Diffraction and Low-Q^2 Physics Including Two-Photon Physics

36 Pages·0.87 MB·English

by  Martin Erdmann

DESY-98-209b ISSN 0418-9833
December1998
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Diffraction and Low-Q Physics
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9 Including Two-Photon Physics
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Martin Erdmann

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Universita¨t Karlsruhe, Engesserstr. 7, D-76128 Karlsruhe
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E-mail: [email protected]
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e Abstract
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e Recentexperimentalresultsonthepartonicstructureofthephotonandonthecolorsin-
h gletexchangeinstronginteractionprocessesarereviewed. AttheLEPe+e−andHERAep
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colliders, complementary and consistent measurements have been achieved on the quark-
i
X gluon structure ofquasi-real andvirtual photons. AttheHERAepandTevatronp¯pcollid-
r ers,thequark-gluon configuration ofthediffractiveexchange isconsistently foundtohave
a
a large gluon component. The rate of diffractive interactions observed by the HERA and
Tevatronexperiments, however,islargely differentandchallenges explanation.
Invited plenarytalkat theXXIX InternationalConference on High EnergyPhysics, Vancouver,
B.C. Canada(1998)
1 The Partonic Structure of the Photon
The motivation behind studying the structure of the photon results from the interest in under-
standing the formation of hadronic matter. Permitted by the Heisenberg uncertainty relation,
the photon can fluctuate for some time into a quark–anti-quark state. This fluctuation can be
disturbed,e.g.,byanelectronorprotonprobewhichallowsthedensityofquarksandgluonsof
thepartonicstateofthephotonto bedetermined.
At the LEP e+e− and HERA ep colliders, photons are emitted by the leptons which gives
accesstothepartonicstructureofalmostrealphotons[1]aswellashighlyvirtualphotons. The
measurementsto obtaininformationon thepartonicstateofthephotonsdiscussedhereare
1. thephotonstructurefunctionfrom deep inelasticelectron–photonscattering(Fig. 1),
2. jet and particlecross sections(e.g. Fig. 2),and
3. thetotalphoton–photoncross section.
e
tag
θ
e tag
γ*(q)
W
γγ
γ(p)
e
e
untag
Figure1: Feynmandiagramofdeep inelasticelectron–photonscattering: thepartonicstructure
of the quasi-real photon from the untagged lepton is probed by the virtual photon from the
taggedelectron.
( a ) ( b )
e e
p p
Figure2: ExamplesofFeynmandiagramsforphotoproductionofjetsinepcollisionsinleading
orderQCD: a)direct photon–protonprocess, b)resolvedphoton–protonprocess.
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1.1 MeasurementsRelatedtotheQuarkDistributions ofQuasi-RealPho-
tons
NewFγ structurefunctionmeasurementshavebeenperformedintheinterestingregionofsmall
2
partonmomentax 10−2bytheL3collaboration [2]. Fγ isdeterminedfromthemeasurement
∼ 2
ofthedoubledifferentialinclusivecross section
d2σ 2πα2
= (cid:0)1+(1 y)2(cid:1) Fγ(x,Q2) , (1)
dxdQ2 xQ4 − 2
where α is the electro-magnetic coupling constant, Q2 denotes the virtuality of the probing
photonandgivestheresolutionscaleoftheprocess,and y istheinelasticityy = Q2/(xs ). In
eγ
Fig.3, thexdependenceofFγ isshownintwo binsofQ2.
2
A major challenge in this analysis is the determination of x: since the lepton that emitted
the target photon remains undetected, the energy of the target has to be determined from the
hadronicfinal state. Using anew improvedreconstructionmethodfor x, two resultsfor Fγ are
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presentedbytheL3collaborationusingtwodifferentMonteCarlogeneratorsforthecorrection
of detector effects (Phojet [3], Twogam [4]). These two data sets demonstrate that over a
large region in x the structure function result does not depend on the details of simulating the
hadronicfinal state. Only belowx 10−2 thislimitationbecomessizable.
