Measurements of diffractive processes at HERA

11 Pages·0.64 MB·English

by  Aharon Levy

Measurements of diffractive processes at
HERA
Aharon Levy
for the H1 and ZEUS Collaborations
3
0
0 1 Introduction
2
One of the main objectives of ep scattering is to study the structure of the
n
a proton. This is done by performing a deep inelastic scattering (DIS) process
J in which the virtual photon probes the partonic structure of the proton. All

7 events are studied, like in a total cross section experiment.
2 If, however,the finalstate consists of events in which the protonremains

intact,orthereis alargerapiditygap(LRG),wehavediffractiveevents,me-
2
diatedbyacolorsingletexchange.Thesecanbefurtherclassifiedasinclusive
v
2 diffractiveevents,asdepictedin Fig.1,orasexclusive ones,showninFig.2.
2 In this talk, these two classes of processes will be studied.
0
1
0 e Q2 e
3 e (k’)
e (k)
0 γ* V (γ)
x/ Q2
X W
e W
-
p
e P P p (P) t p (P’)
h
t
: Fig.2.Schematicdiagramforexclusive
v Fig.1. Schematicdiagram forinclusive diffractive electroproduction of vector
Xi diffractive DIS ep reaction, where the mesonsV,wheretherapiditygapisbe-
LRGisbetweentheprotonandthefinal tween V and p.
r state X.
a
In the Regge theory of strong interactions [1], the color singlet exchange
isdue to the softPomeron,IP,introducedbyGribov[2],andthe parameters
of its trajectory have been determined by Donnachie and Landshoff [3]. In
contrast to the universal nature of this exchange, in the language of Quan-
tum Chromodynamics (QCD), the color singlet exchange is described as a
two gluon exchange [4]. Since its properties depend on the scale involved
in the interaction,the QCD Pomeronhas a non-universalcharacter.We will
discusstheresultswithrespecttothesoftandthehardbehaviorofthesetwo
approaches, which manifest themselves in the energy behavior of the cross
sections.
2 Aharon Levy
2 Kinematics of diffractive scattering
The variables used in diffractive scattering can be defined using the four
vectors presented in Fig. 3. The usual DIS variables are the negative of the
masssquaredofthevirtualphoton,Q2 =−q2 =−(k−k′)2,thesquareofthe
centerofmassenergyofthe γ∗p system,W2 =(q+p)2,the Bjorkenscaling
Q2
variable,x= 2p·q,whichinthe QuarkPartonModelcanbe thoughtofthe
fraction of the proton momentum carried by the interacting quark, and the
q·p
inelasticity, y = k·p.
,
k
In addition to the above variables, the
k e
e variables used to describe the diffrac-
q quark tive finalstate are
β MX xIP = q·(qp·−pp′) ≃ QQ22++MWX22
x ,t LRG
p IP p, Q2 Q2
p p β = ≃
2q·(p−p′) Q2+M2
X
Fig.3. Schematic diagram of diffrac- t = (p−p′)2.
tiveep interaction.
The fractional proton momentum which participates in the interaction with
γ∗ is x , and β is the equivalent of Bjorken x but relative to the exchanged
IP
object. M is the invariantmass of the hadronic finalstate recoiling against
X
the leading proton, M2 =(q+p−p′)2. The approximate relations hold for
X
small t and large W.
3 Diffraction as soft or hard process
IntheReggedescription,diffractionisasoftprocess.Itspropertiesaredeter-
′
minedbytheuniversalPomerontrajectory,α (t)=α (0)+α t,withα (0)
IP IP IP IP
= 1.081 and α′ = 0.25 GeV−2. Therefore the energy behavior of the total
IP
γ∗p cross section is expected to be σ ∼ (W2)αIP(0)−1 ≃ W0.16. Both the
tot
elasticandtheinclusivediffractioncrosssectionareexpectedtohaveafaster
rise with energy ∼ (W2)2αIP(0)−2/b, where b is the slope of the differential
cross section in t [5].
In the perturbative QCD picture, the diffractive process is viewed, in
the proton rest frame, as follows: the virtual photon fluctuates into a quark-
antiquarkpair,whichinteractdiffractivelywiththeprotonbyexchangingtwo
gluons.Therefore,inthis case,the diffractivecrosssectionis proportionalto
the square of the gluon density. Since the gluon density, xg(x,Q2) ∼ x−λ ∼
(W2)λ, where λ depends on the scale Q2, the diffractive cross section has an
energy behavior ∼ (W4)λ(Q2). At Q2 = 10 GeV2, for example, λ≈ 0.2, and
thus the cross section would have a W0.8 dependence.
