Revisto Mexie",,,, de Fisim 38, Supleme7lto 2 (1992) 196-209

The Production of Higgs Bosons and ZO BosonsHeavy-Ion Colliders

.In

G. SorrGescllsehaf! für Sehwrr'io7le7lforsehu7llj (GSf) , Phl1lekstmpe 1, Poslfaeh 1/0 552, /).6100

Dar71l.';/lUit, G'ermany

D. IlILHERG, CH. 1l0I'MANN, CII. UEST, S. SCIINEIDER, M. VIDOVlé

f7lstilul f'¡" Theo,.ctiseh, Physik, Joh"'l7l Jlfolho7llj Goelhe- U7liversi!,;!,Postfoeh 1/1 .9.12. 0-6000 FlTl7lkf1l7'1"''' Moi7l, Ge7'flul7lY

M. GIlElNER

/)'porI71l'7l1 of Phy-,ie.<, U7li,.crsily of Ari:o,,,,, Tlleso7l, AZ 8572/, USA

ABSTHACT. \Ve illv{':-;tigat.c l.he fOrlllat.ioll of exot.ic particks in ultrarelativistir heavy-ion collisions.\Ve calculat(> lhe illlpart.-pararnetcr dcpendcnce of t.JICelectrolnagnetic production of illt.ermediale-mass lIiggs hosons. For an asslIllwd scalar lIiggs IIJ<L';5of Alu = 100 GcV "\o'e obtain a n'ducedcross sectioll C1J1 = 57 Ph for a P¡'.Pb collision al Lile (,IH'rgics wit.h r = 3500. In additionwe study a pos..,ible gCIlt:'fat.iolJ of lIIagnctic monopolcs in t.he slIperstrong elcctromagnelic fieldof rdativistic heavy iOlls. Also hadronic react,iolls ill Ct~lItral collisions of Iludei are cOllsidered.Theoretical results for t.he produrtioll cross secl.ioll of tO)) qtlarks, lIiggs bosons and ZO uosons willbe presented. Relevant quantities of the t.opollilltll are calrulat.rd within a nonrelat.ivisti<'. potentialrnodel. Jt is demonstra!.ed tllaí the Illllltiplicity dis! ribution of produced lept.on pairs can he utilizedto determine the impact paramf'ter of 1.111"heavy-ioll (ollision.

RESU~1F:N. Investigamos la formación de partículas exótica.o:;;en colisiones ultrarelat.ivistas de ionespesados. Calculamos la dl'pell<icncia del parámetro de impacto de la producción electromagnéticade bosones de Higgs COIl1I\a.<;asintf'rllledias. Para ulla masa supuesta del boson escalar de HiggsAlu = 100 GeV, Obt.<.'IH'1II0Suna sección I:'ficaz reducida (1/1 = 57 £lb para \Ina colisión de Pb.Pba energía ..",d('1 Lile con r = 3.100.Adiriollallllt'll1.c (~stlldialllos la posihle gene-ración de mono polosInagnéticos en el call1po e1ect.romagllét ico slIpcrfllcrt.e dI:' iOlles pesados re!ati\'istas. Tambiénconsideramos reacciOlws hadránic(ls CII colisiolH's ccutrales de núcl",os. Presentamos resultadosteóricos para la sección eficaz de producción de t.op quarks, bosones d(' 11iggs y hosones ZO.Calculamos cant.idades r(')('vanl.es dl.'11.0poniUlII dcnt.ro de \1111Il0delo de potencial non-relativista.Demost.rarllos que la dist.rihución dI;' la lIlult.iplicidad de producción de pares de Icptones se puedenutilizar par<\ dderrllinar ('1 par<lllldro dI' illlpacto ell la colisión de iones p('sados.

