s\%\INTERNATIONAL CENTRE FOR

THEORETICAL PHYSICS

A PRBON MODEL WITH HIDDEN ELECTRIC AND MAGNETIC TYPE CHARGES

INTERNATIONALATOMIC ENERGY

AGENCY

UNITED NATIONSEDUCATIONAL

SCIENTIFICAND CULTURALORGANIZATION

Jogesh C. Pati

Abdus Salam

and

J. Strathdee

19R0 MIRAMARE-TRIESTE

• * ?

IC/80/180

International Atomic Energy Agency

and

United Nations Educational Scientific and Cultural Organization

INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

A PHEON MODEL WITH HIDDEN ELECTRIC AND MAGNETIC TYPE CHARGES

Jogesh, C. Pati

International Centre for Theoretical Physics, Trieste, Italy,and

Department of Physics, University of Maryland, College Park,Maryland 20732, USA, ••*

Atdus Salam

International Centre for Theoretical physics, Trieste, Italy,and

Imperial College, London, England

and

J. Strathdee

International Centre for Theoretical Physics, Trieste, Italy-

MIRAMABE - TRIESTE

November I960

• To be submitted f«r publication..

*,* Research supported in part by the M.S. National Science Foundation.

"»» Address after 1 December 1980.

ABSTRACT

The U(j.) * U(l) binding forces in an earlier preonic composite model

of quarks and leptons are interpreted as arising from hidden electric and

magnetic type charges. The preons may possess intrinsic spin zero; the

half-integer spins of the composites being contributed by the force field.

The quark-lepton gauge symmetry is interpreted aa am effective low-energy

symmetry arising at the composite level. Some remarks are made regarding

the possible composite nature of the graviton.

1. The proliferation exhibited by three families of quarks and leptons and

the associated spin-1 gauge and the spia-0 Higgs particles strengthens the need

for a oore elementary and more economical set of objects, of which these nay be

regarded as composites ' ' ' . In 197!* and 1975 a class of composite models of

quarks and leptons was proposed whose salient features are the following.

i) (Jua.rk.8 and leptons are composites of three sets of elementary

ent i t i es : the rlwons ' f. • (u .d . c . s , ) , the chromons ' C = ( r ,y ,b , l )

and a third set of ent i t ies ^y.

Each set i s characterized by apeciflc values of the binding charges stated*)fcelow. The thi rd set S^ may contain aa few as a single member. ' Collectively

the ent i t ies {f.C,S} are named "preons". I t is to be noted that the fl&vonBand chromons directly define flavour and colour attr ibutes of quarks and

leptons ' .

i i ) The forces responsible for binding preons to make quarks and leptons

are assumed to ar ise through two vectorial abelian symaetriea U(l), * "(1),,

generating two spin-1 gauge par t ic les . The assigned charges {Q»IQD) f ° r t h e

sets of f, C aad S are (g,0) , (0,h) and (-g,-h) , respectively. Quarks and

leptons are assumed to be fCS composites. These axe the only three-particle

composites neutral with respect t o both Q, and &, .

*) Four fl&vcas . were introduced in 1971* and 1975 (Ref.l); at that

time four quark flavours were known. Now with the possible existence of

six flavours, it is attractive to treat two flavons (u.,d) as basic and to generate

three families dynamically, or alternatively, let S 'a pl*y the role of

family quantum nunibeis (see text).

••' Four chromons are chosen to go with the idea of lepton number as the fourth

colour. However, in general, using preon ideas, one can consider leptons to

differ from qunrks by more than one attribute.

•»») <jhe g particles in the original formulation carried spin 5- (assuming th*t

chromona and flavons carry the same unit of spin^ Thus they vere named "spinons11.

In thia note ve consider situations where g-particle spin may be zero. A -

humble suggestion for the S particle*is call them esaons"; a name more In

keeping with "flavons" and "chromona" is "somons" - for the neetas of the

Gods in Sanskrit (soma-ras).

*•*•) "Charges" or "attributes" may in general arise in two alternative ways.

