I + tl[ll I +;~k',ll '-J | l¢+'J [Ik"ll 3

PROCEEDINGS SUPPLEMENTS

Nuclear Physics B (Proc. Suppl.) 2513 (1992) 142--151 North-Holland

TIts'. ODDI~RUN - PAST, PRESI~NT A N D F U T U R E

Basarab NICOLESCU

Division de Physique Th~'ique*, IPN, 91406 Orsay Cedex and LPTPE, Universit4 Pierre et Marie Curie, 4 Place Jussien, 75252 Paris Cedex 05, Frmice

After presenting some short historical considerations concerning the evolution in time of the Odderon approach (from asymptotic theorems to QCD), we di:~.-uss the experimental finite-energy effects induced by the presence of the 0dderon. The general agreement with the present experimental data is also briefly discussed. The last part of the talk is devoted to the predictions of the Odderon approach at LHC energies. We expect new physics to occur at LHC energies. We will therefore present strong arguments in favour of the adoption of both pp and l~p options at LHC.

1. I N T R O D U C T I O N

The Odderon approach became popular after the

discovery, in 1987, of a large p~P value at the CERN

SppS collk!er I and it was widely discussed in the lit-

eratuz~. I will therefore not give in this talk historical

details of the Odderon approach (a short description of

its long and complex history can be found in Ref. 2).

Also, I will not present here the formalism and the phe-

nomenological consequences of the maximal o d d ~ n

approach, because they were already discussed by E.

Leader s, B. Nicolescu 4 and P. Gauron s at the previous

Blois Workshops.

In this talk I prefere to concentrate upon some

basic qualitative aspects of the Odderon approach lead-

ing to the conclusion that one can safely expect new

physics to occur at LHC energies. In order to test this

new physics both pp and pp options at LHC have to be

adopted.

2. S H O R T H I S T O R I C A L C O N S I D E R A T I O N S

I present in Table 1 a list of some relevant dates

and references from the point of view of the Odderon ap-

proach. Of course, a bibliographical selection is always

a dangerous exercise and involves a somewhat subjec-

tive choice. However, what I wanted to point out in

Table 1 is the more and more pronounced link in time

between the Odderon concept and QCD : in our days

the Odderon (or, at last, the perturbative Odderon)

naturally arises in QCD (LLA) as a compound state

of 3 reggeized giuons. Recently, by studying the con-

formal properties in QCD, we gave a semi-quantltative

argument is indicating that the intercept of the Odd-

eron in LLA is probably bigger than 1. We therefore

expect at very high energies important expenme,tal ef-

fects, induced by the presence of the Odderon. The fact

that there are already quite strong indications of Odd-

eron effects at ISR and CERN-collider energies is, of

course, very encouraging.

* Unit4 de Recherche des Universit~s Paris 11 et Paris 6 Associ~e au CNRS

.~. Nicolesc~: / Odderon -pasL presen~ and f,';ture 143

Le~. me go backwards in ~ime ir~ -c,r*{er -;o make

r e m a r k s •

i) Stimulated by the extraordinary ~limate gener-

ated in 1972-1973 by the discovery =t ISR of increasing

pp total cross-sections and also stimulated by exciting

discussions with Andr~ Martin and Jean-Louis Basde-

vant, Lukasznk and I thought that the OaT p increase is

just a sign of a very general property of "maximality"

of strong interactions e. By "maximality" I understand

here the following simple, but powerful statement : ev-

erything that can happen, happens. The analytic self-

consistent saturation of axiomatic bounds becomes, in

such a way, a dynamical principle. There are many con-

sequences of this prihciple. One of them is the maximal

Odderon.

ii) One may think that the maximality principle

involves early nsymptoticity. This statement is simply

wrong. The axiomatic bounds are used only as bound-

ary conditions as s --, co for the scattering amplitudes.

In fact, there is a very delicate balance between the non-

asymptotic (Regge) contributions and the asymptotic

contributions. The Regge contributions are dominating

at low energies and become smaller and smaller at high

energies, while the asymptotic contributions are small

at low energies and become bigger and bigger at high

energies. This delicate balance generates spectacular

finite-energy effects, which are generally very different

from the asymptotic effects.

Let me give just one example. Let us suppose that

A~ --, --co as s --, co, where

However, ~Lv > 0 at the ex~e,qmental Dre-iSR er~er~es,

concludes that A~ must go through zero and change its

sign just beyond ISR energies. In fact, this feature of

Act was already present in our fLrst 1973-1975 papers e'7

and became much later indirectly contlrmed by the high

p~ UA4 value 1.

