IC/T8/88

INTERNATIONAL CENTRE FOR

THEORETICAL PHYSICS

SIGNATURES FOR AXIAL CHROMODYTTAMICS

Jogesh C. P a t i

and

Abdus Salam

INTERNATIONALATOMIC ENERGY

AGENCY

UNITED NATIONSEDUCATIONAL,

SCIENTIFICAND CULTURAL

ORGANIZATION 1 9 7 8 MIRAMARE-TRIESTE

IC/78/86

I n t e r n a t i o n a l Atomic Energy Agency

and

United Nations Educational Sc i en t i f i c and Cul tura l Organization

INTERNATIONAL CENTRE FOR THEORETICAL FHTSrCS

SIGNATUHES FOR AXXAL OffiaMODYHAMICS *

C. Fa t i *•

Department of Physics and Astronomy, Univers i ty of Jfcryland, College Park,Ml. 207^2, DEA,

andInternational Centre for Theoretical Physics, Trieste. Italy,

and

Abdus Salam

International centre far Theoretical Physics,1 Triest« t I t a ly ,and

Department of Theoretical PhyBics, Imperial College, London, England.

KRAKARE - TRIESTE

July 1978

• To be submitted for publication.

** Supported in part by the National Science Foundation, under Grant Jo.GPi*3662I.

I. THE HEED FOE CHIRAL COLOUR

Tour-component quarkspossessing flavour and colour exhibit chiral

flavour gauge interactions. It appears surprising to us that it haa

essentially teen taken for granted that colour gauge interactions are

vectorial only and not chiral.

ABSTRACT

Within the context of basic left-right symmetry and the hypothesisof unification of weak, electromagnetic and strong forces at a mass level

SflO -10 GeV, relatively light "mass" axial gluons, confined or liberated,must be postulated. We remark that the existence of such "light" axialgluons supplementing the familiar vector octet preserves the successes ofQCD, both for deep inelastic processes and charmonium physics. Through thecharacteristic spin-spin force, generated by their exchange, they may evenhelp resolve some of the discrepancies betveen vector QCD predictions andcharmonimn physics. The main remark of this note i s that if colour isliberated, not only vector but also axial-vector gluons are produced inhigh-energy e~e experiments, e.g. at PETRA and PEP, with fairly largeeross-section. Distinctive decay modes of such liberated axial gluonsare noted.

A priori,there are several theoretical motivations for postulating

- 1 -

,2' - [SU(1t)A x SU(*0B] f l a v o l i r x

. or more generally [su(n)] with n ). k) to-

that basic colour gauge interactions are chiral Just like the flavour ones.But perhaps the most important one is this)introduction of chiral colourgauges {for. example,'

[sti(U)p x s u ( % J o o l o u rf 1

gether with the assumption that the quark chiral colour subgroup SU(3)L * SU(3)jis preserved as a good low-energy symmetry,permits a unification of weak,electromagnetic as veil as strong interactions to become manifest at a massscale as low as 10-10 GeV.3' Experimentally this implies that there could bedirect signature*of this unification already at Isabelle. By contrast,alternative unifying symmetries ' (e.g. SU(5)> 30(10), E, and E_) devoidof chiral colour, predict ultraheavy unifying mass scales >, 10 GeV.

As will be elaborated later, there i s nothing in . present loir-energy regime to exclude colour being chiral Just like flavour. ID factan underlying ehiral colour symmetry, by providing an octet of axial vectorgluqns 'tin addition to the familiar vector octet, may even help resolve someof the lingering discrepancies between predictions of vector QCD andcharmonium physics.

How ehiral colour SU(3)T x SU(3)_ cannot be preserved as an exactLi R

local syametry, since quarks possess mass. We expect that i t breaks at thesecondary stage of SSB to vectorial colour symmetry SU(3)T' _ ganerttinga massive octet of axial-vector gluons V(8) together with the familiar octetof vector gluons v(8J. in accordance with the low mass unificationhypothesis, the breaking of chiral colour must be at • themass level no bigger, thiin the breakdown o£ the. "electro-weak" •symmetrySU(2)t "x ufij . Correspondingly^ should expect a "relatively light" octet Ofaxial gluons with "masse!" which at the one extreme may be as Bmall as mearly 1 G«Vand at the other , periiaps as high as". 100 GeV. (By "mass" here,

we mean the Archimedes mass 5) which the gluons would seen to possessinside nadronic bags, just as constituent (p,n) quarks inside flavour »ingletbaryons exhibit Archimedes' masses ~300 MeV and b-quark masse»"~ 5 GeV.) Ifthe gluons are liberated, their outside physical masses would, of course,be higher than their inside effective masses - see remarks later.