PACS: 27.70.+'1

l. INTHOIlUCTION

ClIrr~ntly, the possibility of arre1"rating h"avy ions with the high-energy ro]]iders LIIC(CEHN) and SSC (T"xas) is IIlld"r dis(,lIssioll. Th~ major motivatioll for the constrnetioll

TIIE PROOUCTION OF !lIGGS BOSONS ANO ZO BOSONS IN IIEAVY-ION COLLIDERS 197

of these collíders is the detectioll alld illvestigatioll of top quarks and !liggs bosons, but inthe avaílable energy regíon (:I.!j TeV fn for LIIC alll18 TeV fu for SSC; both for accclerating208Pb) otl,er electroweak pl"'lIomena could also play an important role.82 .. o b . IIn this report we concentrate on the formatlOn of IIlggs hosons and Z - osons In centraas well as in pNiplleral nltrarelativistic heavy-ion collisions. \Vhile peripheral collisionshave been investigated already in previous publications we present here first estimates forthe production cross sertions of exotic particles in central nuclens-nucleus collisions, whichin the considered energy domain are dominated hy parton interactíons. Furthermore, weevaluate the production rate for top-quark pairs in heavy-ion reartions. The possiblegeneration of magnetic monopoles in the superstrong e!ectromagnetic field of heavy.iontransits is hriefly outlined. Fiually we d"monstrate that the high multíplirity of about1000 created e1ectron-positron pairs may be utiliz"d to determine the impact paramet.'rof the collisiou.

2. H'GGs-l3oS0N PIlOllUCTION IN CENTIlAL lIEAVV-loN COLLISIONS

The search for the lIiggs particle(s) predicted hy the Standard ~Iodel (and its exten-sions) is one of the tapies in contcmpora.ry pliysics. Here ,ve fC'strict ourselvcs lo theMinimal Standard Mod,,] where ouly one IIig~s bosoll is involved. Tlle lIiggs-boson massenters the theory as a free parameter and is bouuded from belnw by recent experimenta!results to be larg"r than :'0 CeV. Au upper houlld of abont 1 TeV may be deriv"dfr01l\ th£'oretical fonsidcratiollS 5\1(,}¡ as triviality of lh£' sraJar fjí'ld sf'clor of Lile theoryand the loss of unitarity. Th,' r<'maiuing em'l'gy range is generally divided into threeregions d<'ll'lmined by collider capahilities alld decay modes of the lIiggs boson. \Ve arebasically interested in the intermedia!e mass I'ang" (mz ::; Mil ::; 2m;¡-), in whieh thebranching ratio of the lIiggs deeay into b, b r¡narks is large. 1I0wever, in this energy rangeonly the proton colliders SSC and LIIC will he available in tl,e foreseeable futnre. !lutal so an option to collide heavy ions is ullder ,Iiscussion. Ceutral collisions presumablyproduce an overwhelming I,adronic backgronnd which will hide the bb signal for the lIiggsdecay completely. Thus it wa.s proposed [1 - 4] to ereate lIiggs particles in the strongelectromagnetic fields of periphera! heavy-ion eollisions. flut reeently it turned out [:',6]that the Iliggs-boson produetioll rate is too s",all and that the background proeessesare not negligible. Sinee there exist calculations [7J for the lIiggs-boson production inproton-proton collisions which iucorporate a chauee for the detection of lIiggs bosonsby their photon decay, we inv('stigated the production rate of lIiggs bosons in centralheavy-ion collisions at Lile ('n('rgies.

\Ve first caleulated the total eros s section for producing lIiggs particles in nucleon-nueleon collisions. For this reason we mnltiplied the clementary cross sectiolls for tlleprocesses 99 - II aud ,,¡¡ - 1/ with the col'I'espondillg glllon-distrihutiou fllnctionG(x) aud '1l1ark-distriblltioll flluetious ,,(x) amI ¡¡(x) of a ullcl('ou [11] aud performedthc integralioll ovcr tite sraling variahles

0', = J dx J da:' (;(,,)(.'(x') O'gg_J/(x,:r'), (1)

198 G. SOFF ET AL.

2

10'5

100 150 200 250MH [GeV]

FIGURE l. Tolal cross scction ror lIiggs-boson produdion in central Pb-Pb collisions al 3.5 TeV fu.The gluon (g)- ami quark (q) - fusion conlribuliou is indicaled by lhe full and dashed line,respectively.

