The present experimental situation regarding neutrino oscillations is first
summarized, followed by an overview of selected grand unified models which have
been proposed to explain the various scenarios with three active neutrinos and
their right-handed counterparts. Special attention is given to the general
features of the models and their ability to favor some scenarios over others.Comment: 11 pages, talk given at the Joint U.S./Japan Workshop on New
  Initiatives in Lepton Flavor Violation and Neutrino Oscillations with Very
  Intense Muon and Neutrino Sources (Honolulu), October 2-6, 200

Albright, Carl H.

English

arXiv

UNT Digital Library

Fermilab FERMILAB-Conf-00/278-T  October 2000FERMILAB-Conf-00/278-Thep{ph/0010268October 2000Neutrino Oscillation Scenarios and GUT Model Predictions1Carl H. Albright2Fermi National Accelerator LaboratoryP.O. Box 500, Batavia, IL 60510AbstractThe present experimental situation regarding neutrino oscillations is rst summa-rized, followed by an overview of selected grand unied models which have been pro-posed to explain the various scenarios with three active neutrinos and their right-handedcounterparts. Special attention is given to the general features of the models and theirability to favor some scenarios over others.1Talk given at the Joint U.S./JapanWorkshop on New Initiatives in Lepton Flavor Violation and NeutrinoOscillations with Very Intense Muon and Neutrino Sources (Honolulu, HI), October 2-6, 2000.2E-mail: albright@fnal.gov1 Three-Active-Neutrino Oscillation Scenarios1.1 Atmospheric NeutrinosRecent results from the Super-Kamiokande Collaboration [1] involving atmospheric neutrinosconvincingly favor muon-neutrinos oscillating into tau-neutrinos rather than into light sterileneutrinos. The latter possibility is ruled out at the 99% condence level. In terms of theoscillation parameters, m2ij  m2i  m2j and sin2 2atm, the best t values obtained arem232 = 3:2 10 3 eV2;sin2 223 = 1:000; (1)with the latter related to the neutrino mixing matrix elements by sin2 2atm = 4jU3j2jU3j2.1.2 Solar NeutrinosThe situation regarding solar neutrinos is considerably less certain. The recent analysis [2]by the Super-Kamiokande Collaboration involving their 1117 day sample together with thedata from the Chlorine [3] and Gallium [4] experiments favor the large mixing angle MSW [5]solution (LMA) and possibly the LOW solution over the small mixing angle (SMA) andvacuum (VAC) solutions, with the latter two being ruled out at the 95% condence level.Several theory groups analyzing the same data suggest instead that while the LMA solutionis favored, the other solutions are still viable at the 95% c.l. In fact, a continuum solution{ the quasi-vacuum solution (QVO) { stretches between the LOW and VAC regions withtan2 sol>1:0. The best t points in the various parameter regions found in a recent analysisby Gonzalez-Garcia and Pe~na-Garay [6] are given bySMA : m221 = 5:0 10 6 eV2;sin2 212 = 0:0024;tan2 12 = 0:0006;LMA : m221 = 3:2 10 5 eV2;sin2 212 = 0:75;tan2 12 = 0:33;2LOW : m221 = 1:0 10 7 eV2;sin2 212 = 0:96;tan2 12 = 0:67;QV O : m221 = 8:6 10 10 eV2;sin2 212 = 0:96;tan2 12 = 1:5;(2)Note that 12 is in the second octant or \dark side" for the quasi-vacuum region. An evenmore recent analysis, [7] which includes the CHOOZ reactor constraint, [8] modies theabove numbers slightly, and sets tan2 13 = 0:005.1.3 Maximal and Bimaximal MixingsThe Maki-Nakagawa-Sakata (MNS) neutrino mixing matrix, analogous to the CKM mixingmatrix, can be written asUMNS =0@c12c13 s12c13 s13e i s12c23   c12s23s13ei c12c23   s12s23s13ei s23c13s12s23   c12c23s13ei  c12s23   s12c23s13ei c23c131A (3)in terms of c12 = cos 12; s12 = sin 12, etc. With the oscillation parameters relevant tothe scenarios indicated above, we can approximate 13 = 0o and 23 = 45o whereby Eq. (3)becomes essentiallyUMNS =0@c12 s12 0 s12=p2 c12=p2 1=p2s12=p2  c12=p2 1=p21A ; (4)where the light neutrino mass eigenstates are