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Proc. Nati Acad. Sci. USA Vol. 79, pp. 3371-3375, May 1982 Review

Neutrino , decay, and oscillations as crucial tests of unification models (A Review)

R. E. MARSHAK Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Contributed by R. E. Marshak, September 14, 1981 ABSTRACT Several crucial tests of three popular unification hence predicts M(WL) = 77.9 GeV and M(Z0) = 88.7 GeV. models (of strong, electromagnetic, and weak interactions) are The standard electroweak model unifies the weak and elec- described. The models are SU(5) and SO(10) at the grand unifi- tromagnetic interactions by accepting as given the maximal par- cation theory (GUT) level and SU(4)c SU(2)L x SU(2)R at the ity violation (left-handed character) of the up partial unification theory (PUT) level. The tests selected for dis- to the highest energies. This, in turn, implies acceptance ofthe cussion are the finiteness ofthe mass in the volt masslessness of the neutrino, the surrender of the full region, the decay ofprotons into antileptons in the range of 1031±1 - principle for weak interactions (since yr, and the detectability of neutron oscillations at all. The PUT there is no neutrino analog to the "up"* quark in the right- group can also be tested by establishing the existence offour gen- handed representations ofthe standard electroweak group) and erations of and . afuzziness in the physical meaning ofthe weakhypercharge that is part of the standard electroweak group. This last point is re- The development ofa unified theory ofelectromagnetic, weak, flected in the rather accidental cancellation of the triangle and strong interactions (and possibly the gravitational interac- anomalies associated with the SU(2)L x U(1) electroweak group, tion as well) is one ofthe grandiose goals ofparticle physics. The a condition essential for the maintenance of a renormalized past decade has seen much progress in the achievement ofthis spontaneous broken . This cancellation is achieved goal through the unification of electromagnetic and weak in- by using the definitions ofYL = 2(Q - I3L) (where YL is the left- teractions on the basis of the electroweak group SU(2)L x U(1) handed , Q is the electric , and I3L is the (1-3). Here SU(2)L is the left-handed (L) weak group-of third component of IL) and YR = 2Q (where YR is the right- which the two generators, JL+ andJLj, explain handed hypercharge), and then imposing the condition that all the charged weak current experiments up to the present time J(yL3 - YR3) = 0 where the sum is taken over the leptons and [V-A theory (4-6)] andJ3L is the neutral weak current generator quarks (of all three colors) of a single generation. Despite the that completes the group; U(1) is the group. wide variation in the values ofYL and yR ofthe different leptons A series ofneutral weak current experiments (neutrino-, and quarks, this sum miraculously vanishes (8). It seems likely charged lepton-hadron, and neutrino-electron), culminating in that there is a more natural explanation of the cancellation of the Stanford Linear Accelerator Center experiment (7), all can the triangle anomalies (see below). be explained by a total neutral weak current structure P(J3L Despite the caveats mentioned above, the success ofthe stan- - sin2OWjEM) where the two parameters are p (the ratio of dard electroweak model is highly impressive and has encour- neutral to charged weak current) and sin20W (0W is the Wein- aged theoretical attempts to unify the with berg angle) and JEM is the electromagnetic current. This struc- the by adjoining the color group SU(3)c ture is predicted by the SU(2)L X U(1) group when TL(e) (e (presumably representing the strong quark- interaction) stands for the leptons ofa single generation) and TL(q) (q stands to the SU(2)L X U(1) electroweak group and looking for the for the quarks ofa single generation where it is understood that smallest simple group of which SU(3)c X SU(2)L X U(1) is the each quark exists in three colors) are placed in doublet repre- maximal subgroup. This led to the SU(5) grand unified group sentations of SU(2)L and TR(M) and TR(q) (R denotes right- (9, 10) of the strong, electromagnetic, and weak interactions. handed) are placed in singlet representations ofSU(2)L (thereby The two representations {5} and {10} ofSU(5) represent