The abovediscussionshowsthatwe expecta transitionfromsoftto hard
processes when the virtuality of the probing photon increases.
Diffractiveprocesses at HERA 3
4 Inclusive diffraction
Onecanexpresstheinclusivecrosssectionbyadiffractivestructurefunction
FD which is a function of four variables, x ,t,x,Q2. It was shown [6,7,8]
2 IP
that QCD factorization holds also in case of diffraction. Thus FD can be
2
decomposed into diffractive parton distributions, which would follow the
same DGLAP evolution equation that apply in the DIS inclusive case. If,
inaddition,one postulatesReggefactorization,inthe spiritofIngelmanand
Schlein [9], FD may be decomposed into a universal IP flux and the struc-
2
ture function of the IP. One usually integrates over the t variable, and this
decomposition is written as
dFD(3)(x,Q2,x )
2 dx IP =fIP(xIP)F2IP(β,Q2),
IP
where the x dependence of the flux is universal, independent of β and Q2
IP
and is given by fIP(xIP)∼xI1P−2αIP(0).
ZEUS
xFD(3)IP20000....00002468 β=0.007 β=0.03 β=0.13 β=0.48 (Q2G.42eV2) DiffHHr11a pcrteilivme effeZZcEEtUUivSS epr eαlimIP(0)
0.008 0) 1.3
00..0046 3.7α(IP ALLM97
0.02
0.008 1.2
0.06
0.04 6.9
0.02
0 1.1
0.08
0.06 soft IP
0.04 13.5
0.02 1
100Z-4EUS (prel.1) 097-200..0068 39 10-310-210-1 1 Q120 [G1e0V22]
0.04
Regge fit
0.02
0
10-4 10-2 10-4 10-2 10-4 10-2x Fig.5. Q2 dependence of αIP(0) de-
IP rived from measurements of diffractive
Fig.4. xIP dependence of xIPF2D(3) at andtotalγ∗pcrosssections.Thecurve
fixed β and Q2 values, as denoted in (ALLM97) is a representation of the
thefigure. results obtained in inclusive DIS mea-
surements.
Fig. 4 shows the x dependence of x FD(3) at fixed β and Q2 values, as
IP IP 2
measured by the ZEUS collaboration [10]. The curves are the best fit to the
data(restrictedto x <0.01usingauniversalflux,asdescribedabove,with
IP
α =1.16±.01(stat)+.04(syst).Thisvalue,togetherwithacompilationfrom
IP −.01
other measurements [11], is displayed in Fig. 5. For comparison, also shown
is the Q2 dependence of α (0)derivedfrom the inclusive DIS measurements
IP
4 Aharon Levy
andconvenientlyrepresentedbytheALLM97parameterization[12].Clearly,
theinclusiveDISdataarenotcompatiblewithauniversalIP trajectory.The
diffractive measurements seem to point to some Q2 dependence, though the
uncertaintiesaretoolargeforafirmconclusion.ForQ2 >10GeV2,thevalue
of α (0) is significantly higher than that expected from the soft Pomeron.
IP
TheβandQ2dependenceofthePomeronstructurefunction,asmeasured
by the H1 collaboration [11], are shown in Fig. 6. It is the Pomeron struc-
turefunctionundertheassumptionthatthelongitudinaldiffractivestructure
function is zero, FD = 0, and that Regge factorization holds, and therefore
L
one divides-out the Pomeron flux. One sees that, just like in the inclusive
DIS case, as Q2 increases,the Pomeronstructure function is consistent with
a risingbehaviortowardslowβ.However,unlike the inclusive DIScase,pos-
itive scaling violations are observed up to large β values, and only for β >
0.6, the scaling violations turn negative.