The purpose of this note is two-fold: (a) to make some general

remarks regarding the consequences and the consistency of the hypothesis of

light axial colour gluons, whether they are confined or liberated. s.nd

(b) to point out that if axial colour gluons are liberated rather than

confined, they would exhibit unambiguous signatures for high-energy e~e

experiments, e.g. at PETRA and PEP. They vould be produced vith cross-sections

corresponding to electronic partial widths of order 100 keV to few MeV

and can be distinguished by their rather distinctive decay modes-

II. MANIFESTATIOHS OF CHIRAL COLOUR FOR CONFINED OK LIBERATED GLUONS

Within unified theories like [SU(n)] , quarks m»y be fractionally or

integrally charged. For the fractional charge case, the vector gluona are

necessarily massless . In this case, exact colour confinement is generally

postulated; for the integer-charge ease with necessarily finite mass gluons,

the confinement would only be partial, with coloured quarks and gluons

exhibiting the Archimedes effect 5), with different "masses" inside and

outside htdronic bags.

By "inside" mass ve mean the following. In a renormalizatde gauge

theory, with mass generation through SSB, one can define running masses u(q )2

q2

as functions of momenta q , fron renormalization group considerations. We

shall define "inside" masses (m±n) as values of y(q2) for q2 as I/H , where

H is the radius of hadronic bags of the order of a Fermi. For exact

confinement the outside mB.se {m t) is infinite; for partial confinement it

is finite. The precise link between mout

and m. , involving as i t does longindistance, possibly non-perturbative physics, is an unsolved problem. Semi-

quaatit*tinM». considerations based on the picture of a partially confining

pervious bag model have been offered, for example in a formula like 7)

(mquars'out **".-2\where a?' i s the Kegge trajectory slope (in GeV~ )

and is the inside vector gluon mass. In the sequel, for the case of

partial confinement we shall, for orientation purposes, use an ansatz

at . - m. m : r ~ — . Note that m. (from SSB) will depend not only onOut in 2ira iky In

particular (colour) multlpleta but also possibly on the flavour components

concerned. For example, m for (n,p) quarks is <v 300 HeV, while ( mi n ) b

i s & 5 GeV. Vith uy varying between 100 and 10 HeV, m -m. is of orderout in

GeV. Since, from ifro lav mass unification hypothesis sad the SSB

implied by it, a_riori, we cannot place sharper bounds on (m ), for axial

gluons, except that (mA) in range between nearly one and 100 GeV, we expect

that (m.) . would range between few to 100 GeV for the part ia l ly confined

integer-charge quark case. (Since from any SSB arguments we expect

a l s o t o b e >(™V)ouf'(mA}out

But irrespective of whether axial gluons are exactly or partially

confined, light axial gluons would generate an effective lov-energy axial

chromodynamics supplementing the familiar vector QCD. We remark that the

presence of the axial gluon octet with either very light running masses

V (<q.">2)<< a few hundred MeV or. very heavy y2( <q >2) » <q 2 > lrlll not

disturb the familiar successes of QCD. ' (Here <£<i > denotes averagt typical

(momentum transfer)2 for deep inelastic scaling, i .e . ,/q > > 1 OeV2.) This

is because in the case of vanishing p"A(q ), together vith vanishing ffquark^* )

one recovers unbroken chlral SU(3)' colour. In this case left and right quarks

couple to separate octets of gluona VT(8) and V,,(8) with eqi»l coupling constants.2 2

Hence all applications of QCD remain unaltered.(With 2 2 2

y ? ( q « <q ^departures from QCD predictions In respect of moments and structure functions

would only be of order uj/ K.1 ^ 4. 1*-)

For the case of heavy axial masses ji ( ^q.> ) >>ignore A r

one can effectivejj^the contributions of the axial octet altogether. Only vector

chromodynamics would be relevant with a coupling which is lA/51 of the chiral

colour coupling. Thie too leaves QCD applications unaltered. Thus from the

> , Sa'Qie o-bher handt

sueceeses of QCD,ve would infer that either

Vij(<1> } >* ^q. > —100 GeV .

) « 1 GelP or that

Exchanges of axial gluons xouli hovever lead to a B-piD-apin force in

the leading order In contrast to vector exchanges,where the spin—spin forceeffective

i s suppressed aa a non-relativiBtic effect, particularly for loWaxial masses.

The net strength of such a spin-spin force depends on (m,)> • With masses •

M./2-2 GeV the spin-spin force could Indeed be relevant for the splitting

of 3S1 and 15Q qq states, e.g. (*(3100) and n,(2800)) and also •'for. radiative

transitions. One must bear in mind,however, that in general.multi-axial ex--

changes would play an Important role, as would the multi-vector exchanges.

Such a spin-spin force may resolve some of the discrepancies vhlch appear to8Y

be developing between vector QCD predictions and charmonium physics . Acomplete calculation involving the contribution of the axial spin-spin forcefor the charmonium system i s yet to be carried out. We urge such » ca l -culation. This vould no doubt involve, in general, at least two nev parameters

- 3 -

corresponding to the range and strength of the new spin-spin force. We stress ,

however, that the full potential and signature of th is nev force vould easily

be manifest (in spite of the introduction of nev parameters) through a Joint

exploration of the speetroscopies of the eharmonium as well as of the heavier

bottomonium system! which should be available vithin the next few years.