∼
In the same figure, previous results of the OPAL collaboration are shown [5]. Within the
errors, good agreement is observed between the two experiments. Also shown are different
parameterizations of the quark density in the photon demonstrating that the data give new in-
formationonthequarkdistributionsatlowx(LAC [6],GRV [7],SaS [8]). Scalingviolations
caused by gluon emission off the quark before the scattering process occurs results in a rise of
Fγ below a small value of x. The data are not yet precise enough to confirm or reject such a
2
riseat x 10−2.
∼
In the momentum region around x 0.5, where the quark and the anti-quark each carry
∼
halfofthe photonenergy, results on thestructurefunction Fγ exist from manyexperiments. A
2
compilation of these measurements is shown in Fig. 4 as a function of the resolution scale Q2
[9]. The data are compatible with an increasing quark density in the photon as Q2 increases.
ThisQ2 dependenceis very different fromthat ofhadronicstructurefunctionsat large x and is
expectedbyperturbativeQCD(Fig.5anddiscussioninSection2.2): thesplittingofthephoton
intoaquark-anti-quarkpairgivesrisetotheprobabilityf offindingaquark inthephotonto
q/γ
increaseas
Q2
f ln (2)
q/γ ∼ Λ2
QCD
inleadingorder.
In the same figure an effective parton distribution xf˜ of the photon is shown which has
γ
been extracted from di-jet measurements in photon–proton collisions by the H1 collaboration
[10]. Thiseffectivepartondistributioncombinesthequarkandthegluondensitiesofthephoton
withaweightofcolorfactors [11]:
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xf˜ = x (f + f ) . (3)
γ q/γ g/γ
4
2
0.4
〈Q2〉 = 1.9 GeV2 L3(Phojet)
L3(Twogam)
0.3
α OPAL
/
)
2
Q
0.2
,
x
(
γ2
F 0.1
SaS-1d
0
-2 -1
10 10
0.6 〈Q2〉 = 5.0 GeV2 GRV-LO
GRV-HO
α LAC1
/
) 0.4
2
Q
,
x
(
γ2 0.2
F
SaS-1d
0
-2 -1
10 10
x
Figure3: ThephotonstructurefunctionFγ,measuredintwo–photoncollisionatLEP,isshown
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asafunctionofthepartonfractionalmomentumxintwobinsofthevirtualityQ2 oftheprobing
photon. The squared symbolsand thecircles represent themeasurementsoftheL3 experiment
using two different Monte Carlo generators for correcting detector effects. For comparison,
previous results of the OPAL experiment are shown (triangle symbols). The curves represent
differentparameterizationsofthepartondistributionsin thephoton.
The vertical scale for xf˜ on the right side of Fig.4 has been adjusted relative to the Fγ scale,
γ 2
since in contrast to the Fγ measurements the jet processes are independent of the electric
2
charges of thequarks. Therelevantresolutionscale is thetransversemomentump2 of thescat-
t
tered partons which is here taken to have the same resolution power as Q2. The results of the
di-jet measurements are in good agreement with the Fγ data. The jet data probe the partons of
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thephotonat largeresolutionscales and competewell inprecisionwiththeFγ measurements.
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The quark density close to the kinematic limit x 1 is analysed in photoproduction of
∼
two jets. Here the contributions of the direct and resolved photon–protonprocesses need to be
understood(Fig. 2). Theydifferintheirmatrixelementsand thereforeinthedistributionofthe
partonscatteringangleθ∗.