H1 preliminary H1 preliminary
x)IP00.0.18 xQIP2==60.5.0 G0e0V23 xIP=Q02.=080.51 GeV2xIP=0.0Q02=312 GexV2IP=0.01Q2=15 GeV2 x)IP0.1 xβI=P0=.001.30003 xβ=IP0=.0020.001 βx=I0P.0=302.003 β=x0IP.0=430.01 β=0.050
(P0.06 (P0.05
/ f3)I00..0024 / f3)I0.1
σD(r0.1 Q2=20 GeV2 Q2=25 GeV2 Q2=35 GeV2 Q2=45 GeV2 σD(r β=0.067 β=0.080 β=0.107 β=0.130 β=0.167
0.08 0.05
0.06
0.04 0.1
0.02 β=0.200 β=0.267 β=0.320 β=0.433 β=0.500
0.1 0.05
0.08 Q2=60 GeV2 Q2=90 GeV2 Q2=120 GeV2 10-2 10-1
0.06 β 0.1
0.04 β=0.667 β=0.800
0.02 0.05 H1 97 (prel.) y<0.6
H1 97 (prel.) y<0.6; M<2 GeV
10-2 10-1 10-2 10-1 10-2 10-1 H1 2002 σrD NLO QCDX Fit (FLD=0)
H1 97 (prel.) y<0.6 10 102 10 102
HH11 9270 0(2p rσerlD.) N yL<O0. 6Q; CMDX <F2it G (FeLVD=0) Q2 [GeV2]
Fig.6. ThePomeron structurefunction dependenceonβ (left) andon Q2 (right).
D
The curvesare a result of a NLO QCD fit, assuming FL = 0.
An NLO QCD fit, assuming FD = 0, was performed to the data and a
L
gooddescriptionofthe data is obtained.The resulting partondensity distri-
butions in the Pomeronare shownin Fig. 7. They do not differ muchfrom a
LO QCD fit, andhave the feature of a sizable contributionof the gluonden-
sityatlargez (whichissameasβ).UsingthepartondensitiesfromtheNLO
fit, one gets a gooddescriptionof the β andx distribution ofdiffractive jet
IP
∗
production [13] and diffractive D production [14].
Onecancalculatethemomentumfractiontakenbythegluons.Thisturns
out to be a large fraction, about 0.75 ± 0.15 at Q2 = 10 GeV2, and almost
Q2 independent, as can be seen in Fig. 8. Frankfurt and Strikman [15] used
this to calculate the probability that a gluon from the proton will produce
a diffractive process. The find that at x = 10−3 and Q2 = 4 GeV2, this
probability is as high as 0.4, which is very close to the unitarity limit of 0.5.
Diffractiveprocesses at HERA 5
H1 2002 σD NLO QCD Fit
r
H1 preliminary
2Q) Singlet 2Q) Gluon Q[G2eV2] H1 preliminary
z, 0.2 z, 1
Σz ( 0.01 z g( 0 6.5 2z,Q) 1.12 Gfolru 0o.n0 1M<oz<m1entum Fraction
(
]
0.2 1 g
15 + 0.8
0.1 [Σ
z
0 0 z 0.6
d
00..12 1 90 2∫Q) / 0.4 H1 2002 σrD NLO QCD Fit
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 (z, 0.2 ((eexxpp.. +etrhreoor)r. error)
z z g
(He1x p2.0 e0r2r oσrr)D NLO QCD Fit dz z 0 10 102
(exp.+theor. error) ∫ Q2 [GeV2]
H1 2002 σrD LO QCD Fit
Fig.7. The resulting parton density Fig.8. The gluon momentum fraction
distributions in the Pomeron, using a fromaNLOQCDfit,asfunctionofQ2.
NLO QCD fit (shaded line) compared
to a LO fit (solid line).
The ratio of the diffractive cross section to the total γ∗p cross section is
showninFig.9,asfunctionofQ2,forfixedβ values.Thisratio,isremarkably
flat over a wide kinematic range. The ratio is flat also as function of W for
fixed M values [16], contrary to expectations from Regge phenomenology.
X
H1 preliminary
x =0.0003 x =0.001 x =0.003 x =0.01 x =0.03
σ / D(3)r11100023 βI=P0.011 β=IP0.013 β=I0P.017 β=0IP.020 β=0.I0P27
σr 1
103 β=0.032 β=0.043 β=0.050 β=0.067 β=0.080
102
10
1
103 β=0.107 β=0.130 β=0.167 β=0.200 β=0.267
102
10
1
103 β=0.320 β=0.433 β=0.500 β=0.667 β=0.800
102
10
1
10 102 10 102 10 102 10 102 10 102
H1 97 σrD (prel.) / H1 96-97 σr Q2 [GeV2]
Fit (a + b log Q2)
Fig.9. TheratioofthediffractivetototalcrosssectionasfunctionofQ2,forfixed
β values.