given in terms of the avor states by3 =1p2( +  );2 = e sin 12 +1p2(    ) cos 12;1 = e cos 12   1p2(    ) sin 12;(5)For the SMA solution, 12 = 1:4o, while the three large mixing solar solutions dier frommaximal in that the angle is approximately 30o for the LMA, 39o for the LOW, and 51o forthe QVO solutions. In contrast, the CKM quark mixing matrix is approximatelyVCKM =0@0:975 0:220 0:0032e i 0:220 0:974 0:0400:0088  0:040 0:9991A : (6)3An important issue to be answered is why U3 ' 1=p2 is so much larger than Vcb ' 0:040.Maximal mixing of two neutrino mass eigenstates can arise if the two states are nearlydegenerate in mass, i.e., the neutrinos are pseudo-Dirac. It can also arise if the determinantof the 2 2 submatrix nearly vanishes. For example,x2 xx 1!  = 0; 1 + x2;  0 1 x;  + x1; (7)and the components are comparable for x ' 1. The rst situation is relevant for the QVOand LOW near maximal mixings, while the second is more relevant for the atmospheric andLMA mixings where a sizable hierarchy is expected to be present.Finally, it should be noted that the UMNS mixing matrix is the product of two unitarytransformations diagonalizing the charged lepton mass matrix L and the light neutrino massmatrix M :UMNS = UyLU ; (8)where by the seesaw mechanism M =  NTM 1R N is given in terms of the Dirac neutrinomatrix N and the right-handed Majorana matrix MR. The structure of UMNS is thendetermined by the three matrices N; MR and L, one of which or in concert can play a rolein the maximal or bimaximal mixing pattern.2 Types of Neutrino Models and Possible UnicationsNeutrino models can be characterized as belonging to one of three types for the purpose ofthis talk. Those involving only left-handed elds leading to a left-handed Majorana mass matrixwith no Dirac neutrino mass matrix present. The Zee model [9] is a prime example.Typically lepton number is violated by two units, or an L =  2 isovector Higgs eldis introduced. A newly-dened lepton number L  Le   L   L is often taken to beconserved. The ultralight neutrino masses, however, are not easily understood. Models in which both left-handed and right-handed elds are present. With no Higgscontributions to the left-handed Majorana mass matrix, the seesaw mechanism readilyyields ultralight neutrino masses, provided the right-handed Majorana masses are inthe range of 105 1014 GeV. Such masses are naturally obtained in SUSY GUT modelswith G = 2 1016 GeV.4 Models in which neutrinos probe higher dimensions. Right-handed neutrinos which aresinglets under all gauge symmetries can enter the bulk. With large extra dimensionsand the compactication scale much lower than the string scale, a modied seesawmechanism can generate ultralight neutrino masses.I shall restrict my attention in this overview to models involving both left-handed and right-handed neutrinos. In this workshop, Tobe [10] addresses purely left-handed neutrino modelsin the context of R-parity violation, while Mohapatra [11] considers models involving higherdimensions.Both the nonsupersymmetric standard model (SM) and the minimum supersymmetricextended version (MSSM) involve no right-handed neutrinos and just one or two Higgsdoublets, respectively. Hence no renormalizable mass terms can be constructed for theneutrinos; moreover, the renormalizable mass terms which are present for the quarks andcharged leptons have completely arbitrary Yukawa couplings. In order to reduce the numberof free parameters and thereby achieve some detailed predictions for the mass spectra ofthe fundamental particles, some avor and/or family unication must be introduced. Thisis generally done in the context of supersymmetry for which the desirable feature of gaugecoupling unication obtains.Flavor or vertical symmetry has generally been achieved in the framework of GrandUnied Theories (GUTs) which provide unied treatments of quarks and leptons, as (some)quarks and leptons are placed in the same multiplets. Examples involve