Inclusive and exclusive diffraction: overview of the experimental presentations at Diffraction2004

0.49 MB·English

by  Aharon Levy

Inclusive and exclusive diffraction: overview of the experimental
5 presentations at Diffraction2004
0
0 Aharon Levya ∗
2
n a Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv
a University, Tel Aviv, Israel
J

6 Someissues in inclusiveand exclusivediffractive processes are discussed.

1
v
8
0 1. Introduction colorless,howevertherapiditygapproducedbya
0 Reggeon is exponentially suppressed, while that
1 There were 20 experimental presentations at ofthePomeronremainsconstant. Thisprompted
0 this conference, all by expert people in the field.
Bjorken [1] to define diffraction as processes in
5 Allthesetalkswereplenary,sothereisnopointof
which the large rapidity gap is not exponentially
0
me summarizing again the contents of each talk.
/ suppressed.
x Instead, I would like to present a personal view
How practical is this definition? This we shall
e and touch upon few selected issues which were
- see in the following sections.
p presented here.
e
3. Diffraction in inclusive processes
h
: 2. What is diffraction?
v 3.1. Kinematical variables
Xi In spite of the fact that diffractive processes Iwilltrytodefinehereallthevariablesneeded
have a long history, it is still not easy to give a in the following sections. Let us first look at a
r
a precise and concise definition of what one calls diffractivereactionep→epX atHERA,depicted
a diffractive reaction. It is clearly a process in figure 1. A virtual photon γ∗ (Q2 ≡ −q2) in-
where, in an exchange picture, no color is ex-
changed. This however includes all the color-
,
less particles. A further requirement is that the k
exchanged messenger has the quantum number k e
of the vacuum, which, in the Regge picture is e
q
named the Pomeron. Elastic scattering is usu- quark
b
ally presented as an example of a diffractive pro- M
X
cess. However,atlowenergiesitcanproceedalso
throughanexchange with quantumnumbers dif- x ,t LRG
IP
ferent from the vacuum, called a Reggeon. At p p,
high energies, where the kinematics allows for p p
a large rapidity range, it is more useful to talk
aboutrapiditygaps. Duetothefactthatnocolor
is exchanged, there is a suppression of gluon ra-
Figure 1. Schematic representation of the deep
diation and therefore a rapidity gap is produced
inelastic diffractive scattering.
between the two vertices of the interaction. Of
course, both the Pomeron and the Reggeon are
∗SupportedinpartbytheIsraelScienceFoundation(ISF). teracts with the proton through a colorless ex-
1
2
change with vacuum quantum numbers. A mass timated. In the analysis of the H1 collaboration,
MX of the hadronic system recoils against the processeswithprotondissociationintomassesbe-
proton. The squareofthe momentumtransferat low 1.6 GeV amount to about 10% [7].
the protonvertexis t. The fractionofthe proton The MX method which subtracts the expo-
momentumcarriedbytheexchangeisdenotedby nentially suppressed large rapidity gap events, in
x . The quark struck by the virtual photon car- principlesubtractsalsotheReggeoncontribution
IP
riesafractionβ ofthemomentumofthecolorless andisleftonlywiththeprotondissociativeback-
exchange. (Notethatsometimesz isusedinstead ground. These can not be removed for masses
of β). The last two variables are connected to below 2.4 GeV, which constitutes about 30% of
Bjorken x as follows: x=βx . the selected diffractive events [8].
IP
Atthe Tevatron,where onestudies the diffrac- AttheTevatron,singlediffractiveevents,p¯p→
tive reactionp¯p→p¯X,the equivalent variableto p¯X, are selected by tagging the scattered p¯.
x is denoted by ξ.
