document: in recent time people are too much interested to find some flavor symmetry in order to generate mass and mixing pattern of fermions . 
   continuous symmetry like @xmath9 @xcite , @xmath10 @xcite symmetry and most popular discrete symmetry , @xmath11 exchange symmetry ( @xmath12@xcite have got some success to describe mass and mixing pattern in leptonic sector . to avoid mass degeneracy of @xmath13 and @xmath14 under @xmath15 symmetry , 
   e. ma and g. rajasekaran in @xcite have introduced first time the @xmath1 symmetry . 
   after this paper , a lot of work have done with this symmetry @xcite-@xcite . 
   after introduction of tri - bi maximal mixing pattern ( @xmath16 , @xmath17 , @xmath18)@xcite , people have tried to fit this mixing pattern through the @xmath1 symmetry . in an well motivated extension of the standard model through the inclusion of @xmath1 discrete symmetry tri - bi 
   maximal mixing pattern comes out in a natural way in the work of altarelli and feruglio @xcite . 
   more precisely , the leptonic mixing arises solely from the neutrino sector since the charged lepton mass matrix is diagonal . 
   the model @xcite also admits hierarchical masses of the three charged leptons whereas the neutrino masses are quasi - degenerate or hierarchical . 
   although the model gives rise to @xmath19 ( @xmath20 ) which is consistent with the chooz - palo verde experimental upper bound ( @xmath21 at 3@xmath22 ) , however , the non - zero and complex value of @xmath0 leads to the possibility to explore _ 
   violation in the leptonic sector which is the main goal of many future short and long baseline experiments . within the framework of @xmath23 model , non - zero @xmath0 
   is generated either through the radiative correction @xcite or due to the introduction of higher dimensional mass terms @xcite . 
   generation of non zero complex @xmath0 and possibility of non - zero cp violation has been extensively studied in @xcite for the proposed model of altarelli - feruglio @xcite with explicit soft breaking of @xmath1 symmetry @xcite .    in the model 
   @xcite the authors showed that the tri - bi maximal mixing pattern is also generated naturally in the framework of see - saw mechanism with @xmath23 symmetry . 
   exact tri - bi maximal pattern forbids at low energy cp violation in leptonic sector . 
   the textures of mass matrices in @xcite could not generate lepton asymmetry also . in the present work , 
   we investigate the generation of non - zero @xmath0 through see saw mechanism by considering a small perturbation in @xmath2 , the dirac neutrino mass matrix , keeping the same texture of the right - handed majorana neutrino mass matrix as proposed in ref.@xcite . at first , we have studied in detail perturbation of @xmath2 by adding a small parameter at different entries of @xmath2 and see the variations of three mixing angles in terms of other model parameters considering all of them real . 
   we extend our analysis to the complex case for a suitable texture . 
   we study detailed phenomenology of neutrino mass and mixing including cp violation at low energy , neutrinoless double beta decay and leptogenesis . 
   our approach to get nonzero @xmath0 is minimal as we break @xmath1 symmetry explicitly by single parameter in single element of @xmath2 . 
   generation of cp violation at low energy as well as high energy is also minimal as we consider only one parameter complex . 
   we consider the model proposed in @xcite , which gives rise to diagonal @xmath2 and @xmath24 ( the charged lepton mass matrix ) along with a competent texture of @xmath25 and after see - saw mechanism and diagonalisation gives rise to tri - bimaximal mixing pattern . 
   the model consists of several scalar fields to generate required vacuum alignment to obtain tri - bimaximal mixing . in table i. 
   , we have listed the scalar fields and their vev s and representation content under all those symmetries . 
   .list of fermion and scalar fields used in this model , @xmath26 . [ cols="^,^,^,^",options="header " , ]     the model is fabricated in such a way that after spontaneous breaking of @xmath1 symmetry , the @xmath15 symmetry remains on the neutrino sector and the charged lepton sector is invariant under @xmath27 symmetry . 
   consider the lagrangian of the model @xcite , @xmath28 after spontaneous symmetry breaking , the charged lepton mass matrix comes out diagonal with @xmath29 , @xmath30 , and @xmath31 . 
   the neutrino sector gives rise to the following dirac and majorana matrices @xmath32 where @xmath33 , @xmath34 . 
   the structure of light neutrino mass matrix can be obtained from see - saw formula : @xmath35 where , @xmath36 this is clear from eq.[ssf ] that @xmath37 is the diagonalising matrix for light neutrino mass matrix @xmath38 . 
   the form of @xmath37 is in eq.[tbmix ] which is nothing but the so called tribimaximal mixing matrix . from eq.[ssf ] we have the eigenvalues of @xmath38 : @xmath39 from eq.[tbmix ] we have the mixing angles @xmath16 , @xmath40 and @xmath18 and from eq.[a4ev ] we get the solar and atmospheric mass squared differences as @xmath41 where @xmath42 , @xmath43 and all parameters are real . from the experiments we know @xmath3 is positive and dictates either @xmath44 or @xmath45 . 
   if @xmath44 , then it has to be small in order to generate small value of @xmath3 provided @xmath46 is not too small as @xmath3 . but small positive @xmath47 corresponds to same order of magnitude of @xmath3 and @xmath4 which is not acceptable according to the experimental results . 
   now @xmath44 only acceptable for @xmath48 and hierarchy of @xmath3 and @xmath4 obtained with the singular nature of @xmath4 as in eq.[a4msd ] near @xmath49 . 
   this corresponds to normal hierarchical mass spectrum . 
   again for @xmath50 , @xmath45 is the physical region . 
   this region of @xmath47 makes @xmath51 which is so called inverted ordering of neutrino mass pattern . 
   again @xmath52 should take small value in order to generate small value of @xmath3 . 
   for one complex parameter @xmath53 , we can write the mass differences in the following form @xmath54 in the complex case , positivity of @xmath3 can be obtained either with @xmath44 and @xmath55 or with @xmath56 and @xmath57 . for the first case with @xmath48 and with @xmath58 one can have normal hierarchical mass spectrum . for the second case hierarchy will be inverted and @xmath59 have to be small . in both case @xmath47 should take the value such that the @xmath60 range also satisfy . the mixing pattern is tri - bi maximal eq.[tbmix ] and it is independent to the fact whether the parameters are real or complex . in this mixing 
   pattern @xmath61 and non - zero complex @xmath0 is a basic requirement to see the non - zero dirac cp violation . 