In Fig. 6, a new di-jet cross section measurement of the ZEUS collaboration is shown dif-
ferentiallyin cosθ∗ forlarge di-jetmassesandcorrespondinglylargex [12]. Alsoshownare
| |
next-to-leading order QCD calculations [13] using two different parton parameterizations of
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p2 [GeV2]
T
2 3
1 10 10 10
2.5
α α
dsc) / 2.25 OAMPAYL ( 0(0.3.1 < < x x < < 0 0.8.6)) TAOLEPAPHZ (p0r.e3l .< ( 0x. 3< <0 .x8 )< 0.8) 8γx f /γeff
u
2Q, JADE (0.1 < x < 1.0) L3 prel. (0.3 < x < 0.8)
γF (2 2 DELPHI prel. (0.3 < x < 0.8) 7
TPC (0.3 < x < 0.6) H1 fγ (0.4 < x < 0.7)
1.75 eff 6
GRV LO (0.1 < x < 0.6)
1.5 GRV LO (0.2 < x < 0.9)
5
GRV LO (0.3 < x < 0.8)
1.25 SaS1D (0.1 < x < 0.6)
4
HO (0.1 < x < 0.6)
1
ASYM (0.1 < x < 0.6)
3
0.75
2
0.5
1
0.25
0 0
2 3
1 10 10 10
Q2 [GeV2]
Figure 4: The structure function F of the photon is shown as a function of the virtuality Q2
2
of the probing photon for parton fractional momenta around x 0.5. Measurements of the
photonstructurefunctionFγ frome+e− dataareshownincompa∼risonwithan effectiveparton
2
distribution extracted from photoproduction of di-jets in ep collisions (H1 data). The curves
represent differentparameterizationsofthepartondistributionsofthephoton.
thephoton(GRV [7],GS [14]). Thedirectphotoncontribution(notshowninthefigure)isnot
sufficient to describe the measured jet cross section either in shape or in the absolute normal-
ization. Contributionsof resolved photon processes are required to describe thedata which are
sufficientlypreciseto discriminatedifferent partonparameterizationsofthephotonat large x.
1.2 Measurements Related to the Gluon Distribution of Quasi-Real Pho-
tons
New measurements of the inclusive charm production cross section at the large LEP beam
energies are shown in Fig. 7 by the L3 collaboration [15]. The cross section has been de-
termined using semi-leptonic charm decays in the electron and muon channels. In the same
figure, next-to-leading order QCD calculations [16] using two different charm masses and the
GRV parameterization [7] of the parton distributionsin the photons are shown. The dominant
contribution to the cross section results from gluon induced processes with an average gluon
momentumas smallas x 0.03 [17].
h i ∼
4
0.3
p2
F
NMC BCDMS SLAC
H1 94-97 Preliminary
NLO QCD Fit
0.2
0.1
x=0.4
0
2 3 4 5
1 10 10 10 10 10
Q2 /GeV2
Figure 5: The structure function F of the proton is shown as a function of the virtuality Q2
2
of the probing photon for the parton fractional momentum x = 0.4 from fixed target data and
preliminaryH1 data.
Also di-jet data are used to access the low-x gluon distributions of the photon. In Fig. 8, a
new measurement of the di-jet cross section is shown as a function of the parton momentum x
by the H1 collaboration [18]. The histograms represent a leading-order QCD calculation [3]
showingthecontributionsofthedirectphoton-protoninteractionsandquarkandgluoninduced
processesusingtheGRV partonparameterizations forthephotonand theproton.
Both the charm and di-jet measurements give compatible conclusions on the low-x gluon
densityofthephotonand are precisetothelevelof30%.
New information on the gluon distribution of the photon results from di-jet production in
photon-photoncollisionswhichhas been measured by theOPAL collaboration [19]. In Fig. 9,
the cross section is shown differentially in the transverse jet energy Ejet. At sufficiently large
t
Ejet the measurement can well be described by a next-to-leading order QCD calculation [20]
t
usingthepartondistributionfunctionofGRV [7].
InFig.10,thedi-jetcrosssectionsareshowndifferentiallyinthejetrapidity ηjet . Thedata
| |
exploredifferent regions of the parton fractional momentum x > 0.8,x < 0.8 with a precision
of 20%. They are compared to leading order QCD calculations (Phojet [3], Pythia [21])
∼
anddiscriminatedifferentparameterizationsofthegluondistributionsofthephoton(LAC [6],
GRV [7], SaS [8]).
