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the seesaw mechanism  @xcite seems to provide a simple way to understand the smallness of neutrino masses . the simplest among the various seesaw mechanisms is the type - i seesaw , which requires the introduction of standard model ( sm ) gauge - singlet right - handed ( rh ) neutrinos ( @xmath3 s ) . the majorana mass @xmath4 of these rh neutrinos explicitly breaks the global @xmath5 symmetry of the sm by two units and gives rise to a light neutrino mass matrix of the form @xmath6 where @xmath7 is the dirac mass generated due to the neutrino yukawa couplings @xmath8 after the electroweak symmetry breaking . if one assumes maximal allowed values for the third - generation dirac mass @xmath9 , as is implied by certain grand unified theories such as @xmath10 , then the seesaw scale is pushed up to @xmath11 gev making it virtually inaccessible to both collider experiments at the energy frontier and other low energy searches at the intensity frontier . such naive (  dimensional counting " ) considerations however can be misleading in the context of specific ultraviolet ( uv ) complete seesaw models where there may be dynamical suppressions of neutrino dirac masses . one class of such models that are based on the sm gauge group generally go by the name of radiative seesaw models ; see e.g.  @xcite . within the type - i seesaw framework , there exists another possibility to suppress the light neutrino masses by assigning specific textures to the dirac and majorana mass matrices in the seesaw formula  @xcite . the stability of these textures can in principle be guaranteed by enforcing some symmetries in the lepton sector . extending the sm gauge group to the left - right ( l - r ) symmetric gauge group @xmath0 provides a simple uv - complete seesaw model  @xcite . here , the rh neutrinos are a necessary part of the model and do not have to be added ` by hand ' just to implement the seesaw mechanism . an important point is that the rh neutrinos acquire a majorana mass as soon as the @xmath12 symmetry is broken at a scale @xmath13 . this is quite analogous to the way the charged fermions get masses in the sm by the higgs mechanism when the @xmath14 gauge symmetry is broken at a scale @xmath15 . the higgs field that gives mass to the rh neutrinos becomes the analogue of the 125 gev higgs boson discovered at the lhc .    in this proceedings , we focus on a new class of l - r seesaw models  @xcite , where in addition to the rh gauge bosons as well as other higgs fields , light ( tev scale ) rh neutrinos with sizable mixing with the left - handed ( lh ) neutrinos may be accessible at colliders and other low energy experiments ( for a review , see e.g.  @xcite ) . with the lhc ramping up to a higher center of mass energy @xmath16 tev and later to 14 tev , our model as well as other low scale seesaw models , should provide motivation for testing the origin of neutrino mass in the coming years . for the collider phenomenology of tev - scale lrsm , see e.g.  @xcite , and for the current experimental status , see  @xcite . such considerations should also be of interest  @xcite for setting physics goals for future higher energy colliders such as the @xmath17 or 100 tev vlhc  @xcite . it is also important to mention here that the new class of l - r seesaw models with relatively large left - right neutrino mixing can be distinguished from the minimal lrsm using different kinematic variables  @xcite . an attractive consequence of the seesaw mechanism is the possibility that it could solve another important puzzle of cosmology ,  i.e.  the origin of matter - antimatter asymmetry in our universe , via a mechanism called leptogenesis  @xcite . at the heart of this mechanism is the out - of - equilibrium decay of the rh majorana neutrinos via the decay modes @xmath18 ( where the superscript @xmath19 denotes the @xmath2-conjugate ) , which violate @xmath20 , @xmath21 and @xmath2 , thereby dynamically