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the sm predicts the @xmath9 branching ratio to be @xcite    [ sm : bs ] ( ) = ( 3.21.5)10 ^ -9 , and the ratio of branching fractions [ rsm ] r_sm .
|_sm ~o(10 ^ -2 ) , where @xmath10 is the lifetime of the @xmath11 meson , @xmath12 and @xmath13 are the corresponding mass and decay constant .
however , given the sm prediction of @xmath14 , the @xmath15 decay is experimentally remote unless it is significantly enhanced by new physics .
thus , the purely leptonic decays of neutral @xmath16 mesons provide an ideal testing ground for physics outside the sm , with the current experimental upper bounds @xcite
@xmath17 and @xmath18 , both given at @xmath19 .
the main interest in this talk is in a qualitative comparison of the @xmath5 branching fractions in the presence of non - standard interactions , which can be made by using the ratio [ ratio : bdbs ] r. referring to , it is important to note that the suppression of @xmath6 in the sm is largely due to the ratio of the ckm elements .
this dependence on the ckm factors allegedly pertains to all models in which the quark mixing matrix is the only source of flavour violation .
it is therefore interesting to ask if @xmath6 could be of the order unity in some non - standard models where flavour violation is governed exclusively by the ckm matrix .
working in the framework of the minimal supersymmetric standard model ( mssm ) with a large ratio of higgs vacuum expectation values , @xmath8 ( ranging from @xmath20 to @xmath21 ) , we show that such a scenario does exist , and study its consequences for the @xmath5 branching ratios .
the outline is as follows .
first , in , we define modified minimal flavour violation ( @xmath4 ) and discuss briefly three distinct scenarios within the mssm .
second , the effective hamiltonian describing the decays @xmath5 in the presence of non - sm interactions is given in .
furthermore , in , numerical results for the branching fractions @xmath0 and the ratio @xmath6 are presented .
finally , we summarize and conclude .
there exists no unique definition of minimal flavour violation ( mfv ) in the literature ( see , e.g. , ) .
the common feature of these mfv definitions is that flavour violation and/or flavour - changing neutral current ( fcnc ) processes are entirely governed by the ckm matrix . on the other hand ,
they differ , for example , by the following additional assumptions : i ) there are no new operators present , in addition to those of the sm , ii ) fcnc processes are proportional to the same combination of ckm elements as in the sm @xcite or iii ) flavour transitions occur only in charged currents at tree level . while these ad hoc assumptions are useful for certain considerations , such as the construction of the universal unitarity triangle @xcite , they can not be justified by symmetry arguments on the level of the lagrangian .
for example , the number of operators with a certain dimension is always fixed by the symmetry of the low - energy effective theory .  whether the wilson coefficients are negligible or not , depends crucially on the model considered and on the part of the parameter space .
furthermore , the requirement that fcnc processes are proportional to the same combination of ckm elements as in the sm fails , for example , in the mssm and can be retained only after further simplifying assumptions . the last statement in iii ) is of pure phenomenological relevance in order to avoid huge contributions to fcnc processes .
using symmetry arguments , we propose an approach that relies only on the key ingredient of the mfv definitions in , without considering the above mentioned additional assumptions i)iii ) .
we call an extension of the sm a modified minimal flavour - violating ( @xmath4 ) model if and only if fcnc processes or flavour violation are entirely ruled by the ckm matrix ; that is , we require that fcnc processes vanish to all orders in perturbation theory in the limit @xmath22 . for a motivation of this definition using symmetry arguments
we refer the reader to .
as will become clear , the advantage of @xmath4 is that it is less restrictive than mfv , while the ckm matrix remains the only source of fcnc transitions .
our definition of @xmath4 is manifest basis independent .
however , in order to find a useful classification of different @xmath4 scenarios within the mssm , we will work in the super - ckm basis .
in this basis the quark mass matrices are diagonal , and both quarks and squarks are rotated simultaneously .
the scalar quark mass - squared matrices in this basis have the structure [ squark : mass ] _
u^2 = (    cc ^2_u_ll & ^2_u_lr + ^2_u_lr & ^2_u_rr    ) , _
d^2 = (    cc ^2_d_ll & ^2_d_lr + ^2_d_lr & ^2_d_rr    ) , where the @xmath23 submatrices are given in @xcite . here
we present the two important entries only : @xmath24 @xmath25 because of su(2 ) gauge invariance , the mass matrix @xmath26 is intimately connected to @xmath27 via [ su2 ] = ^ , which is important for our subsequent discussion .
the above given definition of @xmath4 requires that the soft susy trilinear couplings @xmath28 , @xmath29 and the soft susy breaking squark masses @xmath30 , @xmath31 are diagonal .    taking into account the relation in ,
one encounters three cases of @xmath4 .