6 Aharon Levy
5 Exclusive Vector Mesons
It has been suggested [17] that a good way to see more clearly the different
behavior of soft and hard processes is to study diffractive production of low
masses,inparticularvectormesons.Exclusivevectormeson(VM)production
showsaclearinterplaybetweensoftandharddiffractiveprocesses.Oneofthe
niceexamplestothiseffectcanbeseenincaseoftheelasticphotoproduction
of VMs, whose cross section measurements as function of W are presented
in Fig. 10. There is a clear change in the W dependence when going from
the light VMs, like ρ0,ω and φ, to the heavier ones like J/ψ,ψ(2S) and
Υ. In the latter case, a hard scale is provided by the mass of the heavy
quarks. The shallower W dependence of the light VMs is consistent with
that expected from a soft process, mediated by the IP trajectory, while the
steepW dependenceincaseoftheheavyVMsisconsistentwithexpectations
from a two-gluon exchange hard diffractive process calculated in pQCD.
Fig.10. Compilation of elastic photoproduction of vector mesons, as function of
W.The total γp cross section is plotted for comparison.
Another soft-hard transition can be obtained by using Q2 as a scale in
caseofexclusiveelectroproductionofρ0 [18,19].ThisisdemonstratedinFig.
11,wheretheδ parameter,oftheWδ behaviorofthecrosssection,isplotted
as function of Q2. While at low Q2, δ is consistent with expectations of a
Diffractiveprocesses at HERA 7
soft process, at higher Q2 the values of δ reach those expected from a hard
process.
H1 ρ production
1.6
δ
H1 preliminary
1.4 H1 96
ZEUS 96-97 prel.
1.2 H1 J/ψ δ 3 ZEUS (prel.) DIS 98-00 H1 DIS 95-97
2.5 Wδ ZEUS (prel.) BPC 99-00 H1 PHP
1 ZEUS PHP
2
0.8 1.5
1
0.6
0.5
0.4 0
0 2.5 5 7.5 10 12.5 15 17.5 20
Q2 [GeV2]
0.2
soft pomeron
Fig.12. The parameter δ from a fit of
δ
0 the form W to the cross section data
0 5 10 15 20 25 30 35 40
of J/ψ electroproduction, as function
Q2 [GeV2] of Q2.
Fig.11. The parameter δ from a fit of
δ
the form W to the cross section data
of ρ0 electroproduction, as function of
Q2.
However, in case of exclusive electroproduction of J/ψ [20,21], the hard
scale is provided by the heavy quark mass and thus the value of δ is already
large even at Q2 = 0, as shown in Fig. 12.
ZEUS
J/Ψ H1 Another way of seeing this different
14 ρJ/ ΨZE ZUESU (Sp r(eplr.)el.) behavior of the light and heavy vec-
12 ρ H1 tor mesons, is through the study of
the Q2 dependence of the slope b of
10
the differential cross section dσ/dt of
8 ρ0 and J/ψ. Fig. 13 displays the mea-
sured value of b as function of Q2, for
6
bothvectormesons. Onesees theclear
4 soft-hard transition in case of the ρ0,
whiletheJ/ψproductionisahardpro-
2
cess even in case of photoproduction.
010-3 10-2 10-1 1 10 102 At Q2 ≥ 20 GeV2, both mesons have
the same small size, and the b value is
as expected from the proton size [22].
Fig.13.Theslopebofdσ/dtforρ0and
J/ψ.
8 Aharon Levy
Contraryto the photoproduction case, in the electroproduction of vector
mesons both transversely and linearly polarized photons participate. In the
picture discussed above, where the photon fluctuates into a quark-antiqark
dipole, it can do so in two configurations: a large spatial one, resulting in a
soft process, and a small spatial one, resulting in a hard process [23]. While
thelongitudinalphotonisbelievedtofluctuateintoasmallconfiguration,the
transverse photon can fluctuate into both. It is of interest to study how the
differentconfigurationsofthevirtualphotoninfluencethesoft-hardtransition
discussed above. To this end, one can use s-channel helicity conservation to
measure the ratio R=σ /σ of the cross sections produced by longitudinal
L T
to transverse photons.
H1 ρ production
σσ= / LT1102 H1 preliSmCiHnaCry approximation σσR=/LT Q23..245 [GeV2] MMRRSTT(99)
R H1 7
12
8 ZEUS 19
6
4
2
Martin, Ryskin, Teubner ZEUS 96/97 (Preliminary)
0
0 10 20 30 40
Q2 [GeV2] W [GeV]
Fig.15. The W dependence of R for
Fig.14. TheratioRasfunctionofQ2
ρ0 electroproduction,forfixedQ2 bins.
for ρ0 electroproduction. The curve is
The curves are the predicions of the
theexpectationoftheMRTmodel[26].