To conclude! even for confined axial chromodynamics, one can findq\

signatures for axial gluons perhaps through departures from vector QCD

predictions for deep inelastic processes! but more promisingly through an

exploration of the spectroscopy of the heavy quarkonium systems. However,

their oiost spectacular debut wuld be for the liberated case which we consider

next.

The secondary stage of SSB is induced through fundamental BHltlplets•.

Only four such multiplets (related by discrete symmetry1 ) are needed:

A * (14,5,1,1), B = (1 , I t ,1 ,0 , C = ( im.&.D. H - ( l . l . l t . I ) . Assume th« pattern

of VEV: <A> • (a1 ,a1 ,a1 ,a l t) , B - (0,0,0.b^), <C> - ( e ^ c ^ . e ^ ) ,

<H>* (h.,h . h - . h j , where the entries denote VEV of diagonal elements.

Consistent with the low mass unification hypothesis, assume the hierarchy

\ » ( w V s> ci« bi< \ ana *t ~lai+ a^- The ac* le° f theBe

parameters is fixed by the combination c + a2 . 2 .

vhere

Note that b,

— . £ . 3 .

being the largest makes the right-handed charge (I gauge

particles Wjj ana a neutral gauge particle BR (see below) supertaavy leaving

an abeliaa U(l)_ invariant

I I I . LIBERATED AXIAL GLUONS

Consider t h e ease of In teger-charge quarks and l i b e r a t e d co lour . We

s h a l l mainly be concerned with the production and decays of

a x i a l gluons in e + e~ c o l l i s i o n s . The in t e rp l ay between the f lavour and

colour gauge p a r t i c l e s i s bes t exhibi ted through the neu t r a l masB matrix i

which we nov construct . .

Gauge mass mat r ix i To be speci f ic consider spontaneous breakdown of [SU(M] =

[SU(10A x S U ( M B ] n a T O U r x [sutlOc S U ( M , ; ] c 0 l o u r . Here A,B denote l e f t

and r i g h t f lavour and C,D l e f t and r i g h t colour in the space of bas ic fermions.

The primary breaking through VEV of 15 -p le t s of each SU(lt) reduces the symmetryu to 2 ) ' 3 > ' 1 0 )

SU(2)

U(l) couples to the appropriate diagonal sum of Wr and S {see bfllov).

The parameter h2 5 3h? + h? breaks U(l)'T X U(l)'_ to U(l)T . n giving

mass to the colour-singlet axial combination (SJ - S°)A/1" . The parajMrter

breaks cljiral quark colour SU(3) 5U(3)R to vector colour

and thereby gives mass to the octet of axial colour gluons VA(_8) ( while theparameter c, breaks left flavour SU(2)T and lef t colour SU(3). (and thereforevector colour SU(3) ) giving ma.sa to the octet of vector gluom V(8) (e.being the smallest of a l l VEV'a makes the vector octet VC ) the lightest apart fro*the photon). The parameter c^ breaks SU(2) x U(l)L to the diagonalabelian sum U(l) (ftnalogouB to (5)), vhile a^ breaks fl*TOur SU(a)L x SU(2)R

to SU(2) . A summary of these symmetry breakings is given below:

U(D.(VV

vhere SU(S)T are the left and right 6IH flavour subgroups and U(l)T denote4-j, L » R , L,R

the 15 generators of SU(4) „ colour. The gauge particles of SU(2)T ,,,

SU(3}' „ and U(l)' „ are denoted In the notat ion 1 1 of Eef.2 by(vr,W3)T _,

V(8) and ST _ , respectively, while their respective coupling constantsare denoted by g = g, fs • f and (f. C)T „ * fnr, (We are assuming that

L,K L,K S lp L,n 15

the unieonstant symmetry [sy(lt)]1* breaks in such a manner that lef t-r ight

symtietry is preserved at the primary stage of SSB , thus theradiative differences between gL and gR and ( f 1 5 ) L and ( f 1 5 )H are small.)

SU(3)L x SU(3) SU(3)L+H

UCD,

Here U(l) is the familiar abelian generator of su(2) x u(l),

Lt!(l)™, contains flavour and SU(3) ' colour generators appropriate to thecase of integer-charge quarks. (Uote that for the case of fractionallycharged quarks the above pattern of SSB applies with the exception thatc^ = 0.) We now present belov the consequences of this breaking patternon the neutral gauge mass matrix

- 5 -

Heutral elgenat&tea; There are BIX relevant neutral gauge particles

* SL B * n d UL R ' v h l c h m i x w l t h e a c h UL,R = 2

they denote the canonical ehiral gluon f ields, which enter into the photon.

