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.