implying a massless left-handed neutrino). When the further the left-handed quarks and antiquarks (of three colors) and the restriction is made that only one Higgs doublet spontaneously left-handed leptons and antileptons of the first generation as breaks the initial gauge symmetry, the parameter p becomes follows 1 and the value of sin2Ow directly determines the mass of WL (9, 10): [WL is the (left-handed) charged weak -i.e., { } =e-{ d {10} {e+ ud: i i = 1,2,3 color. [1] M(WR) = s373 GeV] sinew The superscript c in Eq. 1 is the charge conjugate. The fact that and that of Z0 [the neutral weak boson-i.e., quarks and leptons are in the same representation opens up the possibility of number and nonconser- vation. We note that there is no room in these two represen- = 74-6 GeV]. Mq sin2oW tations for a left-handed antineutrino [which, of course, can be The electroweak group SU(2)L x U(1) with only one Higgs doub- Abbreviations: GUT, grand unification theory; PUT, partial unification let is called the standard electroweak model (1-3). Fitting the theory. expression for the total neutral weak current with the experi- * The nomenclature "up" ("down") quark or lepton is used for the quark mental data yields sin20W = 0.229 ± 0.009 (±0.006) [the first or lepton with the third component of its 13 = +1/2 error is experimental and the second is theoretical (8)] and (-V2). 3371 Downloaded by guest on September 27, 2021 3372 Review: Marshak Proc. Natd Acad. Sci. USA 79 (1982) given the status of an SU(5) singlet], thereby implying that we cillations or in otherways-the standard electroweak model and are still constrained to a massless left-handed neutrino. And we SU(5) GUT will have to be modified. Although it is true that also note that we must utilize two representations of SU(5) to both of these models can accommodate miniscule-mass neutri- cover all the left-handed leptons, antileptons, quarks, and an- nos (Dirac or Majorana) through additional neutrino or Higgs tiquarks of a single generation. boson representations, the elegant versions would be killed. With this said, some of the attractive features of the SU(5) Furthermore, ifthe neutrino has a nonminiscule mass, it seems grand unification theory (GUT) should be spelled out. SU(5) more plausible to use doublet representations for all right- GUT is the only group with a single coupling constant that has handed leptons (and afortiori quarks) ofeach generation. This SU(3)c x SU(2)L x U(1) as a maximal subgroup. The electric leads immediately to the left-right symmetric group-namely, charge is quantized (i.e., the quark and lepton charges are re- SU(2)L x SU(2)R x U(1)-as a serious alternative to the standard lated) in SU(5) GUT because the operator is an SU(2)L x U(1) group [with the left-handed leptons and quarks SU(5) generator; this, however, is nota unique property ofSU(5) of each generation being placed in doublet representations of GUT. The unification mass associated with SU(5) GUT, of the SU(2)L-and singlet representations of SU(2)R-and the right- order of1015 GeV, serves several purposes: it is the approximate handed leptons and quarks placed in the doublet representa- mass at which the very different coupling constants for the tions of SU(2)R-and singlet representations of SU(2)L]. strong, electromagnetic, and weak interactions (in the energy The left-right symmetric group has several interesting prop- regime in which we have thus far been operating) attain the erties that immediately distinguish it from the standard elec- same value (as is required by the concept of grand unification) troweak group. First, the "weak" Gell-Mann-Nishijima set of and it is also the mass that leads to a reasonable prediction for relations for the standard electroweak group-namely, Q = I3L sin20w (0.21, which is close to the experimental lower limit) and + YL/2 and Q = YR/2-are replaced by the single relation: Q this, in turn, leads to a prediction for the lifetime ofproton decay = '3L + I3R + (B-L)/2 [B is the of each quark that exceeds the present lower limit ofapproximately 103' years, (1/3) and L is the lepton number ofeach lepton (1)] (16, 17). The encouraging the hope that this baryon number-violating process left-right symmetric group was initially studied (18-20) with will be observed in the next round of experiments, say at the U(1) as U(1)L+R. The