3. EXPERIMENTAL FINITE-ENERGY EF-

FECTS I N D U C E D BY THE PRESENCE OF

THE ODDERON

In this section, for the sake of generality, I will con-

sider all kinds of Odderons, not only the maximal one.

By "Odderon" I mean a J-plane singularity near J = I

in the odd-under-erossing amplitude F - . The Odderon

is the natural companion d the Pomeron which cor-

responds to a J-plane singularity near J = I :r- ~ the

even-under-crossing amplitude F+. Both are exw~ssed

dynamically in te~c~s of multigluon exchanges.

Taking into account that

F , , = F+ + F_ and F~, = F+ - F - (2)

we can define ,wo important cases :

a) There is no Odderon, i.e. F - = 0 at high

energies, leading to Fpp = F~p. The physical meaning is

that pp and/~p scattering are identical at high energies.

Let me call this case the "symmetrical" case.

b) The Odderon is present, i.e. F_ ~ 0 at high

energies, leading to F~,p ~ F~r. The physical meaning is

that pp is di~erent from ~p scattering at high energies.

Let me call this ease the "asymmetrical" case.

Ao =o~? - ~ P . (1)

144 B. Nicolescu / Odderon -past, present and future

TABLE i . c ~ n e # r n ~ n ~ ~ ~ d d ~ r a n a n ~ e n ~ c ~ , ~

Year Ref. C o m m e n t s

1 9 7 3

1 9 7 5

1 9 7 5

1980

1984

1985

1987

1 9 8 7

1 9 8 7

1988

1988

1988 -1990

6 First paper on the Odderon as a con- sequence of the maximal;ty principle

7 The only model that predicted a high value of p~P at CERN-eollider energies (seen 12 years later). Derivation d the derivative relation for the case J = 1 in F - .

8 The case of a simple pole at J = I in F_ was considered (later identified as 3-gluon Odderon in QCD). The name "Odderon" was invented.

9 The Odderon naturally arises in QCD {LLA) as a compound state of 3 regge- ized gluons

10 Minimal Odderon-pole linked to 3 gluon exchange, leading to a quantita- tive prediction of A(d¢/dt) # 0 at ISR energies

11 Experimental discovery of A(d~/dt) 0 at vfs = 52.8 GeV in the structure region (itl " 1.3 Geg 2)

1 Experimental discovery of a high p~P value at vf~ = 546, in agreement with predictions made in 1975 (ReL 7)

12 Discussion of the Odderon interpreta- tion of the UA4 pPP datum (Ref. I)

13 A dynamical quark-model interpreta- tion of the Odderon

14 A rigorous extension of the maximal Odderon approach at t ~ 0

15 Multiparticle unitarity indicates that probably the slope b(s, t = - 0 . 0 2 GeV 2) crosses over the slope b~p(s,t = -0.02 GeV 2) above the ISR energies

16 Tevatron data - E710 Collaboration. High values of aT, as expected by ~1, most all threshold models, are excluded

t n o ~ l O ~G1h l . ~ u 1 ~ . 1 1 1

-1991

end 20,21 1990

De i f i ed comparison of the Odderon approach w{-~,h -~F-: ~,he ex'sting expei~ m e n ---:- ~.]--- dae~

t ~ D _ _ _ ~ . . . . 1 1 _ . _o . . . . . 2 - - i . . . . . . . . . t • I ' L l ) 1 ) ] r l l i l c [ I i ~

QCD of the Odderon problem

Theoretical challenge for having both pp and pp options at LHC

T A B L E 2.

CrT

Gel/GT

Maxima] Odderon (GLN) approach pre-

dictions 17 at V~ = 17 TeV.

o~T p ---- 121 rob, ~T ~' ---- 127 m5--*

~OT = ~T P -- ~ T p = - -6 m5

o ~ = 27 .4 rob, o ' ~ = 29 .6 mb ..~

A ~ , I = ¢r~e ~ - ~r~ = - 2 . 2 mb

(~ , t / ¢T) ~p = 0 .227 , ( ~ , i / ~ 7 , ~ TM = 0.233

A(~,dUT) = (#,dUT) ~p - (u,I/OT) ~ =

--0.006

p~P = 0 .25, f ' ~ = 0.05--*

Ap _-- p~P -- pPP = 0.2

Mean-slope in the region 0.01 _< Itl

0.16 GeV 2,

b,~p = 29 GcV -2, bpp = 30 GeV -2

I~bl- - 1 G~V -2

B. Nicolescu / Odderon --past, present and future 145

in the ~ymmet r ic~ c~e ~most MI ~" . . . . " ~

. . . . A a . I give -~-me ex~mpl~ : i t % , - ~ t - r - -

i) For a large class of Odderons, Ao" - , const, or

]Ae[ -'~ co , as s "-* oo, i.e.

