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the discovery of the higgs boson at atlas and cms experiments @xcite made a revolutionary impact on the field of particle physics . it not only confirmed the so - called higgs mechanism for the electroweak symmetry breaking , but also opened a new possibility to perform a precise test of the standard model ( sm ) by studying the properties of the higgs boson . in the sm , the coupling constants of the higgs boson with other particles are well understood using the fact that the masses of quarks , leptons , and weak bosons originate in the vacuum expectation value ( vev ) of the higgs field , resulting in the prediction of the partial decay widths of the higgs boson into various particles .    in models with physics beyond the sm ( bsm ) , measurements of the higgs couplings provide even exciting possibilities . in large class of bsm models , there exist new particles at the electroweak to tev scale , which affect the properties of the higgs boson . thus , with the detailed study of the higgs properties at collider experiments , we have a chance to observe a signal of bsm physics . such a study will be one of the major subjects in forthcoming collider experiments , i.e. , the lhc and future @xmath1 colliders like ilc and tlep @xcite . low energy supersymmetry ( susy ) is a well - motivated candidate of bsm physics . compared to the sm , the particle content is enlarged in susy models . even in the minimal setup , i.e. , in the minimal susy sm ( mssm ) , there exist two higgs doublets , @xmath8 and @xmath9 , as well as superparticles . the lightest higgs boson @xmath10 , which plays the role of the `` higgs boson '' discovered by atlas and cms , is a linear combination of the neutral components of @xmath8 and @xmath9 , while there exist other heavier higgses . in the case where the mass scales of the heavier higgses and the superparticles are high enough , the properties of @xmath10 are close to those of the sm higgs boson . on the contrary , if the heavier higgses or superparticles are relatively light , deviations of the higgs properties from the sm predictions may be observed by future collider experiments . with the precise measurement of the partial decay widths ( or branching ratios ) of the higgs boson , information about the heavy higgses and/or superparticles may be obtained even if those heavy particles can not be directly discovered .    in this paper , we discuss how low the mass scales of the heavier higgs bosons and superparticles should be to observe a deviation . we evaluate the partial decay widths of the lightest higgs boson in the mssm , taking account of the following phenomenological constraints : higgs mass , flavor constraints of the @xmath11 mesons , stability of the electroweak ( sm - like ) vacuum against the transition to charge and color breaking ( ccb ) vacua , and perturbativity of coupling constants up to a high scale . these constraints exclude large fraction of the parameter region giving rise to a significant deviation . even so , we will see that the deviations of the partial widths from the sm predictions can be of @xmath12 for some of the decay modes in the parameter region allowed by the above - mentioned constraints . in particular , the deviations may be large enough to be observed by future future @xmath1 colliders like ilc and tlep even if superparticles are so heavy that they would not be observed at the lhc . the organization of this paper is as follows . in sec . [ sec : mssm ] , we briefly overview the properties of the higgs bosons in the mssm . we also summarize the phenomenological constraints that are taken into account in our analysis . then , in sec .  [ sec : width ] , we calculate the partial decay widths of the lightest higgs boson in the mssm and discuss how large the deviation from the sm prediction can be . [ sec : discussion ] is devoted for conclusions and discussion . we review some of the important properties of the higgs sector in the mssm . there are two higgs doublets , @xmath8 and @xmath9 . as the neutral components acquire vevs , the electroweak symmetry breaking ( ewsb ) occurs . the ratio of the two higgs vevs is parameterized by @xmath13 . assuming no cp violation in the higgs potential , the mass eigenstates are classified as lighter and heavier cp - even higgs bosons ( denoted as @xmath10 and @xmath14 , respectively ) , cp - odd ( pseudo - scalar ) higgs @xmath15 , and charged higgs @xmath16 . in the following , we concentrate on the case where the masses of the heavier higgses ( @xmath14 , @xmath15 , and @xmath16 ) are much larger than the electroweak scale . then , the lightest higgs boson @xmath10 should be identified as the one observed by the lhc . on the other hand , the masses of the heavier higgses are almost degenerate . we parameterize the heavier higgs masses using the pseudo - scalar mass @xmath17 .    at the tree level , the lightest higgs mass is predicted to be smaller than the @xmath18-boson mass , while it is significantly pushed up by radiative corrections @xcite . the mass matrix of the neutral cp - even higgs bosons is denoted as @xmath19 where @xmath20 represents radiative corrections .    at the one - loop level , the top - stop contribution dominates the radiative correction to the lightest higgs mass , and is approximated as @xmath21,\end{aligned}\ ] ] where @xmath22 is the sm higgs vev , @xmath23 is the top - quark mass , @xmath24 ( with @xmath25 and @xmath26 being the lighter and heavier stop masses , respectively ) , and @xmath27 ( with @xmath28 and @xmath29 being the tri - linear scalar couplings for stop and the susy invariant higgsino mass parameter , respectively ) . in this paper , we adopt the convention of the slha format @xcite . the top - stop contribution can significantly enhance the lightest higgs mass . on the other hand , the bottom - sbottom contribution to the lightest higgs mass becomes sizable when the bottom yukawa coupling is large . it is likely to decrease the lightest higgs mass . when stop masses are @xmath30 , there are up to four solutions for @xmath28 to satisfy the observed value of the higgs mass @xmath31 , for which we use @xmath32 @xcite . let us call these four solutions as    * ns : negative @xmath28 with smaller @xmath33 , * nl : negative @xmath28 with larger @xmath33 , * ps : positive @xmath28 with smaller @xmath33 , * pl : positive @xmath28 with larger @xmath33 . assuming universal sfermion masses at the susy scale , the value of @xmath33 is typically a few times larger than the stop mass for nl and pl cases . such a large value of @xmath33 has significant phenomenological implications , as we will discuss in the next section . since the one - loop correction to the higgs mass is comparable to the tree - level value , higher order corrections are necessary to obtain reliable results . in particular , qcd correction , which appears at the two - loop level , and a large hierarchy between the susy scale and the electroweak scale require the resummation of the leading and sub - leading logarithms . we use feynhiggs 2.10.2 @xcite for the precise evaluation of the higgs masses ( as well as the mixing parameters and the partial decay widths of @xmath10 ) .    