   now we concentrate on the issue of leptogenesis in this model . 
   the decay of right handed heavy majorana neutrinos to lepton(charged or neutral ) and scalar(charged or neutral ) generate non - zero lepton asymmetry if i ) c and cp are violated , ii)lepton number is violated and iii ) decay of right handed neutrinos are out of equilibrium . 
   we are in the energy scale where @xmath1 symmetry is broken but the sm gauge group remains unbroken . 
   so , the higgs scalars both charged and neutral are physical 
   . the cp asymmetry of decay is characterized by a parameter @xmath62 which is defined as @xmath63 spontaneous @xmath1 symmetry breaking generates right handed neutrino mass and the mass matrix @xmath25 obtained is shown in eq . 
   we need to diagonalize @xmath25 in order to go into the physical basis ( mass basis ) of right handed neutrino . 
   this form of @xmath25 gives the diagonalising matrix in the tri - bi maximal form @xmath37 in eq.[tbmix ] : @xmath64 however , the eigenvalues are not real . 
   we need to multiply one diagonal phase matrix @xmath65 with @xmath37 . 
   hence , diagonalising matrix @xmath66 relates the flavor basis to eigen basis of right handed neutrino : @xmath67 in this basis the couplings of @xmath68 with leptons and scalars are modified and it will be : @xmath69 at the tree level there there are no asymmetry in the decay of right handed neutrinos . due to the interference between tree level and one loop level diagrams , 
   the asymmetry is generated . 
   there are vertex diagram and self energy diagram to contribute to the asymmetry @xcite . 
   the vertex contribution is : @xmath70 \label{vertex}\end{aligned}\ ] ] and the self energy part is : @xmath71 where @xmath72 and @xmath73 the key matrix , whose elements are necessary to calculate leptogenesis , is @xmath74 . in this model 
   @xmath2 is diagonal and proportional to identity . 
   hence , @xmath74 matrix is real diagonal and it is also proportional to identity matrix and it is independent of the form of @xmath75 . 
   the terms for decay asymmetry generated by `` i '' th generation of right handed neutrino @xmath76 for both vertex and self energy contributions are proportional to @xmath77 ( where @xmath78 ) as in eq.[vertex ] and eq . 
   all off - diagonal elements of @xmath74 are zero . 
   so , decay of all three generation of right handed majorana neutrinos could not generate lepton asymmetry . 
   so , in this model of @xmath1 symmetry tri - bi maximal mixing pattern is not compatible with the low energy dirac cp violation as well as high energy cp violation . in order to obtain non - zero @xmath79 , 
   low energy dirac cp violation and leptogenesis we need to break the @xmath1 symmetry through not only spontaneously but also explicitly introducing some soft @xmath1 symmetry breaking ( soft in the sense that the breaking parameter is small to consider @xmath1 as an approximate symmetry ) terms in the lagrangian . 
   we consider minimal breaking of @xmath1 symmetry through a single parameter in a single element of @xmath2 keeping @xmath25 unaltered as @xmath80 we introduce the breaking by small dimensionless parameter @xmath81 to the @xmath82 element of dirac type yukawa term for neutrino . 
   after spontaneous @xmath83 symmetry breaking it modifies only one element @xmath82 of @xmath2 of neutrino . 
   there are nine possibilities to incorporate the breaking parameter @xmath81 in @xmath2 . we know that after spontaneous @xmath1 symmetry breaking , a residual @xmath15 symmetry appears in neutrino sector . 
   there is a special feature of @xmath15 symmetry which ensures one @xmath84 and one maximal @xmath85 mixing angles . 
   there is one task to check whether our newly introduced explicit breaking term can break @xmath15 symmetry or not . 
   this is important because we need non - zero @xmath79 . 
   we have seen that in one case out of the nine possibilities , residual @xmath15 symmetry remains invariant . 
   this is @xmath86 case . in other cases 
   @xmath15 symmetry is broken and one expect non - zero @xmath79 from those cases . primarily , we consider that all parameters are real . 
   we want to study the mixing pattern and want to see its deviation from tri - bi maximal pattern considering experimental value of mass squared differences of neutrinos . 
   we explore all nine cases including @xmath86 case . 
   although @xmath86 case could not generate non - zero @xmath79 , however , we want to see whether this breaking can reduce the tri - bi maximal value of @xmath87 ( @xmath88 ) to its best fit value ( @xmath89 ) or not along with the special feature @xmath90 and @xmath91 . here 
   , we explicitly demonstrate the procedure for a single case and for the other cases expressions for eigenvalues and mixing angles are given in apendix . 
   \(i ) breaking at 22 element : in this case , the structure of @xmath2 is given by @xmath92 and after implementation of see - saw mechanism keeping the same texture of @xmath25 , three light neutrino mass eigenvalues come out as @xmath93 and the three mixing angles come out as @xmath94\nonumber\\ \sin\theta_{13 } & = & { \frac{\epsilon}{3 } } \left({\frac{d}{{\sqrt 2}a } } -{\frac{{\sqrt 2}d}{4a - 2d}}\right ) \label{angel22 } \end{aligned}\ ] ] assuming a relationship between the parameters @xmath95 and @xmath96 as @xmath97 we rewrite in a convenient way the above three mixing angles as @xmath98 \qquad\sin\theta_{13 } = \frac{\e k(1-k)}{3{\sqrt 2}(2-k ) } \label{mangel22 } \end{aligned}\ ] ] and the mass - squared differences are @xmath99\nonumber\\ \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-2\e(2k^2 - 4k-1)\right ] \label{masd22}\end{aligned}\ ] ] where @xmath100 . 
   defining the ratio @xmath101 in terms of mass - squared differences we get @xmath102 }      { \left[3k(2-k)-2\e(2k^2 - 4k-1)\right ] } \label{r22 } \end{aligned}\ ] ] which in turn determines the parameter @xmath81 as @xmath103 }      { \left[(k-1)^2(2k^2 + 4k+1)+      r(k+1)^2(2k^2 - 4k-1)\right ] } \label{ep22 } \end{aligned}\ ] ] similarly , we have evaluated all other possible cases which we have listed in the appendix . 
   plot of @xmath87 with respect to @xmath47 . 
   we keep @xmath104 and @xmath105 to their best fit values . , height=302 ]     plot of @xmath106 with respect to @xmath47 . 
   we keep @xmath104 and @xmath105 to their best fit values . 