IP
3.3. Diffractive structure function
In figure 2 the diffractive structure function
3.2. Selecting diffractive processes
measurements with all three HERA methods are
There are three methods used at HERA to se-
lect diffractive events. One [2] uses the Leading presented. The MX data have been multiplied
by a factor of 0.69 to correct for the proton dis-
Proton Spectrometer (LPS) to detect the scat-
sociation background. No correctionwas done to
tered proton and by choosing the kinematic re-
theH1data. Allmethodsseemingeneraltoagree
gion where the scattered protonlooses very little
witheachotherintheiroverlappingkinematicre-
of its initial longitudinal energy, it ensures that
gion.
the event was diffractive. A second method [3]
simply request a large rapidity gap (LRG) in the
event and fits the data to contributions coming
ZEUS (prel.)
from Pomeronand Reggeonexchange. The third
method [4] uses the distribution of the mass of FD(3)20.05 b =0.007 b =0.03 b =0.13 b =0.48 (QG2eV2)
the hadronicsystemseeninthe detector,MX,to xIP0.025 2.4
isolate diffractive events. We will refer to these 0
threeasLPS,LRGandMX methods. AttheFer- 0.05 3.7
milab Tevatron[5] diffractive processes are being 0.025
studied by tagging events with either a rapidity 0
0.05
gap or a leading hadron. 6.9
0.025
The LPS method has the advantage of detect-
0
ing the scattered proton and thus excluding pro-
0.05
ton dissociative processes. However, in order to 0.025 13.5
ensure that the scattered proton resulted from a 0
diffractiveprocess,onerequiresx <0.01,where LPS 0.05
IP MX * 0.69 39
xIP is the amount of longitudinal momentum lost H1 0.025
by the scattered proton. This cut removes con- 0 10-3 10-3 10-3
tributions coming from Reggeon exchanges [6]. x
IP
The LRG method selects events which also
include some proton dissociative processes and
Reggeon contributions. The latter can be re- Figure 2. Comparison of x FD(3) measured by
moved by the same x < 0.01 cut as above. The IP 2
IP H1 andZEUS,as afunction ofx inoverlapping
protondissociativeprocessescanberemovedpro- IP
bins of β and Q2.
vided their mass is large enough to produce sig-
nalsinsomeforwardtaggingdevices. Thecontri-
bution oflowmassprotondissociationcanbe es-
3
3.4. Q2 dependence of λ 3.5. NLO QCD fits to x FD(3)
IP 2
Thexbehaviouroftheinclusivestructurefunc- It has been proven [9] that QCD factorization
tionF ata givenQ2 is welldescribedby anx−λ worksfor diffractiveprocessesatHERA. This al-
2
form. ThevalueofλisconnectedtothePomeron lows to use the DGLAP [10] evolution equations
intercept, λ = α (0)−1. The value of λ is ap- to get diffractive parton distribution functions.
IP
proximatelyconstanttill Q2 ≈ 1 GeV2, and then Given the fact that for describing diffractive pro-
rises almost linearly with lnQ2. cessesoneneedsmorevariables,t,x ,β,Q2,one
IP
Itisofinteresttoseewhetherthex behaviour wouldactuallyliketoevolveinβ andQ2 forfixed
IP
of x FD(3) shows a similar pattern. To this end, t and x . t is usually hard to measure and one
IP 2 IP
a fit of the form x FD(3) ∝ x−λ was performed, integrates over it. Thus, ideally one would like
IP 2 IP
for different Q2 intervals. to evolve for fixed xIP values. The statistics of
Figure 3 shows the value of λ as function of the presently available data is not sufficient for
Q2 from fits to the x behaviour of F and from carrying this out.
2
D(3) Ingelman and Schlein [11] suggested to con-
thex behaviourofx F . Theprecisiondata
IP IP 2
of F makes it possible to see a very significant sider the exchanged Pomeron as a particle hav-
2
rise with Q2. The x FD(3) data does not have ing internal structure. Under this assumption,
IP 2 the diffractive process is described as a multistep
the precision needed for a clear Q2 dependence.
event: the proton ’radiates’ a Pomeron having a
There is a trend similar to that of F , but given
2
fractionx oftheprotonmomentum. Thevirtual
the large errorsof the data, the behaviour is also IP
photoninteractsinadeepinelasticprocessoffthe
consistent with no Q2 dependence.
