DESY ISSN
January
A Measurement of the
Proton Structure Function F x Q
H Collab oration
Abstract
2
A measurement of the proton structure function F x Q is rep orted for mo
2
2 2 2
mentum transfers squared Q b etween GeV and GeV and for Bjorken
4
x b etween and using data collected by the HERA exp eriment H in
It is observed that F increases signi cantly with decreasing x con rming
2
our previous measurement made with one tenth of the data available in this analy
2
sis The Q dep endence is approximately logarithmic over the full kinematic range
covered The subsample of deep inelastic events with a large pseudo rapidity gap
in the hadronic energy ow close to the proton remnant is used to measure the
di ractive contribution to F
2
submitted to Nucl Phys B
H Collab oration
3 13 35 40 24 28 11
T Ahmed S Aid A Akhundov V Andreev B Andrieu R D Appuhn
36 26 35 17 24 29 11
M Arpagaus A Babaev J Baehr J B an P Baranov E Barrelet W Bartel
4 29 37 11 24 1
M Barth U Bassler H P Beck H J Behrend A Belousov Ch Berger
1 29 36 4 9
H Bergstein G Bernardi R Bernet G Bertrand Coremans M Besan con
11 22 27 13 8 4
R Beyer P Biddulph J C Bizot V Blob el K Borras F Botterweck
28 14 11 1 27 17
V Boudry A Braemer F Brasse W Braunschweig V Brisson D Bruncko
15 11 13 11 13 11 39
C Brune R Buchholz L Bungener J Burger F W Busser A Buniatian
18 26 11 26 11 5
S Burke G Buschhorn A J Campb ell T Carli F Charles D Clarke
18 4 8 8 19 5
A B Clegg B Clerbaux M Colomb o J G Contreras C Cormack J A Coughlan
27 9 9 11 5 30
A Courau Ch Coutures G Cozzika L Criegee D G Cussans J Cvach
29 19 23 16 34 9
S Dagoret J B Dainton M Danilov W D Dau K Daum M David
11 27 29 11 4 32
E De ur B Delcourt L Del Buono A De Ro eck E A De Wolf P Di Nezza
37 3 2 23 29 13
C Dollfus J D Dowell H B Dreis V Droutskoi J Dub o c D Dullmann
13 12 34 19 11 23 37
O Dunger H Duhm J Eb ert T R Eb ert G Eckerlin V Efremenko S Egli
35 37 36 14 20
H Ehrlichmann S Eichenb erger R Eichler F Eisele E Eisenhandler
22 11 14 36 4 4
R J Ellison E Elsen M Erdmann W Erdmann E Evrard L Favart
23 13 11 9 15 32
A Fedotov D Feeken R Felst J Feltesse J Ferencei F Ferrarotto
11 11 26 2 24 23
K Flamm M Fleischer M Flieser G Flugge A Fomenko B Fominykh
7 31 22 11 12 19
M Forbush J Form anek J M Foster G Franke E Fretwurst E Gabathuler
33 26 3 11 8 11
K Gabathuler K Gamerdinger J Garvey J Gayler M Gebauer A Gellrich
1 11 11 6 24 29
H Genzel R Gerhards U Go erlach L Go erlich N Gogitidze M Goldb erg
8 29 23 23 36 2
D Goldner B Gonzalez Pineiro I Gorelov P Goritchev C Grab H Gr assler
2 19 26 26 16 35
R Gr assler T Greenshaw G Grindhammer A Grub er C Grub er J Haack
11 6 29 1 18 11
D Haidt L Ha jduk O Hamon M Hamp el E M Hanlon M Hapke
5 20 13 18 35
W J Haynes J Heatherington G Heinzelmann R C W Henderson H Henschel
1 30 26 11 5 35
R Herma I Herynek M F Hess W Hildesheim P Hill K H Hiller
22 30 22 8 33 3
C D Hilton J Hladky K C Ho eger M H oppner R Horisb erger V L Hudgson
4 8 14 22 1 9
Ph Huet M Hutte H Hufnagel M Ibb otson H Itterb eck M A Jabiol
27 21 27 15 11 21
A Jacholkowska C Jacobsson M Ja re J Janoth T Jansen L J onsson
13 4 18 29 20 20
K Johannsen D P Johnson L Johnson H Jung P I P Kalmus D Kant
2 12 16 14 35
R Kaschowitz P Kasselmann U Kathage J Katzy H H Kaufmann
11 3 25 1 26 35
S Kazarian I R Kenyon S Kermiche C Keuker C Kiesling M Klein
13 11 7 1 26 8 7
C Kleinwort G Knies W Ko T K ohler J K ohne H Kolanoski F Kole
22 11 8 35 24 8
S D Kolya V Korb el M Korn P Kostka S K Kotelnikov T Kr amerk amp er
6 29 11 2 11 11
M W Krasny H Krehbiel D Kruc ker U Kruger U Kruner Marquis
26 2 26 17 8 34
J P Kub enka H Kuster M Kuhlen T Kur ca J Kurzh ofer B Kuznik
29 28 7 20 35 26
D Lacour F Lamarche R Lander M P J Landon W Lange P Lanius
9 24 11 11 24 2 8
J F Lap orte A Leb edev C Leverenz S Levonian Ch Ley A Lindner
12 11 13 11 27 21
G Lindstr om F Linsel J Lipinski B List P Lo ch H Lohmander
