Neutrino mixing and masses in a left right model with mirror fermions

Eu . Phys. J. C (2012) 72:1859 DOI 10.1140/epjc/s10052-012-1859-7 Regula A icle - Theo e ical Physics Neu ino mixing and masses in a le – igh model wi h mi o e mions R. Gai án2,a, A. He nández-Galeana1, J.M. Ri e a-Rebolledo1, P. Fe nández de Có doba3 1Depa amen o de Física, Escuela Supe io de Física y Ma emá ica, I.P.N., U.P. Adol o L. Ma eos, México D.F. 07738, Mexico 2Cen o de In es igaciones Teó icas, FES, UNAM, Apa ado Pos al 142, Cua i lán-Izcalli, México 54700, Mexico 3Ins i u o de Ma emá ica Pu a y Aplicada, Uni e sidad Poli écnica de Valencia, Valencia 46022, Spain Recei ed: 1 July 2011 / Re ised: 18 No embe 2011 / Published online: 31 Janua y 2012 © Sp inge -Ve lag / Socie à I aliana di Fisica 2012 Abs ac In he amewo k o a le – igh model con ain- ing mi o e mions wi h gauge g oup SU(3)C⊗SU(2)L⊗ SU(2)R⊗U(1)Y, we es ima e he neu ino masses, which a e ound o be consis en wi h hei expe imen al bounds and hie a chy. We e alua e he decay a es o he Lep on Fla o Viola ion (LFV) p ocesses μ→eγ ,τ→μγ and τ→eγ . We ob ain uppe limi s o he la o -changing b anching a ios in ag eemen wi h hei p esen expe imen- al bounds. We also es ima e he decay a es o hea y Ma- jo ana neu inos in he channels N→W±l∓,N→Zνland N→Hνl, which a e oughly equal o la ge alues o he hea y neu ino mass. S a ing om he mos gene al Majo- ana neu ino mass ma ix, he smallness o ac i e neu ino masses u ns ou om he in e play o he hie a chy o he in ol ed scales and he double applica ion o seesaw mech- anism. An app op ia e pa ame e iza ion on he s uc u e o he neu ino mass ma ix imposing a symme ic mixing o elec on neu ino wi h muon and au neu inos leads o i- bimaximal mixing ma ix o ligh neu inos. 1 In oduc ion The e idence o neu ino oscilla ions ob ained in expe i- men al esul s om a mosphe ic, sola , eac o and accele - a o neu inos leads one o conclude ha he neu inos ha e a mass di e en om ze o. The cu en neu ino expe imen- al da a (Supe Kamiokande, SNO, Kamland, K2K, GNO, CHOOZ) can be desc ibed by neu ino oscilla ions ia h ee neu ino mixings [1–7]. The p esen da a gi e he sola neu- ino lep on mixing angle an2θ12 =0.45 ±0.05, he a - mosphe ic angle sin22θ23 =1.02 ±0.04 and sin22θ13 = In e disciplina y Modeling G oup, In e Tech. ae-mail: gai an@se ido .unam.mx 0±0.05 [8–10]. The complex phase has no ye been mea- su ed. The expe imen al in o ma ion on neu ino masses and mixing poin s ou new physics beyond he S anda d Model (SM) o pa icle physics, wi h a g ea ac i i y on he conse- quences. Among he possible mechanisms o neu ino mass gene a ion, he mos simple and a ac i e one is he see- saw mechanism [11–20], which explains he smallness o he obse ed ligh neu ino masses h ough he exchange o supe hea y pa icles; an al e na i e explana ion is gi en by ex a dimensions beyond he usual h ee ones [21]. I