Either (i) each charge is associated with one elementary entity as for flavona

and chromons or (ii) charges are generated (at least for sone.) dynaadcally aX tb4

composite level. An example of (ii) is the dynamical generation of "fandlyj!____

charge (see text). / ~

- 1 -- 2 -

iii) Low energy electroweak and strong interactions are generated in the

model by postulating a local symmetry § = SU(2). * SU(2)D « SU(!»)?.„ for theo ij n urn

preonic I^grangian and introducing the required spin-1 gauge as well as the spin-0Higgs particles as elementary. This was in addition to the U(l)A * UU)B

symmetry generating the preon binding forces, which commutes with ^i .The purpose of this note is to propose certain elaborations of this model,

motivated by our desire to retain non-proliferation of fundamental couplingconstants and of preons. In the new scheme we obtain (i) a new interpretation forthe origin and the link between the binding charges Q and (L, (ii) a raisonfor spin 5- for quarks and leptons starting with just spin-0 preons and (i i i) aplausible raison for the existence of families of quarks and leptons. The electro-weak strong gauge symmetry sueh as SU(2) * SU(2)_ * SUfO „ or its extensionfor example to SU(l6),is viewed as an effective low energy symmetry valid atenergies below the inverse size of the composites. Certain possible experimentalconsequences of this class of preonic model are noted at the end.

2- We preserve the central feature of the old scheme that quarks and leptonsare composites of three sets of preons f,, C and S as well as the

• ^ 1 J kassignment of binding charges ' (g,0), (0,h) and (-g,-h) to these sets. Wemodify the scheme in the following respects:

(l) It has recently been observed ' that ordinary "electric" typeforces **) (abelian or non-abelian) arising within a simple or semi-simple grandunifying symmetry are inadequate to bind preons to make quarks and leptons ofsmall size rQ (< 10" cm) without proliferating preons unduly. Following±b* spirit- of a suggestion made in Ref.3, we propose that the .

two primordial charges Q, and t , ( or rather g and h ) are not unrelated.They are reciprocal charges analogous to (but not identical with) the fundamentalelectric and magnetic charges. Thus they satisfy Birac-Uke quantizationcondition

(H = 1,2,3,...) (1)

• ) Other? enjupge assignment* are in general permissible (see for

example Hef.3),though in this note we shall restrict ourselves to this particular

assignment.

•*) By "electric" type forces arising within a grand unifying symmetry, we mean—2

forces whose effective strength is of order 10 at the grand unifying mass M.

- 3 -

The two charges a g^^ a may correspond to a. UdK x u ^ ' t j Sa"ge symmetry5) *)subject to a subsidiary condition sueh that there exists only one primordial

spin-1 gauge boson (A ) (rather than two) coupled to "both QA and Q . The

integer H for the specific model introduced here must be unity (see below).

Thus the two coupling constants g and h related by e.g. (l) represent just

one fundamental parameter.2 1

We assume that h is of order unity or larger (h Air >, j to 1) at shortdistances r . < 10~ or 10 cm or equivalently at running momenta M ; l/r_ > 1

0 *•*• u u ^**

or 10 TeV, so that it may bind preons to naXe composites of small size r0. To-

gether with the constraint H = 1 this would imply that g (MQJ/'HT^ [J to £•).

For the specific assignment of the binding charges (Q^.tjg) - namely (g,0),

(0,h) and (-g,-h) for f, C and S, both QA and Qg are zero for quark, and

lepton composites (fCS). Since ordinary eleetrie charge is:non-van1ahing on

quarks and leptons, ve see that we cannot identify either Q A or Qg with

ordinary electric charge. We therefore interpret both ^ and Q_ to be nev

conserved charges which are operative only at the preon level, but are hidden

at the q uark lepton level. They are analogous to electric and

magnetic charges in being reciprocals of each other; however,clearlyjthey have

to be distinct from them. The associated primordial gauge particle A is thua

distinct from the ordinary photon. "*' In the present model, the ordinary photon

must be regarded as composite like the gluons, the W's and the Z (see remarks

below). This is to be contrasted from the specific model presented in the text

of Ref.3, where one of the two reciprocal charges was identified with ordinary

electric and the other with magnetic charge; and the primordial gauge

particle was the known photon. These two alternatives, while sharing many common

features, can be distinguished experimentally .