generating an asymmetry in the lepton sector . this primordial lepton asymmetry undergoes thermodynamic evolution as the universe expands and finally gets converted to a baryon asymmetry via equilibrated electroweak sphaleron interactions  @xcite . the attractive aspect of this mechanism is that the _ same _ yukawa couplings @xmath8 that give rise to neutrino masses via the seesaw mechanism in eq . are also responsible for the origin of matter , thus implying an intimate connection between two seemingly disparate pieces of evidence for beyond the sm physics . this beautiful idea can be tested , provided the seesaw scale , and hence , the scale at which leptogenesis takes place , is accessible to current and near future laboratory experiments . low - scale leptogenesis is possible when at least two rh majorana neutrinos have a small mass difference comparable to their decay widths , thus resonantly enhancing the @xmath22-type @xmath2 asymmetry  @xcite due to rh neutrino self - energy effects  @xcite . an important question to explore is whether it is possible to falsify the leptogenesis mechanism by laboratory experiments  @xcite . in particular , it is worth investigating if the leptogenesis mechanism works in a tev - scale realization of l - r seesaw and whether an observation of a rh gauge boson at the lhc could falsify this scenario . this problem was analyzed in detail in  @xcite and it was pointed out that the additional dilution and washout effects on the lepton asymmetry due to @xmath23-mediated @xmath24 scattering processes become important for a tev - scale l - r seesaw . since in generic versions of the seesaw model , sub - ev neutrino masses would require the dirac yukawa couplings to be @xmath25 , the washout effects would lead to an efficiency factor @xmath26 ( @xmath27 being the @xmath12 gauge coupling , which is assumed to be equal to the @xmath14 gauge coupling in the minimal scenario ) which is too small for a low - scale leptogenesis to work . through a detailed analysis of the relevant boltzmann equations , it was concluded in  @xcite that even for maximal @xmath2-asymmetry @xmath28 , the observed value of the baryon asymmetry can be explained by leptogenesis in these l - r models , only if @xmath29 tev . turning this argument around , if a positive signal for @xmath23 is observed at the lhc , this will falsify leptogenesis as a mechanism for understanding the origin of matter in l - r seesaw framework . since this is such an important issue , we have reanalyzed this  @xcite to examine the robustness of the lower bound on @xmath30 and to investigate if there exists _ any _ allowed parameter space with successful leptogenesis for smaller values of @xmath30 . we find that for the generic class of l - r seesaw models with large light - heavy neutrino mixing , successful leptogenesis requires @xmath1 tev for the maximal @xmath2 asymmetry . for illustration , we will present an explicit neutrino mass fit which satisfies the observed baryon asymmetry . the main new results presented here should supersede those reported in  @xcite . this proceedings is organized as follows : in section  [ sec2 ] , we review the basic features of the generic l - r seesaw models as well as our new l - r seesaw model with special dirac and majorana textures resulting in light neutrinos via type - i seesaw with large light - heavy neutrino mixing generated in a natural manner . in section  [ sec3 ] , we present an alternative neutrino mass fit relying on cancellations in the seesaw formula . in section  [ sec4 ] , we discuss resonant leptogenesis in this model and the impact of a tev - scale @xmath23 on the lepton asymmetry . our conclusions are given in section  [ sec5 ] . in the minimal l - r symmetric model ( lrsm ) , the fermions are assigned to the gauge group @xmath0 as follows : denoting @xmath31 and @xmath32 as the quark and lepton doublets of the @xmath33th generation respectively , @xmath34 and @xmath35 ( also denoted