We propose a new seesaw mechanism for neutrino masses within a class of
supersymmetric SO(10) models with broken D-parity. It is shown that in such
scenarios the B-L scale can be as low as TeV without generating inconsistencies
with gauge coupling unification nor with the required magnitude of the light
neutrino masses. This leads to a possibly light new neutral gauge boson as well
as relatively light quasi-Dirac heavy leptons. These particles could be at the
TeV scale and mediate lepton flavour and CP violating processes at appreciable
levels.Comment: 4 pages, 3 figures, revtex4, references added, typos corrected,
  sharper discussion of the RGEs give

J. C. Romão

J. W. F. Valle

M. Malinský

T. Yanagida

English

arXiv

Crossref

Supersymmetric SO(10) Seesaw Mechanism with Low
                    
                      B

We propose a new seesaw mechanism for neutrino masses within a class of supersymmetric SO(10) models with broken D-parity. It is shown that in such scenarios the B-L scale can be as low as TeV without generating inconsistencies with gauge coupling unification nor with the required magnitude of the light neutrino masses. This leads to a possibly light new neutral gauge boson as well as relatively light quasi-Dirac heavy leptons. These particles could be at the TeV scale and mediate lepton flavour and CP violating processes at appreciable levels

Malinsky, Michal

Romao, J. C.

