You are an expert at summarizing long articles. Proceed to summarize the following text: 
the standard model is flawed by the large number of free parameters , for which there is at present no explanation . there is no prediction of the family replication pattern , nor of the number of families . all the families are really treated on the same footing . most of the standard model free parameters reside in `` flavour space '' - with six quark masses , six lepton masses , four quark mixing angles and ditto for the leptonic sector , as well as the strong cp - violating parameter @xmath0 . the structure of flavour space is determined by the fermion mass matrices , i.e. by the form that the mass matrices take in the `` weak interaction basis '' where mixed fermion states interact weakly , in contrast to the `` mass bases '' , where the mass matrices are diagonal . one may wonder how one may ascribe such importance to the different bases in flavour space , considering that the information content of a matrix is contained in its matrix invariants , which in the case of a @xmath1 matrix @xmath2 are the @xmath3 sums and products of the eigenvalues @xmath4 , such as @xmath5 , @xmath6 , @xmath7 these expressions are invariant under permutations of the eigenvalues , which in the context of mass matrices means that they are flavour symmetric , and obviously independent of any choice of flavour space basis . even if the information content of a matrix is contained in its invariants , the form of a matrix may also carry information , albeit of another type . the idea - the hope - is that the form that the mass matrices have in the weak interaction basis can give some hint about the origin of the unruly masses . there is a certain circularity to this reasoning ; to make a mass matrix ansatz is in fact to define what we take as the weak interaction basis in flavour space . we denote the quark mass matrices of the up- and down - sectors in the weak interaction basis by @xmath2 and @xmath8 , respectively . we go from the weak interaction basis to the mass bases by rotating the matrices by the unitary matrices @xmath9 and @xmath10 , @xmath11 @xmath12        the lodestar in the hunt for the right mass matrices is the family hierarchy , with two lighter particles in the first and second family , and a much heavier particle in the third family . this hierarchy is present in all the charged sectors , with fermions in different families exhibiting very different mass values , ranging from the electron mass to the about @xmath13 times larger top mass . it is still an open question whether the neutrino masses also follow this pattern @xcite . in the democratic approach @xcite , @xcite , @xcite the family hierarchy is taken very seriously . it is assumed that in the weak basis the fermion mass matrices have a form close to the @xmath14 symmetric `` democratic '' matrix @xmath15 with the eigenvalues @xmath16 , reflecting the family hierarchy . the underlying philosophy is that in the standard model , where the fermions get their masses from the yukawa couplings by the higgs mechanism , there is no reason why there should be a different yukawa coupling for each fermion . the couplings to the gauge bosons of the strong , weak and electromagnetic interactions are identical for all the fermions in a given charge sector , it thus seems like a natural assumption that they should also have identical yukawa couplings . the difference is that the weak interactions take place in a specific flavour space basis , while the other interactions are flavour independent . the democratic assumption is thus that the fermion fields of the same charge initially have the same yukawa couplings . with three families , the quark mass matrices in the weak interaction basis then have the ( zeroth order ) form @xmath17 where @xmath18 and @xmath19 have dimension mass . the corresponding mass spectra @xmath20 reflect the family hierarchy with two light families and a third much heavier family , a mass hierarchy that can be interpreted as the representation @xmath21 of @xmath22 . in order to obtain realistic mass spectra with non - zero masses , the @xmath14 symmetry must obviously be broken , and the different democratic matrix anstze correspond to different schemes for breaking the democratic symmetry . we can apply the democratic approach to the lepton sector as well , postulating democratic ( zeroth order ) mass matrices for the charged leptons and the neutrinos , whether they are fermi - dirac or majorana states , @xmath23 relative to the quark ratio @xmath24 , the leptonic ratio @xmath25 is so extremely