(12 = J dx J dx' ¿(q(x)q(x') + q(x)q(x')) (1•• _II(X,X')

•The elemenlary cross ser.tions read (7)

(2)

(3)

(4)

where GF is lhe weak coupling conslanl and A. is lhe amplitude of the quark loop in lhelriangle diagram for lhe proress 99 - l/. Tlle quark masses "'. were approximaled innext-lo-leading-Iog order.

In order lo derive the tolal lIiggs-boson production cross seclion (11and (12were mulli-plied with the lolal number of individual nucleon-nucleon reactions during lhe heavy-ioncollision. This number was compuled el11ployiug a simplified version of lhe RQMD model(8) which yields up lo 1250 nucleon-nucleon collisions al LIlC energies.

In Fig. 1 the total lIiggs-boson production rross section is plotted versus the Higgs-boson mass assuming a Pb-Pb collision at LIlC (E;o" = 3..5 TeV ju). The fullline corre-sponds lo the gluon-fusion process wllich dominates lhe qq ~ l/ process (represenled

THE PRODUCTIONOF IIIGGS BOSONSANDZO BOSONSIN IIEAVY-IONCOLLIDERS 199

• SSC REDSSC-WW

+ LHC RED- LHC-WW

1 ........•.',*,.••.•.•...•.••..w..

.•••...-- ....-.---.--- .•.......•••.

0.1

0.01

'O

~.oe•...•

50 150[GeV]

200

FIGURE2. Total (fu)) curve) and r.duced (dash.d curve) cross seetion for IIiggs-boson formationvia gamma fusion at Lile and SSC energies for nlt = 150 GeV. Stars and crosses representeaJculated points.

by the dashed line) by about two orders of magnitudes. With a luminosity of [,1028 em-2s-1 one tiuds an annual rate up to about ~!jOOlIiggs bosons in the eonsideredenergy range.

3. HIGGs-BOSON PRODUCTION IN PERIPIIERAL COLLISIONS

The strong eleetromagnetie fields prevailing in ultrarelativistic heavy-ion eollisionscoold give rise to the possihle produetion of exotie particles, partieularly lliggs bosonsin the intermediate mass region 11lz < mil < 211l\V. First ealculations [1-5] lead toproduetion eros s seetions in the I nb regio n for SSC energies. AII previous ealeulationsrely on the \Veizsaeker- \Villiams or equivalent photon method leading to the total erosssection

(5)

with the photon-distribution funetion n(w) ana the elementary eross seetion (fn_H forthe prod uetion of a lliggs boson vía two real photons.

Looking c10ser on the produetion of lliggs bosons, one might qoestion whether the maineontríbution to the eleetromagnetie eross seetion really results from impaet parametersbeing larger than twiee the nuclear radius. Central colJisions shoula be omitted beeause of

200 G. SOFF ET AL.

nuelear reaetions, whieh wonld mask a ciean experimental signa!. The equivalent photonmethod whieh has been employed to ealcnlate the produetion eross seetions only yieldstotal eross seetions, because the wave front of the equivalent photons is by definitionextended to infinity in transverse direetions. In order to oVereome this short-eoming, wedeveloped an impact-parameter dependent equivalent photon method for the Iliggs-bosonproduetion [4,9J. The impact-parameter dependent eross seetion reads

(6)

with the two-photon distribution funetion 7I(w) ,w2,b) of the two nuelei eolliding at adistanee b. lntroducing a sharp cut-off impaet parameter, be = 2R, and thus diseardingcentral collisions, the redneed eross seetion

(7)

for the sealar Iliggs-boson produetion in Pb-l'b eollision was ealculated. R denotes thenuelear radius. Fig. 2 displays tl,e total (full curve) and the redueed (broken curve) erossseetion for the maximum LIIC energy (Iower curves) and SSC energy (upper curves). Theredueed eross seetion for the sealar Iliggs-bosou produetion is only by a factor of2.:1(3.1)at LII C energies and 1.6( 1.8) at SSC energies for a Iliggs mass of 1OO(1.')0) CeV smallerthan the eorresponding equivalent photon eross seetion.