•) While we provisionally follow the formalism in the first paper of Ref,5,a field theory of electric and magnetic type charges with manifest Lorentiinvariance s t i l l needs elaboration. In this note we do not consider the' t Hooft-Folyakov type of magnetic monopoles nor their non-abelian extensions.••) We provisionally leave the question of masslessaess of A' open.We note that:even with a, MS*1«S» A* there is- no conflict with thelimits from EotvoB type experiments, since quarks and

leptons are neutral with regard to Q, and Q-, and have small sizes rQ. HieVan-der-WaaJ. force between neutral matter is proportional to ~- a (r /R)7or r-, * 10~ cm, this force i3 very much smaller than the gravitational eve»if B is atomic <vio" cms.

-U-

•. ' (2) The seeend new feature in this note•concerns the generation of spin -r

for quarts and leptons. We consider the possibility here that the flavons, chromons

and 8-particlea may a l l be scalar particles. Quarks sad leptona, which arefCS composites nevertheless possess spin j due to half-integral angular momentum

associated with the field created 'by the tvo reciprocal charges (g and h) . This

la entirely analogous to the case of angular momentum possessed by the electro-

magnetic field of an electric charge in the presence of a magnetic monopoly.

To obtain precisely half-integer angular momentum from the fieia as

opposed to higher values, we set

(2 )

This i s the reason for choosing If - 1 in Eq.(l). The problem of making three-tody composites allowing for angular momentum of the field is discussed later.

(3) We propose '' that the- abelian foree generated by thecharges (Q .ttp) i s the only primordial force, and al l other forces including thenon-abellan electrowea*£strong forces (leaving out gravity for the present, onWhich we comment later) are derived effectively only at the composite level . Weadopt this plint of view in the interests of non-proliferation of fundamentalcoupling constants and_ non-proliferation of preons.

10™-10~The primordial force being strong at very Bhort distances ( ; £

em) binds three preona (fCS) t o make spin r- quarks and leptons of small s ize***'— I T —~\ ft

r^ $, 10" to 10~ cm; i t can also bind even numbers of preons including anti-preons to moke a hoat of Bpin-1 and spin-0 composites, which are neutral *••• '

with respect t o the binding charges Q. and Ve assume that theBe spin-0

and sptn-1 composites also possess small s izes <v r n , with the masses of the

«oafpositea being much smaller than their inverse s ize l&-~ — . Hote that (•!„18 r 0 "

easeeds 10 Te¥ for r < 10" cmand may be as large as P l c k i fexeeeds 10

~i<T3 3Te¥ for < 10 cm.and may be as large as Planck mass if

• ) We are aware that the usual treatment (see Ref.6) i s non-relativiaticand that i t would need further elaboration for application to the present situation.

• • ) >ote that had we introduced fa. * U(l)A x U(l)B as a fundamental symmetry{subject to hS(M )/lt» £ 1) where €^ contains the familiar SU(2) * U{1) * SU(3)C

aynmetry we would not be in a position to embed such a symmetry into a simpleqr_ semi simple group larger than £ j ^ * U(l) x U (1) wlthoat_prqll feratlng, preons. " • ) The size r_ of the composites is perhaps as large as ~10~1 > r~' 10 cm;

~33i t may even be aa small as 1/Hpianct"** i 0 CIB- *n general, i f preons arecomposites of prepreonsana pre-pi-e-preona (see Ref.7), there may be a hierarchyof sizes of these composites ranging from 10~ cm. down to gravitational length

••••) The spin-O, 9pin-l composites, neutral with regard to (Q .Qg) are of the

fora

", 2t ^ 1 «te.)

Starting with the observation, that q.uarks and leptons possess smalisizes.compared to which inverse masses of theBe objects are irrelevantand -ta^ an effective field theory of these composites *)

shouia be etpresattle as a series of terms in powers of the size parameter-i t has been conjectured fwe believe plausibly and agreeably) that the effectivefield-theoretic interactions of these composites of spins .0, 5- and t at moment*:<<M0 = ^ • m u s t "be renormalizable at least •• ;•- for ••' a perturbative •'": •.' • • rSicapproach. • Adopting this philosophy, non-renormalizable interactions (which

incidentally are the only ones available for composites of spins****!will be damped out at low energies by powers of %b& s ize, L/lt..