We know the exact composition of the massless photon aa veil as the composition

of one heavy gauge part icle Z. . They are:

cos* 0)

(1)

- 3°)where tan* - (Ur/(3r+l})l/a (g/fg), ^ R ; C3r+l)~1/a ( ^ F w 3 - 3°) andBL,E E < 3 r + i r l / 2 (¥3 + V3r* S0)L>H. The ratio r = f^ /2g 2 i s related tothe veak angle by sin ey = 3r/(6r+2). Extracting out the two eigenttatea— photon and Z -we are left with i li x li symmetric matrix, vtdch in units of

(g£A) i s gtren Tjiyi

" 1 [.9r£h2+*2

15 15

In the above we have not exhibited correction terms of order (g It,.),

(ffL/f2) and C2(h2+a2) compared with unity.

-T-

Uy A =Here U y = cos* (^ + U R ) / t^ - 8ia« (^ + A ^ / t^1 and

Since (c +a ) iB determined by the mass of W* , there are three parameters

which determine the complexion of the eigenstates of (2). These are:

«x = c2/(c 2

+ a2), 5 2 5 hf/(c

2+a

2) and ^ E (h2+a

2)/(c2+a

2), where

2 2 2h ~ (3h1 + hjj). The general constraints on these ratios, in accordance with

the requirements of low vector gluon mass and low mass unification hypothesis,

are; ^ « l, ££ < 1 and 1 < ^ < ».

To exhibit some of the main physical consequences which arise due to

the presence of axial gluons, we shall assume (for illustration Only) the

following hierarchy consistent with the constraint mentioned above:

2 2 2 2This amounts to assuming that BL « m.' « nu « m- , where Z, and Zfi

UV U A *A ^

are the two "weak" neutral gauge eigenstates to emerge from (2) . .faete-for

guidance that such a hierarchy holds for masses aueh as n^ —10 G«T,

n^ ~ 30 GeV, m ~ TO GeV, m~ fclUo GeV,-though we must atresa t t a t - l a generalA A ' " ,

may he comparable to EL ~, few to 20 GeV on the one hand and to m^ ti 60 to 85

on the other • 1 Subject to the above i l lus t ra t ive hierarchy, the elgenstatea

of the mass matrix are approximately given by:

*

UA ss (cosa) UA + (sino) (A

2, w coeB C(-sina) UA + (cosa) (k^-k^lJS } + (sinB) ^ +©!;«")

-.inn {(-Bin*) UA * (cose) UA

- 8 -

The masses are: f C2

V16)

= {h2+a£)/(c2+a£) £ 1/2, m2 x {k sin2etf]

(1 +6f(E_)). For £ » 1, mz •* m Q =AS

with 2^ becoming much

heavier then

The parameters e , «:' and s." are small quantities given by

) 2 «' (g/f ) (m /m ) 2 C" (g/f ) (m An ) £

':

e 5 (m /m.,.)2, «' = (g/f ) (m.. /m ) 2 , C" = (g/f ) (m.. An ) £ • Subject to

the hierarchy (8), C' <v £," << G << 1. The coefficients of the small

components of the eigenstates are defined such that J ©•(£)[ sj |e | etc. The

angles aina and sing are given by;

slna~(g/f ) (mf. /»„ f , sing ~ a2/(h2+a2) . (5)8 V ZA

We are now in a position to observe four crucial features of this

complex of eigenstates,

(A) parity-violating component in u : Hie composition of the dominantly

vector gluon EL is the same as in Ref.l,except for one notable change. I t

has picked up an axial componient UA of order € = (m /IIL ) . This i s ,

of course, ». parity-violating mixture, which could show i tself in the hadron-

hadron system, e.g. i» the nuclear force. Let us estimate the effect. There

are two types of contributions.

violating amplitude is given by T'(tree)

i ) Firs t there is the tree eontrihution with a single Uy exchange

tetveen two nucleons. The contribution T' of this exchange to pari ty-

Vm^ ) (c* ) , vhere i i s the

colour octet Oij ynnent In the dominantly colour singlet nucleon (S < 1/10).

Thus T'(tree) ^ 10~5 GeV~2 for I L « 10 GeV and C • {m /m^ } 4 (1/10).

We see that this amplitude i s suppressed in large part due to the colour

Binglet nature of the nucleon.

i i ) Second, there is the loop contribution with double U . exchange.

This i s a convergent loop. Even if we neglect form factors in nucleon-gluon

vertex, the contribution to the parity-violating amplitude is T'(loop)»w

(a2/m? ) (m. /-a, ) • Given the mass ranges discussed above together with

-9-

a K> 0.2, we obtain T'(loop) < h x 10 GeV~ . If we use form factors,s o

T'(loop) will be suppressed by another pover of (m^ / I GeV)^ Thus, in spite

of the Sizeable mixing between U . and U,, i t s parity-violating effects for

colour singlet hadrons appear to be suppressed numerically to the level of (L , .

Parenthetically, we observe the following feature. Q^ark-antiquark

(or quark-quark) scattering can proceed, of course, through single [L, exchange.