simply by @xmath36 ) are assigned to doublets under the @xmath14 group , while @xmath37 and @xmath38 ( also denoted by @xmath39 ) as the doublets under the @xmath12 group . the higgs sector of the model can consist of one or several bidoublets @xmath40 and triplets @xmath41 : @xmath42 the gauge symmetry @xmath43 is broken by the vacuum expectation value ( vev ) @xmath44 to the group @xmath45 of the sm . the lh counterpart ( @xmath46 ) to @xmath47 is not considered here , assuming that parity and @xmath12 gauge symmetry scales are decoupled . in this case , the @xmath46 fields become heavy when the discrete parity symmetry is broken , and disappear from the low energy theory  @xcite . the vev of the @xmath48 field given by @xmath49 breaks the sm gauge group to @xmath50 . the fermion masses are obtained from the following yukawa lagrangian : @xmath51 where @xmath52 ( @xmath53 being the second pauli matrix ) . after electroweak symmetry breaking , the dirac fermion masses are given by the generic formula @xmath54 for up - type fermions , and for down - type quarks and charged leptons , it is the same formula with @xmath55 . the yukawa lagrangian ( [ yuk ] ) leads to the dirac neutrino mass matrix @xmath56 and the majorana mass matrix for the heavy rh neutrinos @xmath57 which go into the seesaw formula for calculating the neutrino masses and the heavy - light neutrino mixing . since the higgs sector relates the neutrino yukawa couplings with the charged - lepton ones in the lrsm , it is interesting to see how a tev - scale l - r seesaw can be realized in nature . there are essentially three ways to do so : ( i ) by choosing one set of yukawa couplings to be @xmath58 for a particular vev assignment for the bidoublet higgs fields ; ( ii ) by choosing particular symmetry - motivated textures for the yukawa couplings which ensure that the leading order seesaw contribution to neutrino masses vanish ; and ( iii ) by choosing large yukawa couplings as allowed by specific textures and invoking cancellations in the seesaw formula . the strategy ( i ) with small yukawa couplings does not lead to any new interesting phenomenology over the minimal lrsm . therefore , we will focus on strategies ( ii ) and ( iii ) in the following sections , and in particular , use strategy ( iii ) for our numerical analysis for the calculation of lepton asymmetry . a similar analysis can be performed following strategy ( ii ) as well . for the phenomenological implications of this new class of l - r seesaw models , see e.g.  @xcite . as mentioned above , the basic strategy for understanding small neutrino masses with a low - scale type - i seesaw is to have the appropriate textures for @xmath7 and @xmath4 in eq .  . there are several examples of this type  @xcite in the context of the minimal seesaw extensions of the sm . here , we discuss the embedding of one such texture ( from ref . @xcite ) in the l - r model using an appropriate family symmetry  @xcite . the symmetry must not only guarantee the special leptonic textures but also must be free of light scalar bosons which can result if the effect of the discrete symmetry is to automatically lead to a @xmath59 symmetry . moreover in lrsm , the charged - lepton mass matrix @xmath60 is related to @xmath7 which puts additional constraints on phenomenological viability of the model . therefore , we find it remarkable that the model presented below remains a viable tev - scale l - r type - i seesaw model for neutrinos , and as a result , has interesting phenomenological implications beyond the minimal lrsm . the dirac and majorana mass matrices @xmath7 and @xmath4 considered here have the following form : @xmath61 with @xmath62 and @xmath63 . in the limit of @xmath64 , the neutrino masses vanish , although the heavy - light mixing parameters given by @xmath65 can be quite large . the light neutrino masses given by the seesaw formula become proportional to either @xmath66 , @xmath67 or their products . if the smallness of @xmath67 and @xmath66 can be guaranteed by some symmetry , then we have a `` natural '' tev - scale seesaw model with tiny neutrino masses . as we show below , the mass textures   can be successfully embedded into the l - r framework , while satisfying all current experimental constraints . note that the choice of texture for the rh neutrino mass matrix in eq .   