Proc. Nati Acad. Sci. USA Vol. 79, pp. 3371-3375, May 1982 Review Neutrino mass, proton decay, and neutron 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 x SU(2)L x SU(2)R at the ity violation (left-handed character) of the weak interaction 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 neutrino mass in the electron volt masslessness of the neutrino, the surrender of the full region, the decay ofprotons into antileptons in the range of 1031±1 quark-lepton symmetry 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 quarks and leptons. 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 gauge theory. 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 hypercharge, Q is the electric charge, and I3L is the (1-3). Here SU(2)L is the left-handed (L) weak isospin group-of third component of IL) and YR = 2Q (where YR is the right- which the two charged current 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 weak hypercharge group. wide variation in the values ofYL and yR ofthe different leptons A series ofneutral weak current experiments (neutrino-hadron, 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 strong interaction with berg angle) and JEM is the electromagnetic current. This struc- the electroweak interaction 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-gluon 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 fermion 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 boson-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 baryon number and lepton number 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 weak isospin 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 electric charge 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 baryon number 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 quantum number 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).