at the tree level , @xmath8 ( @xmath9 ) couples only to up - type quarks ( down - type quarks as well as leptons ) . however , this is not the case once radiative corrections due to superparticles are taken into account . the higgs couplings to bottom quark and tau lepton can be subject to sizable corrections even when susy breaking scale is very large . let us parameterize the effective @xmath34 and @xmath35 vertices including radiative corrections as @xcite @xmath36 where @xmath37 , @xmath38 , and @xmath39 are right - handed bottom , right - handed top , and third - generation quark - doublets , respectively . in addition , @xmath40 , @xmath41 and @xmath42 are @xmath43 indices , while the color indices are omitted for simplicity . here , @xmath44 and @xmath45 are non - holomorphic radiative corrections to the yukawa coupling constants . for a detailed treatment of the non - holomorphic corrections , see refs .  @xcite . after the electroweak symmetry breaking , the yukawa couplings are related to the quark masses as these relations hold at the susy breaking scale . thus , the quark masses and yukawa couplings in the formula should be understood as the running parameters at the scale . @xmath46 where , at the leading order in the mass - insertion approximation , @xmath47 is given by @xmath48 \tan\beta    , \\ \delta_t & \simeq    \left [      \frac{2\alpha_s}{3\pi } m_3 \mu\ , i(m_{\tilde t_1}^2,m_{\tilde t_2}^2,m_3 ^ 2 )      + \frac{y_b^2}{16\pi^2 } \mu a_b\ , i(m_{\tilde b_1}^2,m_{\tilde b_2}^2,\mu^2 )    \right ] \cot\beta,\end{aligned}\ ] ] with @xmath49 being the gluino mass . the loop integral is defined as @xmath50 notice that @xmath51 is enhanced when @xmath52 is large , while @xmath53 is suppressed by @xmath54 . the mass eigenstates of the higgs bosons are given by linear combinations of @xmath8 and @xmath9 . the cp - even parts of their neutral components are related to the mass eigenstates as @xmath55 the mixing angle @xmath56 depends on the pseudo - scalar mass @xmath17 , and shows a decoupling behaviour , i.e. , @xmath57 as @xmath58 . in this limit , @xmath10 behaves as the sm higgs boson . using eq . , we obtain @xcite @xmath59 in fig .  [ fig : cosba ] , we show the behavior of @xmath60 as a function of @xmath17 with the masses of superparticles being fixed . here , all the sfermion mass parameters , @xmath61 , @xmath62 , @xmath63 , @xmath64 , and @xmath65 , are taken to be universal at the susy scale @xmath66 , where these mass parameters are soft susy breaking masses of sfermions with gauge quantum numbers of @xmath67 , @xmath68 , @xmath69 , @xmath70 , and @xmath71 , respectively , with the numbers in the parenthesis being quantum numbers for @xmath72 , @xmath43 , and @xmath73 . throughout our study , we take @xmath74 . in addition , the sfermion masses are assumed to be universal in generation indices . we can see that radiative corrections can enhance @xmath60 by an order of magnitude when @xmath28 is large , while it is comparable to the tree - level value with the smaller @xmath33 solutions . is plotted as a function of @xmath17 with @xmath75 , @xmath76 , and the approximate gut relation among gaugino masses ( see eq .  ) . all the sfermion masses are assumed to be universal at @xmath66 , and are also taken to be @xmath77 . the red and blue lines correspond to the cases of the pl and ps solutions of @xmath28 , respectively . the black dashed line is the tree - level value . ]    denoting @xmath78 coupling ( with @xmath79 being the sm fermions ) as @xmath80 we obtain the @xmath34 coupling constant as @xmath81    g_{h\bar{b}b}^{\rm ( sm ) } ,    \label{g_hbb}\end{aligned}\ ] ] where the superscript `` ( sm ) '' is used for the sm prediction . when @xmath17 is relatively large , @xmath82 is almost unity , while the second term proportional to @xmath60 induces a sizable deviation from the sm value . similar relation holds for @xmath83 vertex , and @xmath84 is approximately given by @xmath85 with @xmath86 being the wino mass . quantitatively , @xmath84 is smaller than @xmath51 in the parameter space of our study . as we will see later , @xmath87 and @xmath88 may show sizable deviations from the sm predictions even if @xmath17 is above tev . the @xmath35 coupling constant is obtained as @xmath89    g_{h\bar{t}t}^{\rm ( sm)}.    \label{g_htt}\end{aligned}\ ] ] the deviation from the sm value mainly comes from the second term in the bracket and is not enhanced by @xmath52 , since @xmath53 is proportional to @xmath54 . the gauge - boson final states are also important . in order to calculate the partial decay widths of the higgs to gauge bosons , we have modified feynhiggs 2.10.2 package to properly take account of the effect of non - holomorphic correction to the higgs interaction . we use eq .   for the @xmath34 coupling to calculate the partial decay widths of @xmath90 , @xmath91 and @xmath92 . we found that the factor of @xmath93 was missing in feynhiggs 2.10.2 package ( see eq .  ) . we have also modified the package to take the @xmath94 approximation  @xcite for calculating the partial widths , in which the renormalization scale of the higgs wave functions is set to be @xmath95 , and the effects of radiative corrections are included in the mixing between the light and heavy higgs bosons . then , as we will see below , the partial decay widths show proper decoupling behavior in the large @xmath17 limit . in particular , the partial width @xmath96 converges to the sm value in the limit of large @xmath17 and squark masses . this behavior looks inconsistent with the result shown in ref . the processes induced by triangle loops , @xmath97 and @xmath98 , have been important for the higgs discovery at the lhc . they are also important in studying new particles that couple to the higgs boson . in susy models , the stop and sbottom loops contribute to the @xmath99 coupling . it is expressed by an approximate formula ( cf . @xcite ) @xmath100 up to @xmath101-term and bottom - loop contributions . here , @xmath102 . in the right - hand side , the first term comes from the top loop , while the second term is given by the stop and sbottom loops . the correction is positive in the non - mixing limit ( i.e. , @xmath103 ) , whereas it becomes negative when the mixing terms are sizable . we also note here that @xmath104 couplings ( with @xmath105 and @xmath106 ) are approximately given by @xmath107 . this ratio is very close to unity , and hence the deviations in these modes are very small .      before discussing the possibility of observing a deviation of the higgs partial widths from the sm prediction at future colliders , we summarize phenomenological constraints on the mssm parameter space which are adopted in our analysis .      in the sm , the flavor - changing decay , @xmath108 , proceeds by virtual exchanges of the @xmath18 and @xmath109 bosons . they are suppressed by the final - state helicity . in contrast , susy contributions can be enhanced considerably by large @xmath52 , when virtual exchanges of the heavy higgs boson contribute to the decay @xcite . the branching ratio is expressed as @xcite @xmath110,\end{aligned}\ ] ] where @xmath111 is the fermi constant , @xmath112 is the @xmath113-meson mass , @xmath114 is the decay constant of @xmath113 , @xmath115 is the muon mass , @xmath116 is the lifetime of @xmath113 , and @xmath117 is cabbino - kobayashi - maskawa matrix element . in the above expression , @xmath118 , @xmath119 and @xmath120 are the wilson coefficients of the effective operators , @xmath121 , @xmath122 , and @xmath123 , respectively , while @xmath124 are obtained by flipping chiralities , @xmath125 . among them , the sm contribution appears only in @xmath118 . including higher order contributions and taking account of effects of the @xmath126 oscillation , the sm prediction becomes @xcite @xmath127 this can be compared with the lhcb measurements @xcite @xmath128 defining @xmath129 , where the first term in the right - hand side includes both the susy and sm contributions , the 95% c.l .  bound is estimated as @xmath130 we will adopt this constraint in our numerical analysis .    even when superparticles are heavy , they affect the branching ratio through non - holomorphic contributions to the heavy higgs couplings . including radiative corrections and diagonalizing the quark mass matrices , effective couplings of the heavy higgs bosons to the down - type fermions become @xcite @xmath131 where @xmath132 . the flavor - changing coupling is induced by @xmath133 as @xmath134 here , soft scalar masses are assumed to be universal in generation , and @xmath135 is obtained by substituting @xmath136 in eq .  . then , the wilson coefficients receive higgs - mediated contributions , @xmath137 where @xmath138 is the bottom - quark mass , @xmath139 is the weinberg angle , and @xmath140 . the non - holomorphic correction @xmath133 as well as @xmath51 does not decouple even for very heavy superparticles . we will see later that the corrections to @xmath141 can be sizable and that the constraint excludes some part of the parameter space of our interest . the branching ratio of the inclusive decay of @xmath142 may also be sensitive to the non - decoupling contributions to the ( charged ) higgs boson . in the numerical analysis , defining @xmath143 , we adopt the 95% c.l . bound , @xmath144 where the experimental value @xmath145 @xcite and the sm prediction @xmath146 @xcite are combined . at the current accuracies , @xmath147 imposes more stringent bound on the parameter space than @xmath142 except when superparticles are light .    in the numerical analysis , superiso 3.4 @xcite is used for evaluating the susy contributions to the branching ratios as well as the sm predictions . in our analysis , we assume that the squark masses are universal in generations . if the squark masses are non - universal , there are extra contributions to @xmath133 , and the flavor constraints are affected ( see e.g. , ref . @xcite ) . such a non - universality is expected even in the model with the universal scalar masses at the gut scale . thus , it should be noted that the flavor constraints that we will show below are just for a particular choice of the squark - mass parameters and may change if the squark mass matrices have non - universal structures .      with sufficiently large @xmath33 , ccb vacua arise , and the minimum of the scalar potential with the correct ewsb becomes a false vacuum @xcite . when @xmath148 , stop and the up - type higgs fields acquire large vevs at the ccb vacua , while the vevs of other fields are relatively small . recently , the decay rate of the sm - like vacuum has been studied in detail for such a case @xcite . on the other hand , if @xmath29 is as large as the stop masses , the down - type higgs boson also has a large vev at the ccb vacua due to the tri - linear scalar coupling among stops and the down - type higgs , which is proportional to @xmath149 . the vacuum stability condition is important in such a case because significant deviations of the higgs partial widths from the sm prediction may occur . in order to study the sm - like vacuum stability , we consider the tree - level scalar potential in the field space involving @xmath150 , @xmath151 , @xmath152 and @xmath153 ( which are canonically normalized scalar fields embedded in the left - handed stop , right - handed stop , the up - type higgs and the down - type higgs , respectively ) .    