Pomeron, scattering of a parton in the Pomeron
carryingafractionβ ofthePomeronmomentum.
There is thus a flux factor at the proton vertex,
dependent only on x (t is integrated out), and
IP
a Pomeron structure function FD(2). This pic-
2
ture assumes Regge factorization, an assumption
which has to be checked by the data.
Using the proven QCD factorization together
with the assumed Regge factorization, one gets
diffractive parton distributions.
3.6. Regge factorization
The assumption of Regge factorization clearly
does not hold in the inclusive case. The value
of λ is clearly Q2 dependent. However both the
diffractive H1 data and the LPS data can be de-
scribed by an NLO QCD fit with one fixed value
of α (0), as shown by Scha¨tzel [7] and by Ca-
IP
pua [8] at this meeting. In case of the LPS data,
a cut on x < 0.01 has to be made. For the H1
IP
analysis,one needs to add the Reggeoncontribu-
tion. ThestatisticsoftheLPSdatawerenotsuffi-
cienttorepeatthefitindifferentQ2bins. TheH1
analysis,showssomeindicationofariseofλwith
Figure3. The Q2 dependence ofλ obtainedfrom Q2 (see figure 3), though with quite large error
fits to F ∝ x−λ and x FD(3) ∝ x−λ. The bars. The uncertainty comes not only from the
2 IP 2 IP
bandindicatesthevaluecorrespondingtothesoft statistics but also from the way one needs to iso-
Pomeron. late the Pomeroncontributionfromthe Pomeron
4
+ Reggeon fit. H1 preliminary
proWceessceasn, fcoorncxlud<e t0h.a0t1,inthiencdlautsaivecadniffbreacctoivne- 2z,Q) 1.12 Gfolru 0o.n0 1M<oz<m1entum Fraction
sistent with RegIPge factorization. There is a clear ]g(
+ 0.8
need for more precise data. [Sz
z 0.6
d
3.7. Dtioiffnrsactive parton distribution func- 2∫Q) / 0.4 HZE1 U20S0 2Q sCrDD NfiLtO QCD Fit
The H1 data, which have a wide kinematical z, 0.2 (exp. error)
dcoiffvrearactgievienpQar2taonnddiinstβri,bhuatvioenbsee(dnpudsfesd),tsoheoxwtrnaicnt dz z g( 0 (ex1p0.+theor. er1r0or2)
figure4. Oneseesadominanceofthegluondistri- ∫ Q2 [GeV2]
Figure 5. The gluon momentum fraction from a
H1 2002 s rD NLO QCD Fit NLO QCD fit, as a function of Q2.
H1 preliminary
2Q) Singlet 2Q) 2 Gluon Q[G2eV2]
z, z,
( 0.2 g( 6.5
Sz z 1 kinematic region: Q2 > 3 GeV2, MX > 2 GeV
0 0 andxIP <0.05. Arethesedpdfsportablejustlike
2 in the inclusive pdfs case? In other words, does
0.2 15 QCD factorization work?
1
0 0 3.8. QCD factorization test
2 The diffractive parton distributions, obtained
0.2 1 90 by H1 from the NLO QCD fit, were used to
calculate expectations of other diffractive pro-
0 0
10-2 10-1 10-2 10-1 cesses. The agreement with data is very good
z z ∗
for diffractive D as well as for diffractive dijet
H1 2002 s D NLO QCD Fit
(exp. errorr) production [12]. However, the expectations for
(exp.+theor. error) the Tevatron results are by one order of mag-
H1 2002 s rD LO QCD Fit nitude too high [13]. This is not surprising as
QCD factorizationshouldnot holdfor diffractive
hadron-hadronreactions. Furthermore,theTeva-
tron data is measured in the kinematic region
Figure 4. The resulting parton density distri-
0.035 < ξ < 0.095, where the Reggeon exchange
butions in the Pomeron, using a NLO QCD fit
dominates and thus would not be called diffrac-
(shaded line) compared to a LO fit (solid line).