The force thus generated will involve a parity-violating component due toU -U mixing- In case the qq or (qq) system i s inside a normal hadron,

2 2the parity-violating amplitude thus arising would be given by "[f / ( i , ) ]"( i . / i ) , where the bar denotes "inside" Archimedes' masses. Relative to

V A 2 2the parity-conserving amplitude ~ "[f / a ) ] " , the parity-violating amplitude

at the quark level is suppressed by the factor (m. /S ) ^ 10 for

JL "-10 MeV and SL j , 1 GeV.

I t is not clear how to detect such a possibly large ( "10 ) pari ty

violation for the qo_ and qq systems when they are constituents inside a

hadron, except possihly through the effects of the corresponding potentials

on energy levels of nuclei. At any rate, if £ . were larger than 3 GeV, theA

effect would be rather small even a t the quark level .

(B) Leptonic coupling of the axial ffluon U : The state U, is dominantlythe axial colour gluon [} , However, i t necessarily couples to leptonic eeand Jjp currents through the small components (Af-A-)/ V? , B as well as themore important component U . (Uote that TJ contains the vector flavourcomponent (A + A_)/ /? of an amount sin^i «; (g/f ) .) I t s coupling toleptons i s given by

where

and

2|e2/f I ( ^ An )8 V UA

(6)

(Ta)

\

-10-

17) 2 2m^ >> my

The factor 2 arises by substituting "'' g «j 2e. If E L >> m,. > we see

A Athat the vector coupling will dominate over the axial-vector coupling. Note

,that the small but finite leptonic coupling of U is a direct consequence

of the gauge nature of the basic theory as well as of the photon being

generated through SSB so as to carry flavour as well as colour components.

The coupling (6) would lead to a leptonic partial width given by;

•* e+e") GeV) (75 (8)

If we take {BL /n^ )" «s (1/2 to l/lO), m^ a 30 GeV and (f^/lnr) * 0.2 atV^ A A

HL , we get F(U -+ e e") S (100 keV to 3 MeV), which re la t ive ly speaking, i s^ A A

r i ther l a rge .

(C) Decay and production of the axial gluon U : The allowed decay modes

of U with the corresponding orders of magnitude of the amplitudes are

listed below:

Amplitude

normal hadrons "V A

<-* e " e + , u~V+ i hadrons + y (see Ref. 5)

(9b)

Uy +(ml,#, KK, 3TT or (u+n) ©(s t rong) )

L-» e~e , u~M • hadrons + y i e t c . (Ref. 5) .

(9c)

U —» q + 9(Btrong) ( i f tt^ > 2 m ) (9a)

L.v + mesons (see Ref.18)

-11-

Here we have assumed that the vector gluon U is lighter than the axial gluon

if in accordance with our previous discussions. We have in l is t ing the above

decay modes taken into account the faeta that (i) I = 0 for U and CL»

(i i ) C = -1 and +1 for U and UA, ( i i i ) ^ = 1" and 1+ for u and UA> (iv) they

are both colour octets but flavour singlets a^d (v) both a and $ have Stl(3)

singlet components. In addition to the decay modes l is ted &bove» i f the

axial gluon tf has a mass more than twice that of the charged vector gluons v ,~ 191 + -

i t will decay through i ts U component ' into a pair of TV . The2corresponding amplitude is of order2) , which is thus suppressed

relative to (9c) and (9d). We therefore expect mftasa* permitting the decay

modes (9c) and (9d) or, at the very least (9b),to be the dominant decay modes

of the axial giuon u . As long as a modest Q value (£,fev hundred MeV)

is available for the decay modes (9c), we expect that the width of U^

would be (conservatively) greater than 10 MeV, but perhaps as large ae 100

to a few hundred MeV. Taking r(UA -» e"e+) % 100 keV to 1 MeV, we thus

expect leptonic branching ratio of UA to l i e between nearly 10 and 10 .

Note that a major advantage of producing the axial gluon U A is

that it in turn becomes a dominant source of the vector gluon ffy and possibly

also of quarks and antiquarks. (Decay modes of U y l*fl of quarks are

l i s ted in Hefs.5 and 18,respectively.)

Referring to the production of U , i t should eventually be produced,

of course, in high-energy hadronic collisions in association with other

colour octet objects. But associated production cross-sections of such

heavy objects would presumably be much below the level of T production.

Fortunately, due to the leptonie coupling of U of order 2(e /f ) (ny,/**, ) t

which yields a leptonic part ial width r(U, •* e"e+) « 100 keV to few MeVA

(for m. a 30 GeV, see Eq..(8)), we expect that if would be produced withA - +

a fairly decent cross-section as a resoiaint particle in high-energy e ecollision. In other words, if DL, l ies between 10 and 1*0 GeV, PSTHA and PEP

A v

would be ideally suited to produce the liberated axial gluon U. and there-A

by the vector gluon U as well as possibly liberated quark-antiquark pa i r s .