Since the only renormalisable theory of interacting "charged" apin-1fields i s a Yang-Hills theory based on a spontaneously broken non-abelian localsymmetry, i t follows from the above remark that the effective interactions ofthe composites > of spins 0, j a n d 1 of small size must be generated by anon-abelian spontaneously broken gauge theory upto energies < M_ • — . Thespin-0 composites can now play the role of the Higga fields. °

The economy of this picture ia appealing. The basic theory, as in Hef.3,involves a single gauge coupling constant g, a single primordial spin-1partbsle A , and. a reasonably mall nuabar (leas than at most nine) of preoa#«The prol iferate qjuark-lepton gauge structure, 3U(l6) or bigger, with th«associated proWfirated spin p spin-1 as well as spia-0 quanta (auarks, leptoni,Higgs, etc . ) derives i t s origin only at the compo«it« level. All of it«parameters ahouHtfl* cbmputabltf l a principle In term* of t i e basic theory* -;

The renormalizabl* Tang-Hills theory i s a consequence of the small sizeof the composites and applies, . only at low energies « — .

,. etc.

•) Composite* possessing non-zero values of QA and/or (L can also form.They may possess higher masses. Such composites can effectively play therole of technifermions 3 ^ 8 >.

••) Unpublished remarks due to M. Veltman, 0. 't Hooft, M. Parisl andK. Wilson, In the present context this conjecture i s stressed in Bef.3. W*are of course assuming that preon masses (evaluated at t^) are also very muchsmaller than MQ. Any departure in this respect from experience with <JCD mayhave i t s origin in the abelian (rather than non-abelian)preon dynamic*.

• " ) This may provide a raison for the absence of spin j and higher spincomposite quarks and leptons with noticeable strong interaction at low energies.•*••) This idea of composite spin-1 gauge fields was proposed in a generalcontext in Hef.?..

-6-

3. We now vish to build spin j" three-body composites. One naive picture

la of "shell structure" where a two-body composite of smaller size is formed

first tto which the third entity binds. Consider the pair CS, which can form

two-body composites X^ • , Q» with charges indicated by a subscript.

Here the pair can bind both through Q * Q_ coupling as well as through Q,* Q_a a AD

coupling. With C and S carrying charges (0,h) and (-g,-h), the field of

the (CS) pair has an angular momentum -gh/UTT = =• (see Eq.(2)). Thus X madeNow the third entity

Since both 1 and X,

f binds

carry

of two spln-0 components has half integer spin

to X, to make composites (fCS) ~ (fX. ),Q -> . U.U^E I,V.II J. »UM «,

only Q. charge, the field of the (fX^) system carries zero angular momentum.

With X^ of spln-i-and^ of spin-O, the (fX.^ composite has spin ~, if v ~ J

f bind in S wave. Hence spin ~r for quarks and leptons.

and

Pursuing the picture of forming two-body composites first, two other

such "composites" may be possible:X2« (fS)(Q _nj and Xg • (fc'(g h ) ' e a c h o f

which possesses spin 3- for reasons mentioned above. These quasi-two-body

composites may then form the cores to which C and S may, respectively, bind.

These could provide two additional spin j (fCS) composites which may be viewed

approximately as (<Xj) and (SX,) composites. We would then have three sets

of fCS composites, possibly distinguished from each other by the sizes of

the inner cores and the outer radii, representing three distinct families.

With f containing two flavons (u,d), C containing four chromons

(r,y,btl) and 3 being a single member set, there would be exactly eight members

(2 * U * 1) in each of the three seta { f ^ S } . Each of the eight members

having spin j can appear with either left or right beliclty depending

upon the orientation of the field spin relative to the direction of motion of

the composite. The eight members in each set natch by construction the flavour

•) In 19WS Harlah Chandra (Ref.10), on the basis of a classical calculation

showed that an electric charge cannot bind with a magnetic monopole. This

result has been questioned by A.S. Goldhaber who shows that

both zero and non-zero mass composites can form classically. (The former

may possibly represent neutrinos.) In this context R. Jackiw10)

has shown that the dynamics of the monopole charge system possesses

ft hidden 0(2,1) symmetry and that it is characterized by & simple irreducible,

unitary (hence infinite dimensional) representation of this group. One wonders

whether this could have any relevance to the number of families and whether

this number is infinite; see also A. Barut, Ref.10. for the question of

binding In dyonium systems based on classical considerations.

• V We observe that this mechanism is not applicable to three-body composites

of "identical" objects like the three-quark composites. The preons f, C and

3 do differ from each other in respect of their binding charges.

and colour quantum numbers of tie six quarks plus two leptons in each family.

