measured

Measurementofthe...

arXiv:hep-ex/03070

66

v1

25Jul2003

1

MeasurementoftheCross-SectionfortheProcessγγ→pˉp

at√

e=183GeVand189GeVwiththeOPALdetectorat

sareprentedforpˉp

invariantmass,W,intherange2.15<=""on=""p=""

previous=""quark-diquark=""recent=""the=""with="">

UCTION

Theexclusiveproductionofproton-antiproton(pˉp)pairsin

thecollisionoftwoquasi-realpho-tonscanbeudtotest

hephotonsareemittedbythebeam

elec-trons1andthepˉppairsareproducedinthepro-ces

+e?→e+e?

γγ→e+e?pˉp.

TheapplicationofQCDtoexclusivephoton-photon

reactionsisbadontheworkofBrod-skyandLepage

[1].Calculationsbadonthisansatz[2,3]uaspeci?cmodelof

theproton’sthree-quarkwavefunctionbyChernyakandZhit-

nitsky[4].Thiscalculationyieldscross-ctionsaboutoneorder

ofmagnitudesmallerthantheex-istingexperimentalresults

[5,6,7,8,9,10,11],forpˉpcentre-of-masnergiesWgreaterthan

lnon-perturbativee?ects,theintro-ductionof

quark-diquarksystemshasbeenpro-pod[12].

Recentstudies[13]haveextendedthesys-tematic

investigationofhardexclusivereac-tionswithinthequark-

diquarkmodeltophoton-photonprocess[14,15,16,17].

Thecalculationsoftheintegratedcross-ctionforthe

processγγ→pˉpintheangularrange

|cosθ?|<0.6(whereθ?

istheanglebetweentheproton’smomentumandthe

electronbeamdi-rectioninthepˉpcentre-of-masssystem)and

forW>2.5GeVareingoodagreementwithex-

e=183GeVand189GeVat

egratedluminositiesforthetwoen-ergiesare

62.8pb?1and186.2pb?ELECTION

Thee+e?→e+e?pˉpeventsarelectedbythefollowing

tofcuts:

oftheenergiesmeasuredinthebarrelandendcap

ctionsoftheelectro-magneticcalorimetermustbelessthan

halfthebeamenergy.

ytwooppositelychargedtracksarerequiredwith

eachtrackhavingatleast20hitsinthecentraljetchamberto

ensureareliabledeterminationofthespeci?cenergylossdE/d

ntofclostapproachtotheinteractionpointmustbe

lessthan1cmintherφplaneandlessthan50cminthezdirection.

htrackthepolaranglemustbeintherange|cos

θ|<0.75andthetransvermomentump⊥mustbelargerthan

utnsureahightriggere?ciencyandgood

particleidenti?cation.

2

ariantmassWofthepˉp?nalstatemustbeinthe

range2.15<=""measured=""momenta=""of=""p=""proton=""

the=""tracks=""two=""using="">

ntsareboostedintotherestsystemofthe

measuredpˉp?tter-ingangleofthetracksinthis

systemhastosatisfy|cosθ?|<0.

6.

nts

must

ful?lthetriggerconditionsdescribedin[11].

gebackgroundfromotherexclusive

process,mainlytheproductionofe+e?,μ+μ?,andπ+π?pairs,is

reducedbypar-ticleidenti?cationusingthespeci?cenergyloss

dE/dxinthejetchamberandtheenergyintheelectromagnetic

/dxprobabilitiesofthetracksmustbe

consistentwiththepand

e=183GeVand128eventsat

√

dWd|cosθ?|

=

Nev(W,|cosθ?|)

eisobtainedfromthedi?erential

cross-ctiondσ(e+e?→e+e?pˉp)/dWusingthe

luminosityfunctiondLγγ/dW[20]:σ(γγ→pˉp)=

dσ(

e+e?→e+e?pˉp)

dW

.(2)

3TheluminosityfunctiondLγγ/dWiscalculated

bytheGalugaprogram[21].Theresultingdif-

ferentialcross-ctionsfortheprocessγγ→pˉp

inbinsofWand|cosθ?|arethensummedover

|cosθ?|toobtainthetotalcross-ctionasafunc-

tionofWfor|cosθ?|<0.6.

ANDDISCUSSION

Themeasuredcross-ctions[11]asafunction

rageW

ineachbinhasbeendeterminedbyapplyingthe

proceduredescribedin[22].Themeasuredcross-

ctionsσ(γγ→pˉp)for2.15

p="">

andfor|cosθ?|<0.6arecomparedwiththe

resultsobtainedbyARGUS[8],CLEO[9]and

VENUS[10]inFig.1aandtotheresultsob-

tainedbyTASSO[5],JADE[6]andTPC/2γ[7]

rk-diquarkmodelpredic-

tions[13]ableagree-

mentisfoundbetweenthismeasurementand

theresultsobtainedbyotherexperimentsfor

W>rWourmeasurements

agreewiththemeasurementsbyJADE[6]and

ARGUS[8],butliebelowtheresultsobtained

byCLEO[9],andVENUS[10].Thecross-

ctionmeasurementsreportedhereextendto-

wardshighervaluesofWthanpreviousresults.

Fig.1cshowsthemeasuredγγ→pˉpcross-ction

asafunctionofWtogetherwithsomepredic-

tionsbadonthequark-diquarkmodel[12,13].

Thereisgoodagreementbetweenourresultsand

theolderquark-diquarkmodelpredictions[12].

Themostrecentcalculations[13]lieabovethe

data,butwithintheestimatedtheoreticaluncer-

taintiesthepredictionsareinagreementwiththe

measurement.

Animportantconquenceofthepurequark

hardscatteringpictureisthepowerlawwhichfol-

lowsfromthedimensionalcountingrules[23,24].