SU(5); SU(5) U(1); SO(10); E6, etc.The introduction of a family or horizontal symmetry, on the other hand, enables one tobuild in an apparent hierarchy for masses of comparable avors belonging to dierent families.Such a symmetry may be discrete as in the case of Z2; S3; Z2  Z2, etc. which results inmultiplicative quantum numbers. A continuous symmetry such as U(1); U(2); SU(3), etc.,on the other hand, results in additive quantum numbers and may be global or local (andpossibly anomalous).Combined avor and family symmetries will typically reduce the number of model pa-rameters even more eectively. On the other hand, the unication of avor and familysymmetries into one single group such as SO(18) or SU(8), for example, has generally notbeen successful, as too many extra states are present which must be made superheavy.53 Froggatt-Nielsen-type Models with Anomalous U(1)Family SymmetryIn 1979 Froggatt and Nielsen [12] added to the SM a scalar singlet \avon" f , which getsa VEV, together with heavy fermions, (F; F ), in vector-like representations, all of whichcarry U(1) family charges. With U(1) broken at a scale MG by hi=MG    (0:01  0:2),the light and heavy fermions are mixed; hence  can serve as an expansion parameter forthe quark and lepton mass matrix entries. No GUT is involved, although MG is some highunspecied scale.This idea received a revival in the past decade when it was observed by Ibanez [13] thatstring theories with anomalous U(1)'s generate Fayet-Iliopoulos D-terms which trigger thebreaking of the U(1) at a scale of O() below the cuto, again providing a suitable expansionparameter. The n structure of the mass matrices can be determined from the correspondingWolfenstein  structure of the CKM matrix and the quark and lepton mass ratios, wheredierent U(1) charges are assigned to each quark and lepton eld.By careful assignment of the U(1) charges, Ramond and many other authors 3 haveshown that maximal mixing of  $  can be obtained, while the SMA solution for e $;  is strongly favored. Since then, other authors [15] have applied the technique inthe presence of SU(5) or SO(10) to get also the QVO or LOW solutions. Very recently,Kitano and Mimura [16] have considered SU(5) and SO(10) models in this framework withan SU(3)U(1) horizontal symmetry to show that the LMA solution can also be obtained.But with these types of models, the coecients (prefactors) of the  powers can not beaccurately predicted.4 Predictive SUSY GUT ModelsWith the minimal SU(5) SUSY GUT model extended to include the left-handed conjugateneutrinos, the matter elds are placed in 5 and 10 representations according to5i  (dc; `; `)i; 10i  (u; d; uc; `c)i; 1i  (c)i;  = 1; 2; 3: (9)while the Higgs elds are placed in the adjoint and fundamental representations(24); Hu(5); Hd(5): (10)3For reference listings in two more comprehensive reviews, see [14].6The SU(5) symmetry is broken down to the MSSM at a scale G with hi pointing inthe B   L direction, but doublet-triplet splitting must be done by hand. The electroweakbreaking occurs when the Hu and Hd VEV's are generated.The number of Yukawa couplings has now been reduced in the Yukawa superpotential,and the fermion mass matrices exhibit the symmetries, MU =MTU ; MD =MTL . This impliesmb = m at the GUT scale, but also md=ms = me=m which is too simplistic since no familysymmetry is present. One can circumvent this problem by introducing a family or horizontalsymmetry, but more predictive results are obtained in the SO(10) framework.In SO(10) all fermions of one family are placed in a 16 spinor supermultiplet and carrythe same family charge assignment:16i(u; d; uc; dc; `; `c; `; c` )i; i = 1; 2; 3: (11)Massive pairs of (16; 16)'s and 10's may also be present. The Higgs Fields may containone or more 45H 's and pairs of 16H ; 16H which break SO(10) down to the SM, while 10Hbreaks the electroweak group at the electroweak scale. A 126H or eective 16H  16H eldcan generate superheavy