The lIIinimal supersymmetrie extension of the standard model requires five Iliggsbosons: two sealar, one pseudosealar. and lwo oppositely eharged bosons. The reduetionfaetors for the two sealar Iliggs bosons are the same as for lhe standard Iliggs boson.In the case of the pseudosealar Iliggs boson one has to take into eonsideration that theeleetrie fie1ds of the two photons have to be perpendicular. The redueed eross seetionfor the pseudosealar Iliggs-boson produetion is only by a factor of 2.3(3.3) at the LIICenergy and 1.5(1.7) at the SSC energy for a Iliggs mass of 100(1-')0) CeV smaller lhan theeorresponding total equivalent photon eross seetion.

4. zO AND DILEPTON PRODUCTION

This seetion deals wilh the evaluation of ti", produetion rale for neutral intermediateZO bosons during an high-energy heavy-ion collision. This proeess can contribute to thebackground for Iliggs-boson produetion and, in general, can serVe for investigations ofelectroweak phcnomena in heavy-ion collisiolls.OUT calculatioll comprises several steps:• First the possible elementary proeesses lhat eould eontribute signifieantly were seleeted.Quarks (q), gluons (g) and pholons (f) as inpul partieles were taken into aecount .• The elementary lotal eros s seetions \Vere ealculated using Mandelstam variables.C. Kao [10] performed the calculation for the proeess gg ~ ZaZo, partially by incorpo-rating a triangle graph with an intermediale Iliggs boson.

TUE PRODUCTION OF IIIGGS BOSONS AND ZO BOSONS IN IIEAVy-ION COLLIDERS 201

• In a next step tite total nucleon-nucleou eross sections (10-0 were derived employing titepartan model w¡th the partan distrihutiou fuurtions of Duke and Oweus [11].

• The incohNPnee "''5umptiou nuderlying tite partou model was also applied on the nexthigher level, i.c., the uuclens-nuclpns collisions were treated •••, an ineohereut sum over allbiuary uucleou-uuc1eon collisions which oecur during au heavy-iou collisiou. To estimatetite average nnmber n(b) of binary rollisions during a nuc1pus-nuc1ens collision witlt animpact parauwter b, again a simplified version of the RQMD model [81 was pmployed.The total cross sectious for ª~8I'b_ª~8Pb collisions were ealrnlatpd aecordiug to

a>2H(1U_1I J

(1Pb_Pb = 211"-- Il(b) b rlb .(1tol

°(8)

This exprpssiou givps tite total iutpgrated nuclear interaction arpa normalized to the areaof the total Itadronie intNaetion (i.c. tlw total ¡",dronie eross spetion (110')' whiclt yipldsthe rNjupstpd total heavy-ion cross section. R denotps thp nnclear radius .

• Alternatively, we utilizpd tite Pqnivalent photon metltod to calculate tite Iteavy-ion crosssection for ZO production in peripheral collisions that proeeed via the process q"l _ qZO,which only plays au important role for collisious of higltly eltargNI particlps since theintegrated photon spectrum risps quadratieally witlt tite cltargP nnmher Z of tite collisioupartners .

• The detection ofprodueed ZO hosons is snpposed to proeeed via their deeay int.o dilpptous,which willlead to a dpteetahle clpar signa!. Rpsults of the latest LEP measurpmeuts [12)were used to fix tite partial deray rate of the ZO h050n to

= 3.3.';% . (9)

All results of our aud Kao's ealcnlatious for LIIC energies are summarized in Table 1.The respective columns illdirate the lluc1pon.nuricon cross s('ctions (1U-U1 the total heavy-ion cross scctions aph_PL, the' numbers N ZO of the produrcd ZO hosans during a one ""year"(= 107 s) ruu of the LIIC collidN witlt au assumed Inmiuosity of £- = 1028 CJU-2S-1 andtite numbers N¡,+¡,- of tite ZO hosons whielt eould he deterted via tlteir deeay into adilepton pairo

202 G. SOFF ET AL.

ZO-Produetion via ~JIC(.1.• 2 3..5TeV /u L - 1028 cm -2S 1 )