is necessary to keep the model compatible with strong bounds from tree - level @xmath68 decay via tev - scale @xmath47 exchange  @xcite . in order to obtain the special dirac and majorana textures given in eq . , we supplement the l - r gauge group @xmath0 with a global discrete symmetry @xmath69  @xcite . for the higgs sector , we choose three bi - doublets ( @xmath70 ) with @xmath71 and two rh triplets ( @xmath72 ) with @xmath73 . the fermion and higgs multiplets are assigned the @xmath74 quantum numbers as shown in table  [ tab1 ] . the leptonic part of the yukawa lagrangian invariant under the @xmath74-symmetry is given by @xmath75 in the symmetry limit , the vevs of @xmath76 have the form @xmath77 . this is because the terms of the form tr@xmath78 which would change the @xmath48 vev to the form diag@xmath79 are forbidden by the @xmath74-symmetry from appearing in the scalar potential . thus in the symmetry limit , the @xmath7 elements in one column are big and non - zero , and the charged lepton mass matrix has one eigenvalue zero which can be identified as the electron flavor . the rh neutrino majorana mass matrix has the form in eq . ( [ eq : texture ] ) with @xmath80 . to make the model realistic , we add small soft symmetry - breaking terms of the form @xmath81 to the scalar potential . this will induce the @xmath82 vevs of the form @xmath83 , where @xmath84 with @xmath85 respectively being the scalar self - couplings of the bidoublet and triplet fields in the scalar potential . choosing appropriately small @xmath86 , we can get very small @xmath87 as required to satisfy the neutrino oscillation data . .the discrete symmetry assignments for the fermion and higgs fields in our l - r model that lead naturally to the special dirac and majorana textures given in eq . ( [ eq : texture ] )  @xcite . [ cols="^,^",options="header " , ]     since @xmath88 and @xmath89 , the yukawa couplings @xmath90 are easily calculated using vev s chosen as above , and they are found to be @xmath91 the leptonic @xmath2 asymmetry generated by the rh neutrino decays is governed by these yukawa couplings . if we assume that the two sm doublets in the lr bi - doublet i.e. @xmath92 and @xmath93 are approximate mass eigenstates with @xmath94 , the dominant contribution to the @xmath2 asymmetry comes solely from the self - energy correction by the @xmath93-loop to the decay process @xmath95 . therefore , only the yukawa coupling matrix @xmath96 determines the flavor effect in rh neutrino interactions relevant to resonant leptogenesis . the rh neutrino mixing effect at resonance can be captured by the one - loop resummed yukawa couplings  @xcite . explicitly , in the heavy - neutrino mass eigenbasis , we obtain for the resummed yukawa couplings @xmath97 and their @xmath2-conjugates @xmath98 the following values : @xmath99 the heavy neutrino decay rates for the yukawa - mediated two - body processes @xmath100 are calculated with these resummed yukawa couplings : @xmath101 which are crucial parameters for the calculation of lepton asymmetry , as we will see in the next section . as eluded to above , for low scale seesaw models , a simple way to generate enough lepton asymmetry is to use resonant leptogenesis  @xcite . it requires at least two rh neutrinos to be nearly degenerate , which is guaranteed in our model by the choice of the texture in the rh neutrino mass matrix given by eq .  . thus , in addition to guaranteeing suppression of lepton flavor violating processes such as @xmath102 , this choice of rh neutrino texture also provides a necessary condition for resonant leptogenesis . as far as the dirac neutrino mass matrix @xmath7 is concerned , we choose the pattern given in eq . so that it fits neutrino oscillation data . since our focus is on the feasibility of low scale leptogenesis in a realistic model for neutrinos , we do not stress here on the naturalness of the texture , although a similar exercise can be performed with the fit presented in section  [ sec2.1 ] . the details of leptogenesis in this class of models was discussed in  @xcite and we do not repeat the basic equations here . however , we have extended the work of  @xcite and also present here some revised numerical results due to a computational error in the code used there . the basic steps in our analysis are as follows : first we calculate the flavored @xmath2 asymmetry @xmath103 \ ; , \label{epsilon}\end{aligned}\ ] ] where the partial decay widths are given by eq .   and the total decay width is given by @xmath104 + 2\ : \gamma(n_\alpha\to l_r q_r\bar{q}'_r ) \ ; . \label{tot_width}\end{aligned}\ ] ] note that in lrsm , there is an additional contribution to the total decay width due to the three - body decay mediated by @xmath23 : @xmath105 where @xmath106 is the total decay width of @xmath23 , assuming that all three heavy neutrinos are lighter than @xmath23 . the @xmath2 asymmetry   in our case is determined by the rh neutrino texture , specifically , the magnitudes of @xmath107 and @xmath108 in eq .   as well as the magnitudes of the yukawa couplings , and these parameters are constrained by the neutrino fit . the second step in our calculation is to calculate the thermodynamic evolution of the normalized heavy neutrino and lepton doublet number densities @xmath109 and @xmath110 respectively , where @xmath111 and @xmath112 is the photon number density , @xmath113 being the riemann zeta function . for simplicity and for a fair comparison with the results of  @xcite , here we use the flavor - diagonal boltzmann equations  @xcite : @xmath114 where @xmath115 is a dimensionless variable ( @xmath116 being the temperature of the universe ) and @xmath117 is the heavy neutrino equilibrium number density , @xmath118 being the @xmath119-th order modified bessel function of the second kind . the various decay ( @xmath120 ) , scattering ( @xmath121 ) and washout ( @xmath122 ) rates appearing in eqs .   and are given by @xmath123 \nonumber \\      & \ \equiv \ \frac{1}{2 \zeta ( 3 ) } z^3 k_1 ( z ) k_l^\text{eff } ( z ) \ ; , \label{wash}\end{aligned}\ ] ] where @xmath124 is the hubble parameter at @xmath125 , assuming only sm degrees of freedom in the thermal bath , @xmath126 gev is the planck mass and @xmath127 is the branching fraction of the rh neutrino decays relevant for the generation of @xmath2 asymmetry : @xmath128 \ ; . \label{br}\end{aligned}\ ] ] the various @xmath129 s appearing in eqs . - represent the reaction rates that involve the rh neutrino decays and inverse decays as well as other @xmath130 scattering processes in the model ( see  [ app ] ) . only the two - body decays of the rh neutrinos involving complex yukawa couplings are responsible for building up the asymmetry , whereas all other processes lead to washout effects . we present in figure  [ fig : gnh ] the evolution of the various collision rates as given in  [ app ] . the left panel of the figure is relevant to the first boltzmann equation , while the second one is relevant to . the vertical dashed line shows the critical value @xmath131 beyond which the sphaleron processes become ineffective . the horizontal dashed line is shown for easy comparison with the hubble rate . here we have used @xmath132 tev which is the lowest value of @xmath30 we found in this model with an _ explicit _ neutrino fit that satisfies the leptogenesis constraints . recently , it was pointed out  @xcite that the scattering process @xmath133 mediated by the doubly - charged component of the rh triplet @xmath134 might spoil leptogenesis , if @xmath30 and @xmath135 are relatively small . we have explicitly calculated the washout effect due to this process for various values of @xmath30 and @xmath136 . as shown in figure  [ fig : glhwe ] and also in figure  [ fig : gnh ] ( right panel ) , this effect is negligible compared with the decay rate and other scattering rates when @xmath30 and @xmath136 are in the regime of interest .    