has been sugges ed ha igh -handed (RH) neu inos expe ience one o mo e o hese ex a dimensions, such ha hey only spend pa o hei ime in ou wo ld, wi h appa en ly small masses. A he p esen , i is no known whe he neu inos a e Di ac o Majo ana e mions. Models wi h hea y neu inos o mass o o de 1 TeV can gi e ise o signi ican ligh -hea y mixing and de i- a ion om uni a i y o he Pon eco o–Maki–Nakagawa– Saka a (PMNS) ma ix [22–24]. The nonuni a i y na u e o he neu ino mixing ma ix due o mixing wi h ields hea ie han MZ 2can mani es in ee-le el p ocesses like π→μν, Z→¯νν,W→lν o in cha ged lep on decays μ→eγ , τ→μγ , e c. which a e la o iola ing and a e and p o- ceed a one loop le el [22–26]. The TeV scale seesaw mod- els a e in e es ing because hey can ha e signa u es in he CERN La ge Had on Collide (LHC) in he nea u u e [27– 29]. Neu inos also a e impo an in as ophysics and cosmol- ogy [30] and p obably hey con ibu e o ho da k ma e in he Uni e se and in i s e olu ion. Pa i y P iola ion was one o he g ea es disco e ies o pa icle physics [31–33]. Be o e his obse a ion, acco ding o Fe mi’s hypo hesis i was belie ed ha weak in e ac ions ha e pu ely ec o ial V o axial ec o ial (V–A) pa i y con- se ing Lo en z s uc u e [34,35]. The heo y o Lee and Page 2 o 8 Eu . Phys. J. C (2012) 72:1859 Yang in 1956 [36] p oposed a e mion cu en wi h V and A s uc u e. I is known ha in he s anda d model (SM) he elec oweak in e ac ions ha e a V–A o m, wi h only le -handed (LH) (o dina y) e mions coupling o he weak gauge boson W±. Bu one can include also mi o e mions [37] wi h a V +A coupling, such ha P is conse ed. In his sense, he e m “mi o e mion” is equi alen o “ ec o - like e mion”, whe e o a heo y wi h gauge g oup G,ina ep esen a ion Rone has se s o LH and RH e mions. In he li e a u e a second meaning o ha e m is used. Gis ex ended o a G×Ggauge heo y, and o e e y mul- iple (R,1)a mi o pa ne (1,R)is added, such ha he e is no gauge in a ian mass e m connec ing he LH and RH mul iple s [38–41]. Thus i is na u al o conside he exis- ence o mi o gene a ions. Masses o mi o pa icles a ise om symme y b eaking; o mi o gene a ion hey may lye below one TeV, and easi- ble o be disco e ed in Fe milab Te a on Collide and LHC. A solu ion o he s ong CP p oblem has been p oposed wi hin a L–R symme ic con ex [46,47]. The elec oweak g oup is ex ended o SU(2)L⊗SU(2)R⊗U(1)including mi o e mions. These e mions a e conjuga ed o he o di- na y ones wi h espec o he gauge symme y g oup such ha a e mion ep esen a ion including bo h o hem is eal and he cancela ion o anomalies is au oma ic [48]. In his pape we conside a L–R model wi h mi - o e mions (LRMM) wi h gauge g oup G≡SU(3)C⊗ SU(2)L⊗SU(2)R⊗U(1)Y. We discuss in Sec . 2 he o malism o mixing be ween s anda d and new exo ic e mions In Sec . 3we p esen he model and discuss he symme y b eaking p ocess wi h wo scala double s. In Sec . 