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Figure 6: The di-jet cross section in ep collisions involvingquasi-real photons is shown differ-
entially in terms of the cosine of the parton scattering angle at large di-jet mass above 47 GeV
fromZEUSdata. Thecurvesrepresentnext-to-leadingQCDcalculationsusingdifferentparton
distributionsofthephoton.
1.3 Parton Distributions of Virtual Photons
The fluctuation of a virtual photon into a quark-anti-quark pair is suppressed by the photon
virtuality Q2. In comparison with real photons one therefore expects a smaller probability of
findingthevirtualphotoninapartonicstate. Also,thereislesstimetodevelopfromtheqq¯pair
a vector meson bound state such that the hadronic contributions to the virtual photon structure
shouldbesmall.
InFig.11,thefirsttriple-differentialdi-jetcrosssectionisshownasafunctionofthephoton
virtuality Q2 in two bins of the parton momentum x for a fixed resolution scale (Ejet)2 = 50
t
GeV2 [22]. The cross section measurement at x 1 (Fig. 11b) is well described by a leading
∼
orderQCD calculationusingthedirectphoton-protoninteractionprocesses only(dashedcurve
[23]). At x 0.5 (Fig. 11a) the absolute cross section is found to be smaller compared to the
∼
measurementatx 1asexpectedfromtheshortfluctuationtimeofthephoton. Herethedirect
∼
photon contributions are not sufficient to describe the data at small Q2 2 GeV2: the di-jet
∼
process is able to resolve the partonic structure of the virtual photon. As Q2 approaches the
squared transverse energy of the jets of (Ejet)2 = 50 GeV2, the resolution power of the di-jet
t
processbecomes insufficientfor detectingthefluctuationsofthevirtualphotons.
Inanalogytotherealphotoncase,eq.(3),aneffectivepartondistributionforvirtualphotons
xf˜γ∗ = x(fq/γ∗ + 9/4fg/γ∗) has been extracted from the data and is shown in Fig. 12a in the
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b
p

)
X
3
–c 10
c
-
e
+
e

→

-
e
+
e
(
σ
2
10
0 20 40 60 80 100
Beam energy (GeV)
Figure 7: Measurements of the total charm production cross sections from two–photon col-
lisions are shown as a function of the lepton beam energy (L3 experiment). The full curves
represent next-to-leading QCD calculations using the GRV parton distributionfunctions of the
photon and different values for the charm mass. The direct photon contributionis shown sepa-
rately(dashed curves).
interval 0 Q2 80 GeV2 for x = 0.6 and (Ejet)2 = 85 GeV2. The partonic structure of
≤ ≤ t
the virtual photon is only slowly suppressed with the photon virtuality Q2. Such a dependence
is predicted by perturbative QCD: in the region of Λ2 < Q2 < (Ejet)2 the probability
QCD t
of finding a quark in the virtual photon decreases logarithmically as Q2 approaches the jet
resolutionscale:
(Ejet)2
fq/γ∗ ∼ ln Qt 2 . (4)
Theformation ofa hadronic boundstatefrom theqq¯pair ofthe photoncan be studiedwith
the production of ρ mesons. In Fig. 12b, the Q2 dependence of the ρ cross section is shown
which exhibits a fast decrease proportional to (Q2 + M2)−n with n = 2.24 0.09 [24]. As
ρ ±
expected from the short photon fluctuation time into a quark-anti-quark pair, the probability to
develop a hadronic bound state from the quark-anti-quark pair is highly suppressed. At suf-
ficiently large Q2, the partonic structure of the virtual photon can therefore be predicted by
perturbativeQCD. In Fig. 12a, the full curve represents a QCD inspired model of the effective
partondistributionofthevirtualphoton(SaS1d [25]) whichisin agreementwiththemeasure-
mentwithintheexperimentalerrors.
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P >4 GeV, M > 12GeV, -0.5 <η <2.5, |η -η | < 1.