What is striking is that i t is very difficult for any other part icle

we can think of, to mimick the pattern of decay modes l is ted above. A weak

gauge 2 -like part icle would in g»aeral decay to leptons and hadrons with

similar part ial widths and,mast important,neither a. Z - l ike part icle nor a-12-

g.q resonance involving either old or nev flavours would have a. special

affinity to produce the vector gluon U via i t s decay modes. Thus once the

axial gluon U is produced in e e collision ( and i t ireuld have to be at

the appropriate energy if the idea of liberation is correct), i t would be

difficult to identify this particle vith any object other than the axia.1

gluon UA>

In summary, the presence of axial ehromodynamies with either confinedor liberated colour is important for low mass unification. Signatures forsuch axial chromodynamics would be apparent most promisingly fromexploration of the spectroseopies of both the charmonium and the bottomoniumsystems. Electron-positron accelerators, e.g. PETRA and PEP or conceivablysuccessors thereof, give the best promise for producing the liberatedaxial gluon if, . Discovery of liberated axial gluons would make chiralcolour and simultaneously liberated colour compulsive concepts in particlephysic a,

We thank Victor Elias and Subhash Rajpoot for helpful discussions.

-13-

REFEEENCES AHD FOOTNOTES

1) J.C. Pati and Abdus Salam, Phys. Bev. D8, 12^0 (1973); Ibid. Fhys,Rev. DIP, 275 (1971*). Flavour «—» colour discrete symritotry, for

the basic Lagrangian is motivated in the first paper and le f t *-» rightdiscrete symmetry in the second paper.

2) J.C. Pat i , Proceedings of the Second Qrbis Scientiae, Coral Gables,

Florida, January 19T5 (pp. 253-256);

J.C. Pati and Abdus Salam, Phye. Letters 58B, 333 (1975).

3) V. Elias, J.C. Pati and Abdus Salam, Phys. Bev. Letters 1*0, 920 (197B).

1*) H. Georgi and S.L. Glashow, Phys. Rev . l e t t e r s 21> ^38 (197*0;

H. Fritzsch and P. Minkowski, Ann. Phys. (HY) £3_, 193 (1975);F. Gursey and P. Sikivie, Phys. Rev. le t te rs 36, 775 (1976)IP. Ramond, [fuel. Phys. BllO. 2lU (1976).

5) J.C. Pati and Abdus Salam, Proceedings of tbe 1976 Aachen NeutrinoConference (pp.589-629, especially Sec.V);

J.C. Pati and Abdus Salam, ICTP, Trieste, preprint Ic/77/65(unpublished).

6) K.S. Mohapatra, J.C. Pati and Abdue Salam, Phya. Rev. EL3_, 1733 (1976)tE.N. Mohapatra and J.C. pa t i , Phye. l e t t e r s 63B. S$i (1976).

7) A. De Rujula, R.C. Giles and R.L. Jaffe, MIT preprint (1977).

8) In particular, s e e G. Feinberg and J . Sueher, Phys. Rev. Letters 1£,

17^0 (1975);J.D, Jackson, Proceedings of the EPS Meeting held at Budapest(July 1977)*, K. Gottfried, Photon-Eepton Symposium, Hamburg (August1977), and J. Sueher, Review to appear in Reports on Progress inPhysics, university of Maryland, Technical Report (1978),

9)

10)

In this note we have not considered nev features brought about (a) inZveig-like selection rules and (b) in Jet phenomena, where chargedaxial gluons with C ' + l ^ould jnark their presence.

For different complexions in the breakdown of SU(2) x SU(2)_ x U(l). *t u R L

U(1)R without chiral breaking, see Q. Shafi and Car. Wetterich, Puys.Letters Jjm, 65 (1978); V. Elias, J.C. Pati and Abdus Salam, Phys.Letters 73B, 1+51(1978); J.C. pati and S. Rajpoot, ICTP, Trieste,preprint IC/78/1 and Q. Shafi and Chr, Wetterich, University ofFreiburg preprint (June 1978).

-J.il-

CURRENT ICTP PliEPMHTS AND INTERNAL KJ3FORT3

11)

12)

13)

lit)

15)

16)

17)

For canonical couplings of the gauge fields see the second papers ofHef.1 and Ref.10.

A. Davidson and J.C. Pati , in preparation.

A natural realization of the f i r s t stage of this hierarchy, i . e ,of tHe!

^k >> ' ° i ' a i l l l i ' CSJ1 'be sb0WI1 t o arise through a minimum/potential (Eef.12).Whether the subsequent stage! e.g. c, + a, >> c f 0 can "be realizedthrough the radiative or non-perturba.tive origin remains to be examined.Notwithstanding the delicacy of the Higgs system, we shall proceedtentatively assuming such a hierarchy for phenomenologiea.1 purposes.

2In gene ra l , W ' s may get mass almost e n t i r e l y from a r a the r

2than a

In the charged sector,charged vector and axial vectors will mix with W~

L(see Hef.l). They •would also mix with each other to an extent similar to

U -U mixing as discussed in the text with similar consequences.