In view of the naivety of the dynamical picture outlined above,

one may entertain the alternative possibility that the origin of families

lies at a more basic level. Thus one may postulate that there may for

example be three S-partieles (S ,S ,S ) and identify the e, y and

fCS composites,

may app3-«prt«ttj«4y *>* nwnei "famllona".

families as the ground states of fCSB, fCS^ and

this picture, the i

Within.

The effective gauffe symmetry

We shall assume that the effective gauge symmetry at low energies

(K < 1 TeV) i s determined by those spln-1 preonic composites which are neutrjL

with reapect to the binding charges (QA >V- T h e two-body composites neutral

with regard to (QA .V a r e ? i f J ' V f i a n d § S - l t t h e p r e 0 1 " h a V C l n d e * d

spin-0 rather than spin-|-, i t la clear that the corresponding current awouia be purely rectorial at the preonic level . The Bix-body apin-1 composite*(fCS J<§ ) on the other hand can couple to chiral currents (L and R) i f • •

spin - la generated at the level of three-body composites like fCS (corresponding

to quarks and leptons). Allowing for al l six-body composites of the

above sort (neutral with regard to (^.Qg) and allowing for the chiral

nature of the associated quark and lepton currents, one may obtain the . -

maximal gauge :t aynmietry U(l6) or S0(l6) in the space of one family * " ) 6f

composite eight left-handed fermions t^ (comprising six left-handed quarks

and two left-handed leptona) and their antiparticles f£ - The corresponding

composite gauge particles will couple to the fermionle currents t^i

— • -(; -c -i i < M_T.'u L L n L "

one word of qualification 1 B in order. The symmetry U(l6) or SU(l6}

generating chiral currents possesses triangle anomalies, which spoil

renormalizabillty. Thus subject to the renormalizability conjecture

mentioned before, we expect that either the specific dynamics of preon

») For spin j preons, there Is a related mechanism, which together with

different helieity configurations for the preons, generates three families of

quarks and leptona as well as three mirror families 8)

*•) For binding purposes, these six-body composites cannot be regarded as

qq composites, since the latter have "big" sizes -wio"1^ cm. Even though q

and q are shielded from the primordial binding force, the components within

(fCS tCS) are not. Once the six-body composites form with small s izes , the

effective coupling would be to currents q y q and 5_y In at the ouark level.

• • • ) In principle the symmetry may encompass al l families and may be as

as [U(l6)]3 or even u(U8).

-8-

binding generates additional multiplets of composite femions with

masses « M so' as to cancel the anomalies , or else the effective gauge symmetry

at low energies (E <• M.) is restricted **' to an appropriate anomaly-free sub-

group E of 0(16) or SU(l6). The two moat obvious anomaly-free subgroups are

80(10) or the s t i l l smaller SU(2)L* SU(2)R* SU(U)^R, both of which are l e f t -

right symmetric and treat lepton number as the fourth colour. As stated before,

since~the~~pboton i s a composite~field, the electric charge i t se l f is defined ^

?by th is effective gauge summetry; in particular I 3 L + I 3 H

In addition to the gauge particles of the electronuclear (EH)

t 8 *symmetry $m =- (SU(2)L * SU(2)R - SU(lt)£+R or S0(l0)), we expect8* (in fact

for any preon model based on three seta of preons ) that three strongly bound

spin-1 composites Z f , Z,, and Z coupled Respectively ,to the currents Tr f Suf,

TrC<f C and Tr S <f S, should form. These define the vectorial ' abelian

symmetry •& • U(l ) f * U(l) c * U{l)g; the charges defined by these currents

being Just the flavon, the chromon and the g numbers Hf, Hc and Bg. The

net local symmetry ••••) at the composite level i s thus of the form

U(l) f x U(l) c x U( l ) s .

We expect Z., Zf, and Z,, to acquire masses dynamically. These gaugeparticles have the remarkable feature that each one of them couples universallyto a l l quarks and leptona. This is because each quark (or lepton) possessesn • * = » » 1 The existence of three or more such gauge ,at "c *Bpart icles is peculiar to preonic models. If quarks and leptons are assumed tobe elementary and if ve assume a grand unifying non-abelian symmetry for the

") One example of such fermions are the mirror fermions. With spin T-preons, there exists a simple mechanism to generate three families plusthe i r mirror sets

*•) This amounts to saying that the spin-1 gauge particles within the cosetspaces SU(l6)/H must effectively be superheavy >M_, if they form as compositesat a l l -

•*•) For the case of. spin-— preens the abelian symmetry can be chiral unlessanomaly constraint r es t r i c t s i t to t>e vectorial. Bote that the compositegauge particles Z, „ „ are distinct from the primordial gauge particle A1 .• • • • ) I t is worth noting that the symmetry of the preonic Lagrangian was Just[U(1)A « f ( l ) B ] ^ c a l * [U(2)f * U(l()c x U ( l ) s ] g l o b a l , wherethe hat A signifiesthat the two U(l) ' s (of electr ic and magnetic character) are inter-related.

