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the discovery of the higgs boson at the large hadron collider ( lhc ) @xcite completes not only the standard model ( sm ) of particle physics , but gives also new constraints on any extension of it . the most studied extension of the sm to date is supersymmetry ( susy ) , see ref . @xcite and references therein . however , the minimal - supersymmetric standard model ( mssm ) is facing increasing pressure over the last few years . one of the reasons is the measured higgs mass of 125  gev which is not trivial to accommodate in the mssm . the tree - level mass of the higgs has the strict upper limit @xmath0 , and one therefore needs large radiative corrections to push the mass to the required value . the two main possibilities within the mssm are either heavy stops , and/or a large mixing among them . the first option raises immediately the question about naturalness @xcite , while the second one can cause charge and colour breaking minima @xcite . + for these reasons the interest in non - minimal susy models has increased in the last years . a widely studied approach to soften the need for large radiative corrections to the higgs mass is to increase the mass already at tree - level . this is done for instance in different singlet extensions via @xmath1-terms @xcite . the other option is to use @xmath2-terms @xcite . + the simplest realisations of these ideas show the expected decoupling behaviour : as soon as the new sector responsible for the enhanced tree - level mass becomes heavy , the positive effect of the higgs mass shrinks . however , it has been shown that this decoupling can be circumvented at the price of introducing large soft - breaking masses . indeed , valid models with non - decoupling @xmath1- @xcite or @xmath2-terms @xcite have been successfully constructed . + we will consider in this letter the case of non - decoupling @xmath2-terms via a new abelian gauge group @xmath3 . so far , only the leading order effect on the higgs mass was studied in this scenario : the impact of the non - decoupling @xmath2-terms at tree - level in the case of vanishing gauge kinetic mixing was considered . we will show that ( i ) radiative corrections and ( ii ) the presence of gauge - kinetic mixing can give important corrections to this approximation . + this letter is organised as follows : in [ sec : gkm ] a short excursion into gauge kinetic mixing in supersymmetric models is given , before in [ sec : model ] the origin of both effects in a concrete model is described . the impact on the higgs mass is analysed numerically in [ sec : numerics ] , before we summarise in [ sec : summary ] . if more than one abelian gauge group is present , mixing terms between the field strength tensors of the groups are allowed by gauge and lorentz invariance @xcite : @xmath4 here , @xmath5 are the field strength tensors of two different abelian groups @xmath6 , @xmath7 and @xmath8 is in general an @xmath9 matrix if @xmath10 abelian groups are present . for practical applications it is often useful to bring the propagators of the vector bosons back into their canonical form by the redefinition @xcite @xmath11 the trade - off for this redefinition is a change in the covariant derivative : @xmath12 where @xmath13 is the original diagonal matrix of @xmath10 individual gauge couplings associated to the @xmath10 abelian gauge factors , and @xmath14 is the vector of the relevant @xmath15 charges . thus , the @xmath16 factor can be translated into a new set of @xmath17 `` effective '' gauge couplings whose combinations populate off - diagonal entries of a gauge - coupling matrix @xmath18 in supersymmetric models , gauge kinetic mixing appears not only for the vector bosons , but also for both , the @xmath2-terms and the gaugino soft - breaking terms . of particular importance in the following are the new @xmath2-terms which read for the abelian sector @xmath19 while the non - abelian @xmath2-terms remain unchanged . + for the special case of two abelian gauge groups , the most general form of @xmath20 reads @xmath21 in general , one has the freedom to perform a change in basis to bring @xmath20 into a particular form . the most commonly considered cases are the symmetric basis with @xmath22 and the triangle basis with @xmath23 , @xmath24 . the triangle basis has the advantage that the new scalars do not contribute to the electroweak vev , and the entire impact of gauge kinetic mixing is encoded in one new coupling @xmath25 . the relations between @xmath26 ( @xmath27 ) and the physical couplings called @xmath28 , @xmath29 , @xmath25 are given by @xcite @xmath30 in order to show the impact of loop corrections and gauge kinetic mixing on the higgs mass in the presence of non - decoupling @xmath2-terms , we take a model inspired by ref . @xcite as example charges of the new fields to allow for a seesaw type - i via the term @xmath31 . in this model , the particle content of the mssm is extended by a gauge singlet superfield @xmath32 , a superfield for the right - handed neutrino and two fields @xmath33,@xmath34 responsible for the breaking of @xmath3 . it has also been shown that this model , when extended in addition by three generations of vector - like leptons and quarks , provides an attractive explanation for the diphoton excess observed at 750  gev by atlas and cms @xcite . .charges of the superfields under @xmath3 . the superfields in addition to the mssm particle content are singlets under the sm gauge group . [ cols="^,^,^,^,^,^,^,^,^,^,^,^",options="header " , ]     the @xmath3 charges of all superfields are summarised