Expressions for the masses of Z. and 2 for general 5 aregiven in the paper by J.C. Pati and Si Rajpoot, Eef .10.

If ve had taken for generality <B> = (b1,b1,b1.b1)), the parityviolating parameters £ and £' given in the text would be multipliedby a factor (c^-b?)/(c?+b?). In defining these small parameters, we

regard 9(g/f ) &(t^Jts). note that for sin2flw = l A andt^Jts

ss 0.2 (at the physical vector sluon mass) we have g = (3/2)

Ic/78/19 * S . I . OABHAKOV, N.I . PTATOV, B . I . BAZNAT and D.I. SALAMOVi S«lf-irfT.REP. consistent deacription of the iaospin nixing.

Ic/78/20 * 0 . GHERMAN and h, SALIUi Kodela for 3U(N) 1 5U(N) aymmatry TweakingINT.REP. with extremum constraints .

IC/78/21 • R.K. COPTA and K.V. SUBBARAMi Nuclear fusion.INT.REP.

10/78/22 *INT .REP.

IC/78/23 *INT.REP.

ic /78/24INT.HEP.

3,3 . AHMADi The iterative R-matrix method for the acourateation of nuclear reaction cross—sections.

A. AMUSA and 3.K. SUAHMA: On improved variational otlaulitlon* .}involving ttuasi-deganarate intrinsic Haniltonian* in the nuoleue * C».

R.K. GUPTA and T.K. QAMBHIHi HasB-asymnetrv a« ft ool l»otiv« 00-ordinatt in tlne'-dapendent H«rtrae"Foolc oftiaulation* for heavy-Ionool l io ions i A

Ic/78/25 * B.3. LE£i Keliaal ordering In the Jahn-Teller ao-operative phaseINT .REP. transition.

IC/78/26 3 .3 , AHHADi The application of ths iterative R-natrix aethod to theraaotion.

IC/78/28 *INT .REP.

10/78/29INT .HEP.

IC/78/30INT.REP .

L. 3ATPATHY and R. NATAKi On the exletenoe of bound neutrel nuolal .

T.K. QAMBHIR and R. PAHTHASARATHTi P«rtiol« hol« deeorlption of5°Co with rea l iu t io interact ion.

H.I . ABD-EL-GAWAD, A.B. KHALIL and A.A. SELIHt Hon-linear qs h i f t s and explosive i n s t a b i l i t i e s of two modified ordinary nono-chromatio waves.

18) See. J.C. Fat i , Abdua Salam and S. Sakakibara, Phys, Rev. Letters 36^

1229 (1976), and J.C. Pati and Abdus Salam. ICTP, Trieste, preprint

IC/78/5U (to appear in Bucl. Phys,) for a l is t ing of quark decay

modes.

19) I t cannot decay through i ta dominant U component into y V~ because

of charge conjugation plus parity invariance.

20) A weak 2° in general would also lead to parity-conserving forward-

backward asymmetry in e"e+ •+ u~v+ through interference between vector

and axial-vector couplings, which is prominent (£15$) over a wide

range of centre-of-mass energy £ (m Q /2) . I t is easy to see,

by using Eq,(6),that U. exchange by contrast leads to F-B asymmetry,which is much too low {« 1%) for >- 10 l G e V ' a n d

At h a t even f o r E _ , a m , , ± r ( U . ) i t i s a t most of o r d e r I",.

IC/78/31 • H.D. DOEBHEH and J.-E. WERTHi Olobal properties of ayeterne auantlaedINT.REP. via bundles.

Ic/78/32 P. CALOCERO and A. KEGASPBRISi Conservation laws for olaaiee o"f~noo-linear evolution equatione solvable by the spectral transfora.

IC/78/33 * 3,0. LIMi Euclidean massive apin-3 field wbloh ! • X«rkovi«n.INT.REP.

IC/78/35 L- PONDA, 0 ,0 . OHIRARIlI, C. OMSRQ, A. RIMINI end T. HEBEHitheory of sequential decay processes,

* Internal Reportsi Limited dis tr ibut ion.THESE PREPRINTS ARE AVAILABLE FROK THE PUBLICATIOKS OFFICE, ICTP, P . O . BOX5 8 6 , I-341OO TRIESTE, ITALY. IT I S MOT NECESSARY TO WRITE TO THE AUTHORS.

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IC/78/36 *IMT.HEP.

lc/78/37

IC/78/38

Ic/78/39 *IKF.REP.

IC/78/4O

IC/78/41

IC/78/42

10/78/43 •in .REP,

S,P. CHIAi An alternative interpretation of T(9.4).

Z, HORVATH and L, PALl.Ai Spontaneous compactification and "nonopoles"in higher dimensions.

B.L. TEIHBERGi Hypothesis of thermalization of high energy badronproduotion process,

W.A. SAYBDi Monopole solutions for strong gravity coupled to SO(3)gauga fields.