Thedimensionalcountingrulesstatethatanex-

clusivecross-ctionat?xedanglehasanen-

ergydependenceconnectedwiththenumberof

hadronicconstituentsparticipatingintheprocess

ctthatforasymp-

toticallylargeWand?xed|cosθ?|

dσ(γγ→pˉp)

4

wheren=8isthenumberofelementary?eldsandt=?W

2/2(1?|cosθ?|).Theintroductionofdiquarksmodi?esthepower

lawbydecreasingnton=

werlawiscomparedtothedatainFig.1cwith

σ(γγ→pˉp)～W?2(n?3)us-ingthreevaluesoftheexponent

n:?xedvaluesn=8,n=6,andthe?ttedvaluen=

7.5±0.8obtainedbytakingintoaccountstatisticaluncer-

tacoveringawiderrangeofWwouldbe

measureddi?erentialcross-ctionsdσ(γγ→pˉp)/d|cosθ?|in

di?erentWrangesandfor|cosθ?|<

di?erentialcross-ctionintherange2.15<=""factor=""for=""

from=""given=""highest=""integrated=""is=""leads=""

lies=""lower=""=""mea-surements=""

measurement=""measurements=""of=""opal=""other=""

over=""p=""range=""ranges=""ratio=""re-ported=""

rescale=""results=""shapes=""sig-ni?cantly=""still=""than=""

the=""their=""to=""total=""two=""venus=""w=""|cos=""

θ?|bin,where=""θ?|dependence="">

InFig.2b-cthedi?erentialcross-ctionsdσ(γγ→pˉp)/d|cos

θ?|intheWranges2.35<=""di?erent=""di?erential=""

distribution=""=""for=""function=""in=""

measurements=""model=""of=""p=""predictions=""pure=""

quark=""quark-diquark=""=""shapes=""shown=""

similar=""tasso,venus=""the=""tho=""to=""uncer-

=""w=""with=""within=""|cos=""θ?|for="">

InFig.3bthedi?erentialcross-ctiondσ(γγ→pˉp)/d|cos

θ?|isshownversus|cosθ?|for2.15<=""|cos=""θ?|;the="">

6|cos(Θ?

)|

dσ(γγ→pp_

)/d|cos(Θ?

)|(nb)

00.511.522.533.54|cos(Θ?

)|

dσ(γγ→pp_

)/d|cos(Θ?

)|(nb)

00.511.522.53|cos(Θ?

)|

dσ(γγ→pp_

)/d|cos(Θ?

)|(nb)

?erentialcross-ctionsforγγ→pˉp

asafunctionof|cosθ?

|indi?erentrangesofW;a,c)comparedwithCLEO[9]and

VENUS[10]datawithstatistical(innererrorbars)andsys-tematic

errors(outerbars)andb)comparedwithTASSO[5].TheTASSO

apointsareslightly

displacedforclarity.

5

00.511.522.53

|cos(Θ?

)|

dσ(γγ→pp_

)/d|cos(Θ?

)|(nb)

024681012

14|cos(Θ?

)|

dσ(γγ→pp_

)/d|cos(Θ?

)|(nb)

eddi?erentialcross-ction,dσ(γγ→pˉp)/d

|cosθ?|,withstatistical(innerbars)andtotaluncertainties(outer

bars)fora)2.55<=""and=""approximation=""are=""

asymptotic=""b)2.15

dicatesthatforlowWthepertur-bative

calculationsof[2,3]arenotvalid.

Anotherimportantconquenceofthehardscattering

h

exclusivereactionlikeγγ→pˉpthesumofthetwoinitialhelicities

equalsthesumofthetwo?nalones[25].Accordingtothe

simpli?cationudin[12],onlyscalardiquarksareconsidered,and

the(anti)protoncarriesthehelicityofthesingle

(anti)tingquarkmass,quarkandantiquarkand

henceprotonandantiprotonhavetobeinoppositehe-licity

(anti)protonisconsideredasapoint-like

particle,simpleQEDrulesdeter-minetheangulardependenceof

theunpolarizedγγ→pˉpdi?erentialcross-ction[26]:

dσ(γγ→pˉp)

(1?cos2θ?)

.(4)

ThixpressioniscomparedtothedataintwoW

ranges,2.55<=""agreement=""approximations=""are=""as=""

bdsfid="236"best=""by=""ca=""data=""=""

=""describe=""determined=""does=""each=""

exchange=""expected=""experimental=""higher=""in=""

introduce=""invalid=""is=""leading=""low=""lower=""

meson=""model=""normali-sation=""not=""other=""p=""

partial=""pre-diction=""process=""range=""range,the=""

simple=""soft=""such=""that=""the=""this=""to=""

=""w=""waves,so=""with=""within="">

Thecross-ctionfortheproces+e?→e+e?pˉphasbeen

measuredinthepˉpcentre-of-masnergyrangeof2.15<="">

6

measurementsliebelowtheresultsobtainedbyCLEO[9],and

VENUS[10],butagreewiththeJADE[6]and

ARGUS[8]ss-ctionasafunctionofWis

inagree-mentwiththequark-diquarkmodelpredictions

of[12,13].

Thepowerlaw?tyieldsanexponentn=7.5±0.8wherethe

thisuncertainty,the

measurementisnotabletodistinguishbetweenpredictionsfor

theprotontointeractasastateofthreequasi-freequarksoras

redictionsarebadon

dimensionalcountingrules[23,24].

Theshapeofthedi?erentialcross-ction

dσ(γγ→pˉp)/d|cosθ?|agreeswiththeresultsofprevious

experimentsincomparableWranges,apartfromthe

highest|cosθ?|binmeasuredintherange2.15

=""shape=""simple=""soft=""such=""that=""the=""

theoretical=""this=""to=""w=""w

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