in [ tab : u1xmssmparticles ] , while the most general superpotential in agreement with all global and local symmetries is given by @xmath35 for simplicity , we will neglect in the following @xmath36 , @xmath37 , and @xmath8 as well as their soft - breaking terms . in addition , the soft - breaking term of @xmath38 can always be shifted away . the relevant soft - breaking terms in the scalar sector are @xmath39 with @xmath40 . + electroweak symmetry breaking and the breaking of @xmath3 are triggered by the following scalars receiving vacuum expectation values ( vevs ) @xmath41 in addition , a vev for the scalar singlet is induced in general @xmath42 we define @xmath43 , @xmath44 as well as @xmath45 , and @xmath46 . one can use the five tadpole equations @xmath47 to eliminate five free parameters . we are doing this in the following for @xmath48 , @xmath49 , @xmath50 , @xmath51 and @xmath38 . thus , the remaining free parameters in the scalar sector are @xmath52 , @xmath53 , @xmath54 , @xmath36 , @xmath55 and the vevs . in all numerical studies we are going to fix @xmath56  tev , and @xmath57 . the neutral higgs mass matrix can be written in the basis @xmath58 as @xmath59 with the abbreviations @xmath60 and @xmath61 , @xmath62 . we have used the relations @xmath63 , @xmath64,@xmath65 , @xmath66 , and took the limit @xmath67 , @xmath68 . the lightest eigenstate of the @xmath69 sub - system is approximated by @xmath70 here , we made use of @xmath71 and assumed @xmath72 . in addition , we replaced @xmath73 as well as @xmath74 for clarity by the full expressions . we find the expected limits    * @xmath75 : @xmath76 * @xmath77 : @xmath78    thus , we have the desired @xmath2-term enhancement for very large soft - terms , which is , however , modified by the presence of the off - diagonal gauge coupling @xmath79 . as long as @xmath79 is small , the impact of gauge kinetic mixing will be negligible . thus , as long as @xmath79 is treated as free parameter , it can be set to zero at a given scale . however , via renormalisation group effects ( rge ) it will be induced radiatively if the two abelian gauge groups are not orthogonal . orthogonality in this respect means that the anomalous dimension matrix defined by @xmath80 is diagonal . here , @xmath81 and @xmath82 run over all @xmath15 groups and the trace runs over all superfields charged under the corresponding group . in many commonly studied @xmath15 extension as @xmath83 , @xmath84 is not diagonal @xcite . even if the two abelian groups can be embedded in a singlet gut group , gauge kinetic mixing might appear for the remaining _ light _ degrees of freedom @xcite . calculating the anomalous dimension matrix for the model under consideration , one finds large off - diagonal entries @xmath85 where @xmath86 is a diagonal matrix containing the gut normalisation . since we do nt assume any gut embedding here , we use @xmath87 in the following . at the one - loop level one can calculate the value of @xmath25 at the susy scale as function of ( i ) the scale @xmath88 where @xmath79 is assumed to vanish and ( ii ) the value for @xmath29 at this scale . the running of the gauge coupling matrix @xmath20 at one - loop is given by @xcite @xmath89 one has to ensure to bring @xmath20 to the particular basis defined in eq . ( [ eq : basis ] ) after the running . the result is shown in [ fig : gkm ] .     at 1  tev as function of the scale @xmath88 where gauge kinetic mixing vanishes and @xmath29 at the scale . ] one finds that @xmath25 is in general negative , and only for a very low cut - off @xmath88 is the new coupling @xmath79 is much smaller than @xmath29 . for @xmath90  gev and large @xmath29 , @xmath91 can already be as large as 0.1 , while for a gut motivated scenario with @xmath92 and @xmath93 , @xmath79 can even be as large as 0.40.5@xmath94 . are considered , it can be wrong to neglect gauge - kinetic mixing . although the impact on the higgs mass might not be important , crucial effects for instance concerning @xmath95 searches @xcite or dark matter properties @xcite could be missed . ] for completeness , we want to mention that the possibility of positive ratios @xmath96 exists : this can appear for very large , but negative values of @xmath29 at the scale @xmath88 .      because of the non - vanishing charge of the higgs doublets under the new gauge group , many additional radiative contributions to the higgs mass arise already at one - loop . the feynman diagrams with possible contributions proportional to @xmath29 are depicted in [ fig : diagrams ] . since the right - sfermions carry also a @xmath97 charge , they give also non - vanishing diagrams at one - loop . however , it can be shown that the tadpole and self - energy corrections cancel exactly for them . proportional to @xmath98 . the scalar contributions are summarised by @xmath99 , but for the case where only pseudo - scalars ( @xmath100 ) can appear . @xmath101 label the generations in the loop . ] the loop corrected scalar masses are the eigenvalues of the radiatively corrected mass matrix @xmath102 given by @xmath103 where @xmath104 is the sum of tadpole- and self - energy contributions . the pole masses @xmath105 are then associated with the eigenvalues of @xmath106 . + for the calculation of the diagrams it is necessary to diagonalise the mass matrices of the particles in the loop , which have dimensions up to @xmath107 . thus , most contributions can only be calculated numerically . only for the charged higgs contribution we can find an analytical estimate for the impact on the sm - like higgs mass which is mainly given by the change in