Proeess u" " [nbl UPh_Ph (nb] Nzo N ..+ .•-00 _ Z" -/+/ 1.0. 10+0 1.7.10" 169393 169393a7i _ ZO ZO :1.0.10 3 .5.0. 10" 497 1700 _ Z"oy .5.3 . 10+0 8.7.10" 86743.) 30360qq _ zu"Y'

moy. = 10-' GeV 1.6. 10+0 2.6. 103 264820 8872moy. = 10+0 GeV 6.3. 10-1 1.0. 103 104806 3511moy. = 10+1 GeV 1.3.10-1 2.1.102 21116 707m~.= 10+2 GeV 6.3.10-3 1.0. lO' 1038 35a-r _ uZo - 6.4 . 10" 641300 2148499 - Z"ZOwith lIiggs 2.8. 10-4 0.5.100 45 1 - 2without 1Ii~~s 1.5. 10-4 0.3.10° 2.) < 1

TABLE 1. Results for ZO-production in I'b-I'b collisions at Lile energies.

The results in Table 1 demonstrate that the dominant process for ZO produetion is theresonant proeess qq _ ZO - /+ /-. The contribution of non-resonant proeesses is smallerby orders of magnitude, depending on the masses of the additional1y produeed partides(el. qq _ ZO + X). One should emphasize that the process Q"Y - qZO, whieh occurs alsoin peripheral collisions, achieves the second highest yield of all non-resonant processes.This is a direet conse'luenee of the involved high nuclear eharges and wi1l be negligiblein pure hadronie col1isions. The investigate<1 cnergy <auge is too low for a comparable ZOproduetion via gluon-gluon fusion 99 - ZaZo. Aecording to Ref. [10] this wi1l change atstil1 highcr energies.

To resume our results we can state that there will be a suffieient production rate of ZObosons in these high-energy heavy-ion collidcrs which yiclds an important backgroundfor the seareh of top '1uarks and lIiggs bosons, but it al10ws additional1y for furtherinvestigations of electroweak interaetions during ultrarelativistie heavy-ion col1isions.

5. TOP-QUARK PROllUCTION

The ultimate verification of the Standard Model requires the existenee of the top-quark.Current experiments <lid Bot find a clear signa] [Of a pTocluced top.quark below a massof m, < 89 GeV (13). In addition it is relativc1y uncertain whether the top-quark can bedetected in these experiments, because an extraordinarily high integrated luminosity isnecessary to identify a heavy top-'1uark. Likewise the planned energctical1y boosted LEP2with its 100 GeV on 100 GeV c+c--beam wil1 not provide the possibility for top-quarkereation with a mass aboye m, > 100 GeV. Unfortnnately, theoretical predictions prefera top mass of abont m, '" 150 GeV (14J. rol' this reason it wil1 be almost impossible to

TIIE PROOUCTION OF IIIGGS [30S0NS ANI> ZO BOSONS IN IlEAVy-ION COLLIOERS 203

create top-quarks with existing rollid~rs, iucluding the Tevatron. \Ve considered top-quarkand toponium creation in ultrar~lativistic heavy-ion collisions at the LIIC and the SSC[15]. lI~re we present results for fr~e top-quark cr~ation in the two scenarios of centraland peripheral heavy-ion collisions.After reducing the problem of d~scribing a central ultrar~lativistic heavy-ion collision

to an incoherent sum ov~r singl~ nucl~on-nueleon collisious we have to compute the totalcross section for top-quark pair cr~atiou in hadronic rollisions. This is accomplished inthe framework of the parton mode!: the nuel~on is treated as a swarm of non-interactingpartons (valence quarks, gluons and sea quarks). A top-quark pair is produced throughgluon-gluon fusion and quark-antiquark annihilation. The hadronic cross section resultsfroID an integral over the parton distributions of the two impinging nueleons and theassociatcd elementary cross section

ahad(S) =¿J dXldx1 J¡(x"Q1)h(X1,Q1) aij(x¡,X1,S),'.J

( 10)

where S is the squared invariant energy of the colliding nueleons, Q1 is the four-momentumtransfer, and i and j distinguish between the differ~nt partons. As an example the ele-mentary cross section for top-quark pair creation via quark-antiquark annihilation reads

_ 2a(qq ~ tt) = -

9_,-4m; ( 2m;) ( 2m:)--~ 1+- 1+-s - 4m~ s s

(11)

with 0, the ¡unning coupling of the strong interaction and s the squared invariant energyof the parton su bprocess.