the relevant part of the potential is given by @xmath154 where @xmath155    when the ccb vacua become deeper than the sm - like vacuum , the latter is not stable . the vacuum decay rate per unit volume is calculated in the semi - classical approximation , and is expressed as @xmath156 where @xmath157 is the euclidean action of the so - called bounce solution @xcite . for the decay of the sm - like vacuum , @xmath158 is estimated to be @xmath159 . in order for the lifetime of the sm - like vacuum to be longer than the present age of the universe , the euclidean action is required to satisfy @xmath160 in our numerical analysis , cosmotransition 2.0a1 @xcite is used to find the bounce solution in the four - dimensional field space parameterized by @xmath153 , @xmath152 , @xmath161 and @xmath162 , and to calculate the euclidean bounce action @xmath157 . the calculation is done at zero temperature , and therefore thermal effects are not taken into account . the model parameters such as the tri - linear and top yukawa couplings are evaluated at the susy scale @xmath66 .    in fig . [ fig : se ] we show the contours of constant @xmath157 for the ps and pl solutions on @xmath17 vs.  @xmath29 plane . here , @xmath163 , while sfermion masses , @xmath63 , @xmath64 and @xmath65 , are taken to be @xmath164 ( see sec . [ sec : width ] ) . in each plot , the region between the solid ( dashed ) green lines satisfies @xmath165 ( @xmath166 ) . for the ps solution , these lines appear only for @xmath167 . on the other hand , the upper bound on @xmath168 is comparable to the stop masses for the pl solution .     and @xmath169 on @xmath17 vs.  @xmath29 plane for the ps and pl solutions of @xmath28 . here , @xmath163 , @xmath170 , and @xmath171.,title="fig : " ]   and @xmath169 on @xmath17 vs.  @xmath29 plane for the ps and pl solutions of @xmath28 . here , @xmath163 , @xmath170 , and @xmath171.,title="fig : " ] +    the tree - level potential eq . is used for our numerical analysis . radiative corrections may change the scalar potential particularly around the sm - like vacuum . in order to study their effects , we also estimated the decay rate of the sm - like vacuum by including the top - stop and bottom - sbottom one - loop correction to the higgs potential . a better treatment would be to introduce full one - loop radiative corrections to the potential involving stop , sbottom and the higgs boson so that the potential is stable against the renormalization scale at least at the one - loop level . we found that the euclidean action tends to increase by about 10 20% for @xmath172 from that of the tree - level potential . in order to see the sensitivity of @xmath157 to @xmath29 , we show the contours of @xmath173 in the same plot .    when both @xmath29 and @xmath52 are large , we might have to consider other ccb vacua in the sbottom - higgs direction , which is driven by the tri - linear coupling of @xmath174 ( where @xmath175 and @xmath176 are left- and right - handed sbottoms , respectively ) ( cf . if both @xmath29 and @xmath177 are large , the bottom yukawa coupling can be enhanced not only by @xmath52 but also by @xmath178 ( see eq .  ) . however , when the squark masses are universal , such a parameter region is already excluded by the other constraints discussed in this section . therefore we do not consider the constraint coming from the ccb vacuum involving the sbottom sector in this paper . when @xmath52 is very large , the bottom yukawa coupling is sizable . we can impose an upper bound on @xmath52 by requiring perturbativity of the yukawa coupling constants up to , for instance , the gut scale . in the mssm , the bottom yukawa coupling constant @xmath179 is proportional to @xmath178 , and hence , @xmath179 is enhanced when @xmath51 is negative ( see eq .  ) . consequently , the bound on @xmath52 is more severe when @xmath180 .    in our numerical analysis , we estimate the bottom yukawa coupling constant using the following relation : in discussing the perturbative bound , we neglect holomorphic corrections to the yukawa coupling constant , which are orders - of - magnitude smaller than the tree - level value of the yukawa coupling constant for @xmath181 . @xmath182 then , we follow the evolutions of coupling constants by solving the renormalization group equations at the one - loop level and impose a condition that the bottom yukawa coupling is perturbative up to the grand unified theory ( gut ) scale @xmath183 . numerically , we require @xmath184 where we take @xmath185 . this constraint excludes a large @xmath52 region especially when @xmath186 . notice that @xmath51 is a non - decoupling parameter , and hence , this constraint is important even in the limit of heavy superparticles . in this section , we discuss the partial decay width of the lightest higgs boson @xmath10 . we define the ratio of the partial decay width of the lightest higgs boson to that of the sm prediction : @xmath187 where @xmath188 denotes a specific final state . in the following , we show how much @xmath189 can deviate from the sm prediction ( @xmath190 ) for various final states . as we have mentioned , feynhiggs 2.10.2 is used to calculate the partial decay widths of the higgs boson , in which full one - loop contributions are taken into account for the fermionic final states . in the package , a resummation of the @xmath51 corrections is also included in calculating the partial decay width for @xmath191 @xcite .    in our numerical calculation , we adopt ( approximate ) gut relation among the @xmath72 , @xmath43 , and @xmath73 gaugino masses : @xmath192 all the phases in the mssm parameters are assumed to be negligible , and we adopt the convention of @xmath193 . for simplicity , we also assume that the sfermion masses are universal with respect to the generation indices . ( left ) and @xmath194 ( right ) are shown as functions of @xmath195 ; here all the fermion masses , @xmath49 , and @xmath168 are equal to @xmath195 , and @xmath196 . ( the sign of @xmath29 is taken to be negative , while wino and bino masses are given by using the approximate gut relation . ) in the left ( right ) plot , the black , red , and blue lines correspond to @xmath197 ( @xmath198 ) , @xmath199 ( @xmath200 ) , and @xmath97 , respectively . the solid ( dashed ) lines correspond to the pl ( ps ) solutions of @xmath28 . note that the constraints in sec . [ sec : constraint ] are not taken into account . , title="fig : " ]   ( left ) and @xmath194 ( right ) are shown as functions of @xmath195 ; here all the fermion masses , @xmath49 , and @xmath168 are equal to @xmath195 , and @xmath196 . ( the sign of @xmath29 is taken to be