tion. As mentioned above, the validity of the H1
fitisforx <0.05(x atHERAisξ attheTeva-
IP IP
tron). The fact that QCD factorization seems to
bution, which is the outcome of the fact that the fail for hadron-hadron data is also explained by
data show positive scaling violation up to quite introducing the notion of survival probability of
highβ values. Thisisquantifiedinfigure5,which therapiditygap[14]. Takingitatfacevalue,this
shows that for the region 0.01 < β < 1, the glu- would mean that for the Tevatron processes, the
ons carry 80% of the Pomeron momentum. The survival probability is about 0.1. Since the pho-
same conclusion is reached by the LPS analysis. ton has a hadronic part (’resolved photon’), this
Note that the validity of the diffractive parton notion can be tested in diffractive photoproduc-
distribution functions (dpdfs) is in the following tionofdijets[15,12]. Indeeditseemsthatusinga
5
survivalprobability of 0.34 [16], one can describe However, the ratio of σD/σtot is Q2 dependent.
theresolvedphotondata. Thereseemstobesome It can be as high as 20% at Q2 ≈ 3 GeV2, go-
uncertainty about the conclusion concerning the ing down to about 10% at Q2 ≈ 30 GeV2, as
direct part: while the H1 measurement is below can be seen in fig 7, where this ratio is shown
the expectations, the ZEUS result is consistent as a function of Q2, for the kinematic region
with it. 200 < W < 245 GeV, MX < 35 GeV, and
Aninterestingattempttofitthecombineddata MN <2.3GeV.Oneshouldhoweverkeepinmind
ofinclusiveandinclusivediffractiondatawascar-
ried out by Martin, Ryskin and Watt [17], who
included absorption correction to the QCD anal-
ysis. While the quark distributions they get are
not very different from those of H1, their gluon
distributionissignificantlylowerthantheH1one.
This results in expectations which are by almost
factor of 3 lower than the H1 ones for the com-
parison with the Tevatron data (see figure 6). In
Figure 7. The ratio of diffractive to total cross
section as a function of Q2, for a selected kine-
matic region.
that the Q2 dependence might be an outcome of
the factthatinthis presentationofthe ratio,dif-
ferentregionsofβ arecoveredfordifferentvalues
of Q2. Note that this ratio at Q2 = 100 GeV2
goes down to ≈ 5% for x < 0.03 [7].
IP
This ratio has been measuredfor the first time
Figure 6. Effective diffractive structure function for Charged Current diffractive processes [7,18].
for dijet production in pp¯interactions as a func- It is in the range of 2-3 % for x and x< 0.05.
IP
tion of β, compared to expectations of different One can calculate the ratio of diffractive to
sets of diffractive parton distribution functions. total cross section for specific processes and
check whether the parton distributions obtained
from the NLO QCD analysis fulfill the Pumplin
bound [19]. This was done in [16] for diffractive
this case the survival probability would be closer
to inclusive dijet production induced by gluons
to that of the resolved photon case.
and is displayed in figure 8. As seen, the bound
3.9. Ratio of σD to σtot is clearly violated for relatively low scales at low
Diffractive processes were said to constitute x. This might indicate that unitarity effects are
about 10% of the total inclusive DIS processes. already present in the gluon sector.
6
R = diffractive/inclusive dijet production section which decreases with Q2.