This symmetry translates into 5 ™ . " [U(l)] local at the quark lepton leveliit * ** , for example _

in accordance with the renormalizahility conjecture. Why we started wlth ftiro

flavons, four chromons and one-s - or rather why the global preonic symmetry

is U-(2) » Vrlk) x U_(l) - can only tie answered at the level of pre-preons

quark-lepton Lagrangian, i t would be possible to generate one such gauge f>articl«

coupled to a fermion number *) as in the EU(l6) model, but not three.

If the masses of Z , Z and Za are in the range of a few hundred GeV,¥ - - + +

their presence can be felt in e e + y u and e 'e -» qq forward-backward

This opens the possibility for a clear experimental signal for preonic

models. , a r¥ - - + +

y u and e'e

asymmetry measurements even at T ^ energies and similar measurements in pp -*• LIX

and pp + ifX at Iaabelle and the new CERH pp accelerator. Evidence for three

such gauge particles coupling universally to all quarks and leptona, if found,

would call for a preonic basis. We see that such evidence could come (depending

upon the masses of the Z's) even before one may reach the energy scale M_ s — ,

where quarks and leptons would begin showing form factors, or even dissociating.

This preon model, (with both binding charges Q, and a "hidden") can be

distinguished froa those ' in which one of the "binding" charges is ordinary

electric and the other charge is magnetic. .. For the latter,

collisions of ordinary matterfcarrying electric chargeJean lead to emission

of virtual high—energy photons^which through the large magnetic coupling can

convert to a preon-antipreon pair at short distances. The latter in turn can

generate more preon pairs; these could recomljine to give large multiplicity

events of qq and** type in comparable numbers and perhaps also photons.

These processes would take place as long as centre-ppf-maift energies exceed twice

the effective mass of preons at short distances , which need not be much greater

than 200 GeV K Such a threshold may thus be much lower than the inverse]_ - • •• —

size M Q - — > 1 to 10 TeV. For the present nodel with both Q A and Q^ "hidden"f

such a dramatic signal would appear only at an energy scale ^M^, where

simultaneously quarks and leptons would begin showing form factors.

We end this note with a few remarks which are more general than the

specific model proposed here.

(l) To pursue the point of economy one may regard the graviton as a

composite of the prtacrdial spin-1 quanta A1 and of the preona. A composite12)picture for the graviton has been considered by several authors ', It has

also been noted ^ in a general context that a spin-2 particle treated in the

•) The fermion number symmetry may be identified with the diagonal sum of

the three symmetries U( l ) f , U(l) c and U(l)g.

••) gee Ref.3,v

•••) See Eef.B.^-Tor.a thorovigh; dtgawaion ot re la te* paint •.•far-i photons of energies higher thanenergies E

inverse siae will exhibit circular polarization revealing parity

violation if photons couple to electric and magnetic charge. Parity violation

for such energies is t ruly characteristic of a l l theories based on dual

charges, whether hidden or manlfeBt_^__

framework of a local field theory *' must be massless and must uniquely

couple in a generally covariant manner to the energy itoaentum tensor

TUV i n o r d e r t h a t the theory may be ghost-free **'. Since

positive defioiteness {guaranteeing conservation of probabilities H s the minimal

requirement even for an effective field theory of composites, this result serves

to provide credence to a composite picture of the graviton in the sense that the

unique emergence of the Einstein Lagrangian at the composite level is not an

accident;- it is guaranteed on more general grounds regardless of the details of

the binding dynamics.

One may furthermore observe that the renormalizability conjecture

stated before implies - since gravitational interaction is perturbatively non-

renoraalizable -that this interaction must be damped by the small size B s jj

of the composites at energies much smaller than M. (Here S may in general

be much smaller than the size r of quarks and leptons - see remarks below.)