the ( 2,2)-element of @xmath108 : @xmath109 @xmath110 is the renormalisation scale and we used the limit @xmath111 . in order to give an impression of the importance of all other loop corrections , we group all diagrams into four sets : ( i ) diagrams involving only neutralinos ( @xmath112 ) , ( ii ) diagrams involving only neutral cp - even scalars ( @xmath113 ) , ( iii ) diagrams involving only charged higgs scalars ( @xmath114 ) , ( iv ) diagrams with cp - odd scalars , the new gauge boson and the corresponding ghost ( @xmath100 , @xmath95 , @xmath115 ) . one has to consider the fields in the last group together , in order to have a gauge invariant set of diagrams . in [ fig : pis ] we show the values of the corrections to the ( 2,2)-element of the higgs mass matrix as function of @xmath29 for the case of vanishing kinetic mixing , @xmath116  tev and @xmath117  tev .     as function of @xmath29 for the diagrams involving only ( i ) neutralinos ( green , dot - dashed ) , ( ii ) cp - even scalars ( blue , dashed ) , ( iii ) charged higgs ( orange , dotted ) , ( iv ) cp - odd scalars , @xmath95 and its ghost ( red , full ) . ] one can see that the main loop corrections come from the charged and cp - even scalar sector . since both are negative , one can expect that the new loop corrections reduce the sm - like higgs mass , i.e. they might compensate to some extent the positive effect at tree - level . the corrections stemming from neutralinos are comparable small , while the ones involving the @xmath95 , its goldstone boson and its ghost are even smaller . there is also an indirect effect of the extended gauge sector on the mssm - like corrections to the higgs mass : the new force changes the relation between the measured sm parameters and the running @xmath118values which enter the loop calculations . the most important parameter in this respect is the top yukawa coupling @xmath119 . as it can be seen from [ fig : yt ] , the change in the running coupling @xmath120 is only very small when turning up @xmath29 . thus , the change in the loop corrections is only very tiny .     at the susy scale @xmath121  tev as function of @xmath29 . the red , dashed line is for @xmath122  tev and the blue , full line for @xmath123  tev . ] we turn now to the discussion of the impact on the sm - like higgs mass of the two effects described in the last section . for this purpose , we make use of the spheno@xcite output of sarah@xcite . the sarahgenerated fortrancode provides a fully fledged spectrum generator for the model which enables a calculation of the entire mass spectrum at the one - loop level without any approximation : any loop contribution and the full momentum dependence is included . in principle , sphenoincludes also new two - loop corrections for the model under consideration @xcite . however , these are so far only available in the gaugeless limit , i.e. the corrections we are mainly interested in are not covered . + we show in [ fig : gxgtmh ] the shifts of the sm - like higgs mass at tree - level and at the one - loop level for @xmath124  tev in the @xmath125-plane compared to the case @xmath126 . one sees that the enhancement in the higgs mass when including loop effects and/or gauge - kinetic mixing is always smaller than the push at tree - level when neglecting these effects . assuming a fixed ratio @xmath127 , gauge kinetic mixing becomes more important for larger @xmath29 . in contrast the ( relative ) impact of the loop corrections has only a mild dependence on the considered value of @xmath29 . this can be seen in [ fig : rel_t_l ] where the shifts @xmath128 and @xmath129 defined by @xmath130 are shown as function of @xmath29 and for different combinations of @xmath131 and @xmath54 .     as defined in [ eq : d1,eq : d2 ] as function of @xmath29 . here , we put @xmath132 and assumed @xmath133  tev [ red , dashed],@xmath134  tev [ orange , dot - dotted],@xmath135  tev [ blue , dotted],@xmath136  tev [ green , full ] . ] one finds , that the loop effects always reduce the overall enhancement of the higgs mass by 2530% . the radiative corrections are usually more important for small @xmath29 , but also depend to some extent on the hierarchy between @xmath131 and @xmath54 : for larger @xmath54 , which corresponds to a large enhancement at tree - level , the relative importance of the loops decreases faster with increasing @xmath29 . we have revisited here the possibility to push the tree - level mass of the sm - like higgs by non - decoupling @xmath2-terms . it has been shown that a pure study at tree - level can overestimate the positive effect on the higgs mass significantly . namely , new radiative corrections triggered by the extended gauge sector can reduce the higgs mass by several gev . in addition , it has been shown that gauge kinetic mixing , which is a natural effect if the new abelian gauge group is not orthogonal to @xmath137 , reduces the positive shift of the higgs mass at tree - 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non - decoupling d - terms are an attractive possibility to enhance the tree - level mass of the standard model like higgs boson in supersymmetric models . 
 we discuss here for the case of a new abelian gauge group two effects usually neglected in literature : ( i ) the size of the additional radiative corrections to the higgs mass due to the presence of the new gauge coupling , and ( ii ) the impact of gauge kinetic mixing . 
 it is shown that both effects reduce to some extent the positive effect of the non - decoupling d - terms on the higgs mass . 
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