Studying Low-x Dynamics using the Hadronic Final State in DIS at HERA

0.13 MB·English

by  Roman Poeschl

EPJ manuscript No.
(will be inserted by the editor)
x
Studying Low- Dynamics using the Hadronic Final State in DIS
at HERA
Roman Po¨schl a b
4 DESY,Notkestr. 85, D-22603 Hamburg
0
0
Received: February 7, 2008 / Revised version: February7, 2008
2

n
Abstract. This article describes different approaches to investigate the behavior of parton evolution in
a
the proton by exploiting various aspects of the hadronic final state produced in Deep Inelastic Scattering
J
Eventsat HERA.
7

PACS. 13.60.Hb – 12.38.Qk
2
v
5
5 1 Introduction emitted partons, i.e. kt,1 << .. << kt,n << .. << Q2.
0 DGLAP evolution is expected to break down at suffi-
1 Measurementsofthe hadronicfinalstateindeeply inelas- ciently low values of x, when the ordering no longer ap-
1 tic ep scattering (DIS) provide precision tests of quan- plies.
3
tum chromodynamics (QCD). At HERA data are col- At very low values of x it is believed that the theoret-
0
/ lected over a wide range of the negative four-momentum- ically most appropriate description is given by the BFKL
x transferQ2,theBjorkenvariablexandthetransversemo- evolution equations [2]. These resum large logarithms of
e menta p of hadronic final state objects. 1/x up to all orders and impose no restriction on the or-
- T
p Studies of the hadronic final dering of the transverse momenta within the parton cas-
e state may be usedto getinsight cade. Thus off-shell matrix elements have to be used to-
h into the dynamics of the parton gether with an unintegrated gluon distribution function,
v: cascade exchanged in low-x lep- f(x,µ˜2f,kt), which depends on the gluon transverse mo-
i ton proton interactions. Fig. 1 mentum kt as well as x and a hard scale µ˜f. A promising
X
shows a generic DIS process in approachtopartonevolutionatbothlowandlargevalues
r which a gluon from the proton of x is given by the CCFM [3] evolution equation, which,
a
undergoes a QCD cascade. The by means of angular-ordered parton emission, is equiva-
gluon interacts with the virtual lenttothe BFKLansatzforx→0,whilereproducingthe
photon via a hard photon-gluon DGLAP equations at large x.
process which can be calculated
within perturbative QCD using
an exact matrix element. The 2 Forward π0/Jet Cross Sections
cascade itself represents an ap-
proximationforanallorderma-
An extended parton ladder at low x leads to high k par-
t
trixelementcalculationandsev- tonic emission in the region close to the proton remnant
eralprescriptionstodescribethe
(’forward’region)towhichmeasurementsofjetsandlead-
QCD dynamics within the cas- ingparticles,e.g.π0 aresensitive.Productionofaforward
Fig. 1. Diagram of a cade have been proposed. The π0 canberegardedasarefinedversionofforwardjetpro-
generic DIS process at most familiar one is given by duction.Inordertoenhancethesensitivitytolow-xeffects
low x. Here kt denotes the so called DGLAP evolution special selection cuts have been applied such as confining
the transverse momenta equations[1].Intheseequations the ratio p2 /Q2 to values between 0.5 and 2 in-
of theexchanged gluons, the large logarithms in Q2 are T,(π0,Jet)
spired by a proposal in [4].
xg is the fractional mo- resummed, neglecting log(1/x)
mentum of the parton terms. This practically corre-
taking part in the hard
sponds to a strong ordering of
interaction and x is the 2.1 Forward π0 Cross Sections
the transverse momenta of the
Bjorken scaling variable
a For the H1and ZEUS Collaborations Inclusiveforwardπ0crosssectionsfortransversemomenta
b Talk presented at the EPS03, Aachen,July 2003 pT,π0 > 3.5 GeV are shown in Fig. 2 as a function of x
2 Roman P¨oschl: StudyingLow-x Dynamics using theHadronic Final State in DIS at HERA
H1 Forward π0 H1 Forward Jet Data
600
σ[]d/dx nbπ240000 l2. 0DCDH C<II1RR FQ M+(p2L r R<O(e CE8 lDAS.i0mG,S GQCLie2nAA+VaPD42r)pEyT)2 σd/dx(nb)220500 pT,JETH>13CC .d5AAa SStGaCC,e AApVrDDeEEl. JJ22000033--12
0 NLO DISENT
80 8.0 < Q2 < 20.0 GeV2 150
60
40
100
20
0
20 20.0 < Q2 < 70.0 GeV2 50
15
10 pT,π > 3.5 GeV
5 5o < θπ < 25o 0 0.001 0.002 0.003 0.004
0 x
-4 -3
10 10 x
Fig. 2. Forwardπ0 crosssection asafunctionofBjorken-xin Fig. 3. Forward jet cross section as a function of Bjorken-x
different regions of Q2 compared with predictions of DGLAP compared with NLO DGLAP QCD calculations and predic-
tions bythe CCFM Model CASCADE.
and CCFM based QCD Models.
for different regions of Q2. The data are compared with
predictions of the Monte Carlo models RAPGAP [5] and
