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the huge effort on the experimental side at present b facilities ( babar , belle and cdf ) to increase the precision on data measurements force us to revise the strategies on the theory side to produce more accurate predictions . non leptonic b decays offer different strategies to determine the unitarity triangle , to search for new physics ( np)@xcite but also to rule out models @xcite . while a lot of attention has been devoted to the @xmath7@xcite decay modes , here we will focus on @xmath8 decays that has been observed at cdf @xcite ( @xmath3 ) and at babar @xcite and belle @xcite ( @xmath1 ) . there are two main approaches in the literature to describe @xmath9 decays : flavour symmetries and @xmath10expansion methods ( qcd factorisation  @xcite/ soft collinear effective theories  @xcite or pqcd @xcite ) . each of those methods has pros and cons , that we will discuss in turn . flavour symmetries , like u - spin symmetry that relates @xmath11 with @xmath12  @xcite , provide a model independent analysis and extract most of the needed hadronic parameters from data . however , this method has the disadvantage that it relies strongly on the accuracy of data , and , at present , there is still not full agreement between babar and belle data on the cp asymmetries of the @xmath13 mode . as a consequence , error bars are still quite large , see for instance , the prediction @xmath14 @xcite or , more recently , @xmath15  @xcite . also when relating @xmath13 with @xmath11 some of the needed u - spin parameters can only be roughly estimated and they are usually taken to be of the order of @xmath16 . concerning @xmath17-expansion methods , here we will focus on qcd factorisation ( qcdf )  @xcite . the main idea is to exploit the existence of a large scale @xmath18 together with colour transparency , that applies when the outgoing meson that does not contain the spectator quark is very energetic . at leading power in @xmath19 all long distance contributions can be parametrized in terms of form factors and light cone distribution amplitudes , while the contribution from energetic gluons comes in a perturbative series in @xmath20 and it is incorporated into the hard scattering kernels . qcdf predicts some of the hadronic parameters reducing the error bars , however in the computation one has to face chirally enhanced ir divergences . they are formally suppressed by a power of @xmath17 , but can be numerically significant . they are modelled and induce an important uncertainty in the predictions . however , there is a third possibility and it is the proposal presented in @xcite that combines qcdf and flavour symmetries giving rise to rather accurate predictions for the branching ratios of the above mentioned @xmath0 decays in sm and in supersymmetry . moreover , the method predicts some of the su(3 ) breaking parameters which can be useful for other flavour approaches and , at the same time , deals with the problem of the chirally enhanced ir divergences coming at order @xmath19 ( see also @xcite ) . since ir divergences play a central role in this discussion , it is worth to mention the two sources of ir divergences in qcdf :    * hard spectator - scattering : hard gluons exchange between spectator quark and the outgoing energetic meson gives rise to integrals of the following type ( see @xcite for definitions ) : @xmath21 , \nonumber\ ] ] where the second term ( formally of order @xmath19 ) diverges when @xmath22 . * weak annihilation : these type of diagrams also exhibit endpoint ir divergences as it is explicit in the corresponding integrals : @xmath23      + r_\chi^{m_1 } r_\chi^{m_2}\,\phi_{m_2}(x)\,\phi_{m_1}(y)\ ,       \frac{2}{\bar x y } \right\}. \end{aligned}\ ] ]    both divergences are modelled in the same way @xcite : @xmath24    \!\equiv\ ! \phi_{m_1}(1)\,x_{h , a}^{m_1 }      +   { r , } \nonumber\ ] ] where @xmath25 is a finite piece and the divergent piece is cut - off by a physical scale of order @xmath26 with an arbitrary complex coefficient to take into account possible multiple soft scattering : @xmath27 . the sm amplitude for a @xmath29-decay into two mesons can be split into tree and penguin contributions  @xcite and  penguin " the piece proportional to @xmath30 , even if applied to decays with no actual tree diagram . ] : @xmath31 with @xmath32 denoting the charge of the decay products , and the products of ckm factors @xmath33 . tree and penguin contributions in @xmath34 in qcdf are : @xmath35 where @xmath36 , @xmath37 , the super - scripts identify the channel , the normalisation is @xmath38 ( see @xcite for the corresponding expression of the @xmath0 channels ) . following the observation in @xcite that the structure of the ir divergences is the same , independently of the charm or up quark running in the loop , we identified an ir - safe quantity at nlo in qcdf that we called @xmath39 . all chirally enhanced ir divergences cancel exactly in this quantity at this order . its explicit expression in terms of the coefficients in eq.