negative , while wino and bino masses are given by using the approximate gut relation . ) in the left ( right ) plot , the black , red , and blue lines correspond to @xmath197 ( @xmath198 ) , @xmath199 ( @xmath200 ) , and @xmath97 , respectively . the solid ( dashed ) lines correspond to the pl ( ps ) solutions of @xmath28 . note that the constraints in sec . [ sec : constraint ] are not taken into account . , title="fig : " ]    first , we show the soft mass dependence of @xmath201 without taking the phenomenological constraints into account . in fig . [ fig : msoft ] , @xmath201 are shown for @xmath202 , @xmath203 , @xmath92 , @xmath198 , and @xmath200 as functions of @xmath195 , taking @xmath204 and @xmath196 . we have checked that @xmath205 holds in the parameter region of our study . by choosing negative @xmath29 with @xmath206 , the correction to the bottom yukawa coupling becomes significant . remarkably , even though @xmath195 is around several tev , the partial decay widths for @xmath207 , @xmath200 and @xmath92 deviate from the sm prediction by more than @xmath208% for the pl solution . however , susy contributions to the other widths are smaller . note that @xmath209 is as about twice as @xmath210 for the pl solution , which is due to the difference between @xmath51 and @xmath211 . we also note here that the partial decay widths have an appropriate decoupling behaviour , i.e. , @xmath212 as the masses of superparticles and the heavy higgs bosons become infinitely large . are shown for the ps , ns , pl , and nl solutions of @xmath28 . here , all the sfermion masses , @xmath49 , and @xmath168 are taken to be @xmath77 , and the sign of @xmath29 is set to be negative . the left regions of the blue lines are excluded by @xmath213 , while those of the green solid ( dashed ) lines are constrained by the vacuum stability condition , @xmath214 ( 360 ) . the bottom yukawa coupling becomes non - perturbative below the gut scale in the region above the red line.,title="fig : " ]   are shown for the ps , ns , pl , and nl solutions of @xmath28 . here , all the sfermion masses , @xmath49 , and @xmath168 are taken to be @xmath77 , and the sign of @xmath29 is set to be negative . the left regions of the blue lines are excluded by @xmath213 , while those of the green solid ( dashed ) lines are constrained by the vacuum stability condition , @xmath214 ( 360 ) . the bottom yukawa coupling becomes non - perturbative below the gut scale in the region above the red line.,title="fig : " ] +   are shown for the ps , ns , pl , and nl solutions of @xmath28 . here , all the sfermion masses , @xmath49 , and @xmath168 are taken to be @xmath77 , and the sign of @xmath29 is set to be negative . the left regions of the blue lines are excluded by @xmath213 , while those of the green solid ( dashed ) lines are constrained by the vacuum stability condition , @xmath214 ( 360 ) . the bottom yukawa coupling becomes non - perturbative below the gut scale in the region above the red line.,title="fig : " ]   are shown for the ps , ns , pl , and nl solutions of @xmath28 . here , all the sfermion masses , @xmath49 , and @xmath168 are taken to be @xmath77 , and the sign of @xmath29 is set to be negative . the left regions of the blue lines are excluded by @xmath213 , while those of the green solid ( dashed ) lines are constrained by the vacuum stability condition , @xmath214 ( 360 ) . the bottom yukawa coupling becomes non - perturbative below the gut scale in the region above the red line.,title="fig : " ]    next , let us include the phenomenological constraints discussed in sec . [ sec : constraint ] . in fig . [ fig : matanb ] , contours of @xmath209 are shown on @xmath17 vs.  @xmath52 plane . here , all the sfermion masses , @xmath49 , and @xmath168 are set to be @xmath77 . in the cases of the ps and pl solutions , the contours end at around @xmath215 . this is because , when @xmath52 is large , there is no solution for @xmath28 to satisfy @xmath32 . the bottom - sbottom loop contribution interferes destructively with the top - stop contribution , and thus , larger ( smaller ) @xmath28 is required for the ps ( pl ) solution . then , @xmath216 and @xmath217 merge into a single solution at certain @xmath52 , which is the value where the top - stop contributions can not raise the higgs mass anymore for fixed @xmath195 . note that , @xmath51 is negative when @xmath218 and @xmath219 . in such a case , @xmath179 is significantly larger than the tree - level value , and thus , the bottom - sbottom loop contributions are enhanced .    in fig . [ fig : matanb ] , the constraints from @xmath220 , the vacuum stability , and the perturbativity of the bottom yukawa couplings are shown . wide parameter region is excluded when @xmath28 is large , i.e. , in the pl and nl panels . the constraints from @xmath141 and the vacuum stability become weaker for large @xmath17 , while that from the perturbativity is not . for the pl solution , the constraints from @xmath141 and the vacuum stability change drastically as we vary @xmath52 for @xmath221 , where the bottom yukawa coupling is much larger than the tree - level value . .expected accuracies of the determinations of the partial decay widths of the higgs boson in units of percents @xcite . the accuracies of the widths are assumed to be twice the accuracies of the determinations of couplings . [ cols="<,^,^,^,^,^,^,^,^ " , ] even if the masses of superparticles are relatively large ( i.e. , @xmath77 ) , @xmath209 can be as large as @xmath208% . such a large deviation may be within the reach of future collider experiments . expected accuracies at the future experiments have been discussed ( see table 1 - 16 of ref . @xcite and ref . @xcite ) ; the numbers are summarized in table  [ table : experiments ] . the accuracies of @xmath222 , @xmath223 , and @xmath224 are claimed to be achievable at @xmath1 colliders ultimately . therefore , it is found that , even if the superparticles are kinematically unaccessible at the lhc , we may observe the mssm signal by studying the partial decay widths of @xmath10 in detail .    