582 Nuclear Physics B (Proc. Suppl.} 13 (1990) 582-585 North-HoIImd

RARE DECAYS AS CLUES TO THE UNDERSTANDING OF THE FIFTH INTERACTION (GENERATING THE GENERATIONS)

# Yuval NE'EHAH

4-

Ra~nond and Beverly Sackler Faculty of Exact Sciences Tel-Aver Untversit.~-, Tel-Aviv, !srael 69978

The G~nerattons Puzzle

The success in the understanding of the way

in ~1ch the Neak and Electro-magnetic

Interact ions mix (the popular term "un i f i ca t ion "

does not f i t a s i tua t ion In which the gauge

group Is not simple and we s t i l l work wi th two

fndependent couplings) was followed by attempts

to uni fy th is system with QCD wi th in one simple

gauge group such as SU(5). Although some

suggested GUT did t r y to include the observed

generations systen~tlcs, t t was general ly

assumed that the generations represent some less

profound feature, as compared w|th the group

who~ representation is realized by a single

genaration.

We know nothing about the mechanism respon-

s ib le for the emergence of the generations.

Although the problem has been with us since

194617 (when i t was real ized that the muon is

not Yukawa's meson), iL is general ly t r i v i a l i z e d

by the assumpt|on that a l l quark and charged

lepton masses are due to a "Yukawa-Higgs '°

in teract ion - one per mass, or at least 9

such independent In teract ions!

Clear ly , we ought to devote more at ten-

t ion to t h i s puzzle. I would l i ke to show

the kind of clues that could be provided by

a high resolut ion study of the decays of

known pa r t i c les , searching for spectf ic

decays.

TYPICAL MECHANISMS:

(a) Mechanical Exci tat ions

Nature is sometimes repe t i t i ve , and

a f te r four spectroscopies - molecular, ato-

mic, nuclear and hadronlc, we shal l be

forgiven i f we make the assumption that th ts

is "more of the same". In that case, the

generations would represent radial or v ibra-

t iona l exc i ta t ions of the const i tuents from

which quarks and leptons are made - r ishons,

preons, haplons, alphons or whatever ~he

answer to th i s other puzzle - which is

rea l l y the same problem: note that the only

real ind ica t ion for the existence of such a

fu r ther level is prec ise ly the existence of

generations [1]o

~ f o r Par t ic le Theory, Univers i ty of Texas, Austtn Texas 78712, and supported in part by USDOE prant DE-FGO5-85ER40200 Wolfson Chair Extraordlnary in Theoretical PrmysJcs

+ Supported In part by the USA-Israel Science Foundation, grant 87-0000911

0920-5632/90/$03 50 © Elsevier Science Publishers B.V. (North-Holland)

Y. Ne'eman ~Rare decays as clues 583

In a l l previous spectroscopies, the

rotat ional exc i ta t ion bands are the closest,

i . e . t he i r energy increment is the

smallest. This creates s i tuat ions in which

one has a tower of narrowly stacked leve ls ,

s i t t i n g on one radial or v ibrat ional leve l .

At a r e l a t i ve l y large distance one encoun-

ters the next v ibra t iona l leve l , and close

to i t another ro tat ional band, etc.

In the case of the hadrons, we begin to

see a departure from that ru le. Take the

nucleon N(112.;939). The rotat ional exci ta-

t ions are N(3/2-;1520), N(112-;1535),

N(112-;1650), N(51Z-;1675), N(512.;1680)

N(3/2-;1700), N(312.;1720), e t c . . . However,

we also have a couple of " rad ia l " exc i ta-

t ions , a l l with spin 1/2. : N(112.;1440),

N(112+;1710)o Some of the rotat ional exci -

ta t ions may thus correspond to bands " s i t -

t tng" on Roper's N(II2+;1440), etCo [2 ] .

(Note that the radial levels seem to fo l low

M = ~ 1,2,3 GeV=). In any case, the v ibra-

t ional or radial levels lay at about the

sa~e distances as the rotat ional ones (a

f~ct causing some of the confusion).

I f we regard the p or the t as radial

exc i ta t ions of the rishons or other const i -

tuents, we should be lookin 9 for the rota-

t ional levelso Finding them in the quark

case may be complicated because we may con-

fuse them with hadron exc i ta t ions. I t is in

the lepton system that they would show best:

look for a spln 3/Z lepton!

We have to assume that in th is

spectroscopy, the rotat ional levels are more

d is tant than the radial - or v ib ra t iona l ,

since we probably would have seen them

otherwise. I f they are at higher energies,

i t is in the decays of the Z or W that we

should be looking, where there is hopefully

enough energy for the i r production, I t would

be useful to l i s t possible decay schemes

that would lnclude a lepton with spin 312.