([eq4 ] ) is : @xmath40,\ ] ] where electroweak contributions are neglected . this quantity can be safely evaluated in qcdf and the result found in @xcite was : @xmath41 . the largest uncertainty entering @xmath42 comes from the ratio @xmath43 and the scale dependence . interestingly , this quantity can be expressed in terms of observables , providing a relation between the direct induced cp - asymmetry ( @xmath44 ) , the mixing induced cp - asymmetry ( @xmath45 ) and the branching ratio ( @xmath46 ) of @xmath34 : @xmath47 a_{mix}^{d0 }     -[x_2 \cos\phi_d + x_3 \sin\phi_d ] a_{\delta}^{d0 } \}\ , , \nonumber\ ] ] where @xmath48 , @xmath49 is the weak mixing angle for the @xmath50 system , @xmath51 and @xmath52 are functions of @xmath53 and ckm elements . all sm inputs are taken as in @xcite following @xcite . moreover , it was found in @xcite that this sum - rule encodes also a very interesting information . it provides a new way of measuring @xmath54 : @xmath55 ( see @xcite for a recent review on the extraction of @xmath28 ) . in a similar way , it was found in @xcite a corresponding ir safe quantity @xmath56 and sum - rule for the decay @xmath57 : @xmath58 a_{mix}^{s0 }     -[y_2 \cos\phi_s + y_3 \sin\phi_s ] a_{\delta}^{s0 } \}\ , , \nonumber\ ] ] which provides a completely new way to determine the weak mixing angle @xmath5 that we present here ( see @xcite for definitions ) :    @xmath59 this implies that a measurement of the branching ratio , direct cp asymmetry and mixing induced cp asymmetry of the decay @xmath60 automatically translates into a value for @xmath61 . finally , given the relation @xmath62 , where @xmath63 a new relation between @xmath54 and @xmath64 immediately emerges . the sm amplitude of this @xmath66 penguin decay is given by : @xmath67 its dynamics is described in terms of three parameters : @xmath68 , @xmath69 and the relative strong phase @xmath70 ( remember that @xmath71 stands for the piece proportional to @xmath72 but it is not due to an actual tree diagram in this case ) . its hadronic parameters can be related via u - spin with the hadronic parameters ( @xmath73 , @xmath74 and @xmath75 ) of the also penguin governed mode @xmath76 . this has several advantages : first , we can expect similar final state interactions ( although not equal ) , second , the sources of u - spin breaking can be better controlled using qcdf . these sources are : i ) the factorisable ratio @xmath77 ( extrapolated from the lattice ) ii ) u - spin breaking @xmath17 suppressed terms @xmath78 and @xmath79 : sensitive to the difference of @xmath50 and @xmath6 distribution amplitudes and spectator quark dependent contributions coming from a gluon emitted from the @xmath80 or @xmath81 quark . this leads to the relations @xmath82 and @xmath83 . the next step is to determine the hadronic parameters ( @xmath84 , @xmath85 ) of the decay @xmath86 . this is done using as inputs the @xmath87 and @xmath42 ( from qcdf ) . the direct cp asymmetry @xmath88(denoted by @xmath44 ) will be taken as a free parameter . the combination of those constraints gives rise to a set of non - linear equations ( see definitions in @xcite ) : @xmath89-[{\sin\gamma    x_{\delta}&=&y_{\delta}x_p - { \rho_0 ^ 2 a_{dir}^{d0}}/({2|\lambda_u^{(d)}\lambda_c^{(d)}|\sin\gamma})\ , ,   \end{aligned}\ ] ] that determines @xmath90 , then using @xmath42 one gets @xmath84 . two remarks are important here : first , there is a twofold ambiguity in the sign of @xmath91 ( solved in the next subsection ) . second , current data together with our knowledge on @xmath42 limits the @xmath44 asymmetry ( by means of eqs.([circ ] ) ) within a restricted range between @xmath92 . finally , our sm predictions for the branching ratio and cp asymmetries of @xmath93 are obtained using the relations between @xmath94 and @xmath95 mentioned above and including all u - spin breaking sources together with the qcdf uncertainties in @xmath42 . the resulting predictions are @xmath96 , @xmath97 and @xmath98 . the sign of these asymmetries can be fixed once @xmath44 will be measured with enough accuracy . the analysis of the decay mode @xmath11 follows similar steps , but with some important differences : i ) we will use u - spin and isospin to connect @xmath1 with @xmath11 , ii ) @xmath3 contains a tree ( denoted by @xmath100 in qcdf ) with no counterpart in @xmath101 , iii ) @xmath102 has been measured with excellent precision at cdf@xcite and iv ) we will use the information only on the _ sign predictions _ ( not the absolute value ) for the cp - asymmetries of @xmath3 from the strategy that uses u - spin to relate @xmath3 with @xmath12 . the hadronic parameters describing the amplitude : @xmath103 are obtained from the relations containing the sub - leading @xmath17 u - spin breaking : @xmath104 , @xmath105 . those errors , estimated within qcdf , are stretched roughly by a factor two to be conservative . the two - fold ambiguity on the sign of @xmath106 is lifted here using u - spin arguments based on the @xmath107 strategy . while the signs of @xmath91 and @xmath108 are correlated ( being both positive or negative ) , the prediction based on the @xmath107 strategy points towards a positive sign for @xmath108@xcite , discarding then the solution with @xmath109 . our result in the sm for the branching ratio of @xmath3 averaging over all values of @xmath44 is @xmath110 , where the last error in parenthesis stands for a rough estimate of finite , non - enhanced @xmath19 corrections . finally , confronting our predictions for @xmath3 with the data on @xmath13  @xcite : @xmath111 and @xmath112 , @xmath113 , provides a double information . first , we can give predictions for the u - spin breaking parameters : @xmath114 and @xmath115 connecting @xmath3 with @xmath13 . these parameters can be compared with the qcd sum rules predictions in ref . notice that while qcd sum rules gives only the factorizable part , our predictions include , in principle , the full contribution . second , a comparison between the two relative strong phases @xmath116 and @xmath117 selects @xmath118 . then , if we restricts only to positive values of @xmath44 according to the previous arguments , our sm predictions turn out to be @xcite : @xmath119 another argument in favour of @xmath118 comes from the preference of @xmath120 of the u - spin based @xmath13 strategy @xcite ( see the anti - correlation between @xmath44 and @xmath121 in table 1 of @xcite ) . the accuracy on these cp - asymmetries will be substantially improved once a precise measurement on @xmath44 will be available or the error of @xmath122 and the qcd uncertainties on @xmath42 ( mainly @xmath43 and scale dependence ) will be reduced .      the leading gluino - squark box and penguin contributions @xcite to @xmath60 and @xmath3 were evaluated first in @xcite using the u - spin flavour strategy with @xmath123 and , afterwards , in @xcite using the new method combining flavour and qcdf @xcite . the relative size of this contribution compared to the sm penguin is @xmath124 . the amplitude of these decays in presence of np contains an extra contribution : @xmath125 , @xmath126 . these np amplitudes @xmath127 and @xmath128 in terms of wilson coefficients are : @xmath129a\nn\end{aligned}\ ] ] with @xmath130 , @xmath131 and @xmath132 ( see @xcite for definitions ) . these wilson coefficients are sensitive to the @xmath133 mass splitting . after including the constraints coming from @xmath134 , @xmath7 and @xmath135 we found that a large isospin violation controlled by the mass splitting @xmath136-@xmath137 is possible between the np amplitudes @xmath138 and @xmath139 . for the region of parameters considered in this supersymmetric scenario , @xmath138 can be up to a factor three larger than @xmath139 . the specific results in supersymmetry for each decay mode are @xcite :    * @xmath140 : the branching ratio is very little affected by susy . at most , the sm prediction can be increased by 15% for @xmath141 , increasing a bit the already good agreement with the new cdf data  @xcite . the direct cp asymmetry within susy falls inside the range @xmath142 for @xmath143 . the deviation depends on the relative size of the competing sm tree versus the np amplitude . @xmath144 can take any value from [ -1,1 ] . * @xmath145 : the impact of susy on @xmath146 is even smaller , reflecting the reduced allowed region for @xmath147 as compared to @xmath138 . the situation is very different for the cp asymmetries , that are particularly promising , due to the very small size of their sm prediction @xcite . the direct cp asymmetry in susy can be 10 times larger than the sm one . @xmath148 covers the entire range , and so this asymmetry can be large in the presence of susy , contrary to the sm prediction . the method discussed here is being applied to other non - 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the interplay between flavour symmetries connecting @xmath0 decays with the recently measured @xmath1 decay and qcd factorisation opens new strategies to describe the decays @xmath2 and @xmath3 in the sm and in supersymmetry . 
 a new relation , emerging from the sum - rule for the @xmath4 decay mode , is presented offering a new way to determine the weak mixing angle @xmath5 of the @xmath6 system .