   , height=302 ]     plot of @xmath107 with respect to @xmath47 . 
   we keep @xmath104 and @xmath105 to their best fit values . 
   , height=302 ]    now the @xmath108 parameter is determined in terms of @xmath101 and @xmath47 and we substitute it to the expressions for mixing angles . 
   thus it is possible to explore all three mixing angles @xmath87 , @xmath106 and @xmath107 in terms of @xmath101 and @xmath47 . 
   particularly , the deviation from tri - bimaximal mixing depends only on @xmath101 and @xmath47 . for the best fit values of the solar and atmospheric 
   mass squared differences ( @xmath109 ) , we have shown in fig . 
   [ th12 ] , fig . 
   [ th23 ] and fig . 
   [ th13 ] the variations of @xmath87 , @xmath106 , @xmath107 verses @xmath47 , respectively . 
   we have studied all nine possible cases and shown in the plots . 
   first of all , non - zero value of @xmath107 is obtained if we allow @xmath1 symmetry breaking terms explicitly in any one of the 12 , 13 , 21 , 31 , 22 , 33 element of the dirac neutrino mass matrix and those are the cases of our interest . in the present analysis 
   , we have shown that non - zero @xmath107 is generated in a softly broken @xmath1 symmetric model which leads to deviation from the tri - bimaximal mixing . in @xmath1 
   symmetric model @xmath107 is zero because of residual @xmath15 symmetry in neutrino sector after spontaneous breaking of @xmath1 symmetry . 
   apart from the explicit breaking of @xmath1 symmetry at 11 element , @xmath15 is broken for all 12 , 13 , 21 , 31 , 22 , 33 , 23 , 32 cases . 
   furthermore , perturbation around 23 , 32 elements also lead to zero value of @xmath107 at the leading order although @xmath15 symmetry is broken , non - zero value is generated if we consider higher order terms of @xmath110 which are too tiny and hence , discarded from our analysis . 
   we include 11 case for completeness which preserves @xmath15 symmetry and hence generates @xmath111 and @xmath91 . 
   it only shifts @xmath87 from the tri bimaximal value , but it can not be able to go towards the best fit value of solar angle , @xmath112 . 
   if @xmath113 , then we get @xmath114 , and thereby , the value of @xmath107 is very small also @xmath87 will hit the exact tri - bimaximal value in some cases . 
   the effect of variation on the mixing angles around @xmath115 are asymmetric . 
   for some cases ( for example 23 , 32 ) @xmath106 changes very fast in the @xmath116 region . 
   so , we explore the mixing angles with the range @xmath117 . we choose the most feasible cases in which perturbation is applied around 12 , 13 elements , because in those cases , variation of @xmath47 encompasses the best - fit values of @xmath87 and @xmath106 . 
   although , in the 21 , 31 cases , the value of @xmath106 touches the best - fit value @xmath85 , however , @xmath87 far apart from the best - fit value . 
   in order to achieve large @xmath107 , we have to choose the 21 , 31 cases , but we have to allow the variation of @xmath87 around as large as @xmath118 . in case of 22 , 33 , the structure of @xmath2 is still diagonal and also we can get larger @xmath107(upto @xmath119 ) and also @xmath87 is within @xmath120 , however , @xmath106 will reach @xmath121 value .    in summary , we have shown that non - zero @xmath107 is generated in a @xmath1 symmetric model which leads to deviation from the tri - bimaximal mixing through see - saw mechanism due to the incorporation of an explicit @xmath1 symmetry breaking term in @xmath2 . 
   the breaking is incorporated through a single parameter @xmath108 and we have investigated the effect of such breaking term in all nine elements of @xmath2 . 
   some of them generates still zero value of @xmath107 and rest of the others generated non - zero @xmath107 . 
   we expressed all three mixing angles in terms of one model parameter and showed the variation of all three mixing angles with the model parameter @xmath47 . 
   we find breaking through 12 and 13 elements of @xmath2 are most feasible in view of recent neutrino experimental results . 
   in this section , we consider one of the parameter is complex and out of all nine cases as mentioned earlier , we investigate one suitable case arises due to 13 element perturbation . 
   this is one of the suitable positions of breaking justified from real analysis . 
   again this extension is minimal to generate non - zero cp violation because we consider only one parameter complex . 
   we take @xmath95 as complex : @xmath53 . hence , 
   the form of @xmath2 and @xmath25 under explicit @xmath1 symmetry breaking with complex extension are : @xmath122      using the see - saw mechanism we get the light neutrino mass matrix as @xmath123 we need to diagonalize the @xmath38 to obtain the masses and mixing angles . 
   the eigenvalues are same as we have in the real case and only difference is that the @xmath95 is complex now . 
   we explicitly write down the complex phase in the mass matrix . 
   the obtained eigenvalues are : @xmath124 where we keep terms upto first order in @xmath81 . now with @xmath42 , @xmath125 and keeping term upto first order in @xmath81 we get the three neutrino mass squared as @xmath126 using those expressions we get the mass squared differences and their ratio which are , @xmath127 and @xmath128 . 