4. Exclusive diffractive processes
4.1. Introduction
This section describes exclusive processes like
electroproductionofvectormesonsorDeeplyVir-
m 2=6.5 GeV2
tual Compton Scattering (DVCS). The situation
15 GeV2 inthiscasesismuchsimplerastheseprocessesare
Pumplin bound clearly diffractive processes at the high energies
90 GeV2 where they are measured. There still exist the
problemofisolatingthe ’elastic’processfromthe
proton dissociative one. By measuring the cross
sectionforalimitedlowtrange,the contribution
x of the latter is minimized.
g
4.2. Soft to hard transition
One of the nice features seen in these data is
Figure 8. The ratio of diffractive to inclusive di- the transition from soft to hard processes as one
jet production cross section as a function of x of increases the scale. This transition is seen also
the gluon for different scales of the hard scatter-
ing, for the recent H1 diffractive partondistribu-
tion functions. Also shown is the unitarity limit,
called Pumplin bound.
3.10. Summary on inclusive diffraction
This subsection is more a presentationof some
questions than a real summary. Is Regge factor-
ization broken? Also for x < 0.01? There is a
IP
need for more precise measurements to come to
a clear conclusion. Ideally, so as not to be de-
pendent on the Regge factorization assumption
in diffraction, one would like to do a QCD anal-
ysis for fixed values of x . This will need much
IP
higher statistics than presently available.
ThereisabreakingofQCDfactorizationwhen
usingthepartondistributiondensitiestocompare
to hadron-hadron data. This is interpreted by
theintroductionofthelargerapiditygapsurvival
probability. The value of the survivalprobability
Figure 9. A compilation of elastic photoproduc-
seems to be in the range of 0.1-0.3.
tion of vector mesons, as a function of W. The
The presently obtained gluon momentum den-
total γp cross section is plotted for comparison.
sities seem to give results which are violating the
Pumplin bound, in certain kinematical regions.
This could be the indication of the presence of
unitarity effects. for the photoproduction of vector mesons, where
Thereisalargeratioofdiffractivetototalcross the mass serves as the scale. Figure 9 shows the
7
photoproductioncrosssectionasafunctionofthe changed in the process. This way the effective
γp center of mass energy, W, for different vector trajectoryofthePomeronwasdeterminedforthe
mesons. The light vector mesons, ρ, ω and Φ ρ,φandJ/ψ electroproduction. Asummaryplot
show an energy dependence which is character- of the intercepts and slopes for all three VMs, as
istic of a soft process (the total γp cross section function of Q2 +M2, is presented in figure 11.
V
is also shown for comparison). For the heavier TheinterceptofthelowmassVMsareconsistent
vector mesons, the energy dependence becomes
much steeper, as expected from hard processes.
Note also that the real part of the amplitude in-
creases with the hardness of the process and is a
further reason for the sharp energy dependence.
Thesofttohardtransitioncanalsobeseenfor
a given vector meson, by changing the Q2 of the
δ 0)
process. ThecrosssectionisparameterizedasW (P
I
andδ isseentoincreasewithQ2. Tocompareall a
thevectormesonsononeplot[20]oneshowsδ as
functionofQ2+MV2,withMV being the massof
the vector meson. As seen in figure 10, one gets
anincreaseofδ fromvaluesofabout0.2(soft)at
the low scale end to a value of about 1 (hard) at -2V)
high scales. Ge
(P
’I
a
ZEUS
d1.6 ZEUS f 98-00 (prel.)
ZEUS r 96-97 (prel.)
1.4
ZEUS r 94-95
1.2 ZEUS J/y 96-00
1
0.8 Figure 11. Compilation of α (0) and α′ values,
IP IP
0.6 extracted in exclusive VM production, as a func-
0.4 tion of Q2+M2.