(b) "Fmt l tons" - the generations' quanta

A second plausible mechanism would con-

s i s t in assuming that the exc i ta t ion from

the 15 "effect!we" elementary f i e lds ( in

th i s scheme) of the f i r s t generation to the

ne~t ~ c ~ ) o n is achieved through the

addi t ion of a new quantum, a " fami l ion". In

th is ptc ture, the conservation of charm,

strangeness and mu-lepton charge are d l f -

f e r e n t m t e r i a l i z a t t o n s of a single conser-

vation law, the conservation of "H", the

generation number or Ser ta l t t y [1 ] , For

example, taking a quark and a lepton, we can

look for the process in which N is con-

served, but the femil lon is exchanged bet-

ween them: from the Znd generation quark

c=/= to the 2nd generation lepton p-,

c ' / = + e - ~ u ' p + p-

or, in pa r t i c le states, with spectator

(uS/=, d-Z/=)

A + ~ p+ + e + + p- c

The emergence of e + + p- pairs (and not

e- +~+) is character is t ic of these decays,

s - l l = - d- l /= - + e ~ + P

or, tn par t i c les (with the same spectator

quarks as above),

h ~ n + w ÷ + p-

584 Y. Ne'eman / Rare decaye as clues

( ln terms of the Cablbbo-preferred

t r ans i t i on ) . The same goes for K decays,

etc. The assumption, of course, is that we do

not observe such decays abundantly because

the mass of the mediating vector-mason ( tn a

gauge theoo, for instance) is higher than

10 TeV (the present bound). Hararl and Cahn

have made such estimates for bounds of

several as yet unseen decays. The obser-

vation Of such~decays, i f confirmed, would

glve us seriou~ Indicat ions with respect to

the generation - producing mechanism.

THE FIFTH /NTERACTION

In the early s i x t i es , a f ter the disco-

very of Unitary S~nnmeto (the "old" SU(3)),

an often heard c r i t i c i sm was "how can a

stronglnteract ion broken symmetry produce

good resu l ts , with t t s predict ions t reat ing

the s ~ n e t o breaking to f t r s t order in per-

turbatton theory?" In some cases thts could

be understood from current algebra, but in

scatter ing amplitudes, the mass formula,

e tc . . i t remained a mystery. In 1964, I

suggested an explanation according to which

the processes that were considered un t i l

then as "strong" Interact ion processes

rea l l y consisted of two d i f fe rent forces:

(a) an SU(3)-lnvartant force, respon-

s ib le for the Regge t ra jec tor ies (with a

slope of I/GeV2), for the saturation of

Un i ta r i t y , for Dual i ty as a Bootstrap mecha-

nism, e tc . . ; with today's hindsight, we

would say "a non-perturbative r e l a t i v i s t i c

quantum f i e l d t heoo" . This ts the " t rue"

strong Interact ion.

(b) the SU(3)-breaking in te rac t ion ,

which I named the "F i f t h " [ 3 ] , responsible,

for instance, for the mass of the s - l p

quark. I suggested that t h i s component

should be per tu rbat ive ly describable as a

r e l a t i v i s t i c quantum f t e l d theory. Since I t

is not a "strong" i n te rac t i on , I t can presu-

mably act beyond the hadrons. I suggested

that th ts F t f th force might, for Instance,

also produce the muonmass.

QCD, suggested in 1973 as a Yang-Ntlls

gauge theory wl th massless gluons and quark

confinement [4 ] is indeed "f lavour"-SU(3)-

invar |ant° Thts is the strong in terac t ion ,

and i t ts generated at the quark levelo I t

is indeed assumed to generate the Regge

sequences and other r egu la r i t i e s of the

hadrons as such.

At the same time, we now conclude that

the f lavour-SU(3)-F l f th in te rac t ion ts

indeed the generations-producing mechanism

that we discussed tn the previous sections,

probably o r ig ina t ing at the quark-and-lepton

const i tuents leve l .

The postu lat ion of QCD thus rea;Iz~dmy

separation. I t ls the second - or F i f th -

component that remains to be properly mapped

and understood, The key l i es wi th these rare

decays.

Y. Ne'eman / Rare decays as clues 585

REFERENCES

1. Y. Ne'eman, Phys. Letters 82B (1979) 69. See also H° Harari, Phys. Letters

86._BB (1979) 83 and M.A. Shupe, d l t to ,

p.87.

2. Y. He'eman and Dj. Sljacki, PhySo Revo

D37 (1988) 3267.

3. Yo Ne'ernan, Phys. Rev. 134B (1964)

1355. HoLe that the term "Fifth

Interaction" has stnce been

appropriated for the denotation of a

hypothetical mid-range correction to Einstein's gravtty (E° Fischbach eL

a l . , PhySo Rev. Lett° 56 (1986) 3.

. Go ' t Hooft (1972), unpub.; D.O.

Gross and F. Wilzcek, Phys. Revo

Left. 30 (1973) 1343; HoD. Politzer,

d i t to , p.1346. These authors disco

vered asymptotic freedom. The applica

Lion to co|our-SU(3) was suggested by

H. Frttzsch and Ho Gell-Nann, Proc.

XVZ InternaL. Con. High Energy Physo

(J.D. Jackson and A. Roberts eds.,

Fermilab, 1972, VOlo 2, p.135,

modifying the original integer-

charges proposal of M° Han and Y.

Nembu, PhySo Rev. 139B (1955) 1006.