Furtado Valle, José Wagner

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:hep-ph/0506296v3  29 Jul 2005IFIC/05-28Novel Supersymmetric SO(10) Seesaw MechanismM. Malinsky´∗Scuola Superiore di Studi AvanzatiVia Beirut 4, I-34014, and INFN, Sezione di Trieste, ItalyJ.C.Roma˜o†Departamento de F´ısica and CFTP, Instituto Superior Te´cnicoAv. Rovisco Pais 1, 1049-001 Lisboa, PortugalJ.W.F.Valle‡AHEP Group, Instituto de F´ısica Corpuscular – C.S.I.C./Universitat de Vale`nciaEdificio Institutos de Paterna, Apt 22085, E–46071 Valencia, Spain(Dated: February 2, 2008)We propose a new seesaw mechanism for neutrino masses within a class of supersymmetric SO(10)models with broken D-parity. It is shown that in such scenarios the B−L scale can be as low as TeVwithout generating inconsistencies with gauge coupling unification nor with the required magnitudeof the light neutrino masses. This leads to a possibly light new neutral gauge boson as well asrelatively light quasi-Dirac heavy leptons. These particles could be at the TeV scale and mediatelepton flavour and CP violating processes at appreciable levels.PACS numbers: 12.10.-g,12.60.-i, 12.60.Jv, 14.60.StThe origin of neutrino masses is the most well keptsecret of modern elementary particle physics. Thebasic dimension–five operator which leads to neutrinomasses [1] can arise from physics at vastly different scales.One popular alternative is the seesaw mechanism, inwhich case the small neutrino masses are induced by theexchange of superheavy neutral fermions [2, 3, 4, 5] orsuperheavy scalars, or both [6, 7, 8]. The light neutrinomasses are given asMν ≃ −v2YM−1Y T (1)An alternative inverse seesaw scheme has been sug-gested [9] for theories which lack the representation re-quired to implement the canonical seesaw, as happens ina class of string inspired models.In addition to the normal neutrinos ν such inverse see-saw mechanism employs two sequential SU(3) ⊗ SU(2)⊗ U(1) singlets νc, S (these are all left-handed two-component spinors [6]). The effective neutrino mass ma-trix has the following form:Mν = 0 Y v 0Y T v 0 M0 M µ (2)in the basis νL, νcL, SL. Here Y is the Yukawa ma-trix parametrizing the Y ijνiLTC−1νjcL+h.c. interactions,whileM and µ are SU(3) ⊗ SU(2) ⊗ U(1) invariant massentries. When µ → 0 a global lepton–number symme-try is exactly conserved and all three light neutrinos are∗Electronic address: malinsky@sissa.it†Electronic address: jorge.romao@ist.utl.pt‡Electronic address: valle@ific.uv.esstrictly massless. Yet it has been shown [10, 11] that lep-ton flavour and CP can be violated at appreciable levelseven in the absence of supersymmetry, provided the scaleM is sufficietly low. When µ 6= 0 the mass matrix forthe light eigenstates is given byMν ≃ −v2(YMT−1)µ(M−1Y T ) (3)One sees that neutrinos can be made very light, as re-quired by oscillation data [12], even if M is very low,far below the GUT scale MG (M ≪ MG), provided µ isvery small, µ ≪ M . This scheme has a very rich andinteresting phenomenology, since no new scales need tobe added to generate the small neutrino masses, insteada small parameter µ is added. Note that in such SU(3) ⊗SU(2) ⊗ U(1) inverse seesaw the smallness of µ is natural,in t’Hooft’s sense [13], as the symmetry enhances whenµ→ 0. However, there is no dynamical understanding ofthis smallness.Here we provide an alternative inverse seesaw real-ization consistent with a realistic unified SO(10) model.Such embedding brings several issues:• The νcS entryM (generated by the VEV of a Higgsmultiplet χR with SU(3)c ⊗ SU(2)L ⊗ SU(2)R ⊗U(1)B−L quantum numbers (1, 1, 2,−1)) breaksthe B−L symmetry, now gauged. The correspond-ing scale 〈χR〉 must be compatible with gauge cou-pling unification. Together with the requirement oflow-energy supersymmetry to stabilize the hierar-chies, this places rather strong constraints on howwe must fill the “desert” of particles below MG.• The magnitude of the singlet µSS mass.