small that it seems unnatural . one way out is to simply assume that @xmath26 vanishes , meaning that the neutrinos get no mass contribution in the democratic limit @xcite . according to the democratic philosophy , then there would be no reason for a hierarchical pattern  la the one observed in the charged sectors ; the neutrino masses could even be of the same order of magnitude . data are indeed compatible with a much weaker hierarchical structure for the neutrino masses than the hierarchy displayed by the charged fermion masses . unlike the situation for the quark mixing angles , in lepton flavour mixing there are two quite large mixing angles and a third much smaller mixing angle , these large mixing angles can be interpreted as indicating weak hierachy of the neutrino mass spectrum . the neutrino mass spectrum hierarchy could even be inverted ; if the solar neutrino doublet @xmath27 has a mean mass larger than the remaining atmospheric neutrino @xmath28 , the hierarchy is called `` inverted '' , otherwise it is called `` normal '' .    supposing that the neutrino masses do not emerge from a democratic scheme , a ( relatively ) flat neutrino mass spectrum could be taken as a support for the idea that the masses in the charged sectors emerge from a democratic scheme in the case that both the up- and down - sector mass matrices have a purely democratic texture , the quark mixing matrix is @xmath29 , where @xmath30 is the unitary matrix that diagonalizes the democratic matrix ( [ nambu ] ) . we use this to define the democratic basis , meaning the flavour space basis where the mass matrices are diagonalized by ( [ dem ] ) and the mass lagrangian is symmetric under permutations of the fermion fields @xmath31 of a given charge sector .    in the democratic basis the mass lagrangian @xmath32 is symmetric under permutations of the fermion fields @xmath31 , while in the mass basis with @xmath33 the mass lagrangian has the form @xmath34 which is clearly not invariant under permutations of ( @xmath35,@xmath36,@xmath36 ) . we can perform a shift of the democratic matrix , by just adding a unit matrix @xmath37 , @xmath38 , @xmath39 corresponding to the mass spectrum @xmath40 . the matrix @xmath41 has a democratic texture , both because it is diagonalized by @xmath42 , and because the mass lagrangian is invariant under permutations of the quark fields , @xmath43    if @xmath41 and @xmath44 both have a texture like ( [ pert ] ) , there is no cp - violation . this is independent of how many families there are , because of the degeneracy of the mass values . cp - violation only occurs once there are three or more non - degenerate families , because only then the phases can no longer be defined away . we can repeat the democratic scheme with a number @xmath45 of families , where the fermion mass matrices again are proportional to the @xmath46 symmetric democratic matrix which is diagonalized by a unitary matrix analogous to @xmath42 in ( [ dem ] ) . to the @xmath47-dimensional democratic matrix term , we can again add a @xmath47-dimensional diagonal matrix @xmath48 , and get a @xmath47-dimensional mass spectrum with @xmath45 massive states , and @xmath49 degenerate masses . the mass matrix still has a democratic texture , and there is still no cp - violation . in order to obtain non - degenerate , non - vanishing masses for the physical flavours @xmath50 , the permutation symmetry of the fermion fields @xmath31 in the democratic basis must be broken . the proposal here is to derive mass matrices with a nearly democratic texture , not by explicitly perturbing the assumed initial democratic form ( [ nambu ] ) , but instead by perturbing the matrix @xmath42 which diagonalises the democratic mass matrix . this is done by deriving the unitary rotation matrices @xmath9 , @xmath10 for the up- and down- sectors , from a specific parameterisation of the weak mixing matrix @xmath51 . the idea is to embed the assumption of democratic symmetry into the standard model mixing matrix , by expressing the mixing matrix as a product @xmath52 since both the mixing matrix and its factors , according to the standard parameterisation @xcite , are so close to the unit matrix , the rotation matrices @xmath9 , @xmath10 are effectively perturbations of the democratic diagonalising matrix ( [ dem ] ) . in this way , the weak interaction basis remains close to the democratic basis . the cabbibo - kobayashi - maskawa ( ckm ) mixing matrix @xcite can of course be parametrized - and factorized - in many different ways , and different factorizations correspond to different rotation matrices @xmath9 and @xmath10 . the most obvious and `` symmetric '' factorization of the ckm mixing matrix is , following the standard parametrization @xcite with three euler angles @xmath53 , @xmath54 , @xmath55 , @xmath56 with the diagonalizing rotation matrices for the up- and down - sectors @xmath57 and @xmath58 respectively , where @xmath53 , @xmath54 , @xmath59 and @xmath60 correspond to the parameters in the standard parametrization in such a way that @xmath61 , @xmath62 rad , and @xmath63 , while @xmath64 and @xmath65 .    