In order to evaluate total cross s~(tions for top-quark creation via the photon-gluonfusion subprocess in peripberal beavy-ion rollisions, the equivalent photon method isutilized. In this parton-like interpretation of the el~ctromagnetic ¡¡cId of a relativisticmoving charge the total nuel~ar eros s seetion is similar to Eq. (10). It is an integral overthe effectiv~ gluon distribution of the nucleus, the photon distribution und the elementarycross section for the pboton-gluon fusion subprocess. As the effective gluon distributionof the nueleus we used

(12)

g(X,Q2) is tbe gluon distribution of a nucleon and AO.9 is an experimentally deduced factorthat takes into account the nuclear shadowing elrec\. In Fig.3 the results for top-quarkpair creation in central and p~riphcral h~avy-ion rollisions are plotted as function of thetop-quark mass Tnt.

In comparing the display~d data it results tbat central collisions at futUTe collider ener-gies represent a top-quark factory, but it appears to be difficult wbetber the decay products

204 G. SOFF ET AL.

105

10':aoS,:;; 103...,AI4:

lQ34:"O

lO'

100

,.•.~~•..",','

•..~~:~.•.,',

.•.....•........:::::: .•..•.....:::....LHC....•:::, ....•.

.•••.....•..•...::: •......•..•:,•..•.

...•.......','

centrBlpor~

100 150 200 250mI IGeV]

FIGURE 3. Total cross sedions ror top-antitop quark creation in central and peripheral c.ollisionsplotted as function of the top-quark lIlass tu, [or U-U (upper lioe of the double lines) and Pb-Pb(Iower line of the dou!>le lines) rollisiolls at Lile (3.5 TeVfu) alld SSC (8 TeVfu) energies.

of the top-quark can unamhigiously be isolated from the enormous badronie background.Peripheral rollisions with thcir rC'duced cTPalian Tate are au interesting alternative, sincethe hadronie background is drastically suppressed.

6. ELECTROMAGNETlC MONoroLE-ANTIPOLE CREATION

In addition to the fundamental <¡uestion of mass creation the quantization of eleetrieeharge is of definite interest. Dirae demonstrated that the charge quantization can beunderstood by assuming the existence of magnetie monopoles. i1owever, no magneticmonopoles have been detected yet in nature. This may lead to the conclusion that eitherDiraes proposition is wrong and magnetic monopoles are non-existent or that magnetiemonopoles like quarks are prod uced with their total magnetic eharge coupled to zero.One can also provide the simple explanatioll that magnetic monopoles have not yet beenfound because their masses are too Jarge iu order to be generated with existing colliders.

Recently, a lower mass ¡¡mit of 120 GeV for maglletie monopoles has heen derived[16). This energy threshold for ereatiug monopole-antipole pairs exceeds the capabilityof present e+e- colliders. We studied the photoproduetion of magnetic monopoles in thestrong eleetromagnetie fields occu ring in heavy-ion collisions [17-19). This process couldtake place even for an impact parameter of the heavy ions larger than twice the nuclearradills.

THE PROOUCTION OF IIIGGS BOSONS ANO ZO BOSONS IN IIEAVy-ION COLLIDERS 205

Monopole-Antipole Creation

1000800

ssc

600[GeV)

400m

200

,,,,,,,... ... ... ... ...... ... ... ... .... .... .... .... ................

10-2

10-3

10-'

:o 10-5

"O 10-6

10-7

10-8

10-9

10-10

FIGURE 4. Total cross seC'tion roc the creatioll of mOllopole-ant.ipole paies in IIItrarelativisticPb-Pb coJlisions plotted versus the lIlonopole rest mass. The fullline corresponds to Lile energif"S,the dashed one to SSC energies.