for the pl solution , it is also found that the partial width of @xmath191 can deviate from the sm prediction by about 2% even for @xmath225 . on the other hand , we checked that @xmath226 is smaller by about 1% than @xmath227 at the same parameter point , because the non - holomorphic correction @xmath228 is bigger than @xmath229 at this model point . when @xmath52 is smaller , the difference between @xmath227 and @xmath226 decreases , since @xmath51 is approximately proportional to @xmath52 ; in such a case both @xmath227 and @xmath226 are well approximated by @xmath230 . ( blue ) and @xmath226 ( red ) with small @xmath33 solutions ( i.e , the ps and ns solutions for @xmath28 ) . we take @xmath231 , 3 , 4 and @xmath77 . other sfermion masses are set to be @xmath232 . the partial widths are constrained by @xmath233 , the vacuum stability condition ( @xmath214 ) , and the perturbativity of the bottom yukawa coupling ( @xmath234 ) . the black region corresponds to the tree - level prediction for @xmath235@xmath236 . the black dashed line is the sm prediction . , title="fig : " ]   ( blue ) and @xmath226 ( red ) with small @xmath33 solutions ( i.e , the ps and ns solutions for @xmath28 ) . we take @xmath231 , 3 , 4 and @xmath77 . other sfermion masses are set to be @xmath232 . the partial widths are constrained by @xmath233 , the vacuum stability condition ( @xmath214 ) , and the perturbativity of the bottom yukawa coupling ( @xmath234 ) . the black region corresponds to the tree - level prediction for @xmath235@xmath236 . the black dashed line is the sm prediction . , title="fig : " ] +   ( blue ) and @xmath226 ( red ) with small @xmath33 solutions ( i.e , the ps and ns solutions for @xmath28 ) . we take @xmath231 , 3 , 4 and @xmath77 . other sfermion masses are set to be @xmath232 . the partial widths are constrained by @xmath233 , the vacuum stability condition ( @xmath214 ) , and the perturbativity of the bottom yukawa coupling ( @xmath234 ) . the black region corresponds to the tree - level prediction for @xmath235@xmath236 . the black dashed line is the sm prediction . , title="fig : " ]   ( blue ) and @xmath226 ( red ) with small @xmath33 solutions ( i.e , the ps and ns solutions for @xmath28 ) . we take @xmath231 , 3 , 4 and @xmath77 . other sfermion masses are set to be @xmath232 . the partial widths are constrained by @xmath233 , the vacuum stability condition ( @xmath214 ) , and the perturbativity of the bottom yukawa coupling ( @xmath234 ) . the black region corresponds to the tree - level prediction for @xmath235@xmath236 . the black dashed line is the sm prediction . , title="fig : " ]    , but with all the solutions of @xmath28.,title="fig : " ] , but with all the solutions of @xmath28.,title="fig : " ] + , but with all the solutions of @xmath28.,title="fig : " ] , but with all the solutions of @xmath28.,title="fig : " ]    let us see how much @xmath227 and @xmath226 can change in the parameter space consistent with the phenomenological constraints . we have performed the scan in the following parameter space of the mssm :    * @xmath231 , @xmath237 , @xmath238 , and @xmath77 , * @xmath170 , * @xmath239 , @xmath240 , @xmath216 , @xmath217 , * @xmath241 , * @xmath242 , or @xmath243 , * @xmath244 .    here , @xmath28 is determined to satisfy @xmath245 . the other tri - linear couplings ( e.g. , @xmath177 and @xmath246 ) are assumed to be equal to @xmath28 ; we checked that our numerical results are insensitive to this assumption . we take @xmath247 , while sfermion masses other than @xmath61 and @xmath62 are set to be equal to @xmath248 . we have checked that @xmath227 and @xmath226 are almost insensitive to these scalar masses unless they are very small . however , when @xmath168 is much larger than @xmath63 , @xmath64 , and @xmath65 , bottom and stau mixings become sizable which causes additional complexity to our parameter scan , and/or lighter stau become tachyonic . the values of @xmath63 , @xmath64 , and @xmath65 are chosen to avoid this problem . if @xmath168 would become much larger than squark masses ( e.g. , @xmath249 ) , the higgs partial widths could deviate from the sm prediction sizably , since the higgs mixing angle would be enhanced by radiative corrections . however , the vacuum stability condition excludes significant amount of the parameter region with large @xmath168 , as we have shown in fig . [ fig : se ] . in our scan , we set @xmath250 ; this upper bound is large enough to cover the whole region allowed by the vacuum stability .    in figs . [ fig : rbbtaus ] and [ fig : rbbtau ] , we show the minimal and maximal values of @xmath227 and @xmath226 as functions of @xmath17 and @xmath195 , taking into account the phenomenological constraints discussed in the previous section . fig . [ fig : rbbtaus ] corresponds to the small @xmath28 solutions ( ns and ps ) . the largest and smallest values of @xmath227 and @xmath226 are achieved when @xmath168 and @xmath52 are large and are marginally allowed by the phenomenological constraints . the deviations mainly come from radiative corrections to the higgs mixing angle and @xmath51 . in particular , the maximal value of @xmath227 is larger than that of @xmath226 for large @xmath251 . as discussed earlier , @xmath51 becomes negative and sizable with @xmath252 , which results in a significant enhancement of @xmath227 . [ fig : rbbtau ] shows the minimal and maximal values of @xmath227 and @xmath226 , taking all the solutions of ns , ps , nl , and pl into consideration . they change significantly compared to fig . [ fig : rbbtaus ] . the partial widths become extremum when @xmath28 takes the nl or pl solution except the maximal value for small @xmath17 . for @xmath253 , the ns or ps solutions give the maximal value , since the phenomenological constraints , especially the vacuum stability condition , are too severe for the nl and pl solutions ( see fig . [ fig : matanb ] ) . as in the case of fig . [ fig : rbbtaus ] , the maximal value of @xmath227 is much larger than that of @xmath226 because @xmath254 . the maximal value of @xmath227 has a non - trivial bump - like structure . when @xmath17 is small , medium ( i.e. , around the peak of the bump ) , and large , the partial decay width is bounded by the vacuum stability , flavor constraint , and the perturbativity of @xmath179 , respectively . the measurement of the higgs couplings may provide an evidence of bsm , because the values of @xmath227 and @xmath226 may show significant deviation from the sm prediction . in future experiments , the partial decay widths