* scenario ( a ) : * + @xmath27 is proportional to the unit matrix , and so @xmath32 .  as a result , there are no gluino and neutralino contributions to flavour - changing transitions at one - loop level .
this scenario of @xmath4 coincides with the mfv scenario at low @xmath8 as defined in refs . .
* scenario ( b ) : * + @xmath33 is diagonal but not proportional to the unit matrix and , in consequence , @xmath27 has non - diagonal entries .
in such a case , there are again no gluino and neutralino contributions to flavour - changing one - loop transitions involving only external down - type quarks and leptons .
however , additional chargino contributions show up , due to non - diagonal entries of @xmath27 .
* scenario ( c ) : * + @xmath27 is diagonal but not proportional to the unit matrix , which gives rise to off - diagonal entries in @xmath33 .
accordingly , gluino and neutralino exchange diagrams ( in addition to those involving @xmath34 , charged and neutral higgs bosons ) contribute to flavour - changing transitions at one - loop level that involve external down - type quarks .
the common feature of all these scenarios is that the ckm matrix is the only source of flavour violation .
the effective hamiltonian responsible for the processes @xmath35 , with @xmath36 and @xmath37 , in the presence of non - standard interactions is given by [ heff ] h_eff = - v_tb^v_tq^ * _ i=10,s , p[c_i()_i()+c_i()_i ( ) ] , with the short - distance coefficients @xmath38 and the local operators [ operator : basis ] _
10=(|q ^ p_l b ) ( |l _ _ 5 l),_s= m_b ( |q p_r b ) ( |ll),_p= m_b ( |q p_r b)(|l _ 5 l ) , where @xmath39 . the primed operators can be obtained by @xmath40 and @xmath41 .
it turns out that the primed wilson coefficients are negligibly small , and hence can be safely neglected .    at high
@xmath8 the scalar and pseudoscalar operators @xmath42 and @xmath43 become important in addition to the so called sm - operator @xmath44 . in this region of the parameter space an expansion according to @xmath8 is possible and a general expression for @xmath45 looks like c_i o_i = _
n a_n ^n+1 ( ) ^n + _
n b_n ^n ( ) ^n +  , where we call the first term leading and the second term subleading .
@xmath46 denotes lepton and light quark masses while @xmath47 stands for masses of particles that have been integrated out .
explicit expressions for the wilson - coefficients can be found in .
the experimental bounds used in this numerical analysis as well as the ranges of the mssm parameters can be found in ref .
@xcite .      recall that in scenario ( a ) the matrices @xmath27 and @xmath33 are equal and proportional to the unit matrix .
therefore , the gluinos and neutralinos do not contribute at one - loop level .
the scan over the parameter region shows that the ratio @xmath6 is approximately constant and close to @xmath48 .    in scenario ( b )
, the matrix @xmath33 is diagonal , @xmath49 , with at least two different entries .
hence , there are no gluino and neutralino contributions at one - loop level .
employing the relation in , the matrix @xmath50 becomes non - diagonal .
these off - diagonal flavour - changing entries are constrained by experimental data on @xmath51@xmath52 , @xmath53@xmath54 , @xmath55@xmath56 oscillations , and the @xmath57 decay @xcite .
it is important to note that the bounds on these flavour - changing entries@xcite severely constrain the additional chargino contributions in scenario ( b ) , hence we end up with a result similar to scenario ( a ) .
