 0)^2\ , ( \eta^\dagger \eta )   + \left\ {      \lambda_{s\phi\eta}\ , s_1 ^ 0\ , s_2 ^ 0\ , ( \eta^\dagger \phi )      + \text{h.c . }     \right\ } \nonumber\\ & & { }   + \lambda_{s\delta 1}\ , |s_1 ^ 0|^2 { { \text{tr}}}(\delta^\dagger \delta )   + \lambda_{s\delta 2}\ , ( s_2 ^ 0)^2 { { \text{tr}}}(\delta^\dagger \delta ) .\end{aligned}\ ] ] all coupling constants are real because the phases of @xmath92 and @xmath174 can be absorbed by @xmath8 and @xmath5 , respectively 
   .    mass eigenstates of two @xmath1-even cp - even neutral scalars which are composed of @xmath198 and @xmath199 are obtained as @xmath200 their masses eigenvalues are given by @xmath201 where small contributions from @xmath47 are neglected . 
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summary: we extend the higgs triplet model so as to include dark matter candidates and a simple suppression mechanism for the vacuum expectation value ( @xmath0 ) of the triplet scalar field . 
   the smallness of neutrino masses can be naturally explained with the suppressed value of @xmath0 even when the triplet fields are at the tev scale . 
   the higgs sector is extended by introducing @xmath1-odd scalars ( an @xmath2 doublet @xmath3 and a real singlet @xmath4 ) in addition to a @xmath1-even complex singlet scalar @xmath5 whose vacuum expectation value violates the lepton number conservation by a unit . in our model , @xmath0 is generated by the one - loop diagram to which @xmath1-odd particles contribute . 
   the lightest @xmath1-odd scalar boson can be a candidate for the dark matter . 
   we briefly discuss a characteristic signal of our model at the lhc .