in the strong washout regime , the flavored lepton asymmetry is approximately given by  @xcite @xmath137 where @xmath138 is the effective washout parameter as defined in eq .   and @xmath139 is the effective dilution factor . for the numerical fit given in section  [ sec3 ] , we obtain @xmath140 and the total lepton asymmetry is found to be @xmath141 . this is well consistent with the observed value of the baryon asymmetry @xmath142  @xcite , after taking into account the sphaleron conversion rate and the entropy dilution factors .      here we present our procedure to derive a lower bound of @xmath30 which is compatible with successful leptogenesis in a lrsm with all rh neutrinos being quasi - degenerate in mass . the total lepton asymmetry is given by eq . ( [ eq : etal ] ) , which can be rewritten using eq .   as @xmath143 for the purpose of deriving a lower bound on @xmath30 , we assume that the dominant washout effect comes from the @xmath23-mediated scattering processes , i.e. , @xmath144 where @xmath145 . this follows from the fact that gauge interactions are flavor - blind , and hence , @xmath146 has no dependence on lepton flavors . similarly , when all the rh neutrino masses are quasi - degenerate , we can write @xmath147 . we also assume that @xmath148 for simplicity . note that @xmath149 is not summed over lepton flavors while @xmath74 is . we further define @xmath150 and @xmath151 as the @xmath2 asymmetry and branching ratio , respectively , without the 3-body decay width included in the denominator of eqs .   and . for simplicity , we further assume that the branching ratios of the decay process @xmath152 are the same for all the lepton flavors . with all the above - mentioned reasonable assumptions , we can approximate the total lepton asymmetry in eq .   at the critical temperature as @xmath153 } \left| \sum_\alpha \varepsilon_{l \alpha } \frac{\widetilde{d}_\alpha ( z_c)}{d_\alpha ( z_c ) + 3 s_{r \alpha } ( z_c ) } \right| \\      & \approx \frac{9}{4 \zeta ( 3 ) } \frac{z_c^2 k_1 ( z_c)}{s_r ( z_c ) } \frac{r_s r_d^2}{(3 + r_s r_d ) ( 3 + r_s ) } \varepsilon^y_\text{tot }      \label{eq : etal2}\end{aligned}\ ] ] where the ratios @xmath154 and @xmath155 parametrize the relative washout strengths of the 2-body decay , @xmath23-mediated decay and @xmath23-mediated scattering processes . the values of @xmath156 and @xmath157 depend on @xmath158 , @xmath30 , and the yukawa coupling @xmath159 . assuming a specific value of @xmath159 and calculating the 2-body decay width simply as @xmath160 , we can evaluate these parameters as functions of @xmath158 and @xmath30 . figure  [ fig : etalcon ] shows the contour plots of @xmath161 for two different yukawa couplings @xmath162 and @xmath163 . the red curves correspond to @xmath164 which is the total @xmath2 asymmetry in the example fit given in section  [ sec3 ] . any region outside the red curve is incompatible with successful leptogenesis under the assumptions we introduced to obtain it , i.e. @xmath165 , @xmath166 , @xmath164 for the two specific values of @xmath159 . for @xmath162 , we find that the lowest value of @xmath30 allowed for @xmath164 is 13 tev at around @xmath158 = 580 tev . note that the example fit we have presented in the previous section has @xmath167 tev , @xmath168 gev , and the resummed yukawa coulings of order around @xmath169 . thus , our example fit , shown as a green dot in figure  [ fig : etalcon ] , is very close to the minimum value of @xmath30 obtained here in a simplified manner , which justifies the validity of this approach . in other words , we have derived the lower