right-handed Majorana neutrino masses.With an appropriate family symmetry introduced, a number of texture zeros will appearin the mass matrices. These will enable one to make some well-dened predictions for themasses and mixings of the quarks and leptons, for typically fewer mass matrix parameterswill be present than the 20 quark and lepton mass and mixing observables plus 3 right-handedMajorana masses.Yukawa t   b    coupling unication is possible only for tan = vu=vd ' 55 in thisminimal Higgs case described above. However, if a 160H ; 160H pair is introduced with theformer getting an electroweak-breaking VEV which helps contribute to Hd [17], or if the 16Hof the rst pair also gets an EW VEV, Yukawa coupling unication is possible for tan  55.Such breaking VEV's can contribute asymmetrically to the down quark and charged leptonmass matrices. This makes it possible to understand large   mixing, U3 ' 0:707, whileVcb ' 0:040. Moreover, the Georgi-Jarlskog mass relations [18],ms=mb = m=3m and md=mb = 3me=m ; (12)can be generated by the mass matrices with the help of the same asymmetrical contributions.Models based on SO(10) then dier due to their matter and Higgs contents as well as thehorizontal family symmetry group chosen. Several selected illustrative examples of predictiveSO(10) GUT models are presented below, where some of their characteristic features arehighlighted.74.1 SO(10) with U(1)HA model of this type has been presented by Babu, Pati, and Wilczek [19] based on dimension-5 eective operators involvingMatter Fields : 161; 162; 163Higgs Fields : 10H ; 16H ; 16H ; 45H (13)The 16H develops both GUT and EW scale VEV's. With no CP violation, 11 matrix inputparameters yield 18 + 3 masses and mixings. Maximal  $  mixing arises from theseesaw mechanism, while the SMA solar solution is preferred.4.2 SO(10) with [U(1) Z2  Z2]HBarr and Raby [20] have shown that a stable solution to the doublet-triplet splitting prob-lem in SO(10) can be obtained based on this global horizontal group. With an extension ofthe minimal Higgs content involved, Albright and Barr [21] have developed a model involv-ing only renormalizable terms in the Yukawa superpotential with the following supereldspresent:Matter Fields : 161; 162; 163; 2(16; 16)0s; 2(10)0s; 6(1)0sHiggs Fields : 4(10H)0s; 2(16H ; 16H)0s; 45H ; 5(1H)0s (14)Ten matrix input parameters yield all 20 + 3 masses and mixings. A value of tan ' 5 isfavored with sin 2  0:65 obtained for the CKM unitarity triangle. Maximal  $  mixingarises from the lopsided texture of the charged lepton matrix. In this simplest scenario, theQVO solution is preferred, although by modifying the right-handed Majorana matrix theSMA or LMA solar solutions can be obtained with one or four more input parameters,respectively.4.3 SO(10) with [SU(2) Z2  Z2  Z2]HChen and Mahanthappa [22] have based a model on this family group with dim-5 eectiveoperators involving the following superelds:Matter Fields : (16; 2); (16; 1)Higgs Fields : 5(10; 1)H0s; 3(126; 1)H0sFlavon Fields : 3(1; 2)H0s; 3(1; 3)H0s(15)8With no CP violation, eleven matrix input parameters yield 18 + 3 masses and mixings,while tan  = 10 is assumed. Maximal  $  mixing arises from the seesaw mechanismwith symmetric mass matrices. The QVO solar solution is preferred, while the SMA solutionor the LMA solution with tan2 sol < 1 is dicult to obtain.4.4 SO(10) with [U(2) U(1)n]HBlazek, Raby, and Tobe [23] have constructed such a model involving only renormalizableterms in the Yukawa superpotential with the following elds:Matter Fields : (16; 2); (16; 1); (1; 2); (1; 1)HiggsFields : (10; 1)H ; (45; 1)HFlavon Fields : 2(1; 2)H0s; (1; 3)H ; 2(1; 1)H0s(16)Sixteen matrix input parameters yield the 20 + 3 masses and mixings with tan ' 55required. CP violation occurs with sin 2 in the second quadrant for the CKM unitaritytriangle. All solar neutrino solutions, SMA, LMA, LOW and QVO, are possible.4.5 SO(10) with [SU(3) unspecied discrete