MRT model [26].
Fig. 14 shows the ratio R for electroproduction of ρ0, as function of
Q2 [18,25].Thecrosssectioncomingfromthelongitudinalphotondominates
as Q2 gets larger,andthis increaseis welldescribedby the MRT model [26].
What is surprising is the fact that R seems to be independent of W, in the
Q2 range where the measurements were performed, as shown in Fig. 15 [18].
This means that the W dependence of σ is the same as σ , from which
T L
one concludes that the large size configurations of the transverse photon are
suppressed for ρ0 electroproduction. This behavior is well reproduced in the
MRT model, even for the low Q2 data.
Another striking result in case of the electroproduction of ρ0 is shown
in Fig. 16, where the ratio of the electroproduction to the total γ ∗p cross
sections is displayed. This ratio is W independent over the whole measured
Diffractiveprocesses at HERA 9
kinematicregion[27].ThisiscontrarytoexpectationsoftheReggeapproach
aswellasthepQCDone.IncaseoftheJ/ψ,the ratioincreaseswithW,and
the increase is consistent with expectations from both approaches.
ZEUS preliminary
ZEUS preliminary
Fig.17. The ratio of the J/ψ electro-
Fig.16. The ratio of the ρ0 electro-
production cross section to the total
production cross section to the total
γ∗pone,asfunctionofW,atdifferent
γ∗pone,asfunctionofW,atdifferent
scales. The lines are a best fit of the
scales. form Wδ to thedata.
6 Deeply Virtual Compton Scattering (DVCS)
Deeply virtual Compton scattering (DVCS) is a similar process to electro-
productionofVMs, where the finalstate vectoris replacedbya realphoton.
TheDVCSinitialandfinalstatesareidenticaltothoseoftheQEDCompton
process. The diagrams of both processes are shown in Fig. 18.
e e γ
e q γ e e
γ e
q
p p p p p p
Fig.18.DiagramsshowingtheQCDDVCSprocessandtheQEDComptonprocess.
10 Aharon Levy
The big interest in DVCS comes from the fact that the QED and QCD
amplitudes interfere and produces an asymmetry which can be measured,
oncehighstatisticsdataareathand.Thiswouldgiveinformationonthereal
partoftheQCDamplitude.Inaddition,theDVCSprocessisapotentialone
for obtaining generalized parton distributions [28].
ZEUS
b) ZEUS
n
*σγ→γ(p p) ( 10 ZFEFSU4W0S = <( p 8Wr9e <lG. )e1 9V460- 9G7e,9V9-00 e+p →γ p) (nb)10 Q2ZWEδU fiSt (prel.) 96-97,99δ-00 e+p
p 0.44 ± 0.24
H1 97 e+p *γ
1 σ( 6.2 0.89 ± 0.21
9.9
0.80 ± 0.27
-1
10
1
18.0
2
-2 10
10 10 20 30 40 50 60 70 80 90 100 W (GeV)
Q2 (GeV2)
Fig.19. The DVCS cross section as Fig.20. The DVCS cross section as a
function ofQ2.Thebandisatheoreti- function of W for fixedQ2 values. The
δ
cal prediction [31]. lineisafitoftheformW tothedata.
TheQ2 dependenceoftheDVCScrosssectionisshowninFig.19[29,30].
It fall-off with Q2 is well described by the Frankfurt, Freund and Strikman
model [31]. The W dependence of the DVCS cross section is shown in Fig.
20 [29], for fixed Q2 values. Fitting the data to a form of Wδ shows that
the cross section rises steeply as Q2 increases. It reaches the same value of
δ as in the hard process of J/ψ electroproduction. Given the fact that the
final state photonis real,and thus transverselypolarized,the DVCS process
is produced by transversely polarized virtual photons, assuming s-channel
helicity conservation. The steep energy dependence thus indicates that the
large configurations of the virtual transverse photon are suppressed. This is
thesameconclusionasweobtainedaboveinthecaseoftheelectroproduction
of ρ0.
Acknowledgments
I would like to thank the organizers for a very pleasant conference. I would
also like to acknowledgethe partial support of the IsraelScience Foundation
(ISF)andtheGermanIsraelFoundation(GIF),whichmadethiscontribution
possible.