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the type iii seesaw contains leptonic triplets @xmath4 under the standard model ( sm ) gauge group @xmath5 as @xmath6 , @xmath7@xcite . in tensor notation , the triplet can be written as @xmath8 symmetric in @xmath9 and @xmath10 , where @xmath9 and @xmath10 take the values @xmath11 and @xmath12 . @xmath13 , @xmath14 and @xmath15 . the yukawa couplings related to neutrino and charged lepton masses come from the following terms @xmath16 where the super - script `` c '' indicates the charge conjugation . the lepton doublet @xmath17 , @xmath18 , and higgs doublet @xmath19 ( @xmath20 ) have the components given by @xmath21 , @xmath22 , and @xmath23 , @xmath24 . with just one higgs doublet , @xmath25 and @xmath26 are the would - be nambu - goldstone bosons @xmath27 and @xmath28 `` eaten '' by @xmath29 and @xmath30 bosons , respectively . we have @xmath31 in the above , repeated indices are summed over from 1 to 2 . @xmath32 , @xmath33 and @xmath34 . the neutrino and charged lepton mass matrices @xmath35 and @xmath36 , in the basis @xmath37 and @xmath38 , are given by @xmath39 where dirac mass term @xmath40 , @xmath41 and @xmath42 where @xmath43 is the vacuum expectation value ( vev ) of the higgs doublet . note that given @xmath44 and @xmath4 representations , it is also possible to have the necessary dirac mass term @xmath45 from the yukawa couplings of a quadruplet higgs representation @xmath46 : @xmath47 of the following form , @xmath48 the field @xmath46 has component fields : @xmath49 . in tensor notation @xmath46 is a total symmetric tensor with 3 indices @xmath50 with @xmath9 , @xmath10 and @xmath51 taking values @xmath11 and @xmath12 with @xmath52 we have @xmath53 the neutral component @xmath54 can have vev @xmath55 with @xmath56 . a non - zero @xmath55 will modify the neutrino and charged lepton mass matrices @xmath45 and @xmath57 with @xmath58 to the leading tree level light neutrino mass matrix @xmath59 , defined by @xmath60 + h.c . , is given by @xmath61 a model with a different higgs quadruplet @xmath62 has also been studied where neutrino masses only arises from a dimension-7 operator @xcite . this model is very different from the model we are discussing here . in the basis where the charged lepton mass matrix is already diagonalized , the pmns mixing matrix @xmath63@xcite in the charged current interaction is given by @xmath64 where @xmath65 is the diagonalized light neutrino mass matrix . the introduction of quadruplet @xmath46 in the model can have interesting consequences for neutrino masses , mixing and also for lepton flavor violating ( lfv ) processes , @xmath0 and @xmath1 conversion because the vev of @xmath46 is constrained to be small which then can lead to a large yukawa coupling @xmath66 . we also found some interesting collider signatures of the doubly charged higgs boson in the quadruplet . in the following we will study the quadruplet model in more details . we have seen that in type iii seesaw , it is possible to introduce a quadruplet higgs which give additional seesaw contributions to neutrino masses at the tree level . it is , however , well known that electroweak precision data constrain the vev of a higgs representation because a non - zero vev of some higgs may break the @xmath67 custodial symmetry in the sm leading to a large deviation of the @xmath68 parameter from unity . with the constraints satisfied , the higgs doublet and quadruplet may contribute to the neutrino mass matrix differently . the non - zero vev of the higgs representation with isospin @xmath69 and hypercharge @xmath70 will modify the @xmath68 parameter at tree level with@xcite , @xmath71 the sm doublet higgs alone does not lead to a deviation of @xmath68 from unity , but the addition of a quadruplet does . for our case of one doublet and one quadruplet , we have @xmath72 we therefore have , @xmath73 . using experimental data @xmath74(95% c.l.)