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the standard model ( sm ) has to be still extended so as to include massive neutrinos and dark matter ( dm ) , even though the sm higgs has been discovered .
one of the elegant solutions to resolve this issue is known as radiative seesaw models  @xcite , in which active neutrino masses are generated at multi - loop level and exotic fields are naturally introduced in order to get such radiative masses .
such an exotic field can be often identified as a dm candidate .
especially , ma model  @xcite is known as a minimal radiative seesaw model including fermionic and bosonic dm candidates .    on the other hand
the hierarchy problem arises in the sm .
one solution of the hierarchy problem is supersymmetry .
this is a beautiful theory however there are no signals in the lhc experiments . in this paper , we take another approach to the hierarchy problem following bardeen s argument@xcite .
bardeen has argued that once the classically conformal symmetry and its minimal violation by quantum anomalies are imposed on the sm , it may be free from quadratic divergences .
the models based on this idea are called classically conformal models@xcite .
the classical lagrangian for these models has no mass terms and all dimensional parameters are dynamically generated .
the models need an absence of intermediate scales between the tev scale and planck scale .
then the planck scale physics is directly connected to the electroweak ( ew ) physics .
we consider the classically conformal ma model which is combined ma model and the classically conformal model .
this model connects tiny neutrino mass scale and planck scale .
however the minimal classically conformal ma model does nt realize for following two reasons .
first the ew symmetry doest occur for large top yukawa coupling .
second the classically conformal symmetry forbids majorana mass term .
the majorana mass plays an important role in ma model .
we need the extended model . the minimal extension is gauged b@xmath0l model . in this model ,
ew symmetry breaking is triggered by b@xmath0l symmetry breaking and majorana mass term is generated by b@xmath0l symmetry breaking .
this paper is based on our work@xcite .
we discuss the one - loop induced radiative neutrino model with gauged @xmath1 symmetry containing the dm candidates : the lightest field of @xmath2 and @xmath3 which @xmath4 odd are assigned .
the particle contents are shown in tab .
[ tab:1 ] and tab .
[ tab:2 ] .
we add three @xmath5 singlet majorana fermions @xmath2 with @xmath6 charge under the @xmath7 symmetry to the sm fields . for new bosons ,
we introduce a @xmath5 doublet scalar @xmath3 with zero charge under the @xmath7 symmetry , and a neutral @xmath5 singlet scalar @xmath8 with @xmath9 charge under the @xmath7 symmetry to the sm fields .
we assume that the sm - like higgs @xmath10 and @xmath8 have respectively vacuum expectation value ( vev ) ; @xmath11 and @xmath12 .
the relevant lagrangian for yukawa sector and scalar potential under these assignments are given by @xmath13\nonumber\\    & &    + \lambda_{\phi\varphi }   |\phi|^2 |\varphi|^2 + \lambda_{\eta\varphi } | \eta|^2 |\varphi|^2 , \label{hp}\end{aligned}\ ] ] where mass terms are forbidden by the conformal symmetry , @xmath14 , and the first term of @xmath15 can generates the ( diagonalized ) charged - lepton masses . without loss of generality , we here work on the basis that the third term of @xmath15 is diagonalized and of @xmath16 is real and positive .
we discuss the symmetry breakings in our model .
we assume the classically conformal symmetry and the ew symmetry breaking does nt occur by negative mass parameter .
the symmetry breaking is occurred by radiatively@xcite .
we assume the following conditions at the planck scale for simplicity , @xmath17 under this assumption , these couplings are generated by quantum correction . as a result ,
the couplings are very small at low energy scale
. therefore we can consider the sm with inert doublet sector and the b@xmath0l sector separately .
the coleman - weinberg condition is the following , @xmath18 \right ) .
\label{cwcon}\end{aligned}\ ] ] these running couplings should be satisfy this condition at the symmetry breaking scale(@xmath19 ) .
the @xmath10 mass can be obtained by the following form , @xmath20 this mass should be positive for the stable vacuum .
it suggests @xmath21 is negative at the b@xmath0l symmetry breaking scale .
once the b@xmath0l symmetry is broken , all mass terms are generated through the b@xmath0l breaking scale .
the sm higgs doublet mass is generated through the mixing term between the sm higgs and b@xmath0l breaking scalar in the potential .
the effective tree - level mass squared is induced .
if @xmath22 is negative , the ew symmetry breaking occurs as usual in the sm . under our assumption(@xmath23 ) , @xmath22 becomes negative at the b@xmath0l breaking scale because of positive rge . inserting the tadpole condition , @xmath24 ,
the sm higgs mass is given by @xmath25    @xmath3 is the inert doublet and the mass of @xmath3 should be positive . in our model ,
@xmath3 mass is generated by the mixing between @xmath3 and @xmath8 .
consequently , the mixing should be positive at the symmetry breaking scale , @xmath26 and the quartic couplings satisfy the following inert conditions@xcite , @xmath27      the neutrino mass matrix can be obtained at one - loop level as follows  @xcite : @xmath28,\end{aligned}\ ] ] where @xmath29 . in this form ,
observed neutrino mass differences and their mixings are obtained  @xcite , when the mixing matrix of the charged - lepton is diagonal basis .
@xmath30 can generally be written as @xmath31 where @xmath32 is the mns matrix , @xmath33 s are neutrino masses , @xmath34 is an complex orthogonal matrix and @xmath35 is the following diagonal matrix , @xmath36 we use this formula .
we assume the lightest neutrino mass is zero and the neutrino mass spectrum is normal hierarchy . in this case , the complex orthogonal matrix @xmath34 can be written as @xmath37 where @xmath38 is complex parameter .
we numerically solve the rges and find parameters that satisfy the inert conditions , eq .
( [ inert1 ] ) , ( [ inert2 ] ) .
we use the following parameters at the planck scale , @xmath39     axis . ]
l higgs and doublets . ]    the fig .
[ rge1 ] is the running for quartic couplings . in this figure
, @xmath21 becomes negative and satisfies coleman - weinberg condition ( eq .
( [ cwcon ] ) ) at @xmath4010.9 tev . at that scale , other couplings
satisfy inert conditions .
the fig .
[ rge2 ] is the running for mixings between b@xmath0l higgs and doublets . in this case
, z mass is 3.7 tev .
the experimental search for the z boson at lhc gives the limit on z boson mass , @xmath41 tev @xcite .
we have investigated a classically conformal radiative seesaw model with gauged b@xmath0l symmetry , in which we have successfully obtained the b@xmath0l symmetry breaking through the coleman - weinberg mechanism . as a result ,
majorana mass term is generated and ew symmetry breaking occurs . we have also shown some allowed parameters to satisfy several constraints such as inert conditions , coleman - weinberg condition , the current bound on the @xmath42 mass at lhc , and so on as well as the neutrino oscillations experiments .
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we discuss a classically conformal radiative seesaw model with gauged b@xmath0l symmetry , in which the b@xmath0l symmetry breaking can occur through the coleman - weinberg mechanism . as a result , all mass terms are generated and ew symmetry breaking also occurs . 
 we show some allowed parameters to satisfy several theoretical constraints .