   \label{rc13 } \end{aligned}\ ] ] the mixing angles are obtained from diagonalisation of @xmath38 . 
   we solve the equations of the form @xmath129 . these @xmath130 will give the columns of the diagonalising unitary matrix @xmath131 . throughout our calculation 
   we assume that breaking parameter @xmath81 is small . 
   we have the nonzero @xmath132 which is proportional to @xmath81 . 
   so , the values of @xmath133 and @xmath134 will give the solar and atmospheric mixing angles , respectively . 
   the expressions for the mixing angles come out as @xmath135     plot of @xmath87 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in 13 element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values.,height=302 ]    @xmath137    @xmath138^{1/2 } \label{t13c13}. \end{aligned}\ ] ]    from the expression of mixing angles it is clear that the deviations from tri - bi maximal are first order in @xmath81 . 
   the independent parameters in this model are @xmath96 , @xmath95 , @xmath139 , @xmath81 and @xmath136 . 
   alternatively the independent parameters are @xmath140 , @xmath141 , @xmath47 , @xmath81 and @xmath136 ( where @xmath142,@xmath125 , @xmath143 ) . in the above analysis of light neutrino mass and mixing , scale @xmath140 
   did not appear explicitly . 
   we have four well measured observable which are @xmath3 , @xmath4 , @xmath87 and @xmath106 , and , thus , in principle it is possible to determine four parameters @xmath141 , @xmath47 , @xmath81 and @xmath136 and we are able to predict the other less known observable such as angle @xmath107 , cp violating parameter @xmath144 etc . 
   it is difficult to get inverse relations of those observable . from the expression of @xmath101 in eq . 
   [ rc13 ] we easily obtain the expression for @xmath81 as     plot of @xmath106 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in 13 element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values . 
   , height=302 ]     plot of @xmath107 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in `` 13 '' element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values . 
   , height=302 ]    @xmath145}{4\left[r(1+k^2 - 2k\cos\phi)(1+k^2 + 2k\cos\phi)+(2+k^2 + 2k\cos\phi)(1+k^2 - 2k\cos\phi)\right]}.\nonumber\\   \label{epc13 } \end{aligned}\ ] ]    now using the relation of @xmath4 with the parameters eq . [ msdc13 ] we get the expression for @xmath46 : @xmath146 where @xmath81 is in the form of eq . 
   [ epc13 ] . 
   thus , @xmath81 and @xmath46 depend on the parameters @xmath47 , @xmath136 and experimentally known @xmath101 . 
   extraction of @xmath47 and @xmath136 from other two known mixing angles is little bit difficult . 
   rather we have plotted @xmath87 and @xmath106 with respect to @xmath47 and @xmath136 and obtain the restriction on the parameter space of @xmath47 and @xmath136 . from the expression of @xmath147 in eq . 
   [ t12c13 ] we are seeing that there is a factor @xmath59 in the denominator . 
   for @xmath116 there will be a @xmath136 for which the quantity @xmath59 becomes zero . 
   hence , we should keep @xmath45 . 
   again the factor @xmath59 should be small to ensure that @xmath81 is also small . 
   it justifies our whole analysis because we consider first order perturbation as we considered symmetry @xmath1 remains approximate . 
   we consider the range @xmath148 and @xmath149 . from fig . 
   [ th12c13 ] we see that @xmath87 changes from the tri - bi maximal value @xmath150 to @xmath151 . 
   near @xmath152 it crosses the best fit value @xmath112 . 
   we have plotted @xmath106 in fig . 
   [ th23c13 ] . 
   the variation of @xmath106 is from @xmath153 to @xmath154 for the same range of @xmath47 and @xmath136 . 
   the best fit value @xmath155 is remain within range of variation and it is in the low @xmath47 low @xmath136 region . 
   the plot of @xmath107 is in fig . 
   [ th13c13 ] . 
   value of @xmath107 remains within @xmath156 for the same range of @xmath47 and @xmath136 and the model predicts @xmath107 is very small but non - zero . 
   question may arise whether such small value of @xmath107 can generate observable cp violation or not .    keeping all those constraints in view 
   next we explore the parameter space of cp violation parameter @xmath157 . the parameter @xmath157 defined as @xcite @xmath158 }     { \delta m^2_{21}\delta m^2_{31}\delta m^2_{32 } } \label{jcp1}\end{aligned}\ ] ] where @xmath159 , @xmath160 is dirac phase . 
   this @xmath161 is associated with cp violation in neutrino oscillation and is directly related to dirac phase of mixing matrix . 
   plot of @xmath157 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in 13 element of @xmath2 in the unit of @xmath162 . 
   we keep @xmath104 and @xmath105 to their best fit values . 
   , height=302 ]     plot of @xmath163 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in `` 13 '' element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values . 
   , height=302 ]    the from eq . 
   ( [ mnuc ] ) we can express @xmath38 matrix in terms of @xmath81 and @xmath141 and @xmath47 and @xmath136 . 
   with the expressions for @xmath81 and @xmath141 we can easily obtain the @xmath38 and hence @xmath164 completely in terms of @xmath47 and @xmath136 . 
   hence , similar to the mixing angles @xmath144 will be also only function of @xmath47 and @xmath136 . 
   we have plotted @xmath144 in fig . 
   [ fjcp1 ] where the values are normalized by a factor @xmath162 . for 
   the same range of @xmath47 and @xmath136 the model predicts @xmath144 up to the order of @xmath165 which is appreciable to observe through the forthcoming experiments . inverting the expression of @xmath144 , 
   the phase @xmath160 is extracted in terms of @xmath47 and @xmath136 and it is plotted in fig . 
   [ dcp13 ] . 
   we see that the value of @xmath160 is large upto @xmath166 and , thereby , compensates small @xmath107 effect in @xmath144 and makes it observable size . one important discussion we have to make about the range of @xmath136 and @xmath47 . 
   one can ask why we are keeping ourselves small range of those parameters where larger @xmath136 can enhance the @xmath107 and @xmath144 . 
   we have studied that the larger value of @xmath136 and also @xmath47 in negative become responsible for breaking the analytic bound @xmath167 . 
   so , we keep ourselves in shrinked parameter space which keep @xmath87 and @xmath106 in exceptionally good values according to the experiment and also can able to generate observable cp violation instead of small @xmath107 . 
   another thing we want to point out that negative value of @xmath136 equally acceptable as far as it is small . 
   it could not change mixing angles because their expressions depend on @xmath136 through @xmath168 and @xmath169 . only @xmath144 and @xmath160 will change in sign which are unsettled according to the experiments .    at the end 
   we want to check whether the range of @xmath47 and @xmath136 can satisfy the double beta decay bound @xmath170 ev . in our model expression for this quantity is : @xmath171 and it will be also only function of @xmath47 and @xmath136 . 
   we plot this in fig . 