symmetries]HBerezhiani and Rossi [24] have proposed a model based on this group with the followingstructure:Matter Fields : (16; 3); (16; 3); (16; 3); 2(16; 3)0s;2(16; 3)0s; (1; 3); (1; 3); (10; 3); (10; 3)Higgs Fields : (16; 1)H ; (16; 1)H ; (54; 1)H ; 2(45; 1)H0s;2(10; 1)H0sFlavon Fields : (1; 6)H ; 3(1; 3)H0s; (1; 8)H(17)Fourteen matrix input parameters yield 18 + 3 masses and mixings with moderate tanassumed. Maximal  $  mixing arises from the lopsided texture of the charged leptonmass matrix. The SMA solar solution is preferred, while other solutions are possible withmodication of the right-handed Majorana matrix.5 Concluding RemarksThe most predictive models for the 12 \light" fermion masses and their 8 CKM and MNSmixing angles and phases are obtained in the framework of grand unied models with family9symmetries. The SO(10) models are more tightly constrained than SU(5) models and aremore economical than larger groups such as E6 [25], where more elds must be made super-massive. In fact, some SO(10) models do very well in predicting the 20 + 3 \observables"with just 10 or more input parameters, depending on the model and type of solar neutrinomixing solution involved.The SMA MSW solution is readily obtained in many unied models, since only one pairof states,  and  , are maximally mixed. Bimaximal mixing can be obtained in a smallerclass of models, with the QVO solution having the more natural hierarchy with a pair ofpseudo-Dirac neutrinos. The LMA MSW solution, if allowed, requires the most ne tuning,for two nearly maximal mixings must be obtained with a hierarchy of neutrino masses. Forthis latter solution, the right-handed Majorana neutrino masses typically span a range of106 1014 GeV, while the lightest is typically 1010 GeV for the other solar neutrino solutions.Unfortunately, while the experimental solar neutrino solution remains rather uncertain,unied model builders are not able to clarify the situation by predicting the outcome withany degree of certainty.References[1] S. Fukuda et al, hep-ex/0009001.[2] T. Takeuchi, talk at XXX Intl. Conf. on HEP, ICHEP 2000, Osaka, Japan, July 27 -August 2, 2000.[3] K. Lande, talk at XIX Intl. Conf. on Neutrino Physics and Astrophysics, Sudbury,Canada, June 16-21, 2000.[4] V. Gavrin, talk at XIX Intl. Conf. on Neutrino Physics and Astrophysics, Sudbury,Canada, June 16-21, 2000; GALLEX Collab. (W. Hampel et al), Phys. Lett B 447, 127(1999).[5] L. Wolfenstein, Phys. Rev. D 17, 2369 (1978); S.P. Mikheyev and A. Yu. Smirnov, Yad.Fiz. 42, 1441 (1985), [Sov. J. Nucl. Phys. 42, 913 (1985)].[6] M.C. Gonzalez-Garcia and C. Pe~na-Garay, hep-ph/0009041.[7] M.C. Gonzalez-Garcia, M. Maltoni, C. Pe~na-Garay, and J.W.F. Valle, hep-ph/0009350.[8] CHOOZ Collab. (M. Apollonio et al), Phys. Lett. B 420, 397 (1998).10[9] A. Zee, Phys. Lett. B 93, 389 (1980).[10] K. Tobe, contribution to this workshop.[11] R.N. Mohapatra, contribution to this workshop.[12] C.D. Froggatt and H.B. Nielsen, Nucl. Phys. B 147, 277 (1979).[13] L. Ibanez, Phys. Lett. B 303, 55 (1993).[14] G. Altarelli, Nucl. Phys. Proc. Suppl. 87, 291 (2000); S.M. Barr and I. Dorsner, Nucl.Phys. B 585, 79 (2000).[15] Q. Sha and Z. Tavartkiladze, Phys. Lett. B 482, 145 (2000); G. Altarelli, F. Feruglioand I. Masina, hep-ph/0007254.[16] R. Kitano and Y. Mimura, hep-ph/0008269.[17] C.H. Albright, K.S. Babu, and S.M. Barr, Phys. Rev. Lett. 81, 1167 (1998).[18] H. Georgi and C. Jarlskog, Phys. Lett. B 86, 297 (1979).[19] K.S. Babu, J.C. Pati, and F. Wilczek, Nucl. Phys. B 566, 33 (2000).[20] S.M. Barr and S. Raby, Phys. Rev. Lett. 79, 4748 (1997).[21] C.H. Albright and S.M. Barr, Phys. Rev. Lett. 85, 244 (2000); Phys. Rev. D 62, 093008(2000).[22] M.-C. Chen and K.T. Mahanthappa, hep-ph/0005292.[23] T. Blazek, S. Raby, and K. Tobe, Phys. Rev. D 62, 055001 (2000).[24] Z. Berezhiani and A. Rossi, hep-ph/0003084.[25] E. Ma, contribution to this workshop.11

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