bound in two different ways : ( i ) in section  [ sec3 ] by carefully scanning the parameter space in order to find an explicit fit with the lowest possible @xmath30 compatible with leptogenesis , and ( ii ) using the approximate expression in eq . ( [ eq : etal2 ] ) . the remarkable agreement between these two approaches shows that the simplified expression in eq . ( [ eq : etal2 ] ) is very effective in finding the region in parameter space compatible with leptogenesis and predicting the lower bound of @xmath30 as well as the position in the parameter space where it exists . if we use the same expression and take the maximal @xmath2 asymmetry allowed in principle , i.e. @xmath170 , then we obtain the blue curves figure  [ fig : etalcon ] . with this maximal @xmath2 asymmetry , we have found that the yukawa coupling @xmath163 gives the lower bound of @xmath30 = 9.9 tev at @xmath158 = 630 gev . the yukawa couplings can not be increased arbitrarily without spoiling the lepton asymmetry , since not only the source term due to the two - body decay of the rh neutrinos , but also the washout effects due to inverse decay and @xmath171 scattering increase with the yukawa couplings . similarly , for very small values of the yukawa couplings , the branching fraction of the two - body decay mode becomes comparable or smaller than the three - body decay mode due to @xmath23 interactions , and therefore , the washout effect again increases . thus , successful leptogenesis works only in a range of the yukawa coupling parameter space . this is shown in the three - dimensional plot given in figure  [ fig:3d ] , where we see that leptogenesis constraints in our model require the yukawa coupling to be @xmath172 for @xmath173 tev . the robustness of the lower bound on @xmath30 obtained in figure  [ fig : etalcon ] can also be verified from figure  [ fig:3d ] . in this proceedings , we address two issues related to seesaw models for neutrino masses . the first one deals with whether the tev scale can be naturally in the tev range without fine - tuning of parameters . we present a natural tev scale left - right model which achieves this goal and therefore provides a counterexample to the common lore that either the seesaw scale must be superheavy or the active - sterile neutrino mixing must be tiny in a uv - complete seesaw model . the second issue addresses the important question : whether in such low scale models , one can have successful leptogenesis , and if so , what constraints are implied by this on the mass of the rh gauge boson . in an explicit tev - scale lr model , with an explicit fermion mass fit , we find the lower bound to be 13.1 tev and for generic models in this class of l - r seesaw with enhanced neutrino yukawa couplings compared to the canonical seesaw case and with maximal possible @xmath2 asymmetry for each flavor , this bounds becomes 9.9 tev . the work of p. s. b. d. is supported by the lancaster - manchester - sheffield consortium for fundamental physics under stfc grant st / l000520/1 . the work of c. h. l. and r. n. m. is supported by the nsf grant no . phy-1315155 . the various collision rates for decay and scattering processes in eqs . ( [ be1 ] ) and ( [ be2 ] ) are given below : @xmath174 the scattering terms involving two heavy neutrinos in the initial state , e.g. induced by a @xmath175-channel @xmath23 or @xmath176 , and by an @xmath177-channel @xmath178 , are not included here since their rates are doubly boltzmann - suppressed and numerically much smaller than the scattering rates given above  @xcite . the decay rates are explicitly given by @xmath179 , \\ \gamma^{n_\alpha}_{l_rq\bar{q } ' } \ & = \ \frac{m_{n_\alpha}^3}{\pi^2 z } k_1(z)\left[\gamma(n_\alpha\to l_r q_r\bar{q}'_r)+\gamma(n_\alpha\to \bar{l}_r\bar{q}_r q'_r)\right ] \ ; .