Total gamma-gamma and gamma*-gamma* Cross Sections Measured at LEP

4 Pages·0.1 MB·English

by  A. De Roeck

1
Total γγ and γ γ Cross Sections Measured at LEP
∗ ∗
Albert De Roecka
a CERN, 1211 Geneva 23, Switzerland
Recentresultsontotalcross-sectionmeasurementsinγγ andγ∗γ∗ collisionsatLEParereported. Phenomeno-
1
logical fits to thedata are presented.
0
0
2

n
1. Introduction the Monte Carlo model used to correct the data:
a
J it affects the absolute normalization by approxi-
At LEP2 photon-photon collisions constitute
9 mately 20%, as derived from using two different
a large part of the inclusive cross-section.
models, PYTHIA [3] and PHOJET [4]. An im-
1 Quasi real photons are emitted according to a portantuncertaintyisthediffractivecontribution
v Weizs¨acker-Williamsenergyspectrumbythelep-
tothecross-section. Sucheventstoalargeextent
6 ton beams. Two photon events can be tagged by
escape detection; depending on the model only
7
one or both of the scattered electrons, or anti-
0 6% to 20% of the diffractive events are selected
tagged,in which case the electrons remain in the
1 by the standard analysis cuts.
0 beampipe. Tagging detectors measure electrons In Fig. 1 data on σ from the LEP and pre-
γγ
1 typically down to 30 mrad. In this paper we re-
LEPexperimentsareshown,comparedtovarious
0 port results on anti-tagged (i.e. almost real pho-
theoreticalmodelsasreviewedin[5]. ThenewL3
/ ∗ ∗
h tonγγ)anddoubletagged(i.e.γ γ )totalcross- dataarestillpreliminaryandareacombinationof
p sectionmeasurements. Theanalysesarebasedon
- approximately 390 pb−1, from e+e− data taken data takenat√see =189and192−202GeV[6].
p Contrary to previously published data [1], these
e at √see =189−202 GeV in ’98 and ’99. data are determined using both PHOJET and
h
PYTHIA, and are therefore above published val-
:
v ues. The cross-section clearly rises with increas-
2. Total γγ Cross-Section
Xi ing Wγγ. The OPAL and L3 data are consistent
Photons at high energies can fluctuate in two- with each other. This is less so for the pre-LEP
r
a fermion pairs or vector mesons with the same data [7],of whichonlya selectionis shownin the
JPC quantum numbers as for the photon. Hence figure.
a photon can behave like a hadron, with an All models predict a rise with the collision en-
additional pointlike component. Total inclusive ergy, but the strength of the rise differs and the
hadron-hadron cross-sections are known to rise predictions at high energy show dramatic differ-
gentlywiththecentre-of-mass(CMS)energy. An ences. In proton-like-models (dash-dotted [8–10],
outstanding question is whether σ rises faster dashed[11],dotted[12]andsolid[13]curves),the
γγ
than σ , expected from the additional pointlike curvature follows closely that of proton-proton
pp
component in the photon structure. cross-section, in QCD based models (upper [14]
LEP allows to study γγ interaction cross- and lower [5] bands), the rise is obtained using
sectionasfunctionoftheCMSenergyW . L3[1] the pQCD jet cross-section.
γγ
and OPAL [2] have measured σ in the region A large contribution to the errors of the cross-
γγ
5 < W < 145 GeV and 10 < W < 110 section is due to the uncertainty of the model
γγ γγ
GeV respectively. The challenge of this measure- dependent correction factors, which are strongly
ment is the reconstruction of W from the vis- point-to-point correlated and partially hide the
γγ
ible hadronic final state. The result depends on
2
1000 800
Regge/Pomeron, SaS
L3 preliminary
900 GLMN BKKS
BSW
800 Aspen EMM
700 600
600
(nb)tot500 ]b
s n
400 [ 400