4we w i e he gauge in a ian Yukawa couplings which a e spon aneous symme y b eaking gi e he mos gene al Majo ana neu ino mass ma ix. Wi h a double ap- plica ion o he ype I seesaw app oxima ion we es ima e he ligh neu ino masses in e ms o ee Yukawa couplings assuming ex u es o he ligh and mi o ma ices, ob ain- ing consis en no mal hie a chical alues o masses and a i-bimaximal mixing o ligh neu inos. We discuss in Sec . 4 he mixing be ween s anda d and mi o e mions. In Sec . 5we include he adia i e decays μ→eγ ,τ→μγ and τ→eγ and es ima e bounds o hei b anching a ios. Finally, we calcula e such a ios o he hea y Majo ana neu- inos decays N→W+l−,N→Zνland N→Hνl, ge ing a smoo h a ia ion wi h he hea y neu ino mass, e en when i is much la ge han any o he in ol ed masses. 2 Fe mion mixing and la o iola ion To conside he mixing o e mions, we shall ollow [22– 24], g ouping all e mions o elec ic cha ge qand helici y a=L,R in o na+ma ec o column o nao dina y (o) and maexo ic (e) gauge eigens a es, i.e. ψo a=(ψo na,ψo me)T a.The o dina y e mions include he SM ones, whe eas he exo ics include any new e mion wi h sequen ial (mi o o single ) p ope ies beyond he SM. The ela ion be ween he gauge eigens a es and he co - esponding ligh (l) and hea y (h) cha ged mass eigens a es ψa=(ψl,ψh)T a,a=L,R is gi en by he ans o ma ion ψ0 a=Vaψa,a=L,R, (1) whe e Va=AaEa FaGa.(2) In (2), Aais a ma ix ela ing he o dina y weak s a es and he ligh -mass eigens a es, while Ga ela es he exo ic and hea y s a es. Eaand Fadesc ibe he mixing be ween he wo sec o s. F om he uni a y o V VaV+ a=1,a=L,R (3) i ollows ha he subma ix Aais no uni a y. The e m F+ aFa, which is second o de in he small ligh –hea y e mion mixing, will induce la o -changing ansi ions in he ligh –ligh sec o . The acuum expec a ion alues (VEV) o he neu al scala s p oduce he SM e mion mass e ms, which oge he wi h he exo ic mass and mixing ma ices lead o he mass ma ix Mwhich akes he o m M=Kˆμ μˆ K,(4) whe e Kdeno es he SM e mion mass ma ix and ˆ Kco - esponds o he e mion mass ma ices associa ed wi h he exo ic sec o , while μ,ˆμco espond o he mixing e ms be ween o dina y and exo ic e mions. The diagonal mass ma ix Mdcan be ob ained h ough a biuni a y o a ion ac ing on he Land Rsec o s, namely Md=V+ LMVR=ml0 0Mh,(5) whe e ml,mhdeno e he ligh and hea y diagonal mass ma- ices, espec i ely. The o m o he mass ma ix will depend on he ype o exo ic e mion conside ed. The scala - e mion couplings wi hin some speci ic Higgs sec o a e no diagonal in gene al, and one can see ha he couplings a e no diagonal in gene al; hus new phenomena associa ed wi h la o -changing neu al cu en s (FCNC) will be p esen in such model. Eu . Phys. J. C (2012) 72:1859 Page 3 o 8 3 The model In his and nex sec ions we ollow closely [42–45]. The LRMM o mula ion is based on he gauge g oup SU(2)L⊗ SU(2)R⊗U(1)Y. In o de o sol e di e en