physical interpretation of U(1) as U(M)B.L, level of i03' years. based on the baryon-lepton symmetry principle, first discussed It should also be remarked that SU(5) GUT exhibits global by Gamba et aL (21), has led to the single relation. In other B-L conservation (11, 12), thereby permitting decays like p words, the "fluttering" weak hypercharge e+{17, n -> e+ir, etc., but not allowing electron decay chan- depending, in the case of the standard electroweak model, on nels (like p e-+ r++, etc.) or nonleptonic channels (like n the left-handed or right-handed character ofthe representation -ni). This follows in SU(5) GUT because it can be shown that, for leptons and quarks, becomes simply (B-L) in the left-right if baryon nonconservation is mediated by four-fermion graphs symmetric model for both left-handed and right-handed doub- that respect the SU(3)c X SU(2)L x U(1) group of the standard let representations. The "weak" Gell-Mann-Nishijima relation low-energy electroweak and strong interactions, then B-L must for the left-right symmetric model gives an obvious (natural) be a conserved quantum number. The power of the selection cancellation of the triangle anomalies for each generation of rule is connected with the fact that the grand unification mass quarks and leptons, and comparison ofthis relation with the set is so much larger than the weak (left-handed) boson mass WL. of "weak" Gell-Mann-Nishijima relations connected with the Deviations from this selection rule can only be expected ifthere standard electroweak model illuminates in a trivial way the ap- is an intermediate mass [between the mass of WL and the su- parent accidental cancellation oftriangle anomalies in the latter perheavy mass Mx ofSU(5)] that enters the picture. model. If the weak hypercharge is directly equal to (B-L), this An intermediate mass scale is necessary for nonminiscule neu- (B-L) can now be regarded as a local symmetry [which neces- trino and for the detectability ofneutron oscillations, and sarily has to be broken, because ofthe Eotvos experiment (see such possibilities exist within the framework of SU(5) GUT ref. 22)] and not merely as a global symmetry. By gauging SU(2)L through the presence of much more complicated Higgs struc- and SU(2)R [as well as U(1)BL] and then breaking the symmetries tures or fermion representations (13). However, such gross de- spontaneously with a minimal set of Higgs ,t all neutral partures from SU(5) GUT will greatly reduce its elegance-the and charged weak current data can be fitted with a somewhat same elegance, incidentally, that is responsible for the "desert" larger value of sin20w, lower mass values ofWL and Z° (23, 24) between MWL 102 GeV and Mx 1015 GeV, the gauge hi- and necessarily larger mass values of the weak bosons coupled erarchy problem (14), and the possible existence of superheavy to the right-handed currents (larger, that is, than those of the magnetic monopoles (15). Putting aside the highly speculative weak bosons coupled to the left-handed currents). As long as cosmological arguments (baryon asymmetry of the universe, WR and Z° (the neutral counterpart to WR) have finite masses etc.), the key laboratory test ofthe elegant version ofSU(5) GUT (i.e., the left-right symmetric model holds), parity will be re- will be detection of the baryon number-nonconserving process stored at energies large compared to WR and Z°'. of at the 1031l'-yr level. The elegant version of It can now be shown that the physical consequences of the SU(5) GUT is not compatible with nonminiscule neutrino minimal left-right symmetric modelt are quite distinct from masses and detectable neutron oscillations, however. those ofthe standard electroweak model, even though the latter Because SU(5) GUT has a number ofundesirable features that is the limiting case ofthe former when M(WR) -- oo. Thus, con- follow basically from its equal rank with its subgroup SU(3)c sider an energy larger than M(WL); then SU(2)L X U(1) sym- x SU(2)L x U(1), we must be prepared for choosing a metry is expected to be a good symmetry and it follows from grand unified group of higher rank than SU(5) but having ele- the "weak" Gell-Mann-Nishijima relation Q = 13L + I3R + (B- gant features that differentiate it from SU(5). Within the present L)/2 that: conceptual framework, we would expect any successful unified AI3R -- A(B-L) group to pass through the group SU(3)c x SU(2)L x U(1) and 2 [2] end up as the unbroken group SU(3)c x U(l)EM. If the has a mass in the electron volt region (if the neutrino tThe minimal left-right symmetric model is defined bychoosingfor the of one generation has a nonminiscule mass, it is likely that the Higgs bosons the fermion "condensates" - 4LtR, AL "%4'L' C-' others do)-as established by the observation of neutrino os- *L) AR IRTAC- WR (17, 25, 26). Downloaded by guest on September 27, 2021 'Review: Marshak Proc. Natl. Acad. Sci. USA 79 (1982) 3373