300 gg
s
200 TPC
Desy 1984 1999 data
100 LEP2-L3 189 GeV and DESY 86 200 1998 data
192-202 GeV LEP2-OPAL 189 GeV
OPAL
1 10 √s (GeV)102 103
0
Figure 1. Data on σγγ, versus Wγγ (denoted as 50 100 150
√s) compared with models (see text). W [GeV]
gg
Figure 2. Data on σ from OPAL and L3, com-
γγ
pared with fits through the data (see text).
significanceoftheriseofthecross-section. There-
fore Fig. 2 shows the L3 data without the model
dependent errors. The size of the rise is quanti-
fied by a Regge inspired fit, X sǫ1 +Y s−η1,
1 1
· ·
i.e. the sum of a pomeron and a Reggeon term. L3findsY 1000nbfromitsownfits. Hencewe
1
∼
The exponents ǫ1 = αIP 1 and η1 = αR 1 made fitsusingthe publishedOPALandprelimi-
− −
are usually assumed to be universal, whereas the narynewL3datapoints,ignoringcorrelationsbe-
coefficients are process dependent. For η1, which tweenthepointsandignoringtheuncertaintydue
is determined by low energy hadronic data, the to the model dependence. Refitting the OPAL
value of 0.34 is taken [15]. αIP and αR are the data but with Y1 as determined by L3, one finds
pomeron and Reggeon intercept, respectively. ǫ =0.205 0.042(χ2/NDF =1/3). Refittingall
1
±
For its fits, OPAL fixed the coefficient of the the data,leavingY free,givesǫ =0.238 0.029
1 1
±
Reggeon term, while L3 fitted the magnitude of (χ2/NDF = 2.7/9). Is this rise driven by the
Y1. The L3 fit yields for the pomeron term: point at largest Wγγ from L3? Removing this
ǫǫ11 ==0.01.0216+−300±..0022500.[021].4T[6h]ewcuhrilveesOsPhoAwLtphuebLli3shfietds pnooinsitgnfriofimcanthtechfiatnggieveosfǫt1h=e e0x.p22o3ne±nt0..033,hence
withfree(solidline)andfixed(dashedline)value The correspondingvalueforǫ inhadroniccol-
1
of ǫ1,(ǫ1 = 0.095). Correlations between the lisions is in the range 0.08 0.095, hence the γγ
−
pointsaretakenintoaccountinthesefits. L3ob- cross-section appears to rise significantly faster
servedthatthevalueofǫ1doesnotdependsignif- than hadron cross-sections.
icantlyonthemodelusedforcorrectingthedata. Recently, Donnachie-Landshoff [16] proposed
TheslopefoundbyOPALisconsiderablysmaller a model which includes two pomeron terms in
than the L3 one, despite agreement between the an attempt to save the universality of the soft
data points. This can be traced back to the as- pomeron. Thetotalcross-sectionisthenassumed
sumption on the Regge coefficient, Y1, which is to be described by
fixedbyOPALduetoabsenceofitsownmeasure-
ments below W =10GeV toa value of320nb. σ =X sǫ1 +X sǫ2 +Y s−η1, (1)
γγ 1 2 1
3
The second pomeron term was added mainly to
describe the γ∗p data. From fits to pp and γ(∗)p 183GeV
data the exponents ǫ = 0.0808 ǫ = 0.418 and 189-202GeV
1 2 1
η = 0.34 are extracted. An intriguing ques- PHOJET
1
tion is whether the X term is present in the γγ ) QPM
2 b
data. A fit, as described above, to the prelim- (p -1
Y 10
inary L3 data with Wγγ > 20 GeV, and with d
two pomerons only, gives X2 = 2.5 0.6 nb, /ee
±
withχ2/NDF =4.5/3. FittingallOPALandL3 sd -2
10
data to the full expressionof eq.( 1), keeping the
ǫ ,ǫ and η fixed, gives X =5.0 0.9 nb, with
1 2 1 2 ± L3 Preliminary
χ2/NDF =2.3/9. Hence,withinthismodel,and -3
10
within the restrictions of the fits made, the extra
2 3 4 5 6
hard pomeron term appears to be required in γγ Y=ln(S/S )
0
data at the 4σ level or higher.
Whilethecross-sectioninγγ appearstoberis-
ing faster than in pp, the γp cross section can be
Figure 3. The ee eeX cross-section for double
described by a single pomeron term with expo- →
tagged events, measured by L3, compared with
nent 0.0808. It is therefore important that the
model predictions (see text).
rise in the γγ data gets established more thor-
oughly. This canbe accomplishedwithmoreand
improvedcross-sectionmeasurements in the high
W range AND also with better measurements
γγ
at low W from LEP or elsewhere. The latter
γγ
is important because the fit result depends sig-
OPAL preliminary
nAinficeaxnptelyrimonenthteatknVoEwPlePdgineoNfotvhiesiRbiergskgehoanstberemen. []/dY pb10-1 a)
scheduled to measure σ at low W . sd
γγ γγ
-2
10 OPAL QPM
3. Total γ∗γ∗ Cross-Section PHOJET Kwiecinski et al.
-3
10
The study of virtual photon-photon scattering 0 1 2 3 4 5 6
Y
has recently been discussed as a definite probe []Y nb b)
oevfotlhuetiohnaredqu(aBtFioKnLd)espcormibeersosnca[t1t7e]r.inTghperoBceFsKseLs sd/dgVgV10
in QCD in the limit of large energies and fixed,
but sufficiently large momentum transfers. The 1 Kim99
Bartels99
BFKLpomeronhasbeenintensivelyinvestigated
0 1 2 3 4 5 6
in the context of small–x deep inelastic electron- Y
proton scattering at HERA. However, despite
clear hints [18], the presence of so called ln1/x
terms in deep inelastic scattering at HERA has Figure 4. The γ∗γ∗ cross-section, measured by
not been unambiguously established yet. OPAL, compared with model predictions (see
∗ ∗
The γ γ cross-section has been advocated as text).
anexcellentmeasurementtoseelow-xorsocalled
BFKLeffects[19,20]. Thesemeasurementscanbe
performed by tagging both scattered electrons,
which forces the virtuality of both photons to
4
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