p oblems such as he hie a chy o qua k and lep on masses o he s ong CP p oblem, di e en au ho s ha e enla ged he e mion con en o he o m l0 iL =ν0 i e0 iL ,e 0 iR,ν 0 iR, ˆ l0 iR =ˆν0 i ˆe0 iR ,ˆe0 iL ,ˆν0 iL, Q0 iL =u0 i d0 iL ,u 0 iR,d 0 iR, ˆ Q0 iR =ˆu0 i ˆ d0 iR ,ˆu0 iL,ˆ d0 iL, (6) whe e he index i uns o e he h ee e mion amilies and he supe sc ip s 0deno e gauge eigens a es. The quan um numbe s o hese e mions unde he gauge g oup Gde ined abo e a e gi en by l0 iL ∼(1,2,1,−1)iL,ν 0 iR ∼(1,1,1,0)iR, e0 iR ∼(1,1,1,−2)iR,ˆν0 iL ∼(1,1,1,0)iL, ˆe0 iL ∼(1,1,1,−2)iL,ˆ l0 iR ∼(1,1,2,−1)iR u0 iR ∼3,1,1,4 3iR ,d 0 iR ∼3,1,1,2 3iR ˆu0 iL ∼3,1,1,4 3iL ,ˆ d0 iL ∼3,1,1,2 3iL Q0 iL ∼3,2,1,1 3iL ,ˆ Q0 iR ∼3,1,2,1 3iR , espec i ely, and he las en y co esponds o he hype - cha ge (Y) wi h he elec ic cha ge de ined as Q=T3L+ T3R+Y 2. A model wi h gauge g oup SU(2)L×SU(2)R×U(1)V× SU(3)Hand he e mion con en (6) was o iginally sug- ges ed in Z.G. Be ezhiani [49] as he “uni e sal seesaw” model which gene a ed masses o cha ged e mions as well as o he neu inos. He also wo ked on a SU(5)×SU(3)H model o ex ension o SO(10)o Pa i–Salam [50,51], p e- dic ing o ins ance mνe=O(10)eV. A low (elec oweak scale) ene gies he model simula es he s anda d SU(3)C× SU(2)L×U(1)Ymodel, and FCNC a e supp essed na u- ally. 3.1 Symme y b eaking The “Spon aneous Symme y B eaking” (SSB) is achie ed ollowing he s ages: G−→ GSM −→ SU(3)C⊗U(1)Q,(7) whe e GSM =SU(3)C⊗SU(2)L⊗U(1)Yis he “S anda d Model” g oup symme y, and Y 2=T3R+Y 2. The Higgs sec- o o induce he SSB in (7) in ol es wo double s o scala ields: Φ=(1,2,1,1), ˆ Φ=(1,1,2,1), (8) whe e he en ies co espond o he ans o ma ion p ope - ies unde he symme ies o he g oup G, wi h he “Vacuum Expec a ion Values” (VEV’s) Φ= 1 √20 ,ˆ Φ=1 √20 ˆ .(9) The mos gene al po en ial ha de elops his pa e n o VEV’s is V=−μΦ†Φ+ˆμˆ Φ†ˆ Φ+λ1 2Φ†Φ2+ˆ Φ†ˆ Φ2 +λ2Φ†Φˆ Φ†ˆ Φ.(10) In he las exp ession he e ms wi h μ,ˆμa e included so ha he pa i y symme y (P)is b oken so ly, i.e., only h ough he dimension- wo mass e ms o Higgs po en ial. The scala Lag angian o he model is w i en as Lsc =(DμΦ)+(DμΦ)+ˆ Dμˆ Φ+ˆ Dμˆ Φ,(11) whe e Dμand ˆ Dμa e he co a ian de i a i es o he SM and he mi o pa s, espec i ely. The gauge in e ac ions o qua ks and lep ons can be ob ained om he Lag angian Lin =¯ ψiγμDμψ+¯ ˆ ψiγμˆ Dμˆ ψ. (12) The VEV’s and ˆ a e ela ed o he masses o he cha ged gauge bosons Wand ˆ Wby MW=1 2gL and Mˆ W=1 2gRˆ , whe e gLand gRa e he coupling cons an s o SU(2)Land SU(2)R, and gL=gRi we equi e L–R sym- me y. 4 Gene ic Majo ana neu ino mass ma ix Wi h he ields o e mions in oduced in he model, we may w i e he gauge in a ian Yukawa couplings o he neu al sec o :1 hij ¯ ˆνiLνjR +λij ¯ liL ˜ ΦνjR +ηij ¯ ˆ liR ˜ ˆ ΦˆνjL 1To simpli y no a ion we d op he “0” supe sc ip . Page 4 o 8 Eu . Phys. J. C (2012) 72:1859 +ˆ Mij ¯ ˆνiL(ˆνjL)c+σij ¯ liL(ˆνjL)c˜ Φ +χij ¯νiR(νjR)c+πij ¯ ˆ liR(νjR)c˜ ˆ Φ+h.c.,(13) whe e i,j =1,2,3, ˜ Φ=iσ2Φ∗,˜ ˆ Φ=iσ2ˆ Φ∗,hij ,ˆ Mij ,χij ha e dimensions o mass, and σij ,ηij ,λij and πij a e di- mensionless Yukawa coupling cons an s. When Φand ˆ Φ acqui e VEV’s we ge he neu ino mass e ms hij ¯ ˆνiLνjR + √2λij ¯νiLνjR +ˆ √2ηij ¯ ˆνiR ˆνjL +ˆ Mij ¯ ˆνiLˆνjLc+ √2σij ¯νiLˆνjLc +χij ¯νiR(νjR)c+ˆ √2πij ¯ ˆνiR(νjR)c+h.c.,(14) which a e w i en in he gene ic Majo ana ma ix o m ΨνL, Ψ cνLMLMD MT DMR(Ψ c ν)R (Ψν)R(15) whe e (Ψν)L,R =νi ˆνiL,R ,Ψc νL,R =(νc i) (ˆνc i)L,R ,(16) ML=0 √2σ √2σTˆ M,M R=χˆ √2π ˆ √2πT0, (17) MD= √2λ0 hˆ √2η,(18) wi h h,ˆ M,χ,σ,η,λand πunknown ma ices o 3 ×3 dimension. By assuming he na u al hie a chy |(ML)ij | |(MD)ij ||(MR)ij | o he mass e ms, he mass ma ix in (15) can app oxima ely be diagonalized, yielding ΨνL, Ψ cνLMν0 0MR(Ψ c ν)R (Ψ ν)R,(19) whe e, neglec ing O(MDM−1 R) e ms, we may w i e in good app oxima ion [52]ΨνL,R ≈ΨνL,R, and ΨcνL,R ≈Ψc νL,R. The Majo ana mass ma ix o he le -handed neu inos may be w i en in his seesaw app oxima ion as Mν≈ML−MDM−1 RMT D.(20) We assume a scena io whe e he dominan con ibu ion o he ac i e known neu inos comes om he MLma ix ha - ing he same s uc u e o a Type I seesaw. Then in his sce- na io he eigen alues o he ligh neu inos may be ob ained by applying again he seesaw app oxima ion, ha is, Mligh =− √2σˆ M−1 √2σT .(21) Taking ad an age o he ac ha all σij and ˆ Mij en ies in (21) a e ee pa ame e s, we p opose he ollowing pa- ame e iza ions o ˆ Mand Mligh neu ino mass ma ices: Mligh =Y2 2 2ˆm⎛ ⎝ 1+bb b b1+b+cb−c bb−c1+b+c⎞ ⎠, ˆ M=ˆmDiag(Y1,Y2,Y3), (22) whe e Y,Y1,Y2,Y3,b,ca e dimensionless coupling con- s an s and ˆm ep esen s he mi o scale. This pa ame e iza- ion o he ligh neu inos mass ma ix imposes a symme ic mixing o elec on neu ino wi h muon and au neu inos in he i s ow and column o (Mligh )ij , and he 2 ×2 subma- ix i,j =2,3 gene a e maximal mixing o muon and au neu inos. This s uc u e o Mligh makes possible he diag- onaliza ion o ligh neu inos by he so called “ i-bimaximal mixing ma ix” [57], i.e. UT TBMligh VTB =−UT TB √2σˆ M−1 √2σT UTB =Diag(m1,m2,m3), (23) wi h UTB =⎛ ⎜ ⎜ ⎜ ⎜ ⎝ 2 √6 1 √30 −1 √6 1 √3−1 √2 −1 √6 1 √3 1 √2 ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ (24) and he ligh neu ino mass eigen alues (m1,m2,m3)=Y2 2 2ˆm(1,1+3b,1+2c). (25) The supp ession by he mi o scale ˆmin (25) p o ides a na - u al explana ion o he smallness o neu ino masses. The allowed ange o alues o he squa e neu ino mass di e - ences epo ed in PDG [56]: m2 2−m2 1≈7.6×10−5eV2, m2 3−m2 2≈2.43 ×10−3eV2, (26) wi h he inpu o no mal hie a chy o he neu ino masses (m1,m2,m3)=(0.0865,0.0870,.1)eV,(27) ix he pa ame e alues as b=0.00168 and c=0.07757. These neu ino masses a e consis en wi h he bounds mν<2eV[56], and se he mass di e ences m2 3−m2 1≈2.5×10−3eV2.(28) So, om (25), (27) Y2 2 2ˆm≈8.65 ×10−2eV.