This would say that the weakness of the gravitational coupling constant is

related to another known fact - the smallness of the size of quarks and leptoas

. (or of their constituents) and thus to the dynamica of the primordial binding

force.

To identify H with. ~ 2 * CeV' ve tini

*) We are assuming here that the composites including graviton havesufficiently small size ~ 1^Mpianck' So t n a t t h e y "^y116 encompassed within a localfield theory for energy ranges « Up n . We remark that the above statementdoes not of course preclude the existence of massive spin-2 composites like the fgraviton Xk) egnpaaiteperhaps, a? t w gluons., TfHfc. W 5 ? 5 H= « M p ^ ^• l i e s < K--5. Toeaw B«,»-.»l»e-,l>a dMertted /by effective l e e a l . f I d a . theories for

out inverse

ess-tt Hrt»4r lu.vwrse size.••) It is noteworthy that no spin g- or spin 3 interacting theories which are

field theoretically satisfactory have yet been discovered.

natural to envision several layers of increasing elementarity - preons,

pre-preons, pre-pre-preons... within quarks and leptons with their sizes

decreasing progressively from say lcf -10 em to 10 • cm - the size/the last but

one layer which includes the graviton (if it is composite} being of order

ly^PlaMCk " Within this picture the gravitational interaction would be

damped by form factors at momenta approaching Planck mass scale thua rendering

the theory well behaved for these energies. Unfortunately the differences from

the conventional picture where gravitation is included as a fundamental inter-

jtetion would manifest themselves only at and beyond Planck energies if one may

be so daring a3 to contemplate this regime where the graviion may have

dissociated into its more elementary constituents. In such a. theory

the perspective of unification of gravity with the other forces takes a. new

form: the effective Yang-Hills constant of the present gauge theories as well

as_the Newtonian constant would be computable, in principle, in terms of the

primordial [u(l) * U(l)] constant (suitably diiaensionally transmuted). Compare

this with the picture presented for example by 3upergrstvity theories at Planck

energies and beynnd^where gravity plus some form of matter - possibly with

a fundamental Yang-Mills interaction - would survive and the eventual theory

contain . •••two constants {Newtonian and Yang Mills or e^uivalently

Newtonian and a cosmological constant).

(2) One may choose to assign spin _- to the preons f, C and S rather

than spin 0, while assigning them the same binding changes (ft^tQg) *» i n the

text. In this caae one must choose (gh/Uir) = (*•) (2) = 1, no that the fieldpair would *=

generated by ead£,l contribute one unit of angular momentum rather than half a

unit and the composites fCS can still have spin —. Here,for h A n = 1,

we would have g /U» = gh/Uir = l . Thus both Q.'Q. and On* On couplings can be

of the same order. ' This ease will share most of the consequences of the model

presented above ' except that spin ^ will not have its origin in the force

field and that spin 1 (Pip composites can couple to ehiral rather than purely

vectorial currents.

(3) We see that the effective gauge symmetry at the quark lepton level

need not be simple or semisimple; it may in general have a form "W _,. * U(l)~

factors, which cannot be embedded into a simple or semisimple group for reasons

*) This would correspond to having no long extending "desert" or grand

plateau in physics.

*•) Hote that in this ca.se, a l l three familiesfarising through three

different two-body cores in the manner discussed in the text)would have

similar binding energies.

-12--11-

discussed above. Tils however aoes not run counter to the spirit of

grand unification, since the primordial force is governed hy one coupling

constant.

C O Proton decay into leptons (with composite quarks, leptona, gauge

and Higgs particles) will occur and provide an upper lisit to the scale of the

inverse size l/r0 = MQ. This is because the masses of the composites (in-

cluding the gauge and Higgs particles) are.within the picture presented here,

bounded above by Mg.