Aa#O, at TeVenergies. (3)

Of course the most spectacular case is A a < 0, which

has crucial dynamical implications. One can note that

an asymptotic symmetry is still generally kept :

~ P / ~ F - - , 1 , as s--,oo. (4)

ii) Similar finite-energy effects concern d~/dt :

( d a ) f d a ' S " (da~ pp A ~ =k~) -k"di/ #0" (5)

One expects spectacular differences A(da/dt) at TeV

energies. It is important to note that the ISR results n

at v/a = 52.8 GeV are the first experimental indica-

tion in favour of (5). Let us also note the asymptotic

symmetry

( da / d t )PP , 1 , as s --, co, (6)

in thc sy~actr ic~j case p ~ 0 as .s ~ c,~ ,~,~d :P~ --/~'~

T h e case p --, 00 is, o f course, un in teres t ing in

the light of present experimental indications. Let us

therefore consider the ease p -* const. (with different

constants for pp and/~p scattering). One thus expects

Ap = p~P - pPJ' # 0 at TeV energies. (9)

For example, if Re F - < 0 it is seen from eq. (8) that

the Odderon pushes p~P up and f P down, i.e. Ap >

0. This is precisely the case corresponding to the UA4

data 1. Moreover the phase of the F_ amplitude directly

forces Ae < 0 at these energies.

A pedagogical way in looking for all these effects

in o~nnection with general principles is to consider the

t~y model of Cornille 22, valid at t = 0, s --* co :

, f /2 1 #+ F+(s)-~ i G , [In(sO )] , 00}

F-(s) --* - C - s [ l n ( a e - i ' q ' ) ] ' - , (11)

where an overall scale factor is assumed.

Analyticity, unitarity and positivity imply

a* le.~st inside the diffraction peak. ~+_<2, ~ _ < ~ + / 2 + 1 , ~ _ _ < f l + + l . (12)

iii) Very interesting finite-energy effects concern

i.e.

Re F(s , t = O) (7) p(8) = Im F(s , t = O) '

f p = ReF+ + ReF_ and ~ P = ReF+ - R c F _ ($) lmF+ + ImF_ lmF+- ImF_"

The (/~+, B_) domain allowed by general principles

is shown in Fig. 1, where the behaviour of Aa and

p in different regions is also indicated. The maximal

Odderon corresponds to the point (B+ = 2, B_ = 2).

Different classes of other possible Odu~rons fl_ < 2

can be directly explored on Fig. 1. I think that the

most interesting region from the point of view of QCD

would be proved in future to be the upper-right triangle

(~+ <2, q_ >1, ~÷ >~_).

146 B. Nicolescu / Odderon - pas t , presen t and fu ture

i . i i i J i i i i . J i i i i i

i ) / , , / r /s f

/ / i , / i /

=L J I I I I A , ~ I

~, ,~- - 7 - ' ]

S / I 2

,'p--, S /

is÷

Fig. 1 CorniUe's plot

4. C O M P A R I S O N W I T H E X P E R I M E N T A L

DATA

Detailed considerations concer:dng the compari-

son of the Odderon approach with the experimental

data (including the Tevatron data pub:ished before this

Conference) were made elsewhere lz'17 and there is no

need to repeat them here.

I will just quote our general conclusion : the max-

imal Odderon (GLN) approach is the only existing the-

oretical picture which fits all the present elastic p p a n d

#p data, including A ( d ¢ / d t ) at V~ = 52.8 G e V a n d

p~P at q~ = 546 G e V . This conclusion is not changed

by the interesting Tevatron data presented at this Con-

ference by the ET1023 and CDF 24 Collaborations, as

cxplained below.

A first remark concerns thc CT Tevatron datL I

hope that it is obvious to everybody that, because Act

is expected to he small at these energies, the Tevatro~z

absence : they check just the rate of increase of i m F+.