@xcite , we see that @xmath55 is constrained to be less than 5.8 gev which is about 40 times smaller than that of the doublet higgs vev . this vast difference in higgs vev s indeed indicate that the higgs doublet and quadruplet contribute to the neutrino mass matrix differently in the sense that if the yukawa couplings @xmath75 and @xmath66 are the same order of magnitude , they contribute to the neutrino masses can be different by orders of magnitude . turning this around , if both higgs contribute to the neutrino masses with the same orders of magnitude , then the yukawa coupling for quadruplet @xmath66 can be several orders of magnitude larger than that for the doublet @xmath75 . if the seesaw mass is only from the coupling to @xmath76 , just like type iii seesaw with one doublet , the canonical yukawa coupling is of order @xmath77 . with a @xmath78 of order @xmath11 tev , the yukawa couplings would be less than @xmath79 with @xmath59 around @xmath80 ev . this makes it clear that even the heavy degrees of freedom are kinematically accessible at the lhc@xcite , the small yukawa couplings is hard to study their properties and their effects on lfv processes@xcite . although it has been shown that there are solutions with large yukawa coupling in type iii seesaw with just one higgs doublet@xcite , it is interesting to see if large yukawa couplings can more naturally manifest itself . the quadruplet with a small vev provides such a possibility . the natural size of the yukawa coupling @xmath66 is of order @xmath81 . with @xmath55 of order 1 gev , @xmath66 would be enhanced by about 250 times compared with @xmath75 . with a smaller @xmath55 , @xmath66 can be even larger since @xmath82 . the large yukawa coupling @xmath66 can lead to interesting phenomenology , such as the possibility of having large effects in lepton flavor violating ( lfv ) processes @xmath2 and @xmath1 conversion . in the type iii seesaw with just doublet higgs , if there is just one leptonic triplet @xmath83 , the resulting neutrino mass matrix @xmath59 for the three light neutrinos is only a rank one matrix . this implies that only one light neutrino mass is non - zero . neutrino oscillation data show the existence of two distinct mass squared splittings , so a model with just one generation of triplet @xmath83 is in conflict with data . more than one generation of @xmath83 is required to have a higher ranked mass matrix to fit data . we point out that with the introduction of quadruplet @xmath46 , it is possible to raise the rank of neutrino mass matrix by including one loop contributions to the mass matrix . the tree and loop generated mass matrices together can be consistent with present data on neutrino mass and mixing . with both higgs doublet and quadruplet , the tree level light neutrino mass matrix @xmath59 given in eq . is still rank one if there is only one generation of @xmath83 . in the following we show that the inclusion of one loop contribution can raise the rank of the mass matrix to two . the one loop contributions involve exchange of internal quadruplet higgs bosons and heavy leptons . in order to show this mechanism explicitly , we first identify physical higgs states and mixing necessary for one loop generation of neutrino mass from the higgs potential . the most general renormalizable higgs potential is given by @xmath84 , \ ] ] where @xmath85 denotes an index for @xmath67 contractions . the contraction of @xmath67 indices for each of the terms are given by @xmath86 in the above only two terms are independent for @xmath87 . also only two terms are independent for @xmath88 . one can just take @xmath85 to be equal to 1 and 2 as the independent terms for these two types of terms . in the following , we set @xmath89 without loss of generality . the two terms @xmath90 and @xmath91 , break the global lepton number symmetry after the doublet and quadruplet develop non - zero vev s . @xmath91 then mixes @xmath76 and @xmath46 fields . at one loop level majorana masses will be generated for light neutrinos . there are three types of mixing terms which can be characterized to be proportional to @xmath92 , @xmath93 or @xmath94 . we have seen earlier that @xmath43 is much larger than @xmath55 from electroweak precision data , therefore one can just keep terms proportional to @xmath92 for the loop generation of neutrino masses . these terms are @xmath95 + h.c . \ ] ] the above terms will generate a neutrino mass matrix proportional to @xmath96 for the first term and , @xmath97 for the second term . to have a consistent model , the elements in @xmath75 are required