   [ mee13 ] and it remains well below the experimental upper bound . 
   again we want to discuss about the mass pattern . throughout our whole analysis in real as well as complex case 
   we keep @xmath3 and @xmath4 to their best fit value and take the negative sign of @xmath4 . 
   it corresponds to so called inverted ordering of neutrino mass . 
   it is the feature near @xmath115 . 
   it is necessary to keep @xmath172 . 
   why we so fond of this region of @xmath47 instead of region @xmath173 which can give the normal hierarchical mass spectrum . 
   the reason is that the inverted ordering corresponds to the light neutrino mass scale @xmath174 where @xmath175 for normally ordered mass spectrum . 
   so , from the point of view of observable cp violation , it is inevitable to choose larger value of @xmath141 because @xmath176 . 
   so , inverted hierarchical mass spectrum compatible with the observable cp violation . 
   now we extend our study of this model to leptogenesis . 
   we want to see whether we can have appreciable leptogenesis compatible with baryon asymmetry for the same parameter space @xmath47 and @xmath136 after successful low energy data analysis for the feasible value of scale @xmath140 . 
   plot of @xmath177 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in `` 13 '' element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values . 
   , height=302 ]      after successful predictions of low energy neutrino data we want to see whether this model can generate non - zero lepton - asymmetry with proper size and sign to describe baryon asymmetry . 
   we keep the same right handed neutrino mass matrix @xmath25 as before . 
   the change only appear in dirac type yukawa coupling and hence in @xmath2 also . 
   the diagonalisation of @xmath25 gives @xmath178 and hence the masses of the right handed neutrino are @xmath179 and the phases are @xmath180 the explicit form of diagonalising matrix is @xmath181 where the expressions for the phases are given in eq . 
   ( [ majp ] ) . 
   the @xmath2 matrix is no longer diagonal after explicit breaking of @xmath1 symmetry . in the mass basis of right handed neutrino 
   the modified dirac mass term is @xmath182 . 
   hence the relevant matrix for describing leptogenesis is : @xmath183 to calculate lepton asymmetry as in eq . 
   ( [ vertex ] ) and eq . 
   ( [ self ] ) we need to calculate following quantities from matrix @xmath74 : @xmath184 calculating @xmath72 from eq . 
   [ mrev ] , @xmath185 from eq . 
   ( [ hc13 ] ) and taking @xmath77 from eq . 
   ( [ imh ] ) we calculate the self energy part of lepton asymmetry from eq . 
   ( [ self ] ) and vertex part of lepton asymmetry from eq . 
   ( [ vertex ] ) . adding both we obtain the following decay asymmetry of right handed neutrinos for all three generations @xmath186.\nonumber\\ \label{las1 } \end{aligned}\ ] ] @xmath187   \label{las2 } \end{aligned}\ ] ] @xmath188\nonumber\\ \label{las3 } \end{aligned}\ ] ] cp asymmetry parameters @xmath62 are related to the leptonic asymmetry parameters through @xmath189 as @xcite @xmath190 where @xmath191 is the lepton number density , @xmath192 is the anti - lepton number density , @xmath193 is the entropy density , @xmath194 is the dilution factor for the cp asymmetry @xmath62 and @xmath195 is the effective number of degrees of freedom @xcite at temperature @xmath196 . 
   value of @xmath195 in the sm with three right handed majorana neutrinos and one extra higgs doublet is @xmath197 . 
   the baryon asymmetry @xmath198 produced through the sphaleron transmutation of @xmath189 , while the quantum number @xmath199 remains conserved , is given by @xcite @xmath200 where @xmath201 is the number of fermion families and @xmath202 is the number of higgs doublets . the quantity @xmath203 in eq . 
   ( [ barasym ] ) for sm with two higgs doublet . 
   now we introduce the relation between @xmath198 and @xmath204 , where @xmath204 is the baryon number density over photon number density @xmath205 . 
   the relation is @xcite @xmath206 where the zero indicates present time . now using the relations in eqs.([leptasym],[barasym ] , [ yetar ] ) , @xmath203 and @xmath207 we have @xmath208 this dilution factor @xmath194 approximately given by @xcite @xmath209 where @xmath210 is the decay width of @xmath211 and @xmath212 is hubble constant at @xmath196 . 
   their expressions are @xmath213 where @xmath214 , @xmath215gev and @xmath216gev . 
   thus we have @xmath217 for our model @xmath218 , @xmath219 and @xmath220 are @xmath221     plot of baryon asymmetry @xmath222 in unit of @xmath223 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in `` 13 '' element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values and have plotted for mass scale of right handed neutrino @xmath224 gev , height=302 ]     plot of baryon asymmetry @xmath222 in unit of @xmath223 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in `` 13 '' element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values and have plotted for mass scale of right handed neutrino @xmath225 gev , height=302 ]     plot of baryon asymmetry @xmath222 in unit of @xmath223 with respect to @xmath47 and @xmath136 for the breaking of @xmath1 in `` 13 '' element of @xmath2 . 
   we keep @xmath104 and @xmath105 to their best fit values and have plotted for mass scale of right handed neutrino @xmath226 gev , height=302 ]     we combine all three plots of baryon asymmetry for three right handed neutrino mass scale along with the wmap value of baryon asymmetry @xmath7 which is the plane surface.,height=302 ]    where @xmath227 , @xmath228 . using eq . 
   ( [ k1k2k3 ] ) into eq . 
   ( [ kppa ] ) and from the expression of @xmath62 we can say that apart from logarithmic factor , @xmath229 and @xmath230 . 
   so , baryon asymmetry will be independent of @xmath141 and @xmath231 . 
   they only appear through logarithmic factor in @xmath194 . 
   we consider @xmath232 . 
   substituting @xmath141 from eq . 
   ( [ m013c ] ) , @xmath81 from eq . 
   ( [ epc13 ] ) and considering @xmath140 some specific value into the expressions of @xmath62 , @xmath194 we can have baryon asymmetry as function of @xmath47 and @xmath136 only . in fig . 
   [ basymp1 ] , fig . 
   [ basymp2 ] and fig . 