Within the standard approach the (B-L) conserving proton decay(e.gi p •+ e + T ) is mediated by diquark and lepto-antiquark type ofgauge particles, which for a preonic theory of the type presented here areto be interpreted as six rather than two preonic composites. The masses

Ikof these gauge particles are estimated to exceed around 10 Gev to account for the

known lover limit on proton lifetime. For this picture to be consistent with ourapproach the sizes of quarks and leptons and the superheavy gauge particleswouldhave to be less than (10 GeV)"1. There is an alternative scenario which wouldarise i f the dynamics of preon binding does not favour the formation of six preonic

- * ™ + 0 ^

sptn-1 composites *' . In this case, proton decay into e + IT may occur through^ thirdorder ID the effective four preonic transition ((?1 + f g - ^ ^ + ^ + +a

+ <+b>>'

followed by an effective qu&rtic Xlf* coupling^subject to one component of4 having non-zero VEV).**^ The four preonic transitions of the above sortcan be mediated (for the case of Bpin-g- preons) by aipreonic gauge composites

with for example the compositionsfc f ) , (fs) and (sC)-The emitted Biggs (*a)nay have the same composition or may contain four preons. The amusingfeature of such a mechanism is that the characteristic mass scale for thisprocess (yielding AF= -U,p + e* + pions) i s only of the order of 10 -10 GeVin contrast to lO1** GeV for the SU&.6) or SO(10) models. The AF = 0 protondecay mediated by leptoquarfc X of mass 10 GeV would be comparable in Btrengthwith similar remark^fur AF - -2, -6. Within this picture quarks and leptons

need have sizes no smaller than « (10 TeV)" 1 „ A choice between the two scenarios

would need direct experiments with high-energy probes fTtm the region of

energies of order 10 TeV.

•) Unfortuantely the question of binding for such systems of charges and

monopoles is very little understood.

••) This mechanism is analogous to that of the AF = 0 proton decay (p * 3i +

mesons) for the standard case (see Ref. l ).

-13-

(5) Finally we have taken a fairly conservative attitude towards

the physics of preonB. If we are to entertain the .notion of layers of

composlteness and elementsjity, we should be prepared for new physica, relevant

at very small distances. Ideally we shall be looking for the preon, pre-preon,

pre-pre-preon... sequence to end with one single (monotheistic) . entity

endowed perhaps with prf^iw^of, topologies,! nature, ****,

Mote added: After completing this note, we came across a paper of Weinberg and

kitten* in which restrictions on spins-of^ composites are derived, under certain

assumptions, among which Lorentz invarianee plays an important role. If our

preons carrying dual charges are described by a theory like that of Zwanziger ,

Lorentz invariance emerges only non-perturbatively, and it is not clear to u» if

the considerations of Weinberg and Witten should apply to this case.

•) See remarks in the last reference of Hef.1.

*•) We observe that of the three sets of preons (f,C,S), one set can he consideredas composite of the other two so far as their charge assignment is concerned, e.g.f—C5. Alternatively, and perhaps more attractively, one may introduce JuBt two pre-preons, e.g. a with charge (g,0) and B with charge (0,h). Identify S of charge(-g,-h) with (ofj) and i t s mirror S1 of charge (g,-h) with aB. The two flavon*(f 's) may be identified with a and fSS - S(aB) or (and, for 2 families)witha(aot) and B(a3). Likewise one can specify composite constructions for four ormore C'a. One criteria*-for choosing a particular set could be the emergence ofappropriate commutation relations for the composite currents from the canonicalcommutation relations in tvlie approximation vhen composite size is neglected.

With Just two fundamental entitles a and fi , related by duality, one might alreadybe approaching a monotheistic view, but such a model, as i t stands, yields integerspin for quarks and leptons, when viewed as fCS composites. This 1B true for eitherspin assignment (0 or |-) for (a.fl) and either field-spin (ghAir > r o r l ) . Thisdifficulty can of eour*e be reaoved by introducing, in addition, supersymmetricpartnervtrf (spin h) a's and 6's or alternatively a. fundamental splnon withcharges (g,h)j however ve would like to believe that there Is yet another sourcefor spin \ which will obviate the need for introducing these extra entit ies. -

***) W« have In olnd the possible use of the theory of knots built on a fundamentalsubstructure , or the use of higher dimensions where dual charges c a n *•topclogically defined . In this latter context W. £ahm (in a private SiseuMion)has aaphaaised t n*t the N » k Yang-Mills supersymmetrlc theory which can beformulated in ten dimensions is a good candidate for a fundamental local theory ofdual charges. The B function vanishes lupto three loops) in the theory implyinglack of need fa»t>perturbative renormtlizability for either charge (electric ( ormagnetic » - gif * y ^ )•

-lit-

1)

2)

3)

5)

6)

7)

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A. De Rujula, CEPJf p rep r in t TH S9O3 (1980).

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1181 (1977);

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