(29) Eu . Phys. J. C (2012) 72:1859 Page 5 o 8 The e o e, assuming ˆm=mˆν=100 GeV and =246 GeV we ob ain Y≈5.34 ×10−7.(30) The ma ix MLin (17) may be diagonalized by using a uni- a y ans o ma ion, U†MLU=Diag(m1,m2,m3,ˆm1,ˆm2,ˆm3), (31) whe e he mixing ma ix Ucompa ible wi h ou amewo k is w i en in good app oxima ion as U6×6≈UTB √2σˆ M−1 −( √2σˆ M−1)TI3×3.(32) The pa icula nume ical solu ion cong uen wi h he abo e scena io o he neu ino masses and mixing is √2σ≈93041.9eV⎛ ⎝−1.2001 0.6355 1.2952 0.6355 −1.2702 1.3006 1.2952 1.3006 0.5389⎞ ⎠, (33) ˆ M=100 GeV Diag(3.4918,3.2643,3.6043), (34) and √2σˆ M−1≈9.3×10−7⎛ ⎝−0.3437 0.1946 0.3593 0.1819 −0.3891 0.3608 0.3709 0.3984 0.1495⎞ ⎠ (35) o ligh ν–mi o mixing. Since he ligh –mi o mixing is e y small, he mixing ma ix o ligh neu inos beha es in good app oxima ion as he UTB,(24). I is wo h o men- ion he e ha in he limi o e y small ligh –mi o cha ged lep on mixing, (F † LFL)ij ,(E† LEL)ij 1, we may app oach UTB as he usual UPMNS lep on mixing ma ix o h ee gen- e a ions. Then, we ob ain (UPMNS)e2≃1 √3,(UPMNS)e3≃0, and (UPMNS)μ3≃1 √2, which gi e o he sola and he a mo- sphe ic neu ino mixing angles θ12 ≃35.20and θ23 ≃450, wi h θ13 ≃0 in good ag eemen wi h cu en da a, al hough ecen e idence [58,59] shows ha θ13 may ha e a alue di e en om ze o. In ea lie pape s on he s udy o neu inos and le – igh symme y [60–63] appea simila ep esen a ions o he e mions and mass ma ices as ou in (18), bu hese au ho s ob ain masses o he s anda d and mi o neu i- nos some o de s o magni ude di e en om ou s. On he o he hand, he mass gene a ion in he LRMM he e consid- e ed is achie ed wi h he scala ields Φand ˆ Φ,(3), (4), ans o ming as double s unde SU(2)Land SU(2)R, espec- i ely, wi h a mi o scale much lowe han 1012–1013 GeV. 5 Radia i e decays In his sec ion we analyze he lep on la o iola ion p o- cesses μ→eγ ,τ→μγ and τ→eγ a ising in he model by he exis ence o gauge in a ian mixing e ms be ween o dina y lep ons and wi h he mi o coun e pa s. The lowe o de con ibu ion o heses decays media ed by he neu al scala ields comes om he Feynman diag ams whe e he pho on is adia ed om an in e nal line. The co esponding ampli ude is p opo ional o he ope a o u(p2)σμνqνμu(p1), whe e q=p1−p2and μis he pho- on pola iza ion [53–55]. In he limi memμmτ he a e decay is gi en by Γ(l i→lj+γ)=α 512π4GFm2 li2m5 li M4 Hln M2 H m2 li−4 3ij − k xνkVL,jkV+ R,ki 2 ,(36) whe e xνk≡m2 νk M2 W ,ij =|A+ LAR|ij ep esen s he la o - changing couplings, and he second e m is he e y small con ibu ion om he ligh neu ino p opaga ing inside he loop. In he limi α1 and MHMˆ H he b anching a ios a e, espec i ely, B1(μ →e+γ)=3αm4 μ 8M4 Hln M2 H m2 μ−4 3eμ − k xνkVL,ekV+ R,kμ 2 ,(37) B2(τ →μ+γ)=3αm4 τ 8M4 Hln M2 H m2 τ−4 3μτ − k xνkVL,μkV+ R,kτ 2 (38) and B3(τ →e+γ)=3αm4 τ 8M4 Hln M2 H m2 τ−4 3eτ − k xνkVL,ekV+ R,kτ 2 .