@xmath6 varies between @xmath58 and @xmath59 . neglecting the constraints we could have found @xmath6 in the range @xmath60 .      in this case
, the matrix @xmath27 is diagonal , @xmath61 , with at least two different entries . according to the relation in ,
this implies that @xmath33 has non - diagonal entries , so that gluinos and neutralinos contribute to the @xmath62 transition already at one - loop level . as before , we take the constraints of on these off - diagonal elements .    [ cols="^,^ " , ]     an interesting subset of parameter points was considered in ( for details see ) interestingly , in the left ( right ) plot , the ratio @xmath6 ranges between @xmath63 ( @xmath64 ) , while the magnitude of the individual branching fractions decreases drastically with increasing charged higgs boson mass , @xmath65 . note that for small @xmath65 and @xmath8 close to @xmath21 both branching ratios are in a region that can be probed experimentally , in run ii of the fermilab tevatron , babar and belle .
the neutralino wilson coefficients are numerically smaller than those coming from the chargino and gluino contributions .
however , we have found that in certain regions of the mssm parameter space cancellations between the chargino and gluino coefficients occur , in which case the neutralino contributions become important . as a matter of fact , for the susy parameter sets examined
, we found that a large value of @xmath1 always involves such a cancellation .
we have defined @xmath4 using symmetry arguments and have shown that @xmath4 is less restrictive than mfv , while the ckm matrix remains the only source of flavour violation . within the mssm
we have investigated three scenarios that are possible within the context of @xmath4 .
in particular , we have studied the case where the chargino exchange diagrams @xcite as well as the gluino and neutralino exchange diagrams @xcite contribute besides @xmath66 [ scenario ( c ) ] .    including current experimental data on rare @xmath16 decays , as well as on @xmath67 meson mixing
, we found that in certain regions of the susy parameter space the branching ratios @xmath68 and @xmath69 can be up to the order of @xmath70 and @xmath71 respectively .
specifically , we showed that there exist regions in which the branching fractions of both decay modes are comparable in size , and may well be accessible to run ii of the fermilab tevatron as well as @xmath6 can deviate from @xmath72 by orders of magnitude .
we wish to stress that a measurement of the branching ratios @xmath0 , or equivalently , a ratio @xmath6 of @xmath7 , does not necessarily imply the existence of new flavour violation outside the ckm matrix .
nevertheless , any observation of these decay modes in ongoing and forthcoming experiments would be an unambiguous signal of new physics .
i would like to thank christoph bobeth , andrzej j.  buras , thorsten ewerth , frank krger and michael spira for useful discussions and comments on the manuscript .
this work was supported in part by the german ` bundesministerium fr bildung und forschung ' under contract 05ht1woa3 and by the ` deutsche forschungsgemeinschaft ' ( dfg ) under contract        c.  bobeth , t.  ewerth , f.  krger , and j.  urban , .
a.  j.  buras , in _ flavour dynamics : cp violation and rare decays _ , lectures given at international school of subnuclear physics , erice , italy , 2000 , hep - ph/0101336 .
belle collaboration , report no .
belle - conf-0127 ( unpublished ) ; cdf collaboration , f.  abe , .
a.  j.  buras , p.  h.  chankowski , j.  rosiek and  .
sawianowska , .            c.  bobeth , a.  j.  buras , f.  krger , and j.  urban , . m.  misiak , s.  pokorski , and j.  rosiek , in _ heavy flavours ii _ , edited by a.  j.  buras and m.  lindner ( world scientific , singapore , 1998 ) , p.  795
, hep - ph/9703442 . t.  besmer , c.  greub , and t.  hurth , .
see also f.  gabbiani , e.  gabrielli , a.  masiero , and l.  silvestrini , ; d.  chang , w.  f.  chang , w.  y.  keung , n.  sinha , and r.  sinha , .
it is well known that the minimal supersymmetric standard model ( mssm ) can enhance @xmath0 by orders of magnitude @xcite , even if we assume the cabibbo - kobayashi - maskawa ( ckm ) matrix to be the only source of flavour violation . 
 of particular interest is the quantity @xmath1 , since ( i ) the theoretical errors cancel to a large extent , and ( ii ) it offers a theoretically clean way of extracting the ratio @xmath2 in the standard model , which predicts @xmath3 . exploring three different scenarios of modified minimal flavour violation ( @xmath4 ) , we find that part of the mssm parameter space can accommodate large @xmath5 branching fractions , while being consistent with various experimental constraints . 
 more importantly , we show that the ratio @xmath6 can be as large as @xmath7 , while the individual branching fractions may be amenable to detection by ongoing experiments . 
 we conclude that within the mssm with large @xmath8 the decay rates of @xmath5 be of comparable size even in the case where flavour violation is due solely to the ckm matrix .    
 tum - hep-487/02 + psi - pr-02 - 14    0.2 in     +   + _ technische universitt mnchen , d-85748 garching , germany + paul scherrer institut , ch-5232 villigen psi , switzerland _ +