CASCADE[6].RAPGAPimplementsaQCDmodelbased
onLeadingOrder(O(α ),LO)partonshowerswith(‘DIR
s
+RES’) and without (‘DIR’) resolved photon structure.
CASCADEisemployedasanimplementationoftheCCFM
evolution equation introduced above. The prediction by
RAPGAP with a pointlike photon (DIR) is well below
the data. A reasonabledescriptionof the data is achieved
by including contributions from resolved virtual photons
in the predictions and using a factorization scale of Q2+
4pT,π0. Note, that resolved contributions can be consid-
Fig. 4. Inclusive jet cross section as a function of Bjorken-x
ered to mimic a lack of ordering in transverse momen-
compared with NLO DGLAP QCD predictions and DGLAP
tum as required for a DGLAP evolution scheme. CAS-
based QCD Models.
CADE predictions based on the unintegrated gluon den-
sity JS2001[6]onthe otherhand undershootthe data for
lower values of Q2.
3 Inclusive Jet Cross Sections
In the following analysis ofinclusive jet crosssections the
restriction to the forward region and the kinematic con-
2.2 Forward Jet Cross Sections finement introduced in Sec. 2 are removed, leading to a
somewhatmore generalstudy ofjet crosssections.In [10]
itisoutlinedthatthecomparisonofthemeasuredjetcross
sections with matrix element calculations including con-
Results complementary to the ones discussed in Sec. 2.1 tributions up to O(α ) performed with DISENT lead to
s
are obtained by studying jets in the same region of phase significantdiscrepanciesbetweenthedataandthetheoret-
space. Jets are reconstructed with the longitudinally in- ical predictions. If, however, hadronic activity in the for-
variant k cluster algorithm [7]. Fig. 3 shows the forward ward and the backward hemisphere is required and NLO
t
jetcrosssectionfortransversemomentap >3.5GeV (O(α2)) predictions are employed a much better agree-
T,Jet s
as a function of x. The data are compared with NLO ment between the data and the theoretical prediction is
(O(α2)) QCD calculations performed with the program obtained,whichisdemonstratedinFig.4.Thetheoretical
s
DISENT [9] and predictions by CASCADE based on two error represented by the hatched band is due to missing
recent sets of unintegrated gluon distributions [8]. While higher order contributions in the theoretical calculations.
results of the NLO QCD calculations are significantly be- Predictions based on LO DGLAP parton showers, here
low the data, the CASCADE prediction based on the set represented by LEPTO [11], undershoot the data at low-
labelled J2003-1is in good agreement with the data. The x while a good description of the data is obtained by the
difference between the CASCADE predictions indicates CDM [12] model as implemented in the event generator
the sensitivity of forward jet data to low-x dynamics. ARIADNE [13].
Roman P¨oschl: StudyingLow-x Dynamics using theHadronic Final State in DIS at HERA 3
4 Azimuthal Correlations between Jets S S
5<Q2<10 GeV2 10<Q2<15 GeV2
0.1 0.1
Insight into low-x dynamics can be gained from inclusive H1 Data
dijetdatabystudyingthebehaviorofeventswithasmall
∗
azimuthal separation, ∆φ , between the two hardest jets
as measured in the hadronic center-of-mass system [14–
0 0
16]. Partons entering the hard scattering process with 0.2 0.5 1 0.2 0.5 1
x [× 103] x [× 103]
negligible transverse momentum, kt, as assumed in the S S
15<Q2<20 GeV2 20<Q2<30 GeV2
DGLAPformalism,leadatleadingordertoaback-to-back 0.1 0.1
∗ ◦
configuration of the two outgoing jets with ∆φ = 180 .
◦
Azimuthaljetseparationsdifferentfrom180 occurdueto
higher order QCD effects. However, in models which pre-
dict a significant proportion of partons entering the hard
0 0
process with large k , the number of events with small 0.5 1 2 0.5 1 2
∗ t x [× 103] x [× 103]
∆φ should also increase. S S
30<Q2<50 GeV2 50<Q2<100 GeV2
Here we present a measurement of the ratio 0.1 0.1
R120◦N (∆φ∗,x,Q2)d∆φ∗ Lµ2rO= E(–DT*2I,S µE2f=N7T0 )GeV2 (Nµc2roL=r OrEe–c T*(t2eN,d µL f2foO=r7 Jh0aE dGTroe)nViz2ation)
S = 0 dijet ,
R180◦N (∆φ∗,x,Q2)d∆φ∗
0 dijet
0 0
1 2 3 4 1 2 5
of the number of events Ndijet with an azimuthal jet sep- x [× 103] x [× 103]
∗ ◦
aration of ∆φ <120 relative to all dijet events. The
Fig.5. TheobservableS givenasafunctionofBjorken-xand
observable was proposed in [16] and is considered to be Q2 compared with LO and NLO DGLAPQCD predictions.
directly sensitive to low-x effects.
Fig.5presentstheS-distributionasafunctionofxfor
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http://www.desy.de/~jung/rapgap.html.
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