(39) By using he cons ain s ij <1,i =j o he pa ame e s in (37), (39), equi ed by uni a i y o V,see(2), (3), one ge s o he abo e b anching a ios B1<2.2×10−13,B 2<5×10−9and B3<5×10−9 (40) Page 6 o 8 Eu . Phys. J. C (2012) 72:1859 which is cong uen wi h he expe imen al bounds [56] B(μ →e+γ)<1.2×10−11,B(τ →μ+γ)<4.4×10−8 and B(τ →e+γ)<3.3×10−8PDG [56]. 6 Hea y neu ino signals Possible new neu inos can be de ec ed in a ious ways in collide s. I hese neu inos a e hea y hey will be uns able and may be de ec ed di ec ly in hei decay p oduc s. Nex gene a ion o la ge collide s will p obe Na u e up o TeV scales wi h high p ecision, p obably disco e ing new hea y pa icles. Thus, i will be a window o any new physics nea he elec oweak scale which couples o he SM. Such collide s can be used o p oduce new hea y neu inos a an obse able le el o imp o e p esen limi s on hei masses and mixings [64–67]. These e mions wi h new in e ac ions, like in he le – igh models [68], can be p oduced by gauge couplings supp essed by small mixing angles. Fo he anal- ysis o he hea y neu inos signals i is necessa y o know hei decay modes, which a e di e en in he Di ac and Ma- jo ana cases. Hea y Majo ana neu ino single s can be p oduced in he p ocess [69,70] q¯ q→W∗→l±H(41) wi h l=e,μ,τ, which c oss sec ions depend on MNand he small mixing VlN. Hea y Majo ana neu ino decays in he channels N→W±l∓,N→Zνland N→Hνl. The pa ial wid hs o he Ndecays a e ΓN→W+l− =ΓN→W−l+ =e2 64πs2 θw|UlN|2m3 N M2 W1−M2 W m2 N1+M2 W m2 N−2M4 W m4 N, (42) Γ(N→Zνl) =e2 64πs2 θwc2 θw|UlN|2m3 N M2 Z1−M2 Z m2 N ×1+M2 Z m2 N−2M4 Z m4 N,(43) Γ(N→Hνl)=e2 64πs2 θw|UlN|2m3 N M2 W1−M2 H m2 N2 ,(44) whe e UlN is he ligh –mi o neu ino mixing √2σˆ M−1, (35). F om (32), (35) he con ibu ions come om e ms o he o de |VlN|10−7. F om hese exp essions we can con- clude ha he o al b anching o each o he ou channels is independen o he hea y neu ino mixing, de e mined only by mNand he gauge and Higgs boson masses. Hea y neu ino signals a e limi ed by he small mixing o he hea y neu ino equi ed by p ecision cons ain s [73] and masses o o de 100 GeV a e accessible a LHC. Fo his mass ange, SM backg ounds a e la ge and, since p oduc- ion c oss sec ions a e ela i ely small, hea y neu ino sin- gle s a e a he di icul o obse e. The b anching a ios o di e en alues o mN ead as in Table 1(MH=130 GeV); and in all hese cases Bi≈1. He e BW±=B N→W±l∓,B Z=B (N →Zνl), BH=B (N →Hνl). (45) Table 1shows ha hese decays a e no so sensi i e o he hea y neu ino mass, such ha o hea y neu ino signals i is no necessa y o ha e cen e o mass ene gies much la ge han a hund ed GeV. Among he possible inal s a es gi en by (42)–(44), only cha ged cu en decays gi e inal s a es which may in p in- ciple be de ec ed. Fo mN<M W hese wo body decays a e no possible and Ndecays in o h ee e mions, media ed by o -shell bosons. O he simple p oduc ion p ocesses like q¯ q→Z∗→νN, (46) gg →H∗→νN (47) gi e l±and l+l− inal s a