• The presence of a nonzero νS entry in Eq. (2), pro-portional to the VEV of the L-R partner of χR,namely χL ≡ (1, 2, 1,+1).2Let us now discuss one by one these three points andshow that there indeed exists a supersymmetric SO(10)model that addresses all these conditions in a satisfactoryway and offers a new way to understand the smallness ofneutrino masses.First note that there are several mechanisms that couldbe used to get rid of the SS-term in Eq. (2). Forexample we can treat the SO(10) embedding into E6where the fermionic singlet could be a member of a 27-dimensional irreducible representation with the familiarSO(10)⊗ U(1)X decomposition27F = 14F ⊕ 161F ⊕ 10−2F (4)If at the E6-scale there is no 351′ Higgs representationthe U(1)-charge of the 1F1F matter bilinear is so largethat it is very hard to saturate it. Thus, as long as thecorresponding U(1) is unbroken we have µ = 0. Evenif we break the U(1) symmetry at some lower scale itcould be rather complicated to generate an effective SS-entry, which brings further suppression, even at the levelof effective operators. From now on we will neglect µ.Now consider the νS-term. A typical SO(10) superpo-tential contains the following terms,W ∋M1616H16H + ρ16H16H10H +H. c.The fact that in ’standard’ supersymmetric SO(10) mod-els there is a small induced vacumm expectation value(VEV) generated for the neutral component of χL =(1, 2,+1)SM ∈ (1, 2, 1,+1)LR of 16H once the B-L sym-metry is broken can be seen from the structure of theF-terms. For example F †(1,2,1,±1) is proportional toM16(1, 2, 1,∓1)16 + ρ(1, 1, 2,∓1)16(1, 2, 2, 0)10 + . . .After giving a nonzero VEV to the (1, 1, 2,∓1) field (thatsubsequently breaks B-L) and the traditional doubletpair in 10H (to break the SM) the requirements to bein a supersymmetric vaccum lead to〈χL〉 ≡ vL ≃ 〈(1, 2, 1,∓1)16〉 ≃ ρvRvM16(5)Therefore, there is a new contribution to (2) coming froma term of the type F iklνLiTC−1SkLχlL + h.c. so that theneutrino mass matrix readsMν = 0 Y v FvLY T v 0 F˜ vRFT vL F˜T vR 0 (6)instead of Eq. (2). Here F˜ is an independent combinationof the VEVs of the χ′Ls, namely, F˜ijvL =∑k Fijk〈χL〉k,while F ijvR =∑k Fijk〈χR〉k. By inserting vL from (5)into Eq. (6) one sees that the vR scale drops out com-pletely from the previous formula, leading toMν ≃v2MGρ[Y (FF˜−1)T + (FF˜−1)Y T](7)so that the neutrino mass is suppressed by MG irrespec-tive of how low is the B-L breaking scale. This is a keyfeature of our mechanism, illustrated in Fig. 1. In con-trast to both the canonical seesaw in Eq. (1) and theinverse seesaw, Eq. (3), this new seesaw is linear in theDirac Yukawa couplings Y . Note also that, for givenMGand Y , the scale of neutrino masses can be adjusted bychoosing appropriately the value of the cubic scalar sec-tor coupling constant ρ, as well as the FF˜−1 (the lattertends to 1 if there is just one copy of 16H ⊕ 16H). Notealso that the current mechanism, apart from being uni-fied, is also quite distinct from the left-right symmetricattempts in Refs.[19, 20]. From this argument it followsFIG. 1: The proposed supersymmetric SO(10) seesaw mech-anism comes from this graph, up to transposition. The neu-trino mass is suppressed by the unification scale, not by theB-L breaking scale, which can be low.that the B − L breaking scale can in principle be as lowas few TeV.Concerning the stability of the texture zeros at theνcνc and SS entries in formula (6) it can be protectedas long as the U(1)R and the U(1)X (of E6 ⊃ SO(10)⊗U(1)X in E6 inspired setups) are exact. Indeed, U(1)Xmust be broken at the vR scale (16H ⊕ 16H always has aU(1)X charge). However, the charge ofχR’s is such thatthe relevant operators arise only at higher orders andmay be neglected.Now we turn to gauge coupling unification. As wasshown by Deshpande et al [14] the scale at which theSU(2)R⊗U(1)B−L symmetry is broken to U(1)Y can bearbitrarily low if we populate properly the “desert” fromMZ toMG. In their case this is achieved by putting threecopies of (1, 1, 2,+1)⊕(1, 1, 2,−1) coming from 16H⊕16Hright at the vR scale. Then the (one-loop) MSSM runningof the α−1Y can be “effectively” extended above the vRscale (α−1Y =35α−1R +25α−1B−L) by a conspiracy betweenthe runing of α−1B−L and α−1R . However, such a scheme israther ad hoc as we need to push three identical copiesof a Higgs multiplet to a very low scale, at odds with the“minimal fine-tunning”.Here we present a more compelling scheme in whichthe SU(2)R breaking scale VR is separated from the lowU(1)B−L ⊗ U(1)R breaking scale vR, VR ≫ vR in thechain