to be much smaller than those in @xmath66 . we can neglect the contribution from terms proportional to @xmath98 in the above . without terms proportional to @xmath98 and @xmath55 , masses of component fields in @xmath46 are given by @xmath99 we note that a parameter @xmath100 characterizes a mass squared splitting between @xmath101 and @xmath102 , i.e. , @xmath103 . the mass matrix for singly charged scalars is given by @xmath104v^2 \end{pmatrix } \begin{pmatrix } \chi^+ \\ \chi^{- * } \end{pmatrix } = \begin{pmatrix } \chi_1 ^ - & \chi_2 ^ - \end{pmatrix } \begin{pmatrix } m_{\chi^\pm_1}^2 & \\ & m_{\chi^\pm_2}^2 \end{pmatrix } \begin{pmatrix } \chi_1^+ \\ \chi_2^+ \end{pmatrix}\ ; , \ ] ] where @xmath105    the one - loop contributions to the neutrino mass matrix are calculated as@xcite @xmath106 - { \sin(2\theta)\over   \sqrt{3 } } m_e \bigl [ i \bigl(\frac{m^2_{\chi^+_1}}{m^2_e } \bigr ) - i \bigl ( \frac{m^2_{\chi^+_2}}{m^2_e}\bigr ) \bigr ] \biggr\}\ ; , \ ] ] where @xmath107 and @xmath108 are masses of neutral and charged heavy leptons , and @xmath109 . the explicit dependence on @xmath100 is given @xmath110 + \frac12{m_n m_e\over m^2_{\chi^+_1 } - m^2_{\chi^+_2 } } \bigl [ i\bigl(\frac{m^2_{\chi^+_1}}{m^2_e}\bigr ) - i\bigl(\frac{m^2_{\chi^+_2}}{m^2_e}\bigr)\bigr ] \bigr\}\;. \ ] ] neglecting mass splitting in a multiplet , i.e. , @xmath111 , @xmath112 , @xmath113 is given by @xmath114 where @xmath115 . collecting contributions from the tree and loop contribution , one can write the neutrino mass matrix as @xmath116 the mass matrix is now rank 2 in general . this mechanism can also work even when we introduce an additional scalar doublet@xcite . however such a scalar is indistinguishable from a sm higgs doublet without additional quantum charges . the extra doublet fields can interact with other sm fermions and will induce large tree level flavor changing neutral current ( fcnc ) for the charged leptons . in this model , the tree level fcnc are much suppressed for charged leptons . the mass matrix obtained in the previous section , being rank two , has two non - zero eigenvalues . one of the neutrino masses is predicted to be zero . the zero mass neutrino can be @xmath117 or @xmath118 depending on whether the neutrino masses have normal or inverted hierarchy . in this section , we show that the mass matrix obtained can be made consistent with experimental data on mixing parameters . mass squared differences of neutrino masses and neutrino mixing have been measured to good precision@xcite . the mass parameters are determined by global fit as@xcite @xmath119 ev@xmath120 , @xmath121 ev@xmath122 ev@xmath123 for normal ( inverted ) mass hiearchy . here @xmath124 , and @xmath125@xmath126 . for our case , with normal hierarchy , @xmath127 , @xmath128 and @xmath129 . for inverted hierarchy , we then have @xmath130 , @xmath131 , and @xmath132 . the neutrino mixing are given by@xcite @xmath133 , @xmath134 , and @xmath135 . to the leading order , the mixing pattern can be approximated by the tribimaximal mixing matrix@xcite , @xmath136 the light neutrino mass matrix obtained in eq . can be easily made to fit data . we consider the case for @xmath137 , such that terms proportional to @xmath55 can all be neglected for illustration . with this approximation , the cross term proportional to @xmath138 can be neglected .    for normal hierarchy case , by imposing the condition of the tribimaximal mixing , the yukawa couplings can be taken to be the forms @xmath139 , and @xmath140 . in this case @xmath141 and @xmath142 . if the heavy neutrino mass is of order 1 tev , @xmath143 and @xmath144 . we note that relative size of tree level and loop level contributions can be tuned by the parameter @xmath113 , which is proportional to the higgs potential parameter @xmath100 . if @xmath100 is small , quaruplet yukawa coupling @xmath145 can be order of one . this kind of possibility is also studied in the neutrinophilic two higgs doublet model@xcite . the role of the @xmath75 and @xmath66 can be switched . similarly the model can be made consistent with inverted hierarchy . for example with @xmath146 and @xmath140 , the tribimaximal mixing pattern can be realized . in this case @xmath147 and @xmath142 . if the heavy neutrino mass is of order 1 tev , @xmath148 and @xmath149 . again the roles of @xmath75 and @xmath66 can be switched . making perturbation to the above forms , one can get non - zero @xmath150 solutions , which is indicated by recent results at t2k@xcite . for instance , for normal mass hierarchy case modifying @xmath75 to be @xmath151 and keep the same @xmath66 , we can produce non - zero @xmath150 solutions . using the @xmath152 ev , @xmath153ev , we obtain @xmath154 , @xmath155 , @xmath156 , @xmath157 and @xmath158 which are within one @xmath159 error of the data .    