Experimental Consequences of Family Unification

Theories of family unification predict four left-handed and four right-handed families of quarks and leptons, all with masses below 265 GeV. The lightest mirror quark has a mass of less than 140 GeV. All charged leptons are lighter than 55 GeV, and the lightest is below 40 GeV. All five new neutrinos have masses less than 40 GeV and contribute to the width of the Z . We study the decays of these new families, and discuss rare processes such as p, ey. We also examine proton decay, and show that it can proceed into e+m at the observable but acceptable rate of 10 —' yr.

The discovery of the 8'and Z bosons at CERN has confirmed that the standard SU(3) S SU(2) S U(1) model provides an excellent description of the strong, weak, and electromagnetic interactions.However, the standard model is in no sense a fundamental theory.It does not explain why there are three forces, nor why the weak interactions are purely V -A.It does not tell us why quarks and leptons come in families, nor why the families repeat.
Family-unified theories provide a natural answer to these questions.'  They preserve the successful features of ordinary grand unified theories, and more- over, they explain the multiplicity of families.In family-unified theories, the forces and the families are both incorporated into irreducible representations of a simple gauge group G.The most appealing theories of family unification are based on the group O(18).All the known families fit into just one representation, the 256-dimensional spinor.This spinor is complex, and so superheavy masses for ordinary fermions are forbidden.Furthermore, the group O( 18) is anomaly free, so that the spinor anomalies cancel among them- selves.
Previous attempts to construct theories based on O(18) were plagued by serious difficulties.' These stem from the fact that the 256-dimensional spinor contains eight leftand eight right-handed families.
With sixteen light families, the color coupling blows up at a few hundred teraelectronvolts.These theories are not perturbatively unifiable.
To avoid this problem, it is necessary to split the O(18) spinor and give some families mass at the unifi- cation scale M~UT.This was done in Ref. 2, where it was shown that O(18) must break to SU(3) S SU(2) S U(1) S Zz, where Zz is a discrete sym- metry.The Z~family symmetry allows half the left- and right-handed families to gain mass at MGUT.It protects the other four left-and four right-handed families from acquiring mass all the way down to the weak scale M~.
The possible Z~symmetries are seriously con- strained by cosmology and low-energy phenomenology.In Ref. 4 we studied the restrictions that arise from proton decay, big-bang nucleosynthesis, lefthanded Kobayashi-Maskawa mixing, and the stability of right-handed matter.We discovered that family charges of the fermions are essentially unique, and that N equals five or ten.We found that the low- energy theory has two Higgs doublets and precisely three ultralight left-handed neutrinos.The extra fami- lies of O(18) give rise to dramatic experimental signatures, both for proton decay and for present and upcoming particle accelerators.These signatures are the subject of this Letter.

Right handed masses
Sin-ce O(18.)predicts both leftand right-handed families in the low-energy world, it must explain why the right-handed families are heavier than their left-handed counterparts.
It does this via O(8) group theory, which ensures that the Weinberg-Salam Higgs doublets can be chosen to couple only to right-handed families.
The righthanded families receive direct masses at the weak scale M~, while the masses for the left-handed families are generated by one-loop radiative corrections.
Because of the Zz family charges, only one of the two Higgs doublets couples to the right-handed fami- lies.(We denote this field by @.)Its Yukawa cou- plings must be rather large for the induced left-handed masses to be in accord with experiment.As in any grand unified theory, the Yukawa couplings are speci- fied at the unification scale MGUT.The physical right- handed masses are then obtained by evolving of the Yukawa couplings to low energies by use of the SU(3) SU( 2) U(1) renormalization-group equations.When the Yukawa couplings are large, the low-energy masses are given by the infrared fixed points of the renormalization-group equations.The details of the masses do not depend on the Yukawa couplings at the unification scale Mo"T.
In O(18) the essential features of the right-handed masses are given by this fixed-point behavior.We find the low-energy masses by generating uniform dis- tributions for the up, down, electron, and neutrino Yukawa couplings at MGUT, with values chosen ran- domly from the interval 1.0-10.0.We then evolve all Yukawa couplings to low energies.The results are col- lected in Fig. 1, where separate histograms display the up, down, electron, and neutrino Yukawa couplings at the weak scale M~.The fixed-point behavior is evi- dent in the peaking of the distributions.