T,jets jet-jet jets 1 2
1.8
]
b
n H1 preliminary
[ 1.6
)
s
et PHOJET (GRV)
γ-j1.4
x
(
g
o 1.2
l
d
/
σ 1
d
0.8
0.6
gluons
0.4
0.2 quarks
dddiiirrreeecccttt γγγ
0
-1
10 1
x
γ-jets
Figure 8: Photoproduction of di-jets in ep collisions is shown as a function of the parton frac-
tional momentum x from H1 data. The cross section measurement is compared to a leading-
orderQCDcalculationshowingabovethequarkanddirectphotoncontributionsthegluoncom-
ponentofthephotonatsmallx(thehistogramsarecalculatedusingtheGRVparameterizations
ofthepartonsin thephoton).
1.4 Total Photon-Photon Cross Section
The total photon-photon cross section σ is dominated by soft scattering processes in which
γγ
the photons develop a hadronic structure before the interaction occurs. A major challenge of
thismeasurementis theunderstandingofthedifferent contributions,the elastic,diffractiveand
non-diffractive processes. The visibility of the first two contributions in the detectors is small
andrequires reliableMonteCarlo generatorcalculations.
Progress has recently been made by the L3 experiment which succeeded in collecting a
few hundred events of exclusive four pion production which contains contributions of elastic
double-ρ production at center of mass energies below 10 GeV (Fig. 13) [26]. These data test
thetwo generatorcalculationsshown(Phojet [3], Pythia [21]).
A new measurement of the total photon-photon cross section is shown in Fig. 14 using the
two different Monte Carlo generators (L3 collaboration [26, 27]). The data show a rise above
W √s = 10 GeV and are compatible within errors with the preliminary measurement of
γγ
≡
the OPAL collaboration [28]. This observed rise can be described by a power law sǫ with
γγ
ǫ = 0.158 0.006 0.028 [26]. The rise has the tendency to be stronger than expected from
± ±
softPomeron exchangewhichsuccessfullydescribes all hadron–hadronand photon–protonto-
talcross sectionswithǫ = 0.095 0.002 [29].
±
8
]
V
e
G OPAL |ηjet1|,|ηjet2| < 2
b/
p102
jet[ ET data (hadrons)
d
σ/ NLO QCD (partons)
d
direct
10 single-resolved
double-resolved
1
-1
10
4 6 8 10 12 14 16 18 20
Ejet [GeV]
T
Figure 9: The di-jet cross sections from two–photon processes in e+e− collisions is shown as
a function of the transverse jet energy from OPAL data. The curves represent next-to-leading
QCDcalculationsofthedifferentphotoncontributionsusingtheGRVpartondistributionfunc-
tions of the photon. The labels refer to direct photon–photon interactions via quark exchange
(direct),processeswhereonephotoninteractsdirectlywithapartonoftheotherphoton(single
resolved)andprocesses whichinvolvepartonsofbothphotons(doubleresolved).
1.5 Summary 1: Photon
Improvedknowledgeon thepartonicstructureofreal photonsresultsfrom
new structurefunctionFγ measurementsat lowpartonfractional momentax 10−2,
• 2 ∼
di-jetcrosssectionmeasurementsatxvaluesdownto 10−2 andhighx 1inphoton-
• ∼ →
protonand photon-photoninteractions,and
charm productioninphoton–photonprocessesat lowx 10−2.
• ∼
For the first time the partonic structure of highly virtual photons Q2 > 1 GeV2 has been
investigatedin ep collisions. The fluctuations ofthevirtual photon intoa quark-anti-quark pair
is only slowly suppressed with Q2 and is compatible with a logarithmic decrease as predicted
byperturbativeQCD.
The understanding of the total photon-photon cross section has improved by the detection
ofelasticρproduction.
Overall,theresultsonthephotonobtainedine+e− andepcollisionscomplementeachother
and are well compatible. The precision of the measurements remains a challenge for the next
fewyears in ordertobewell prepared forthelinearcollider.
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