for inverted mass hierarchy case , with @xmath160ev , @xmath161ev , we obtain @xmath162 , @xmath163 , @xmath164 , @xmath165 and @xmath166 which are , again , within one @xmath159 error of the data . higher order loop corrections can further raise the rank of neutrino mass matrix in general . therefore , all three light neutrinos can have non - zero masses in this model . it has been shown in ref.@xcite that the rank of the neutrino mass matrix can be rank two at two loop level even with just one triplet lepton and one higgs doublet . however , in this case the heavy triplet lepton mass needs to be @xmath167 gev , and hence its phenomenological consequence for collider physics is out of the scope at the lhc . introduction of more leptonic triplet generations can also increase the rank of mass matrix too . we now study possible effects on lfv processes @xmath0 and @xmath1 conversion . @xmath0 is induced at one loop level . there is a small contribution to @xmath3 conversion at the tree level due to mixing of charged light and heavy leptons . the dominant contribution come at the one loop level due to possible large yukawa coupling @xmath66 , because the size of @xmath75 is constrained to be small by the absolute size of neutrino masses and the doublet higgs vev . the one loop induced effective lagrangian responsible to @xmath0 and @xmath1 conversions is given by @xmath168 with @xmath169 being the electric charge of the @xmath170-quark , and @xmath171 + \tfrac23 \bigl [ \tfrac{s_\theta^2}{m_{\chi^+_1}^2}f_\chi(\tfrac{m_n^2}{m_{\chi^+_1}^2 } ) + \tfrac{c_\theta^2}{m_{\chi^+_2}^2}f_\chi(\tfrac{m_n^2}{m_{\chi^+_2}^2 } ) \bigr ] \nonumber \\ & \qquad + \tfrac1{m_{\chi^{++}}^2 } \bigl [ f_\sigma(\tfrac{m_e^2}{m_{\chi^{++}}^2 } ) + 2f_\chi(\tfrac{m_e^2}{m_{\chi^{++}}^2 } ) \bigr ] \bigr\ } y_\chi^\dag m_\mu,\nonumber\\ a_r & = { m_e\over m_\mu } a_l,\\ b_l & = \frac{e}{16\pi^2 } y_\chi \bigl\ { -\tfrac16 \bigl [ \tfrac1{m_{\chi_r}^2}g_\sigma(\tfrac{m_e^2}{m_{\chi_r}^2 } ) + \tfrac1{m_{\chi_i}^2}g_\sigma(\tfrac{m_e^2}{m_{\chi_i}^2 } ) \bigr ] + \tfrac23 \bigl [ \tfrac{s_\theta^2}{m_{\chi^+_1}^2}g_\chi(\tfrac{m_n^2}{m_{\chi^+_1}^2 } ) + \tfrac{c_\theta^2}{m_{\chi^+_2}^2}g_\chi(\tfrac{m_n^2}{m_{\chi^+_2}^2 } ) \bigr ] \nonumber \\ & \qquad + \tfrac1{m_{\chi^{++}}^2 } \bigl [ g_\sigma(\tfrac{m_e^2}{m_{\chi^{++}}^2 } ) + 2g_\chi(\tfrac{m_e^2}{m_{\chi^{++}}^2 } ) \bigr]\bigr\ } y_\chi^\dag\;,\nonumber\end{aligned}\ ] ] where @xmath172 the lfv @xmath0 decay branching ratio is easily evaluated by @xmath173 the strength of @xmath1 conversion is measured by the quantity , @xmath174 . following ref.@xcite , we have @xmath175 where @xmath176 and @xmath177 with @xmath178     and @xmath179 conversion . the mass of quadruplet scalar is taken as @xmath180 tev . , title="fig:",width=257 ]   and @xmath179 conversion . the mass of quadruplet scalar is taken as @xmath180 tev . , title="fig:",width=264 ]    for many years , the best 90% c.l . experimental upper limit for @xmath181 was @xmath182@xcite . recently , meg collaboration has obtained better result with the 90% c.l . upper limit@xcite @xmath183 . this new bound , as will be seen , provides important constraint for the quadruplet model discussed here . there are several measurements of @xmath1 conversion on various nuclei . the best bound is for au nuclei with the 90% c.l . experimental bound given by @xmath184@xcite . for au , the relevant parameters determined by method i in ref.@xcite are given by : @xmath185 , @xmath186 and @xmath187@xcite . we will use these values to study implication for our quadruplet model . the numerical results are shown in fig.[fig : lfv ] . in obtaining results in fig.