The eJementary photoprod uction cross section for magnetie monopoles has the samestrueture as the photoproduetion eross seetion for eleetrieally eharged partides

2[ (3 ]41l"Um. 4 1 + 2Un_",;;¡(8) = ~ (3 - (3 )]n ] _ (3 - 2(3(2 - (3) , (13)

with (3 = (] - 4m",/8)1/2. m", denotes the unknown mass of the magnetie monopo]e ands is the ordinary Mandelstalll variable. Qne should note that this expression invo]ves theeoupling constant 0'" = 1/40 = 34.26 rather than the eleetromagnetie eoupling constanto = 1/137.04. Therefore the eross seetion for monopo]e prod uction exeeeds the erossseetion for eledrieally eharged partides of the same mass by seven orders of magnitude!

\Ve obtained the total cross sedion for produeing monopole-antipole pairs in heavy.ioneollisions by multiplying the elementary eross seetion with the photon distributions andintegrating over the photon energies

u = J dw n(w) J dw' n(w') u""'_"';;¡- (14 )

The result is plotted in Fig. 4 versus the monopole mass for Pb.Pb eollisions at thetwo collider energies 3.5 TeY /u (LIIC) and 8 TeY /u (SSC). For monopo]e masses near

206 G. SOFF ET AL.

the threshold up to 1 TeV the eros s sectiolls are measurable <¡uantities. Thus we pro-pase to employ the electromagnetic productioll ill heavy-ioll coJlisions for verifying theexistence of mOllopoles in this mass range. Similarly one can also generate the axion (20)and supersymmetric partirles [9) ill the superstrong electromagnetic field of heavy-iollencounters.

7. MULTIPLICITY DISTIUHUTION or DIRECT ELECTRON-POSITRON PAIRS

We investigate the direct creation of electron-positroll pairs out of the electromag-netic fields in ultrarelativistic heavy-ion transits at future heavy-ion facilities. At theseultrarelativistic ellergies, even when the lIuclei do not touch, direct pair creation fromthe electromagnetic fields is ahulldallt. Withill the framework of perturbation theory thepair-creation rate even violates ullitarity. This is evident from the 111

3'1 rise of the per-turbative total cross section which violates the Froissart unitarity hound that prescribesan asymptotical In2'1 rise. In additioll, it has also heell demollstrated [21) that the paircreation probahility at a fixed smaJl impact parameter exceeds unity already at coJliderenergies as low as 10 GeV /u. This might indicate that perturhatioll theory overestimatesthe real cross sectiolls, but it call also imply that the productioll of multiple pairs hecomesdominant over single-pair productioll.

To describe multiple pai r creation llon-pcrtllrbatively, we cmploy a many-particle thcoryof non-interactillg electrolls in all external field. !loth positive and negative energy statesare availahle for the electrons, and the QED vacuum is thus described by a state in whichall negative energy states are filled. Each electroll obeys the Dirac e<¡uation ill the givenexternal field. It can he lifted illto the positive ellergy colltinuum where it is illterpretedas a real electroll. Though it is not 11 [JI"ior.i evident that this theory descrihes QEDcorrectly it can be shown that the n-poi lit functiolls (vacuum expectation values) of thisDirac sea theory (which call he computed from the time evolution of the single-particleDirac e<¡nation) coincide with those calculated from ordinary QED. The latter can bederived explicitly and non-pert,urbatively from the path integral of non-radiative QED inan external field [22] in terms of single-particle amplitudes by a method of <¡uantizationin a time-depelldent basis.