SU(2)R⊗U(1)B−L → U(1)R⊗U(1)B−L → U(1)Y .At each step we assume just those multiplets needed tobreak the relevant symmetry. The first step is achievedby a light admixture of the (1, 1, 3, 0) multiplets living in45 and 210 while the second stage is driven by the light3component of the (1, 1,+ 12 ,−1) ⊕ (1, 1,−12 ,+1) scalars(in SU(3)c ⊗ SU(2)L ⊗ U(1)R ⊗ U(1)B−L notation) of16H⊕16H . Note that to allow for such a L-R asymmetricsetup the D-parity of SO(10) must be broken.Let us further specify the ingredients of our supersym-metric SO(10) model needed to implement the mecha-nism described above. As usual we use three copies of16iF to accomodate the Standard Model (SM) fermionsand for each of them we add a singlet fermion 1iF to playthe role of SL. A realistic fermionic spectrum requiresmore than one copy of 10H Higgs multiplet. Moreoverwe assume one (or more) copy of 16H ⊕ 16H to imple-ment our new supersymmetric seesaw mechanism. Toprevent fast proton decay via dimension 4 operators, weassign the matter fermions in 16F and 1F with a discretematter parity that forbids the mixing of 16F and 16H .Finally, we add a 45H and 210H to trigger the propersymmetry breaking pattern with no D-parity below theGUT scale [15, 16, 17]. The SO(10) invariant Yukawasuperpotential then readsWY = Yaij16iF16jF 10aH + Fijk16iF1jF16kH (8)We do not impose other discrete symmetries to reduce thenumber of parameters that might however be welcome inconnection with the doublet-triplet splitting problem ina more detailed analysis. The Higgs superpotential isWH = Mkl1616kH16lH +Mab1010aH10bH ++ M4545H45H +M210210H210H ++ ρklm16kH16lH10mH + ρklm16kH16lH10mH + (9)+ σkl16kH16lH45H + ωkl16kH16lH210H ++ λ453H + κ452H210H + ξ45H2102H + ζ2103HThe components of 210H and 45H that receive GUT-scale VEVs and trigger the breaking of SO(10) toSU(3)c⊗SU(2)L⊗SU(2)R⊗U(1)B−L are (in Pati-Salamlanguage) 210H ∋ (15, 1, 1)⊕(1, 1, 1) and 45H ∋ (15, 1, 1)As shown in [15, 16, 17] this pattern can accommodatethe desired D-parity breaking allowing for an interme-diate L-R symmetric group with an asymmetric particlecontent, leading to distinct gL and gR below MG. Thesubsequent SU(2)R → U(1)R breaking at VR is inducedby the VEV of a light superposition of (1, 1, 3, 0)210 and(1, 1, 3, 0)45 that can mix below the GUT scale. Next, theU(1)R ⊗ U(1)B−L is broken down at vR by the VEVs ofthe light component of type (1, 1,+ 12 ,−1)⊕(1, 1,−12 ,+1)coming from (1, 1, 2,−1)⊕ (1, 1, 2, 1) of 16H ⊕ 16H . Thefinal SM breaking step is as usual provided by the VEVsof the (1, 2, 2, 0) bidoublet components. Note that unlikethe example given in [14] there is no artificial redundancyin the number of light states living at intermediate scales.Let us finally inspect the one-loop gauge coupling uni-fication. Using the normalization convention 2pit(µ) =ln(µ/MZ) we have (for MA < MB)α−1i (MA) = α−1i (MB) + bi(tB − tA)in the ranges [MZ ,MS ], [MS , vR] and [VR,MG],MS is theSUSY breaking scale taken to be at the ∼ 1 TeV range.Between vR and VR the two U(1) factors mix and the run-ning of α−1R and α−1B−L requires separate treatment. TheCartans obey the traditional formula (with ”physically”normalized B − L and YW ) YW = 2TR3 + (B − L). Notethat the SO(10) normalization of bB−L is b′B−L =38bB−L.Once the D-parity is broken below MG we have gL 6=gR. The Higgs sector in the stage down to VR is as fol-lows: 1 × (1, 1, 3, 0), 1 × (1, 1, 2,+1) ⊕ (1, 1, 2,−1) and1×(1, 2, 2, 0). This gives rise to the b-coefficients b3 = −3,bL = 1, bR = 4 and bB−L = 20.At the subsequent stage from VR to vR we keeponly the weak scale bidoublet (1, 2, 2, 0) (that belowVR splits into a pair of L-doublets with the quantumnumbers (1, 2,+ 12 , 0) ⊕ (1, 2,−12 , 0) under the SU(3)c⊗ SU(2)L ⊗ U(1)R ⊗ U(1)B−L group) and a partof (1, 1, 2,+1) ⊕ (1, 1, 2,−1) that is needed to breakU(1)R ⊗ U(1)B−L to U(1)Y - a pair of the χR fields(1, 1,+ 12 ,−1)⊕ (1, 1,−12 ,+1). Since these fields are neu-tral with respect to all SM charges the position of the vRscale does not affect the running of the “effective α−11 ”(given by the appropriate matching condition) and theonly effects arise from the absence of the righthandedW -bosons at this stage. Using the SU(2)R normaliza-tion of the U(1)R charge the matching condition