[fig : lfv ] , we have choosen the mass of quadruplet component field @xmath188 to be degenerate with a common mass of 1 tev , and the quadruplet yukawa coupling constant is taken as @xmath140 which satisfying neutrino mixing data from our previous studies for illustration . in the left panel of fig.[fig : lfv ] , we show current experimental bounds on the quadruplet yukawa coupling from non - observation of @xmath189 and @xmath190 conversion as a function of ratio of triplet fermion and quadruplet scalar squared masses . we found that current constraints on quadruplet yukawa coupling constant from @xmath179 conversions are weaker than that from @xmath189 . this is very different than the situation in a model with fourth generation where non - zero @xmath29-penguin contribution dominates and @xmath3 conversion gives stronger constraints@xcite . in the quadruplet model discussed here because the triplet heavy lepton @xmath4 does not have hypercharge , no @xmath29-penguin contribution and therefore @xmath1 conversion gives weaker constraint compared with @xmath0 . from the figure , we see that the quadruplet yukawa couplings are constrained by the new meg data to be less than @xmath80 for a wide range of parameter space . as we showed @xmath191 is typically @xmath192 for @xmath11 tev quadruplet scalars in both normal and inverted neutrino mass spectrum . the contribution from @xmath75 is negligibly small . on the other hand , @xmath145 can be enhanced by a factor of @xmath193 with @xmath194tev . to obtain @xmath195 , @xmath196 is required . such a tiny @xmath100 can be naturally understood as a remnant of the lepton number symmetry . the quadruplet model can have yukawa coupling producing @xmath0 closing to the present upper bound . improved experimental limits can further constrain the model parameters .    in the right panel of fig.[fig : lfv ] , we also show the future prospects of lfv bounds . for @xmath2 we take @xmath197@xcite as the near future improved meg experimental sensitivity . for @xmath1 conversion , there are several planed new experiments , such as mu2e@xcite / comet@xcite and prism@xcite for @xmath198 conversion using al and ti . the sensitivities are expected to reach @xmath199@xcite and @xmath200@xcite , respectively . for ti and al nuclei , the relevant parameters for our calculations are given by @xmath201 , @xmath202 and @xmath203 , and @xmath204 , @xmath205 and @xmath206@xcite . we see that improved @xmath2 and @xmath179 conversion experiments can further constrain the quadruplet yukawa coupling constant . also note that searches for @xmath207 conversions can provide better constraints than that for @xmath0 . finally , we would like to make some comments about collider aspects of this model . one of the interesting feature of type iii seesaw is that the heavy leptons with a mass of a tev or lower can be produced at the lhc . the collider phenomenology related to type iii seesaw for the heavy leptons has been studied in great detail@xcite . the introduction of quadruplet also leads to new phenomena in collider physics . an interesting feature is the existence of the doubly charged particle @xmath208 in the model . doubly charged scalar bosons also appear in other models for neutrino masses , for example , higgs triplet in type ii seesaw model@xcite , and zee - babu model@xcite . the doubly charged scalar bosons can be produced at a hadron collider through the drell - yan production mechanism @xmath209@xcite . the vector boson fusion mechanism can also be useful to produce doubly charged particle@xcite if the vev s of the higgs triplet @xmath210 and the quadruplet @xmath55 are not very small . the recently results from lhc exclude doubly charged higgs mass to be around @xmath211 gev if it decay predominantly through leptonic decay@xcite . unlike the type ii seesaw and zee - babu models , the quadruplet scalars do not have direct interaction with a pair of sm fermion and therefore can not decay into them . the lower limit on the mass of doubly charged higgs boson does not apply for our model .    