As it has thus been established that non-radiative external-field QED can be modeledby a Dirac sea tbeary, hoth pair creatian multiplicities alld probabilities are computedfrom the single-particle scattering matrix "qp of the Dirac e<¡uatian. The number of paírsin a state p is tben givell by [23)

ñp = L 1"'1PI2 .q<O

(1.'; )

aqp is the Dirac single-particle scatterillg matrix, while the amplitude to create one pairin the states q and p is approximately

TIIE PRODUCTION OF IIIGGS BOSONS AND ZO BOSONS IN IIEAVY-ION COI.L1DERS 207

Sqp = < aislo> 2:>:,q(t)'l"p(t) (16)n<O

where the factor < aislo> denotes the amplitude that the vaeuum remains unrhanged,i.c. no pairs are created. Continuing along these lines, the general probahility to ereate npairs is, ir interf(,fPlIces are neglected, delennilled by a Poisson dislribution

( 17)

as was to be suspeeted from the idea that tl,,- pairs are rreated independelitly fromeaeh other. The exponenti,,1 factor in front of the expression is in this approximationthe vaeuum-to-vaeuum amplitude < aiSlo> whirh must be assumed to he unity if per-turbatioli theory is employed. Therefore, if n is large the probability exeeeds unity hythe negleetion of this factor alone, even if the perturbatively evaluated Dirae seatteringmatrix is still eorreet. Sinre this factor does not appear iu the expres,ion for the pairmultiplicity, this quantity can he eompllted safely in perturbation theory (as there is astrong suspicion that the single-particle amplitud()'s are pertllrbative duc to lhe very shorttime of interaetion). As it tUfllS out. the multiplieity in lowest order is identieal to theexpression ror the pertllrbative single-pa¡r rr('alían prohahility I\(pcrt) in th(' same arder:

1! = ¿ ¿ l"qpl2 =p>O '1<0

( 18)

\Ve thus conclude t1111tthc pC7'/uI'baliJ>ely caleula/ui/lIlil' elHltirm p1'Ob"biiity is aetually Ihemean multipiieity. Natural!y, if the mu1tiplicities ar<' low, mean multiplieity aud proba-bility coindde. As a COllsC'<¡ucncc, cross sectiolls frolll pertllrha-tive metllods are rOffrclin the sense that they do not describe single-pair ereation but ereation of auy number ofpairs, whieh is natural!y what is wanted.To demonstrate this, we have ealc,dat"d the impaet parameter-dependent pair ereation

mu1tiplicity from a Weizsaeker-Wil!iams method. Though this method has been knownfor long, there lla.s 1I01 heril a gC'tH'ra! formulatioll for the ralrulation of impact parameter-dependent probabilities from two-photon eross seetions. Starting from the Feynman graphexpression. we have derived. by making the usual W"izsiieker-Williams approximation, anexpression for tltis involving the well-kno\\.'n illlpart paramet('r dC'pendent single-photondistributions n(w,b) and lhe polarized two-photon eross section "11 and ".L [24]. Thisexpression iuvolves integration both over thl.:' photoll C'uC'rgiesas \vell as over aH pointsin the plane perpendicular to the mol ion of the ion s where two pholons can fuse, theirnumber givcn by tbe <Iistane" from both nuclei and their polarization by the ra<lial veetorsfrolll these c('lIt('rs.The results as displayed in Fig." indicate tl,at multiplirities are wellup in the thousands

al LIlC 01' SSC for smal! impart parameters (20-100 fm), and d"rreas" sharply for largerdistallct's wllich lIlakes tlle 1Ilf'a.SlIl'f'IllPllt of the impact paralllf'ter [1'0111eiectroll-positron

208 G. SOFF ET AL.

2

.~CI'l 2a..

o 20 40 60 80 100Impact parameter [fml

FIGURE 5. Electron-positron paie Jnultiplirity in U+U collisions al 3£)00 GeV fu ('ollid~renergy.

pair multiplieities feasihle whieh may he important for other e!eetromagnetie proeesses.Also al. RlIIC energies (100 GeV /u) we ohtaincd ahout 1500 e+e--pairs for almost ecntralU-U eollisions. Deam loss from e1cetron capture may he signifieant as total eross seetionscan be taken from well-known Weizsiirker-Williams and other perturbative ealculationswhieh give ahout .500 kharn for U+U al. :1.5 TcV /u.

ACKNOWLEDGEM ENT

Wc are gratcful for stimulating diseussions with W. Greiner, 11. Sorge, J. Reinhardtand A. Sehiifcr.

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