Since
(@) ~175 GeV, we find the following upper bounds on the quark and lepton masses: The bounds (1) and (2) are very stringent.They imply that all four right-handed neutrinos and at least one charged lepton should contribute to the width of the Z .Furthermore, they tell us that at least one right-handed lepton doublet should be seen in the de- cays of the 8'.
Decays of new families.Th-e most striking feature of O(18) family unification is that it predicts five new families below the weak scale.We now summarize the decays of these new families.
The heavier of the eight right-handed quarks cas- cade to their lighter partners by standard chargedcurrent processes, with lifetimes on the order of 10 sec.If kinematically allowed, the lightest right-handed quarks decay into left-handed quarks by dimensionfive operators, Q q+ scalars, (3) with lifetimes of the order of a second.Otherwise, the Cabibbo mixing of right-and left-handed quarks al- lows decays into real and virtual 8'bosons, 0 q+&, 0 q+f+f', with lifetimes on the order of 10 and 10" sec, respec- tively.
The processes (3) and ( 4) ensure that no stable right-handed matter is seen today.The renormalization-group analysis discussed above implies that at least one of the four right-handed charged leptons should contribute to the widths of the 8'and Z .All of the right-handed charged leptons de- cay by ordinary weak interactions with lifetimes on the order of 10 ' sec. 5 The four right-handed neutrinos all have masses less than half that of the Zo.The heavier right-handed neutrinos decay into lighter charged leptons by ordi- nary charged-current processes.The lighter right- handed neutrinos mix with their left-handed partners.
Because of this mixing, the light right-handed neutrinos decay into ordinary matter.The lifetimes for all of these decays are of the order of 1Q '6[(10 GeV)/ MIv] sec.If M& is large enough, the right-handed neutrinos contribute to the visible decays of the Z .
Last but not least, O(18) also predicts a new left- handed family, somewhat lighter than its right-handed counterparts.Its neutrino has mass less than 40 GeV, and decays into standard fermions through ordinary charged-current processes.Depending on its lifetime, the fourth left-handed neutrino might contribute to the visible decays of the Z .turally avoids these problems because one Higgs doub- let couples primarily to up-type quarks, and the other to down-type quarks.This leads to a suppression of Higgs-mediated Ko-K mixing.
8'loop, where the internal fermion is one of the Dirac neutrinos N.This contribution to the branching ratio is given by9 Rtt(p, ey) = 2x10 7[M~j(10 GeV) j i8'"O, i, where HI denotes the Cabibbo mixing between the lep- ton I and the neutrino N. The suppression of p, e y restricts the range of neutrino mixing angles.For the extreme case Mtv --40 GeV, it implies i0'"8, i ( 10When v, mixes with heavy neutrinos, 0'"H, i is estimated to be of order 10 .Thus some versions of our model predict that p, ey might soon be seen. The present limits on other rare processes such as KL p.e, p, eee, v p, y, and 7 ey do not im- pose any further constraints on the theory.Even an improvement on the upper limit of Rtt(KL tu, e) to 10 '2 would only imply i8'"8, i )0.1 for Mz = 40 GeV.
Proton decay.-Limits on the proton lifetime ex- clude a large class of grand unified theories.O(18), however, escapes this fate.Eight families survive down to low energies, and so the color beta function is dominated by its two-loop contribution.With eight families, Mo"r increases from its standard SU(5) value and prolongs the proton lifetime.' For AMs= 150 MeV, the O(18) proton lifetime is a factor of 900 times the minimal SU(5) prediction, and sin 6I~= 0.215.This gives a lifetime on the order of 10 + -' yr.Since experiments now measure r (p e+no) & 2x103z yr, " O(18) predicts that proton decay could soon be seen.
Nucleon decay channels depend on how quarks and leptons are assigned to O(10) multiplets.In ordinary grand unified theories, these assignments are not unique.Unconventional choices can lead to nonstand- ard decay modes.This ambiguity is lessened in the O(18) theory because of the Ztv family symmetry.The form of the fermion mass matrices is known, and unambiguous family assignments can be made for all the quarks on the basis of nearest-neighbor Cabibbo mixing.The lepton family assignments are somewhat more uncertain; but subject to certain assumptions, they permit us to make precise predictions of the nu- cleon decay channels.
In Table I we have listed the neutrino mixing and nucleon decay modes for each of the possible family assignments.
Most of the assignments give compar- able branching ratios for protons into neutrinos and charged leptons.This should be contrasted with super- symmetry, where kaons and muon neutrinos are 12 favored over charged leptons.Note, however, that su- persymmetry mimics those versions of our theory where modes with charged leptons are Cabibbo suppressed.
It is a pleasure to thank Howard Georgi, Sheldon Glashow, Lawrence Hall, Ann Nelson, Stuart Raby, and Robert Wagoner for helpful discussions.This

Flavor
violation.-Two-Higgs models have the po- tential for large flavor-changing neutral currents through tree-level Higgs boson exchange.O(18) na-