in both type ii seesaw and the quadruplet models , if the vev s @xmath210 and @xmath55 are not very small , the doubly charged scalar will mainly decay into a pair of @xmath212@xcite . zee - babu model does not have such decay modes . in the case of type ii seesaw model , if @xmath213 gev , the leptonic pair decay modes will become the dominate one for the doubly charged scalar because the decay to gauge boson pair is suppressed by @xmath214 while leptonic yukawa coupling is scaled as @xmath215 . this is , however , not the case for quadruplet model . the @xmath208 can couple to @xmath216 through yukawa coupling . since the heavy charged lepton @xmath217 can mixing with @xmath218 because mixing in eq . leading to @xmath219 . however , the mixing in this case is proportional to @xmath220 which is small . there is another possible decay for @xmath208 . electromagnetic loop correction@xcite will make @xmath217 to be heavier than @xmath221 allowing @xmath222 . then @xmath221 mixes with light neutrinos to allow @xmath223 decay . since the mixing between light neutrino and @xmath221 is only suppressed by a factor @xmath224 , the decay mode , @xmath225 would be more important than @xmath226 . this is different than type ii seesaw model in the case even the vev s are very small . in type iii seesaw the heavy neutrinos are contained in leptonic triplet representations . being a triplet of @xmath227 gauge group , the heavy leptons have non - trivial structure . concerning yukawa interaction for seesaw mechanism , we find a new possibility of having new type of yukawa couplings by introducing a quadruplet @xmath46 with hypercharge equal to half . when the neutral component field of @xmath46 develops a non - zero vev , a dirac mass terms connecting the light and heavy neutrinos can result to facilitate the seesaw mechanism . it is interesting to note that the vev of the quadruplet higgs is constrained to be very small from electroweak precision data . therefore the yukawa couplings of a quadruplet can be much larger than those in a type iii model with a higgs doublet only . we also find that unlike the usual type iii seesaw model where at least two copies of leptonic triplets are needed , with both doublet and quadruplet higgs representations , just one leptonic triplet is possible to have a phenomenologically acceptable model because light neutrino masses can receive sizable contributions from both the tree and one loop levels . large yukawa coupling may have observable effects on lepton flavor violating processes , such as @xmath0 and @xmath1 conversion . there are also some interesting collider signatures for the doubly charged particle in the quadruplet model . + * acknowledgment * :                  b.  bajc , g.  senjanovic , jhep * 0708 * , 014 ( 2007 ) , b.  bajc , m.  nemevsek , g.  senjanovic , phys . rev .   * d76 * , 055011 ( 2007 ) , r.  franceschini , t.  hambye , a.  strumia , phys .  rev . d * 78 * , 033002 ( 2008 ) , t.  li and x.  g.  he , phys . d * 80 * , 093003 ( 2009 ) [ arxiv:0907.4193 [ hep - 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in type iii seesaw model the heavy neutrinos are contained in leptonic triplet representations . 
 the yukawa couplings of the triplet fermion and the left - handed neutrinos with the doublet higgs field produce the dirac mass terms . together with the majorana masses for 
 the leptonic triplets , the light neutrinos obtain non - zero seesaw masses . 
 we point out that it is also possible to have a quadruplet higgs field to produce the dirac mass terms to facilitate the seesaw mechanism . 
 the vacuum expectation value of the quadruplet higgs is constrained to be small by electroweak precision data . 
 therefore the yukawa couplings of a quadruplet can be much larger than those for a doublet . 
 we also find that unlike the usual type iii seesaw model where at least two copies of leptonic triplets are needed , with both doublet and quadruplet higgs representations , just one leptonic triplet is possible to have a phenomenologically acceptable model because light neutrino masses can receive sizable contributions at both tree and one loop levels . 
 large yukawa couplings of the quadruplet can induce observable effects for lepton flavor violating processes @xmath0 and @xmath1 conversion . 
 implications of the recent @xmath2 limit from meg and also limit on @xmath3 conversion on au are also given . 
 some interesting collider signatures for the doubly charged higgs boson in the quadruplet are discussed .