So the real question is : are the Tevatron data still com-

patible with a In 2 s growth of CT ? A negative answer

to this question was given at this Conference 2s, but it is

in fact based on hidden assumptions and on a particu-

lar way of defining the procedure of fitting the data. It

therefore has no general validity. (Note also that a In s

fit leads to Regge intercepts 2s which have to be rejected

on physical grounds). In fact a ln~s growth predicts

CT ~ 76 -- 78 rob, the maximal Odderon case being

just a particular example of this chLss of models. So,

the Tevatron data presented at this Conference, even

if they look rather low, do not exclude a In 2 s growth

of CT- What they really exclude is the entire class of

threshold models (with one exception2S), which predict

large and even huge o" T at these energies. On an ex-

perimental level, it would be very important to clarify

the p - b - o" T correlations, even if they would lead

to larger experimental error bars. In particular, the

t-dependence of the slope b(f) is crucial in getting ~T.

The experimental quantity which is more relevant

for the Odderon ease is p~P. We predicted p~P = 0.22

at V~ = 1.8 T e V . In Fig. 2 we show our prediction

together with the four p-data sets of the E710 Collabo-

ration (data read from graph 2s) :

pl = 0.215 4- 0.108, P2 = 0.120 -I- 0.173,

p3 = 0.027:t:0.104, p4 = 0.200-1-0.177. (13)

It is seen from Fig. 2 that our prediction is compatible

with sets 1, 2 and 4. The set 3 corresponds to very low

values of p, which are in fact much lower than those

predicted by dispersion relations (with or without the

Odderon). Moreover, the overall p-value 23, computed

B. Nicolescu / Odderon -pasL present and future 147

~A

A A h ~ U ~ V

0.32

0.24

0.16

0.08

-0.08

I I i

I 2 .~ -I | ) a | a .~1 n l l m i ; ~ r

Fig. 2

GLN prediction of p~P at v ~ = 1.8 TeV (dashed line) as compared with experimental data 23. The domain covered by the UA4 data I at Vr~ = 546 GeV is also shown.

under the assumption that the four sets are uncorg-e-

lated,

p = 0.126 4- 0.067 (14)

is almost entirely determined by the sets 1 and 3, cor-

respor, ding to almost incompatible p-data (see Fig. 2).

It is clear that I can not draw any definite con-

clusion concerning p : the Tevatron data are ~either

against nor for the Odderon approach. We have *o

wait for the precise UA4/2 experiment planned 27 at

Vfs -- 546 GeV. One can hope that similar experiments

would be done in the future at Tevatron energies.

Let me also mention our prediction ~or

(~e,./oT)~ = 0.223, at V~ = 1.8 TeV (15)

co.npared with ~he experimental value reported by the

E?IO Collaboration ~.~ this Conference 2a :

(~,/oT)~P., = a 224 + 0.012. (16)

5. C O M P A R I S O N W I T H O'S 'HER T H E O R -

E T I C A L A P P R O A C H E S

I will consider very briefly just two appro~-hes.

The Cbeng and Wu ~ r o a c h 2s is typical for U.~

synunetrieal case. Having F - = ~ at high energies, it

t, 48 .~. Nicolescu / Odderor~ -past, preseat and future

the other da*.a.

The Donnaehie-Landshoff (DL) approach l°ag,

hke the maxiwal Odderon (GLN) approach, belongs to

the abymmetrical class of models.

There ,,,re a lot of similarities in detail between the

DL and GLN aplm~,hes. I will mentiou here only the

main similarities :

i) Both approaches ta~ke into account all the pre-

sent data from v/~ ",, 10 GeV ap to v~ " 1.8 TcV,

including the cosmic ray data. Our common philosophy

is that all data have to c o , t r a i n all the c,,~atributious.

(H.-~wever, an elementary rule has to be respected in the

GLN case : the asymptotic contributions do not have

to be completely determined by the low-energy very

precise data).

ii) Another important con~mon feature is that

both DL and GLN approaches take the Regge approach

(poles + cuts) as a valid dynamical basis.

ill) The 3rd important common feature is the

presence of the Odderon : a simple pole in the DL case

{allowing tofit A(da/dt) ~ 0 but not the UA4 p~ data)

ann a more complicate singularity in the GLN case.

Concerning the differences between the two ap-

proaches, one can think that the I3L approach has a

small number of free parameters, while the GLN ap-

proach has a much bigger number of free parameters.