\end{aligned}\ ] ] the various collision terms for the @xmath130 scattering processes @xmath180 are defined as @xmath181 where @xmath182 with the kinematic threshold value @xmath183/m_{n_1}^2 $ ] , and @xmath184 are the relevant reduced cross sections , whose explicit expressions can be found in  @xcite . the reduced cross section of the additional process @xmath185 mediated by @xmath134 is given by @xmath186 .\end{aligned}\ ] ] 99    p. minkowski , phys . lett . b * 67 * , 421 ( 1977 ) ; r. n. mohapatra and g. senjanovi , phys . rev . lett . * 44 * , 912 ( 1980 ) ; t. yanagida , conf . proc . * c7902131 * , 95 ( 1979 ) ; m. gell - mann , p. ramond and r. slansky , conf . proc . * c790927 * , 315 ( 1979 ) ; s. l. glashow , nato sci . b * 59 * , 687 ( 1980 ) . a.  pilaftsis , z. phys . * c55 * , 275 ( 1992 ) ; e.  ma , phys . lett .   * 81 * , 1171 ( 1998 ) ; e.  ma , phys . d * 73 * , 077301 ( 2006 ) ; p.  s.  b. dev and a.  pilaftsis , phys . rev . * d86 * , 113001 ( 2012 ) ; s.  s. law and k.  l. mcdonald , int a29 * , 1450064 ( 2014 ) ; a.  j.  r.  figueiredo , eur . j.  c * 75 * , 99 ( 2015 ) . j.  kersten and a.  yu . smirnov , phys . * d76 * , 073005 ( 2007 ) . w.  buchmller , c.  greub , and p.  minkowski , phys . lett . * b267 * , 395 ( 1991 ) ; j.  gluza , acta phys .  polon . b * 33 * , 1735 ( 2002 ) ; a.  pilaftsis , phys . lett . * 95 * , 081602 ( 2005 ) ; z .- z . xing , prog . suppl .   * 180 * , 112 ( 2009 ) ; x .- g .  he , s.  oh , j.  tandean and c .- c . wen , phys . d * 80 * , 073012 ( 2009 ) ; a.  ibarra , e.  molinaro and s.  t.  petcov , jhep * 1009 * , 108 ( 2010 ) ; r.  adhikari and a.  raychaudhuri , phys . d * 84 * , 033002 ( 2011 ) ; m.  mitra , g.  senjanovi and f.  vissani , nucl . b * 856 * , 26 ( 2012 ) . a.  ferrari _ et al . _ , phys . d * 62 * , 013001 ( 2000 ) ; m.  nemevsek , f.  nesti , g.  senjanovic and y.  zhang , phys .  rev . d * 83 * , 115014 ( 2011 ) ; j.  chakrabortty , j.  gluza , r.  sevillano and r.  szafron , jhep * 1207 * , 038 ( 2012 ) ; s.  p. das , f.  f.  deppisch , o.  kittel and j.  w.  f.  valle , phys . d * 86 * , 055006 ( 2012 ) ; j.  a.  aguilar - saavedra and f.  r.  joaquim , phys . d * 86 * , 073005 ( 2012 ) . m.  flanz , e.  a. paschos and u.  sarkar , phys . lett . * b345 * , 248 ( 1995 ) ; l.  covi , e.  roulet and f.  vissani , phys . lett . * b384 * , 169 ( 1996 ) . f.  f.  deppisch , j.  harz and m.  hirsch , phys . * 112 * , 221601 ( 2014 ) ; f.  f.  deppisch , j.  harz , m.  hirsch , w.  c.  huang and h.  ps , arxiv:1503.04825 [ hep - ph ] . z.  g.  berezhiani , phys . b * 129 * , 99 ( 1983 ) ; d.  chang and r.  n.  mohapatra , phys . lett .   * 58 * , 1600 ( 1987 ) ; s.  rajpoot , mod . lett .  a * 2 * , 307 ( 1987 ) ; a.  davidson and k.  c.  wali , phys . * 59 * , 393 ( 1987 ) ; k.  s.  babu and r.  n.  mohapatra , phys . lett .   * 62 * , 1079 ( 1989 ) and phys . d * 41 * , 1286 ( 1990 ) .
contrary to the common lore based on naive dimensional analysis , the seesaw scale for neutrino masses can be _ naturally _ in the tev range , with small parameters coming from radiative corrections . 
 we present one such class of type - i seesaw models , based on the left - right gauge group @xmath0 realized at the tev scale , which fits the observed neutrino oscillation parameters as well as other low energy constraints . 
 we discuss how the small parameters of this scenario can arise naturally from one loop effects . 
 the neutrino fits in this model use quasi - degenerate heavy majorana neutrinos , as also required to explain the matter - antimatter asymmetry in our universe via resonant leptogenesis mechanism . 
 we discuss the constraints implied by the dynamics of this mechanism on the mass of the right - handed gauge boson in this class of models with enhanced neutrino yukawa couplings compared to the canonical seesaw model and find a lower bound of @xmath1 tev for successful leptogenesis assuming maximal @xmath2 asymmetry for each flavor . 
 we also present a model with explicit neutrino mass fit , where the lower bound goes up to 13.1 tev due to less than maximal primordial @xmath2 asymmetry predicted by the model .