This basic equation of the left-right symmetric model is ex- = 2 transition within anucleus (30, 31). Clearly, the mixing time tremely interesting because it relates the scale of parity break- is very sensitive to the mass of the right-handed , down to the scale ofbaryon and lepton number breakdown. In but this phenomenon is true of any attempt to make a low-en- fact, in the minimal version of this model,t because the spon- ergy prediction from a unification model that involves much taneous symmetry-breaking is achieved only via fermion con- larger masses-e.g., the lifetime predicted for proton decay densates, one gets AJ3R = 1. Consequently, Eq. 2 leads to the from the SU(5) model is dependent on the fourth power of the following two selection rules in baryon and lepton nonconser- unification mass. One striking prediction of PUT is the vanish- vation: ing ofthe matrix element for proton decay [because ofa hidden 1. AB =0, AL = 2, leading to Majorana (one light selection rule (see ref. 17)]. Whether this crucial prediction at and one heavy per generation; see below). the PUT level is carried over to the GUT level is a question that 2. AB = 2, AL = 0, leading to n -n i (neutron oscillations). we shall now consider. The theory ofMajorana neutrinos in the minimal left-right sym- The simple group of lowest rank that breaks down directly metric model has been worked out (25, 27) and the important to the PUT group is SO(10). The SO(10) GUT option that is result is that the same Higgs triplet responsible for the large proposed as an alternative (23) to SU(5) GUT would then pro- mass of WR also predicts a heavy Majorana neutrino, NR, with ceed through the following chain of spontaneous symmetry a mass comparable to (although somewhat smaller than) the breakings: mass ofWR. The light neutrino-which in this theory must also -* X be Majorana-is predicted to have a mass M(VL) given by the SO(10) {54}Mu SU(2)L XSU(2)R SU(4)c {45}Mc SU(2)L relation M(L)- Me2/M(NR) (Me is the mass ofthe charged lep- ton); this last result makes physical sense because it implies that X SU(2)R X U B-L X SU(3)C {126}M SU(2)L X U [3] M(VL) -O 0 when M(WR) -Xoo. The prediction of a very heavy Majorana neutrino (in addition to a very light Majorana neu- trino) sharply differentiates the minimal left-right symmetric {10}MWL model from the standard electroweak model. Some of the pos- The Higgs boson representation responsible for the breakdown sible tests of this prediction (neutrinoless double 8 decay, JL of the gauge symmetry is displayed in curly brackets, and next -- e + y, conversion into or , etc.) are to it is indicated the mass scale at which the higher symmetry considered elsewhere (28). breaks down. SO(10) GUT, defined by the chain ofEq. 3, leads We are now in a position to appreciate the crucial nature of to anumber ofphysical predictions that distinguish it from SU(5) the neutron oscillation experiment in testing unification models GUT. However, it should be pointed out that there is another in physics. Eq. 2, which contains the new physics ofthe chain of spontaneous symmetry breakings that initially breaks minimal left-right symmetric model, suggests that the same the- down SO(10) to SU(5): ory that predicts Majorana neutrinos (AL = 2 transitions) will also predict neutron oscillations (AB = 2 transitions) at some SO(10) ' SU(5) - SU(3)c X SU(2)L intermediate mass scale in the "desert" between 102GeV {16}MU {45}Mx [M(WL)] and 101'5 GeV [M(X)]. The larger mass ofWR is already X X [4] one incursion into this desert, there is the intermediate mass U1) {}MSWULEM-> UC scale associated with the right-handed Higgs triplet, and there are other possibilities that can give rise to a detectable amount The chain definedby Eq. 4 is more complicated than SU(5) GUT