This is not quite true. The nt, mber of Regge parameters

in the GLN case can be reduced precisely by using the

DL procedure. Also, the valuc~ of most of the param-

eters associated with the asymptotic contributions are

highly constrained by the present data. Paradoxically,

there is very little freedom also in the GLN case.

in iact~ the only one re~ diR~erence is the m_,axi_m~

Odderon~ -=,~i~ is p-=ese~. '-~ ~ e G~} r ~pproach ar_:i -£s

absent in the DL approach. There are therefore two

ways of deciding between the DL and GLN approaches

: 1) see if multighion exchanges with C - 4- in QCD

lead to poles or to more complicated singularities; 2)

test predictions at LHC with both l~p and pp options

: there are dramatic differences between the DL and

GLN at ultra-high energies.

In fact, the crucial question behind all that is the

problem of the coupling of the Odderon in the forward

direction. There is now a quite general agreement about

the existence of the Odderon in the non-forward scat-

tering. However, there is not yet a general and rigorous

proof about the coupling of the Odderon at t = 0. For

the moment, we have to allow us to be guided by the

experimental data.

6. PREDICTIONS OF THE ODDERON AP-

PROACH AT LHC ENERGIES

In the future, interestil~g results concerning the

Odderon approach are expectcd from UNK, Tevatron

and SSC machines. Of special interest are two of the

nine already presented proposals at RHIC. The first

one 3~ concerns the pp measurement (in particular, pPP)

at qrs = 0.5 TeV. This would givc a wonderful com-

piementary information to those of UA4/1 and UA4/2

measurements ofp~P at practically the same energy : we

could directly check if Ap ~ 0. The second proposal 31

concerns the measurement of a~P at several energies up

to V/~ = 0.5 TeV. These data would fill the huge

empty range in pp scattering and would therefore give

an invaluable information concerning the precise rate of

increase of O" r with increasing energies.

B. ¥icolescu / Odderon - past, present and future !49

i ~-.~.~ ~.o s t r e s s f.ha ~ . t h e O d d e r o n eff.~c~s ;~ e n o t

Odaeron effects are also expected in other reactions.

l l n p o r [ a n l S U ~ I , i O r l 8 I n %nls ( l l r e C t l o n w e r e m a d e by

several speakers at this Conference s~.

However, it must be realized that the only way to

have a crucial test d the hadma-hadron - antihadron-

hadron symmetry or asymmetry is to perform the ap-

propriate experiments at LHC with both pp and /~p

options.

16

\ 'x

4

-8

-12

. . . . . . ! . . ! . . . . . . . . . . . .

10 'tO z 40 ~ 10" 10 b v'~. G*'~

I show in Figs. 3-5 the predictions of the maximal

Odderon (GLN) approach 12'"'17 at ultra-high energies,

as an illustrative case of a large class of Odderon models

: aT in Fig. 3, A~ in Fig. 4 and p in Fig. 5.

20C

l o o

b 6 T , m b

. . . . . . pp

107 10 j 10' " ~ ~ ,Ge~

Fig. 3

GLN prediction d ¢7" at ultra-high energies

The maximal Odderon predictions at LHC ener-

gies (other than those for d~/dt) are summarized in

Table 2. One can see from Table 2 that very inter-

eating and measurable Oddenm effects occur at LHC

energies, e.g. A ¢ = - 6 mb and Ap = 0.2. In some

sense the Odderon effects shown in Table 2 are mini-

real experimental effects. If one relaxes the constraints

Fig. 4

GLN prediction of ~ at ultra-high energies

03

O~

94

0

-I

? ..... pp

i //

r S

/ /

T T ' '

Fig. 5

GLN prediction of p at ultra-high energies

coming from low energies, one expects even more copi-

ous experimental effects. For example, the value of A¢

can be as large as - 2 0 mb at LHC energ~s s3.

I also show in Fig. 6 our predictions for d~/dt at

LHC energies. We expect a spectacular finite-energy

Odderon effect to occur at these energies : A(da/dt)

is predicted to be large and positive in the range It I ~-

0.2 - 0.7 GeV 2.

1.~n B . ~ ; ~ ' . . . . . . /"~'q'q . . . . . . . . * p re sen t a n d f u t u r e

i

!} ~/~ ; 17 TeV . . . . . . pp

10

e/

16 0 O.S 1.0 1.5 I fl,(C.-eV)

Fig. 6

GLN predictions of the pp and/~p differential cro~ sec-

tions at the LHC energy V~ = 17 T e V

7. CONCLUSIONS

1) The LHC with both p p and pp options will open

the gate towards new physics, presumably intimately

related with C = - multigluon exchanges in QCD.