of @xmath255 and @xmath256 may be measured at the @xmath257 level ( see table [ table : experiments ] ) . in the case of the ps and ns solutions , @xmath209 can be as large as 2% ( 3% ) if @xmath17 is @xmath258 ( @xmath259 ) for @xmath260 , and @xmath261 ( @xmath262 ) for @xmath263 . on the other hand , @xmath210 becomes larger than 2% ( 3% ) when @xmath17 is smaller than @xmath264 ( @xmath265 ) for @xmath260 , and @xmath262 ( @xmath266 ) for @xmath263 . including the pl and nl solutions , deviations of @xmath267 @xmath237% level are achieved with larger value of @xmath17 . for example , with @xmath263 , @xmath268 can be achieved with @xmath269 . ( left ) and @xmath270 ( right ) are shown as functions of @xmath62 . the parameters are scanned in the same manner as fig . [ fig : rbbtau ] , but @xmath17 is fixed to be @xmath77 while @xmath62 is varied . here , all the solutions of @xmath28 are included in the scan with imposing the phenomenological constraints discussed in sec . [ sec : constraint ] . the black dashed line is the sm prediction.,title="fig : " ]   ( left ) and @xmath270 ( right ) are shown as functions of @xmath62 . the parameters are scanned in the same manner as fig . [ fig : rbbtau ] , but @xmath17 is fixed to be @xmath77 while @xmath62 is varied . here , all the solutions of @xmath28 are included in the scan with imposing the phenomenological constraints discussed in sec . [ sec : constraint ] . the black dashed line is the sm prediction.,title="fig : " ]    in fig . [ fig : msoft2 ] , we show the sfermion mass dependence of @xmath201 with taking the phenomenological constraints into account . the parameter scan is performed in the same setup as fig . [ fig : rbbtau ] , but @xmath62 is varied . here , @xmath17 is fixed to be @xmath77 . in the left plot , the minimal and maximal values of @xmath227 and @xmath226 are shown . they are achieved by the pl or nl solution . since @xmath17 is fixed , the decoupling behaviour is not observed . rather , the non - decoupling contribution to @xmath51 enhances @xmath227 as @xmath62 increases , since larger @xmath33 is required to satisfy @xmath245 for the solutions . on the other hand , it is found that radiative corrections to the higgs mixing angle do not change so much even if @xmath62 increases .    in the right panel of fig . [ fig : msoft2 ] , the minimal and maximal values of @xmath270 are displayed . the maximal value occurs for the ps or ns solution , while the minimal value is achieved by the pl or nl solution . we can see the decoupling behavior , i.e. , @xmath270 approaches to unity as @xmath62 increases . the partial decay width of @xmath97 can deviate from the sm prediction by about 3% for @xmath271 , while it decreases rapidly and becomes 1% for @xmath272 . we have also checked that these values do not change so much for @xmath273 . ( however , they change significantly if @xmath17 is smaller , since the phenomenological constraints exclude the parameter space severely . ) according to table [ table : experiments ] , the partial width of @xmath97 is expected to be measured at the @xmath274 accuracy in future experiments . thus , as far as superparticles are relatively light , we may observe a signal of the mssm in the measurements of this partial width even if the heavier higgses are out of the reach of the lhc .     as a function of @xmath17 ( green histogram ) , as well as that of model points allowed by the phenomenological constraints ( dotted histogram ) . upper - right : the number of model points allowed by the phenomenological constraints on @xmath17 vs.  @xmath52 plane . lower - left : the number of model points accessible with ilc by @xmath275 . lower - right : the number of model points accessible with ilc by @xmath276 . , title="fig : " ]   as a function of @xmath17 ( green histogram ) , as well as that of model points allowed by the phenomenological constraints ( dotted histogram ) . upper - right : the number of model points allowed by the phenomenological constraints on @xmath17 vs.  @xmath52 plane . lower - left : the number of model points accessible with ilc by @xmath275 . lower - right : the number of model points accessible with ilc by @xmath276 . , title="fig : " ] +   as a function of @xmath17 ( green histogram ) , as well as that of model points allowed by the phenomenological constraints ( dotted histogram ) . upper - right : the number of model points allowed by the phenomenological constraints on @xmath17 vs.  @xmath52 plane . lower - left : the number of model points accessible with ilc by @xmath275 . lower - right : the number of model points accessible with ilc by @xmath276 . , title="fig : " ]   as a function of @xmath17 ( green histogram ) , as well as that of model points allowed by the phenomenological constraints ( dotted histogram ) . upper - right : the number of model points allowed by the phenomenological constraints on @xmath17 vs.  @xmath52 plane . lower - left : the number of model points accessible with ilc by @xmath275 . lower - right : the number of model points accessible with ilc by @xmath276 . , title="fig : " ]    finally , we show how large fraction of the parameter space can be covered by future @xmath1 colliders . for this purpose , we define the @xmath277 variable as @xmath278 ^ 2 }    { [ \delta\gamma(h\rightarrow f)]^2},\end{aligned}\ ] ] where @xmath279 is the expected accuracies of the determinations of the higgs partial decay widths at ilc with @xmath280 and @xmath281 ( see table [ table : experiments ] ) . based on this quantity , we define the parameter region which is accessible with ilc at @xmath282 . we perform a parameter scan and study if each model point is accessible with ilc and satisfies the phenomenological constraints . the mssm parameters are scanned in the ranges of @xmath283 ( with the step size of @xmath284 ) , @xmath285 ( with the step size of @xmath286 ) , and @xmath287 ( with the step size of @xmath288 ) . thus , for each set of @xmath289 , 384 model points are studied , taking account of positive and negative values of @xmath29 as well as all four solutions of @xmath28 . in addition , we adopt the relations @xmath290 , and @xmath291 . concentrating on the parameter space where the lhc will have a difficulty in finding superparticles , @xmath62 is taken to be @xmath237 , @xmath238 , and @xmath77 . in fig . [ fig : scan ] , the ilc coverage of the parameter space of our scan is displayed . in the upper - left panel , we show the distribution of the number of model points accessible with ilc by any of the decay modes of @xmath10 as a function of @xmath17 . the green histogram is a distribution of the number of model points which satisfy @xmath292 and the phenomenological constraints , while the dotted one is that satisfying the phenomenological constraints without imposing @xmath293 . we find that the number reduces drastically at @xmath294 . in the upper - right panel , we show the number of model points which survive the phenomenological constraints on @xmath17 vs.  @xmath52 plane . here , @xmath282 is not imposed . then , in the lower panels , we show the numbers of model points which can be accessed by the decay modes of @xmath275 ( lower - left ) and @xmath276 ( lower - right ) with taking account of the phenomenological constraints . they reduce significantly for @xmath295 irrespective of @xmath52 . the accessible points for @xmath295 are mostly with pl or nl solution . in this paper , we have studied the partial decay widths of the lightest higgs boson in the mssm . taking account of relevant phenomenological constraints , i.e. , higgs mass , flavor constraints , vacuum stability , and the perturbativity of coupling constants up to the gut scale , we have calculated the expected deviations of the partial decay widths from the sm predictions . the partial decay widths are enhanced if the @xmath29-parameter is relatively large . however , such a choice may conflict with some of the phenomenological constraints . in particular , the vacuum - stability condition imposes a stringent constraint on the parameter space . we have found that , with too large @xmath168 , there show up ccb vacua where the down - type higgs field as well as the up - type higgs and stop fields acquire large vevs ; existence of such ccb vacua was not seriously considered in the previous studies . in addition , when @xmath296 is large , non - holomorphic correction to the bottom yukawa interaction becomes so large that the bottom yukawa coupling constant becomes non - perturbative below the gut scale . large value of @xmath296 may also cause too large flavor - violating decay of @xmath11-mesons . by taking these constraints into account , the maximal and minimal possible values of the higgs partial widths are restricted . we found that the deviations of the partial decay widths from the sm predictions can be of @xmath208% for some of the decay modes . in particular , those of @xmath87 and @xmath88 may show significant deviations even if the superparticles are out of the reach of 14tev lhc . in addition , the deviation of @xmath96 may also be sizable if the superparticles are relatively light . we emphasize that , although our scan is limited to some part of the mssm parameter space , we have found the regions where the deviations from the sm predictions are within the reach of proposed @xmath1 colliders even if superparticles would not be observed at the lhc . _ acknowledgements _ : the authors would like to thank yasuhiro shimizu for the collaboration in the early stage of this project . the authors also acknowledge yitp for their hospitality , at which this work was initiated . this work is supported by jsps kakenhi no . 23740172 ( m.e . ) , no . 26400239 ( t.m . ) , and no . 26287039 ( m.m.n . ) . the work is supported by grant - in - aid for scientific research from the ministry of education , science , sports , and culture ( mext ) , japan , no . 23104008 ( t.m . ) and no . 23104006 ( m.m.n . ) , and also by world premier international research center initiative ( wpi initiative ) , mext , japan . g.  aad _ et al . _ [ atlas collaboration ] , phys . b * 716 * ( 2012 ) 1 [ arxiv:1207.7214 [ hep - ex ] ] . s.  chatrchyan _ et al . _ [ cms collaboration ] , phys . b * 716 * ( 2012 ) 30 [ arxiv:1207.7235 [ hep - ex ] ] . s.  dawson , a.  gritsan , h.  logan , j.  qian , c.  tully , r.  van kooten , a.  ajaib and a.  anastassov _ et al . _ , arxiv:1310.8361 [ hep - ex ] . y.  okada , m.  yamaguchi and t.  yanagida , prog .  theor .  phys .   * 85 * ( 1991 ) 1 . y.  okada , m.  yamaguchi and t.  yanagida , phys . b * 262 * , 54 ( 1991 ) . j.  r.  ellis , g.  ridolfi and f.  zwirner , phys . b * 257 * ( 1991 ) 83 . j.  r.  ellis , g.  ridolfi and f.  zwirner , phys . b * 262 * , 477 ( 1991 ) . h.  e.  haber and r.  hempfling , phys . * 66 * ( 1991 ) 1815 . z.  skands , b.  c.  allanach , h.  baer , c.  balazs , g.  belanger , f.  boudjema , a.  djouadi and r.  godbole _ et al . _ , jhep * 0407 * ( 2004 ) 036 [ hep - ph/0311123 ] . k.  a.  olive et al . 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motivated by future collider proposals that aim to measure the higgs properties precisely , we study the partial decay widths of the lightest higgs boson in the minimal supersymmetric standard model with an emphasis on the parameter region where all superparticles and heavy higgs bosons are not accessible at the lhc . taking account of phenomenological constraints such as the higgs mass , flavor constraints , vacuum stability , and perturbativity of coupling constants up to the grand unification scale , 
 we discuss how large the deviations of the partial decay widths from the standard model predictions can be . 
 these constraints exclude large fraction of the parameter region where the higgs widths show significant deviation from the standard model predictions 
 . nevertheless , even if superparticles and the heavy higgses are out of the reach of @xmath0 lhc , the deviation may be large enough to be observed at future @xmath1 collider experiments . 
 ut-15 - 02 + ipmu-15 - 0018 + kek - th-1795 + february , 2015 + .75 in    * footprints of supersymmetry on higgs decay *    .75 in     motoi endo@xmath2 , takeo moroi@xmath2 , and mihoko m. nojiri@xmath3    0.25 in    @xmath4 _ department of physics , university of tokyo , tokyo 113 - 0033 , japan _    0.1 in    @xmath5 _ kavli ipmu ( wpi ) , university of tokyo , kashiwa , chiba 277 - 8583 , japan _    0.1 in    @xmath6 
 _ kek theory center , ipns , kek , tsukuba , ibaraki 305 - 0801 , japan _    0.1 in    @xmath7 _ the graduate university of advanced studies ( sokendai ) , + tsukuba , ibaraki 305 - 0801 , japan 
 _    .5 in