of neutron oscillation. The first step in understanding how this [since the SO(10) group is of rank five compared to rank four comes about is to adjoin the color group SU(3)c to the left-right for the SU(5) group] and leads to predictions at low energies that symmetric group, because evidently a AB = 2 transition must are identical to those of SU(5) GUT, including those for proton involve the quarks. The analog of the standard theory at this decay and neutron oscillations. The only advantage ofthis ver- level of unification is SU(2)L X SU(2)R X U(l)BL X SU(3)c [in sion of SO(10) GUT over SU(5) GUT is that a mechanism is place of SU(3)c X SU(2)L X U(1)], and it is obvious that the provided for obtaining a finite mass for the neutrino; this can product of the two groups U()B-L X SU(3)c can be combined be seen by noting that the basic {16} spinor representation for into the single group SU(4)c where B-L is the fourth color. Pati the decomposes into the {3} + {10} representations of and Salam (29) arrived at this group through another line ofrea- SU(5) plus the SU(5) singlet representation {1} for VCL. This soning; their fourth color is L, not B-L. We shall give to the SU(5) singlet representation can be used to generate a finite group SU(2)L x SU(2)R x SU(4)c the name PUT (partial uni- mass neutrino. Because the SU(5) {1} representation is part of fication theory) in contrast to GUT. If PUT is now studied by the irreducible {16} representation of SO(10), we have a more placing the leptons and quarks in the smallest representations natural mechanism for generating a finite mass neutrino (if ex- [(2, 1, 4) and (1, 2, 4)] and the minimal choice of Higgs multiplets perimental results turn out to mandate this) than is possible in is taken as the natural extension of the minimal choice at the minimal SU(5) GUT. electroweak level-namely, = (2, 2, 1), AL = (3, 1, 10), and SO(10) GUT defined by Eq. 3, in principle, can yield larger q5 masses the neutrinos than can GUT de- AR = (1, 3, )0-a quartic self-coupling of the right-handed (Majorana) for SO(10) Higgs bosons is allowed under the local symmetry SU(2)L X fined by Eq. 4. To see this, set Mx = Mu in Eq. 4; then, fol- SU(2)R X U(l)BL that gives rise to the qqq -- qqq (AB = 2 n lowing the argument of Gell-Mann et al. (32), the mass of the n)1 transition. The strength ofthe neutron oscillations is then neutrino m, is of the order: found to be given by Ah3 (AR)/(mA)6 where A is the strength =M 2m [5] of the scalar self-coupling of the right-handed HIgs bosons, (AR) is the of AR (1, 3, 10), h is the where mq is the quark mass and mN is the mass ofthe superheavy strength of the Yukawa coupling of this Higgs boson with the Majorana neutrino (which is the counterpart of the light Ma- fermions, and maR is the mass of the Higgs boson A Using jorana neutrino v in the same generation). To get a crude es- plausible values for these parameters (e.g., maRs = 10 -6 GeV), timate of m^,set mq 10 MeV (first generation) and mN mx one can obtain a mixing time for free neutron oscillations ofthe -- 1015 GeV so that m - 10-10 eV, a miniscule value. To in- order of 107 sec, consistent with a lifetime .1030 years for a AB crease m., Witten (33) has shown how a special choice of rep- Downloaded by guest on September 27, 2021 3374 Review: Marshak Proc. NatL. Acad. Sci. USA 79 (1982)

resentations for the Higgs bosons can reduce mN by as much the proliferation of an equal number of families of quark and as a factor of 108 and thereby increase m, to 10-2 eV. In the case lepton doublets is produced by radial excitations of the preon ofSO(10) GUT defined by Eq. 3, the analog ofEq. 5 at the PUT composites, which, unfortunately, does not seem to work level becomes: either. Y. Tosa and I have recently reexamined the generation prob- meMt2/mNR [6] lem from another point of view and have arrived, interestingly where me is the charged lepton mass. Since mwR can be as small enough, at what appears to be a unique solution of the gener- as 2 X 102 GeV (23), m, 1 eV even when me 0.5 MeV (first ation problem within the framework of the PUT group: SU(2)L generation). x SU(2)R x SU(4)c. We first investigated (37) composite models The issues appear therefore to be sharply drawn if one is of quarks and leptons in which the preons carry the strong pursuing the extraordinarily ambitious goal