es which a e unobse able due o he huge backg ounds. Fo he pai p oduc ion q¯q→Z∗→NN (48) he c oss sec ion is supp essed by |VlN|4, phase space and he Zp opaga o , and is hus negligible. Th ee signals a e p oduced in he wo cha ged cu en decay channels o he hea y neu ino l+N→l+l−W+→l+l−l+¯ν, (49) l+N→l+l+W−→l+l+l−ν(50) and small addi ional con ibu ions om τlep onic decays. Hea y neu ino signals in he inal s a e l±l±a e gi en in he lep on numbe iola ing neu ino decay and subse- quen had onic Wdecay, o lep onic decay when he lep- Table 1 B anching a ios o di e en alues o mN mN(GeV)B W±BZBH 100 0.34 0.1 0.2 390 0.3 0.306 0.09 780 0.3 0.297 0.107 MW,MZ,MH0.293 0.3 0.111 Eu . Phys. J. C (2012) 72:1859 Page 7 o 8 on is missed. LHC p esen ene gies a e enough o disco e hea y Majo ana neu ino wi h e y small VeN [71,72]. 7 Conclusions He e he LRMM wi h gauge g oup SU(3)C⊗SU(2)L⊗ SU(2)R⊗U(1)Yis applied in o de o ind close alues o neu ino masses i ed o expe imen al da a. We ha e wo ked wi h Majo ana neu inos, which mass ma ix was w i en in e ms o blocks ha s and o s anda d and mi - o mass e ms. The la ge numbe o pa ame e s in ol ed induces o make some simpli ica ions on he s uc u e o he ma ix. A double seesaw app oach me hod is used and diag- onaliza ion is pe o med, and wi h he help o neu ino da a we accommoda e neu ino masses wi h no mal hie a chy o he o de o (m1,m2,m3)≈(0.0865,0.0870,0.1)eV. So, we ha e ound a consis en smallness hie a chy o he neu- ino masses. Wi h he LRMM we ha e also analyzed he adia i e decays μ→e+γ,τ→e+γand τ→μ+γ o a Higgs mass o 130 GeV, ob aining bounds o he b anching a ios cong uen wi h he expe imen al ones. De- cay a es o hea y neu inos Nwe e calcula ed o di e - en channels, and we ound ha hei BR a e nea ly equal o MNMW,MZ,MHand also ha hey do no change oo much o o he alues o MN. To ind hea y Majo ana neu inos one has only a ew pa ame e dependence ( o neu- ino single s, he hea y neu ino mass and i s mixing angle) and also he mass scale could be accessible a he LHC. Acknowledgemen s The au ho R. Gai án wishes o hank o he “Sis ema Nacional de In es igado es” (SNI) in Mexico o pa ial sup- po . and also acknowledges suppo by PAPIIT p ojec IN117611. A. He nandez-Galeana is hank ul o pa ial suppo om he “Ins i- u o Poli écnico Nacional” (G an s om EDI and COFAA) and “Sis- ema Nacional de In es igado es” (SNI) in Mexico, and J.M. Ri e a- Rebolledo wishes o hank o EDD-IPN and he “Sis ema Nacional de In es igado es” (SNI) in Mexico o pa ial suppo . Re e ences 1. Y. Fukuda e al. (Supe -Kamiokande Collabo a ion), Phys. Re . Le . 81, 1562 (1998) 2. Q.R. Ahmad e al. (The SNO Collabo a ion), Phys. Re . Le . 87, 71301 (2001) 3. K. Eguchi e al. (KamLAND Collabo a ion), Phys. Re . Le . 90, 021801 (2003) 4. E. Aliu, e al. (K2K Collabo a ion), Phys. Re . Le . 94, 081802 (2005) 5. 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