If .A, SAIEDi Exact Bonopols solutions for 30(3) gauge fields ooupledto f-g theory.

M.A. MARKOYi On the stability of elementary black boles.

P.V, QIAQDIHTA, M. PAHRIKELLO ANDH.P. T03Ii Polaritonio spectraof ionio conductors.

P. BtTDIHIi On oonfornally oovariant epinor equations. (Preliminaryversion)

IC/78/44 ABHJS 3ALAJJ and J. STHATHBEEi Hlggs oouplingm and esyaptotio freedom.

IC/78/45 •IHT.REP.

IC/78/46

IC/78/47 •IFT.HBP,

IC/78/48

IC/78/49

IC/78/50

I0/5O/5X •1ST .HEP.Ic/78/52 *

ts

10/78/53

lc/78/54

IG/7«/55IOT.HBP.

C.K, CHEW and K.X. PHUAi Suppression factor in tbe leptonlo andhadronio decays of the T family,

J.B. HSMHIQi O-fltruoturea and apaoe-time geometry - Ii Oeo»etrioobjectu of higher order.

B,0, 3IEBARTH add A. ABDEL-HAFEZi On the bound itatee for higher«n*ular noaenta.

7.B, PASEMAIfflt Oenersl vector field rsprasantationsi A geoaetriatool for quantization.

3. SAJPOOT and M. SHTQBRi SU(3) 1 U(l) low-energy eymmetry vltbinthe unifying 3U(4)p x 3U(4)C gaupe group.

E. LEJTDVAIi Weak neutral current effeots in e aT., x Un gauge model.

AX inoluaivereactions in the s u |

B.O. SIIHARTBt On the phase shifts for r type potentials.

B.O. SIDBARTHi A reourrenoe relation for the pheee shifts ofh(r>).e*p(-br) type potentials.

3.C. IiIMt Buolideen and Klnkovelci epaoe fornulatione of lineariaedgravitational potential in varloue gaugea.

J.C. PATI and ABSOS SALAKi Liberated quarks and gluone In e"e+

Jets and beao^unp experioents.

8.A. TAOIHOV and I .T, TODOROTi A geonetrio approaob to the solutionof oonformel invariant non-linear field equations.

IC/78/56 * V. JCUMAHi Sagregation at alloy surfaces.IWT.RBP.lc/78/57 * G. ALBERT, C. ALVEAIi, E. CASTELtl, P. POROPAT,_M. 3B33A, L.P. ROSAINT.RKP. and 2.D. THOMEi Reaonanoe3 in p*n system from pB data.

IC/78/59 * C.B. CUBES, J. GOEDES and J.M. MALBOUSSOHt Eleotromapietio absorptionIHT.REP. in antiferroraagnetio chromium.IC/78/60 * C.B. CUBES and A. DA S. RAM03i Ranan scattering of l ight off a super-IKT.HSP. conducting alloy containing paramagnetic impurities.

IC/78/63 V.V. DODONOV and V.I. HAN'KOt Integrals of notion of pure tadmixed quantum systems.

IC/78/64 3. RAJPOOT1 Luft-right asymmetrio modal for weak and eleotromagnetiointaraotiona.

IC/78/67

10/78/68

IC/78/69

10/78/70IHT.REP.

IC/78/71

IC/78/72

IC/78/73

IMT.REP.IC/78/74IHT.REP.10/78/75 * The Bixth Trieste conference on particle physics - 26-30 June 1978.HPT .REP. (Contributions) - Part I .

* The sixth Trieste conference.., . - Part I I .

P. BUDIlfli On conformably oovariant splnor field equations.

M. SINGES 1 3U(4) 1 U(l) and the origin of the Oabibbo angle.

V. de ALFARO, 3. BTTBIHI and a. PDHLAlTi Non-linear cmodels andolasBioal solutions.

* I .A. SAKUABi An angle-dependent lower hound on the solution, o fthe elaatlo unitarlty integral and a ne* uniqueness oonditlonresulting from i t .J.C. PATI and 3 , HAJPOOTi What could PITHA and ttP «xp«riment« uunravel given the parity violation observed at 3LA0?

I. OUIAS r and E.E. RADSSCUi Higher aultipole polar l i a b i l i t i e s ofhadrons froa Compton scattering amplitudes,

* 0 . BAHELOff and M.A. VAHAZXSi On the gfcoet prosiest in a higberderivative Tang-Mills theory,

* A.I. MEHTAi On the structure of sneotic 3^ arid SL phases of HiBPA.

IC/78/76IBT.KBP.IC/78/77IDT .REP.Ic/78/78IHT.REP.

IC/78/79

• V. KAtrsHAI, and K.P, KHAHNAi A new universality and the non-leptonicdecays of CC hyperon,

• C.B. CuHBtT and R. HOTAt Raaan eoattering of light In sntiferro-magnetio ahromiun.

T. BAHME3 and O.I, GEAKEOOTi Orasemann functional 3chr3dingerequation! An application to perturbation theory,

-ii--iii-