of finding the cor- SU(3)c quantum numbers and either the weak SU(2)L X U(1) rect unified theory of strong, electromagnetic, and weak inter- or SU(2)L X SU(2)R X U(I)B-L quantum numbers (see Eqs. 3 and actions. On the one hand, the elegant version of SU(5) GUT 4 above). The constraints imposed on the models were (i) the requires massless neutrinos, maintains the parity violation of absence of color or weak exotics, (ii) cancellation of anomalies the weak interaction up to the highest energies, requires two in the strong and weak sectors, and (iii) an equal number of representations for the leptons and quarks of each generation, quark and lepton generations. Under these conditions, we yields global conservation of B-L (but no possibility of local B- found a "no-go" result for the three-fermion preon model. Since L symmetry) and therefore the detectability ofproton decay but the GUT groups SU(5) and SO(10) shed no light on the gen- not of neutron oscillations, predicts that the masses of WL and eration problem (34), we are left with the PUT group as an avail- Z0 should not go below 76.4 and 87.6 GeV, respectively, and able option (see Eq. 3). We then succeeded in finding (38) a accepts a physics "desert" between 102 and 101'5 GeV. On the three-fermion preon model with two basic massless (Weyl) other hand, S0(10) GUT requires two Majorana neutrinos per fields having the quantum numbers ofthe PUT group-namely, generation (one superlight and one superheavy), can place all (2, 1, 4)L and (1, 2, 4)R-that predicts precisely four generations leptons and quarks ofa single generation in one irreducible rep- of quarks and leptons belonging to the correct representations resentation (even making provision for the extra neutrino which (2, 1, 4)L and (1, 2, 4)R of the PUT group. helps to generate the finite masses of the two Majorana neu- Apart from the obvious consequence that there should be a trinos), contains B-L as a generator and therefore allows for local fourth generation ofquarks and leptons with larger masses-which B-L symmetry and the relation between its breakdown and par- must be tested-a composite model based on the PUT group ity breakdown, predicts the restoration of parity for weak in- predicts that deviations from the pointlike behavior of quarks teractions at sufficiently high energy, populates the physics and leptons (which at present holds down to 1016 cm) should desert with intermediate mass scales that create the possibility set in at distances 10- R-10-20cm (corresponding to the inter- ofdetecting neutron oscillations and ofeliminating the magnetic mediate-mass scale of the PUT group __104_106 GeV (17). An- monopole problem, and can easily reconcile the nondetecta- other consequence of the special role for the PUT group would bility of proton decay with the detectability of neutron oscil- be the possible detectability of neutron oscillations even if pro- lations. Under these circumstances, a careful experiment* to ton decay were unobserved (17). If the fourth generation of search for neutron oscillations is extremely important to throw quarks-and leptons as well as neutron oscillations are found, light on each of the two major GUT options. clearly the "desert would be blooming" up to the level of i04- The SU(5) and SO(10) groups have been treated as the two 106 GeV. One might then be in a position to make the "cou- major GUT options, and rightfully so because of their unique- rageous leap" to the Planck level (- 1019 GeV, corresponding ness under some fairly general assumptions (34)-namely, (i) to 10" cm) and strive to find the "super-GUT" group that lepton and quark doublets in each generation; (ii) absence of would unify all interactions, including (39). non-zero charge for quarks; and (iii) cancellation of triangle I am indebted to L. N. Chang, R. N. Mohapatra, and Y. Tosa for anomalies. However, a serious deficiency of both SU(5) GUT valuable discussions. This work was supported by Department of En- and SO(10) GUT is their inability to explain the "superfluous ergy Grant DE-AS05-80ER10713. replication of generations" (35)-i.e., the repetition of families 1. Glashow, S. L. (1961) Nucl. Phys. 22, 579-588. of quarks and leptons in all respects that seem to differ only in 2. Salam, A. (1968) in Theory, ed. Swartholm, mass. N. 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