from the rotation matrices @xmath9 and @xmath10 we then obtain the mass matrices @xmath66 and @xmath67 , such that @xmath68 where @xmath69 is the trace @xmath70 , and with @xmath71 , @xmath72 , @xmath73 ,    @xmath74    @xmath75    @xmath76    @xmath77\hspace{1mm}+\frac{f}{2}\hspace{1mm}(d - c)\hspace{1mm}(e^{i\gamma}-2\hspace{1mm}e^{-i\gamma})-2t+6\hspace{1mm}m_u$ ]    @xmath78    similarly for the down - sector , @xmath79 with the parameters @xmath80 , @xmath81 , @xmath82 ,    @xmath83 , and    @xmath84    @xmath85    @xmath86    @xmath87+\frac{f'}{2}(j+g)(2e^{i\gamma}-e^{-i\gamma})-2t'+6m_b$ ]    @xmath88    in order to evaluate to what degree these rather opaque matrices are democratic , we calculate numerical matrix elements by inserting numerical mass values . for the up - sector we get the ( nearly democratic ) matrix texture @xmath89\ ] ] where the `` small '' matrix @xmath90 with @xmath91 , is what breaks the democratic symmetry , supplying the two lighter families with non - zero masses . with mass values calculated at @xmath92 ( jamin 2014 ) @xcite , @xmath93 we get    @xmath94 , @xmath95,@xmath96 mev @xmath97 , and    @xmath98 , @xmath99,@xmath100 ,    @xmath101,@xmath102 .    for the down - sector , with @xmath103 we get another democratic texture , @xmath104 where    @xmath105 , @xmath106 , @xmath107 , @xmath108 , and @xmath109 @xmath110 @xmath111 .    just like in the up - sector mass matrix , the matrix elements in @xmath8 display a nearly democratic texture . for both the up - sector and the down - sector the mass matrices are thus approximately democratic . in the mass matrix literature there is an emphasis on `` calculability '' . the ideal is to obtain mass matrices that have a manageable form , but there is nothing that forces nature to serve us such user - friendly formalism . it is however tempting to speculate that there are relations between the elements that could make the democratic matrices more calculable , and in the search for matrices that are reasonably transparent and calculable , we look at a more radical factorization of the mixing matrix , viz . @xmath112 and @xmath113 where , as before , @xmath62 rad , and @xmath114 , while @xmath64 , and @xmath65 . these rotation matrices are still `` perturbations '' of the democratic diagonalizing matrix ( [ dem ] ) , and the up - sector mass matrix has a texture similar to ( [ 1 ] ) , @xmath115 where @xmath69 is the trace , @xmath70 , and    @xmath116 , @xmath117 ,    @xmath118    @xmath119 , @xmath120    with @xmath121 , @xmath122 . this matrix can be reformulated in a form similar to ( [ cu ] ) ,    @xmath123\ ] ] where @xmath124 , @xmath125 $ ] , @xmath126 , and @xmath127 with    @xmath128,@xmath129 ,    @xmath130 ,    @xmath131 ,    @xmath132    inserting the mass values ( [ jam1 ] ) gives    @xmath133,@xmath134 , @xmath135 , and    @xmath136 , @xmath137 , @xmath138    for the down - sector , with @xmath139 the mass matrix @xmath140 reads @xmath141 where    @xmath142    @xmath143    @xmath144 ,    @xmath145 . inserting the mass values ( [ jam2 ] ) we moreover get the numerical values    @xmath146,@xmath147,@xmath148,@xmath149 . by including the democratic rotation matrix in the parametrization of the weak mixing matrix , we obtain mass matrices with specific democratic textures . in this way we make contact between the democratic hypothesis and the experimentally derived parameters of the ckm mixing matrix , avoiding the introduction of additional concepts . h. fusaoka , y. koide , `` updated estimate of running quark masses '' , hep - ph/9712201v2 , dec . 1997 ; r. barbieri , g. dvali , a. strumia , z. berezhiani , l. hall , `` flavour in supersymmetric grand unification : a democratic approach , '' hep - ph/9405428v3 .
within the framework of quark mass matrices with a democratic texture , the unitary rotation matrices that diagonalize the quark matrices are obtained by a specific parametrization of the cabibbo - kobayashi - maskawa mixing matrix . 
 different forms of democratic quark mass matrices are derived from slightly different parametrizations .