at VRis trivial. The relevant b-coefficients of SU(3)c⊗SU(2)Land the matrix of anomalous dimensions of the mixedU(1)R ⊗ U(1)B−L couplings are b3 = −3, bL = 1 and(γ11 γ12γ21 γ22)=(152 −1−1 18). (10)Below the vR scale the model is the ordinary MSSMwith the b-coefficients b3 = −3, bL = 1 and bY =33/5 and finally, the b-coefficients for the SM stage be-low the MS scale are b3 = −7, bL = −3 and bY =21/5. The vR-scale matching condition reads α−1Y (vR) =35α−1R (vR) +25α−1(B−L)′(vR). Recalling that α−11 (MZ) =35 (1−sin2θW )α−1(MZ) and α−12 (MZ) = sin2θWα−1(MZ)the initial condition (for central values of the input pa-rameters) is α−11 (MZ).= 59.38, α−12 (MZ).= 29.93 andα−13 (MZ).= 8.47 [18].Inspecting the results of the numerical analysis (Figs.2and 3) one shows that, indeed, the vR scale does not affectthe predicted value of α−11 (MZ). Its value remains essen-tially free at one-loop level. Thus, the unification patternis fixed entirely by the interplay ofMS and VR. The lowerbound VR & 1014 GeV is consistent with the “standard”minimally fine-tuned SUSY SO(10) behaviour, see for in-stance [21].In summary we have proposed a variant supersymmet-ric SO(10) seesaw mechanism which involves a dynamicalscale vR that can be rather low, as it is essentially unre-stricted both by gauge coupling unification and neutrinomasses. The smallness of neutrino masses coexists with alight B −L gauge boson, possibly at the TeV scale, thatcan be produced at the Large Hadron Collider, by the4FIG. 2: The one-loop gauge coupling unification in the modeldescribed in the text. The D-parity is broken at MG and theintermediate scales VR and vR correspond to the SU(2)R →U(1)R and U(1)R⊗U(1)B−L → U(1)Y breaking respectively.FIG. 3: Same as in Fig. 2 for the case of higher vR. Asexpected, the prediction for α−11(MZ) does not depend onthe position of the vR scale.Drell-Yan process. Moreover, the ”heavy” neutrinos in-volved in the seesaw mechanism, see Eq. (6), get massesat vR and can therefore be sufficiently light as to bring arich set of phenomenological implications. For exampletheir exchange can induce flavour violating processes, likeµ → eγ with potentially very large rates, similar to theinverse seesaw model of Eq. (2)) [10, 11]. We concludethat, within the unified SO(10) seesaw picture, the dy-namics underlying neutrino masses may have observableeffects at accelerators and in the flavor sector.This work was supported by the Spanish grantBFM2002-00345 and by the EC Human Potential Pro-gramme RTN network MRTN-CT-2004-503369. Wethank Rabi Mohapatra and Goran Senjanovic´ for a usefuldiscussion.Note added: after completing this work we came acrossrelated papers by Steve Barr and collaborators, and byFukuyama et al [22] who revive the type-III seesaw sug-gested in [20] and give it a different theoretical context.All of these have indeed elements in common, as well aswith the early work in Ref. [9, 10]. However, the mech-anism we now propose differs crucially from all of theprevious in that our B-L scale can be very low, in con-trast to that of the other models. We show how our newand key feature not only accounts for the oberved neu-trino mass scale, but also fits with the gauge unificationcondition in SO(10).[1] S. Weinberg, Phys. Rev. D22, 1694 (1980).[2] P. Minkowski, Phys. Lett. B67, 421 (1977).[3] M. Gell-Mann, P. Ramond and R. Slansky, (1979), Print-80-0576 (CERN).[4] T. Yanagida, (KEK lectures, 1979), ed. Sawada andSugamoto (KEK, 1979).[5] R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett.44, 912 (1980).[6] J. Schechter and J. W. F. Valle, Phys. Rev. D22, 2227(1980); Phys. Rev. D25, 774 (1982).[7] R. N. Mohapatra and G. Senjanovic, Phys. Rev. D23,165 (1981).[8] G. Lazarides, Q. Shafi and C. Wetterich, Nucl. Phys.B181, 287 (1981).[9] R. N. Mohapatra and J. W. F. Valle, Phys. Rev. D34,1642 (1986).[10] J. Bernabeu et al., Phys. Lett. B187, 303 (1987); G. C.Branco, M. N. Rebelo and J. W. F. Valle, Phys. Lett.B225, 385 (1989); N. Rius and J. W. F. Valle, Phys.Lett. B246, 249 (1990); F. Deppisch and J. W. F. 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Novel Supersymmetric SO(10) Seesaw Mechanism

Novel Supersymmetric SO(10) Seesaw Mechanism

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