V
0.2
0
-0.2
0 5 10 15 20 25 30 with that of the soft Pomeron. This is not the
Q2 + M2 (GeV2)
V case for the J/ψ which has a significantly higher
intercept. As for the slope, all values are lower
that that of the soft Pomeron, as expected from
Figure 10. The parameter δ from a fit of the hard processes.
form Wδ to the cross section data of exclusive
production of VMs, as a function of Q2+M2. 4.4. Sizes of vector mesons
V
The t distribution of the VMs can be well de-
scribed by an exponentially falling cross section,
withaslopeb. Thisslopeisconnectedtothesize
4.3. Effective Pomeron trajectory of the VM. At low Q2 the size of the light VMs
Using the energy dependence of vector meson is large,decreasing with Q2 from a value of ≈ 10
electroproduction at fixed t values, one can ob- GeV−2 to about 5 GeV−2. For the J/ψ the size
tainthe parametersoftheeffectivetrajectoryex- is small already at low Q2. This can be seen in
8
4
figure 12, where the slope b is plotted as function
COMPASS PRELIMINARY
of Q2. The dotted lines are just to guide the eye. 3.5 ZEUS
H1
3 E665
2.5
2
s
1.5 R = s L
14 rr ZZEEUUSS (prel.) 1 T
r H1 0.5
f ZEUS (prel.)
12 f ZEUS 0
J/y ZEUS
10 J/y H1 -0.150-2 10-1 1 10
Q2 (GeV/c)2
8
6 Figure 13. The Q2 dependence ofR for exclusive
ρ0 electroproduction.
4
2
4.6. Configurations of the photon
0 The photon is described as fluctuating into a
-3 -2 -1 2
10 10 10 1 10 10
qq¯ pair. When the relative kT between the pair
is smallwe speak ofa large spatialconfiguration,
while if the relative kT is large, the photon fluc-
tuates into a small spatial configuration. Longi-
Figure 12. Exponential slope of the t distribu- tudinal photons have small configurations, while
tion measured for exclusive VM production as a transversephotonsconsistofbothlargeandsmall
function of Q2. The lines are to guide the eye. configuration. Asmallspatialconfigurationleads
to hard processes and thus to a steep energy de-
pendence of the cross section. A large configu-
The data seem to convergeat highQ2 ona value ration has a shallower energy dependence, as ex-
of b≈ 5 GeV−2. pected in soft processes.
Itcamethereforeasasurprisethatthe ratioR
4.5. R=σL/σT fortheρelectroproductionprocessisW indepen-
The ratio R of the longitudinal photon cross dent for W values up to 120 GeV and Q2 up to
section, σL, to that of the transversephoton,σT, 19GeV2 [23]. The ratioRisW independentalso
can be obtained by studying the decay distribu- for J/ψ [20].
tion of the VM and assuming s-channel helicity ThismeansthatforsomereasonincaseofVM
conservation. Thishasbeendoneforρ[21,22,20], electroproduction the large configurations of the
φ [20] and J/ψ [20]. Figure 13 shows as an ex- transverse photon are suppressed.
ample the very impressive preliminary measure- Another processwhich seems to send the same
ments of R as a function of Q2 for the ρ VM by messageis DVCS.The energydependence ofthis
the COMPASS collaboration [21]. For all VMs, reaction indicates a hard process. The Wδ de-
R is rising with Q2. A compilation of R for all pendenceyields[24]δ=0.98±0.44fortheH1mea-
three VMs is shown in figure 14, as function of surement and δ=0.75±0.15+0.08 for ZEUS. Such
−0.06
Q2. The lines are a fit to the data of the form a steep energy dependence would be expected
R = a(Q2/M2)b, which indicate that R scales from a dominant longitudinal photon. However,
V
with Q2/M2. in DVCS one goes from a virtual photon to a
V
9
Infact,theexclusivediffractiveproductionofthe
Higgs boson has been proposed as a potential
background free method to search for the light
HiggsatLHC.Onecanalsodreamaboutafuture
ep collider which will allow to reach kinematic
region where phase transitions can be observed.
Clearly diffraction is a subject which will occupy
us for quite some time to come.
Acknowledgments
It is a pleasure to acknowledge and thank the
organizersfortheexcellentorganizationofavery
pleasant conference in a most beautiful location.
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V
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