   [ basymp3 ] we have plotted @xmath204 as function of @xmath47 and @xmath136 in the unit of @xmath223 for three @xmath140 values , @xmath224 gev , @xmath225 gev and @xmath226 gev rspectively . 
   we have seen that the experimental value of @xmath233 is obtainable in our model within the same range of @xmath234 and @xmath136 as in the low energy case . 
   to see more explicitly the baryon asymmetry plots we combine all three plots along with the observed baryon asymmetry value @xmath7 which corresponds the plane surface in fig . 
   [ basym0 ] . 
   the observed wmap value of the baryon asymmetry curve intersect the lower curve ( for @xmath224 gev ) near the boundary of @xmath234 and @xmath136 variation . 
   so , lower value of @xmath140 could not generate observable baryon asymmetry . in the intersection region 
   @xmath235 and @xmath236 
   . if we allow that much of variation of @xmath87 and @xmath106 , we can have large low energy cp violation as well as baryon asymmetry with proper size and sign with @xmath224 gev which is near the upper bound of right handed neutrino mass scale for generation of lepton as well as baryon asymmetry . 
   if we more relax , we can easily see that the intersection of experimental and theoretical curve for @xmath225 gev and @xmath226 gev is in the lower value of @xmath47 and @xmath136 where well known neutrino mixing angles are more closer to their best fit value . 
   let us give a close look to the plot of @xmath204 in fig . 
   [ basymp1 ] , fig . 
   [ basymp2 ] and fig . 
   [ basymp3 ] near very low @xmath136 and @xmath237 region . 
   this is the region where @xmath238 become very large . from the expression of @xmath239 and @xmath240 
   it is clear that @xmath239 and @xmath240 both are singular at @xmath241 . 
   this corresponds to equality of the masses @xmath242 or @xmath243 . 
   this singularity can be avoided considering finite decay width of right handed neutrinos . 
   we can able to maximize @xmath239 and @xmath240 and hence @xmath204 using resonant condition @xmath244 . 
   but , as we have already obtained the observed baryon asymmetry without resonance , it is not necessary to think about so finely tuned condition . again in the region where the resonant condition is applicable , the @xmath144 is miserably small to observe through any experiments . 
   contour plot of baryon asymmetry @xmath222 , @xmath87 and , @xmath106 in @xmath136-@xmath47 plane for @xmath104 and @xmath105 to their best fit values and for mass scale of right handed neutrino @xmath224 gev.,height=226 ]     contour plot of baryon asymmetry @xmath222 , @xmath87 and , @xmath106 in @xmath136-@xmath47 plane for @xmath104 and @xmath105 to their best fit values and for mass scale of right handed neutrino @xmath225 gev.,height=226 ]     contour plot of baryon asymmetry @xmath222 , @xmath87 and , @xmath106 in @xmath136-@xmath47 plane for @xmath104 and @xmath105 to their best fit values and for mass scale of right handed neutrino @xmath226 gev.,height=226 ]    we end our analysis with the help of three contour plots of baryon asymmetry @xmath245 for three scales @xmath224 gev , @xmath225 gev and , @xmath226 gev in @xmath136-@xmath47 plane . 
   we insert the contours of @xmath106 and @xmath87 and manage to find the intersection of three contours for some reasonable value of @xmath106 and @xmath87 . 
   case(i ) : @xmath224 gev , from fig . 
   [ fig : contplot1 ] , we are seeing that three contours @xmath246 , @xmath247 and , @xmath245 are intersecting at a point ( @xmath248 , @xmath249 ) in @xmath136-@xmath47 plane . 
   so , the mixing angles are within nearly @xmath156 variation about the best fit values . 
   obtained @xmath47 , @xmath136 value gives @xmath250 , @xmath251 , @xmath252 , @xmath253 ev , @xmath254 ev , @xmath255 and @xmath256 . 
   case ( ii ) : @xmath225 gev , now from fig . 
   [ fig : contplot2 ] , we have the intersection of the contour @xmath245 with the contours @xmath257 , @xmath258 at ( @xmath259 , @xmath260 ) in @xmath136-@xmath47 plane . 
   so , @xmath87 and @xmath106 are more closer to their best fit values ( nearly @xmath261 deviation from their best fit value ) . at this point 
   we have @xmath262 , @xmath263 , @xmath264 , @xmath265 ev , @xmath266 ev , @xmath267 and @xmath268 .    case ( iii ) : @xmath226 gev , from the fig . 
   [ fig : contplot3 ] , the contours @xmath245 , @xmath269 and , @xmath270 have crossed in @xmath136-@xmath47 plane at ( @xmath271 , @xmath272 ) . 
   so , higher scale of right handed neutrino mass helps to have very good value of @xmath87 and @xmath106 . at the intersection point 
   , we get @xmath273 , @xmath274 , @xmath275 , @xmath276 ev , @xmath277 ev , @xmath278 and @xmath279 .    the small value of @xmath81 compatible with all experimental results . 
   so , we can demand that @xmath1 is an approximate symmetry .      in this model 
   everything is determinable in terms of parameter @xmath47 and @xmath136 . 
   well measured quantities fix the value of those parameters . 
   so , value of the rest of the physical quantities ( some of them not so well measured in experiment like @xmath107 , @xmath280 and some of them yet to measure in experiment like @xmath144 , @xmath160 and the majorana phases also ) are obtainable in this model . 
   question may arise whether we can have any relations among the phases in this model or not . 
   first of all , there are two kinds phases , low energy and high energy phases . 
   high energy phases are responsible to generate the lepton asymmetry . 
   the low energy phases are responsible for determining low energy leptonic cp violation . 
   low energy phases are in two type , one is the lepton no preserving cp violating phase @xmath160 and another two are the lepton no breaking cp violating phases . in general , all phases are independent , meaning that there are no correlation among the phases between high and low energy sector , and also phases inside a particular sector are not correlated . for three generations of neutrinos , there are three key phases which are responsible for leptogenesis 
   . those are phases in @xmath281 , @xmath282 , and @xmath283 . from matrix @xmath74 given in eq . 
   ( [ hc13 ] ) , we have @xmath284 it leads to the relation , @xmath285 for a given @xmath47 and @xmath136 the @xmath286 and @xmath287 are known from eq . 