2) The LHC with both pp and pp options will offer

the unique and ultimate crucial test of the fundamental

theoretical problem of ~p -pp symmetry or asymmetry.

This crucial test could lead to a radical change in our

understanding of the. annihilation mechanism in strong

interactkms.

3) The LHC with bott, pp and l~p options is surely

of interest for other fields of pt~ysics, e.g. new physics

connected with the sc~rch for Z*'s.

4) The tip option at LHC is fortunately inexpen-

ation : abie to do iundamental physics for low sums of

money.

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3. E. Leader, Comparison of proton-proton and proton-antiproton scattering at very high ener- gies, in : Elastic and Diffractive Scattering at the Collider and beyond, Proc. of the 1st Blois Work- shop, Blois, France, eds. B. Nicolescu and J. Tran Thanh Van (Fronti~res, Gif sur Yvette, 1985) pp. 183-194

4. B. Nicolescu, The new UA4 pPP datum and the Odderon, in : Elastic and Diffractive Scattering, Proc. of the 2nd Blois Workshop, New York, USA, ed. K. Gouliance (Fronti~res, Gif sur Yvette, 1987) pp.133-144

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l , ~ c o ~ . ~ u / v u u e ~ u . - pa~t , p.rese?|t a.*id f u t u r e lSl

i-3. M.M. isi~m_ ~ ....... ~.,, ~ T..~ a (m-v'~ i83; ?Z.5~. ]~],.~, L~o ]n,...~ :~ . . 2 T- F. _., }~v, R~=.-

=

Phys. B299 (1988)640; Phys. Rev. Lett. $4 (1985) 2656; 65 (1985) 639

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1.9. P. Gau~n, L. Lipatov and pl. Nicolesen, Phys. Lett. B260 (1991) 407; L. Lipatov, talk at this Conference.

20. A. Martin, Elastic scattering and total cross- sections : present and future, Talk given at CERN-Dubna-serpukhov Triangle Seminar, Dubna, USSR, October 1990, CERN-TH 5630/91 preprint

21. Proceedings of the ECFA Large Hadron Collider Workshop, Aachen, Federal Republic of Germany, 4-9 October 19[~), vols. I-Ill, edited by G. Jarl- skog and D. Rein, CERN 90-10/ECFA 90-133, 3 December 1990. See, ~n particular, the talks given by D. Denegri (vo]. I, I~P. 56-117) and E. Leader (vol. II, pp. 22-36)

22. H. Coraille, Th~or~mes asymlAotiques et sections t~caces totalcs croissantes, Comptes-Rendus du Co!!oque d'Aussois (lnstitut de Physique Nuc;~'aire, Orsay, 1973) pp. lI. 1-24~ Nuovo Ci- mento 'rOA (197O) 165

23. Prelimin&-y results on p#P, E710 Collab<,-ation, presented by S Shukla at this Conference

24, Pre~minary . . . . ~*~ a ~ ~'. "~ . . . . . . . . . .

25. M . M . lllnrk~ tRJk --t this Co.-_re~nee;

ANL-HEP-PR 91-38 preprint

26. K. Kang, talk at this Cov.ference; K. Kang and A.R. White, ANL-HEP-PR 91-32/ BROWN-HET-805 preprint

27. Genoa-Palaiseau-Praha-Roma-Valencia Collabor- tion, D. Bernard et al., Minute of the CERN Re- search Board CERN/DG/RB 90-156

28. H. Cheng and T.T. Wu, Phys. Rev. Lett. 24 (1970) 1456; C. Bourrely, J. Sofl'cr and T.T. Wu, Phys. Lett. B252 (1990) 287

P.V. Landshoff, talk at this Conference; for a short review see A. Dunnachie and P.V. Landshofl', Particle World 2 (1991) 1

W. Guryn, S.Y. Ice, S. Majewski, M. Sakitt and A. Sambamurti, BNL-45162 preprint (August 1990), in : Proc. 4th Workshop for a Relativistic Heavy Ion Collider (BNL, Upton, NY, July 1990), to be published

CEILN Courtier 31 (1991) 12

I.F. Ginzburg, B.V. Struminsky and L~. Zhinit- sky, talks at this Conference

29.

30.

31.

32.

33. E. Leader, in Ref. 21.