   ( [ majp ] ) . 
   hence @xmath288 , @xmath289 and @xmath290 are individually determinable phases . 
   but , in this model values of those high energy phases follow the relation given in eq . 
   ( [ hprl ] ) . 
   now , let us give a fresh look to the leptonic mixing matrix . in eq . 
   ( [ mnuc ] ) we have given the tri - bimaximal rotated form of the neutrino mass matrix . 
   keeping terms upto first order in @xmath81 we obtain the diagonalising matrix in the following form , @xmath291 where the @xmath292 , @xmath293 , @xmath294 and the associated phases are completely known function of @xmath47 and @xmath136 . 
   an additional phase matrix @xmath295 is needed to make masses of light neutrino real , from eq . 
   ( [ msevc ] ) we have the phase matrix @xmath296 to obtain the ckm form of mixing matrix we need to rotate @xmath297 by two diagonal phase matrix , let @xmath298 and @xmath299 . 
   so , we have @xmath300 now the with @xmath107 small we can write @xmath301 and more six relations . 
   but these three are sufficient for our discussions . 
   the phases associated to @xmath297 elements , like @xmath302 , @xmath303 , and @xmath304 associated to @xmath305 , @xmath306 and @xmath307 respectively , are completely determinable in terms of @xmath47 , @xmath136 using functional form of @xmath81 , @xmath292 , @xmath293 , @xmath294 and their associates phases . now from the eq . 
   ( [ ckm ] ) we obtain the following phase relations @xmath308 now the form of total mixing matrix is , @xmath309 this phase part in the parenthesis can be absorbed to charged lepton fields and the remaining part gives the leptonic mixing matrix of the form @xmath310 , where the @xmath311 and @xmath312 are the two majorana phases of leptonic mixing matrix . from eq . 
   ( [ ffmv ] ) and using relations in eq . 
   ( [ prl1 ] ) and eq . 
   ( [ phh ] ) , we have the majorana phases , @xmath313 where @xmath314 and @xmath315 are known function of @xmath47 and @xmath136 . in eq . 
   ( [ majp2 ] ) we have the relation of low energy and high energy phases . 
   so , in our model we have correlation among the cp violating phases . 
   we have shown that non - zero @xmath0 is generated in a softly broken @xmath1 symmetric model through see - saw mechanism incorporating single parameter perturbation in @xmath2 in single element . 
   first , we have studied all possible nine cases to explore the mixing angles considering all model parameters real . the extent of @xmath107 investigated , keeping the experimental values of present solar and atmospheric mixing angles . among all nine possible texture of @xmath2 some of them generates non - zero @xmath107 . out of those non - zero @xmath107 generating textures of @xmath2 we find that breaking at 12 and 13 elements are encompassing the best values of @xmath87 and @xmath106 . however , the reach of @xmath107 in those cases are around @xmath261 . 
   considering one of the parameter complex we extend our analysis with one of the most suitable texture of @xmath2 with breaking at 13 element . 
   we have calculated mixing angles and neutrino mass squared differences in terms four model parameters ( @xmath141 , @xmath81 , @xmath47 , @xmath136 ) . 
   we restrict model parameters utilising the well measured quantities @xmath3 , @xmath4 , @xmath87 and @xmath106 and we have obtained @xmath107 ( upto @xmath156 ) and large @xmath144 ( @xmath316)and @xmath317 well below the present experimental upper bound . 
   in addition to that a large @xmath160 is also obtained . 
   further study on leptogenesis is also done and the present wmap value of baryon asymmetry is obtained for a right handed neutrino mass scale @xmath8 gev . in our model , we have seen that the phases responsible for the leptogenesis are correlated . 
   we also find out the relations among low energy cp violating phases and the lepton asymmetry phases . 
   small @xmath1 symmetry breaking parameter @xmath81 , is sufficient to describe the all low energy neutrino data and high energy cp violation ( leptogenesis ) . 
   so , @xmath1 symmetry is an approximate symmetry . 
   here we consider breaking of @xmath1 symmetry in all other entries of @xmath2 . 
   case ( i ) is already discussed in the text . 
   0.1 in ( ii)breaking at 11 element : in this case @xmath2 is given by @xmath318 the mass eigenvalues are @xmath319 and the three mixing angles come out as @xmath320 the solar and atmospheric mass differences and their ratio are @xmath321\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-4\e(k-1)^2\right]\nonumber\\ & & r = \frac{\ds}{\da }     = \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+4\e(k^2 + 2k-1)\right ] }      { \left[3k(2-k)-4\e(k-1)^2\right ] } \label{msd11 } \end{aligned}\ ] ] the obtained expression for @xmath81 in terms of model parameter @xmath47 and experimentally known @xmath101 : @xmath322 }      { \left[r(k+1)^2+k^2 + 2k-1\right ] }   \label{ep11 } \end{aligned}\ ] ] iii ) breaking at 33 element : in this case , the structure of @xmath2 is given by @xmath323 mass eigenvalues are @xmath324 and the angels are @xmath325 \quad   \sin\theta_{13 } =   -\frac{\e k(1-k)}{3{\sqrt 2}(2-k ) } \label{angel33 } \end{aligned}\ ] ] the solar and atmospheric mass differences and their ratio are @xmath326\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-2\e(2k^2 - 4k-1)\right]\nonumber\\ & & r = \frac{\ds}{\da }     = \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+2\e(2k^2 + 4k+1)\right ] }      { \left[3k(2-k)-2\e(2k^2 - 4k-1)\right ] } \label{msd33 } \end{aligned}\ ] ] the obtained expression for @xmath81 in terms of model parameter @xmath47 and experimentally known @xmath101 : @xmath327 }      { \left[(k-1)^2(2k^2 + 4k+1)+      r(k+1)^2(2k^2 - 4k-1)\right ] } \label{ep33 } \end{aligned}\ ] ] iv ) breaking at 12 element : in this case , the structure of @xmath2 is given by @xmath328 mass eigenvalues are @xmath329 and the three mixing angles come out as @xmath330 \quad \sin\theta_{13 } =   -\frac{\e}{3\sqrt 2}\frac{k^2-k-3}{(k-2)}\nonumber\\ \label{angel12 } \end{aligned}\ ] ] the solar and atmospheric mass differences and their ratio are @xmath331\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-4\e(1-k)^2)\right]\nonumber\\ & & r = \frac{\ds}{\da }     = \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+4\e(k^2 + 2k+2)\right ] }      { \left[3k(2-k)-4\e(1-k)^2\right ] } \label{msd12 } \end{aligned}\ ] ] the obtained expression for @xmath81 in terms of model parameter @xmath47 and experimentally known @xmath101 : @xmath332 }      { \left[(k^2 + 2k+2)+      r(k+1)^2\right ] } \label{ep12 } \end{aligned}\ ] ] v ) breaking at 13 element : in this case , the structure of @xmath2 is given by      the mass eigenvalues are @xmath329 and the three mixing angles come out as @xmath334\nonumber\\ \sin\theta_{13}&= &   -\frac{\e}{3\sqrt 2}\frac{k^2-k-3}{(k-2 ) } \label{angel13 } \end{aligned}\ ] ] the solar and atmospheric mass differences and their ratio are @xmath331\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-4\e(1-k)^2)\right]\nonumber\\ & & r = \frac{\ds}{\da }     = \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+4\e(k^2 + 2k+2)\right ] }      { \left[3k(2-k)-4\e(1-k)^2\right ] } \label{msd13 } \end{aligned}\ ] ] the obtained expression for @xmath81 in terms of model parameter @xmath47 and experimentally known @xmath101 : @xmath332 }      { \left[(k^2 + 2k+2)+      r(k+1)^2\right ] } \label{ep13 } \end{aligned}\ ] ] vi ) breaking at 23 element : in this case , the structure of @xmath2 is given by @xmath335 the mass eigenvalues are @xmath336 and the three mixing angles come out as @xmath337 \quad\quad   \sin\theta_{13 } = 0 \label{angel23 } \end{aligned}\ ] ] the solar and atmospheric mass differences and their ratio are @xmath326\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-2\e(2k^2 - 4k+5)\right]\nonumber\\ & & r = \frac{\ds}{\da }     = \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+2\e(2k^2 + 4k+1)\right ] }      { \left[3k(2-k)-2\e(2k^2 - 4k+5)\right ] } \label{msd23 } \end{aligned}\ ] ] the obtained expression for @xmath81 in terms of model parameter @xmath47 and experimentally known @xmath101 : @xmath327 }      { \left[r(1+k)^2(2k^2 - 4k+5)+      ( k-1)^2(2k^2 + 4k+1)\right ] } \label{ep23 } \end{aligned}\ ] ] vii ) breaking at 21 element : in this case , the structure of @xmath2 is given by @xmath338 the mass eigenvalues are @xmath329 and the three mixing angles come out as @xmath339\nonumber\\ \sin\theta_{13 } & = & \frac{\epsilon}{3\sqrt 2}\frac{(3+k^2 - 4k ) } { ( 2-k ) } \label{angel21 } \end{aligned}\ ] ] the solar and atmospheric mass differences and their ratio are @xmath331\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-4\e(1-k)^2\right]\nonumber\\ & & r = \frac{\ds}{\da }     = \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+4\e(k^2 + 2k+2)\right ] }      { \left[3k(2-k)-4\e(1-k)^2\right ] } \label{msd21 } \end{aligned}\ ] ] the obtained expression for @xmath81 in terms of model parameter @xmath47 and experimentally known @xmath101 : @xmath340 }      { \left[r(1+k)^2+k^2 + 2k+2      \right ] } \label{ep21 } \end{aligned}\ ] ] viii ) breaking at 31 element : in this case , the structure of @xmath2 is given by @xmath341 the mass eigenvalues are @xmath329 and the three mixing angles come out as @xmath342\nonumber\\ \sin\theta_{13 } & = & -\frac{\e}{3\sqrt{2 } } \frac{3+k^2 - 4k}{2-k } \label{angel31 } \end{aligned}\ ] ] the solar and atmospheric mass differences and their ratio are @xmath331\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-4\e(1-k)^2\right]\nonumber\\ & & r = \frac{\ds}{\da}= \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+4\e(k^2 + 2k+2)\right ] }      { \left[3k(2-k)-4\e(1-k)^2\right ] }                 \label{msd31 } \end{aligned}\ ] ] the obtained expression for @xmath81 in terms of model parameter @xmath47 and experimentally known @xmath101 : @xmath332 }      { \left[r(1+k)^2+k^2 + 2k+2      \right ] } \label{ep31 } \end{aligned}\ ] ] ix ) breaking at 32 element : in this case , the structure of @xmath2 is given by @xmath343 the mass eigenvalues are @xmath336 and the three mixing angles come out as @xmath344 \quad   \sin\theta_{13 } = 0 \label{angel32 } \end{aligned}\ ] ] the solar and atmospheric mass differences and their ratio are @xmath326\nonumber\\ & & \da = \frac{m_0 ^ 2}{3(1-k)^2}\left [ 3k(2-k)-2\e(2k^2 - 4k+5)\right]\nonumber\\ & & r = \frac{\ds}{\da }     = \frac{(k -1)^2}{(k+1)^2 }      \frac{\left[3k(k+2)+2\e(2k^2 + 4k+1)\right ] }      { \left[3k(2-k)-2\e(2k^2 - 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summary: we have shown that non - zero @xmath0 is generated in a see - saw type softly broken @xmath1 symmetric model through a single parameter perturbation in @xmath2 in a single element . 
   we have explored all possible 9 cases to study the neutrino mixing angles considering the best fitted values of @xmath3 and @xmath4 with all parameters real . 
   we have extended our analysis for the complex case and demonstrated large low energy cp violation ( @xmath5 ) and @xmath6 in addition to mixing and mass pattern . 
   we have also investigated leptogenesis and for a reasonable choice of model parameters compatible with low energy data , wmap value of baryon asymmetry @xmath7 is obtained for right handed neutrino mass scale @xmath8 gev . 
   we have obtained a relation among the phases responsible for leptogenesis and have shown that those phases also have correlations with low energy cp violating phases . 
   pacs number(s ) : 14.60.pq , 11.30.hv , 98.80.cq