20 23 8 11 34 24 7
G C Lop ez V Lubimov D Luk e N Magnussen E Malinovski S Mani
17 4 25 22 34 11
R Mara cek P Marage J Marks R Marshall J Martens R Martin
1 6 2 20 19
H U Martyn J Martyniak S Masson T Mavroidis S J Max eld
19 22 15 22 11 37
S J McMahon A Mehta K Meier D Mercer T Merz C A Meyer
34 11 6 19 28 5 6
H Meyer J Meyer S Miko cki D Milstead F Moreau J V Morris E Mro czko
11 37 17 23 35 13
G Muller K Muller P Mur n V Nagovizin R Nahnhauer B Naroska
35 3 18 29 29 3
Th Naumann P R Newman D Newton D Neyret H K Nguyen T C Nicholls
13 11 1 6 5 21
F Nieb ergall C Niebuhr R Nisius G Nowak G W Noyes M Nyb erg Werther
19 26 8 11 12 4
M Oakden H Ob erlack U Obro ck J E Olsson E Panaro A Panitch
27 19 35 9 22 12 36
C Pascaud G D Patel E Pepp el E Perez J P Phillips Ch Pichler D Pitzl
7 11 11 11 1 30 11
G Pop e S Prell R Prosi G R adel F Raupach P Reimer S Reinshagen
26 8 12 36 13 2 20
P Ribarics H Rick V Riech J Riedlb erger S Riess M Rietz E Rizvi
3 37 35 4 1
S M Rob ertson P Robmann H E Rolo R Ro osen K Rosenbauer
23 7 9 26 24 6 20
A Rostovtsev F Rouse C Royon K Ruter S Rusakov K Rybicki R Rylko
2 26 5 23 26 11
N Sahlmann E Sanchez D P C Sankey M Savitsky P Schacht S Schiek
14 20 11 34 13 11
P Schlep er W von Schlipp e C Schmidt D Schmidt G Schmidt A Sch oning
11 26 14 35 13 11
V Schr oder E Schuhmann B Schwab A Schwind U Seehausen F Sefkow
12 11 23 23 24 26
M Seidel R Sell A Semenov V Shekelyan I Sheviakov H Sho oshtari
24 16 16 28 10 24
L N Shtarkov G Siegmon U Siewert Y Sirois I O Skillicorn P Smirnov
7 24 8 13 1 13
J R Smith Y Soloviev J Spiekermann H Spitzer R Starosta M Steenb o ck
11 2 32 22 11 15 35
P Ste en R Steinb erg B Stella K Stephens J Stier J Stiewe U St osslein
30 37 2 3 15
J Strachota U Straumann W Struczinski J P Sutton S Tapprogge
38 27 23 28 20 37 6
R E Taylor V Tchernyshov C Thiebaux G Thompson P Tru ol J Turnau
14 2 24 31 31 25 4
J Tutas P Uelkes A Usik S Valk ar A Valk arov a C Vall ee P Van Esch
4 11 39 24 30 9 9
P Van Mechelen A Vartap etian Y Vazdik M Vecko P Verrecchia G Villet
8 2 33 18 8 13
K Wacker A Wagener M Wagener I W Walker A Walther G Web er
11 8 11 26 3 7
M Web er D Wegener A Wegner H P Wellisch L R West S Willard
35 11 22 11 11 29
M Winde G G Winter A E Wright E Wunsc h N Wul T P Yiou
31 12 27 23 11 11
J Z a cek D Zarb o ck Z Zhang A Zhokin M Zimmer W Zimmermann
27 15
F Zomer and K Zub er
1 a
I Physikalisches Institut der RWTH Aachen Germany
2 a
III Physikalisches Institut der RWTH Aachen Germany
3 b
School of Physics and Space Research University of Birmingham Birmingham UK
4
Inter University Institute for High Energies ULB VUB Brussels Universitaire Instel ling
c
Antwerpen Wilrijk Belgium
5 b
Rutherford Appleton Laboratory Chilton Didcot UK
6 d
Institute for Nuclear Physics Cracow Poland
7 e
Physics Department and IIRPA University of California Davis California USA
8 a
Institut fur Physik Universit at Dortmund Dortmund Germany
9
CEA DSM DAPNIA CE Saclay Gif sur Yvette France
10 b
Department of Physics and Astronomy University of Glasgow Glasgow UK
11 a
DESY Hamburg Germany
12 a
I Institut fur Experimentalphysik Universit at Hamburg Hamburg Germany
13 a
II Institut fur Experimentalphysik Universit at Hamburg Hamburg Germany
14 a
Physikalisches Institut Universit at Heidelberg Heidelberg Germany
15 a
Institut fur Hochenergiephysik Universit at Heidelberg Heidelberg Germany
16 a
Institut fur Reine und Angewandte Kernphysik Universit at Kiel Kiel Germany
17 f
Institute of Experimental Physics Slovak Academy of Sciences Ko sice Slovak Republic
18 b
School of Physics and Materials University of Lancaster Lancaster UK
19 b
Department of Physics University of Liverpool Liverpool UK
20 b
Queen Mary and West eld Col lege London UK
21 g
Physics Department University of Lund Lund Sweden
22 b
Physics Department University of Manchester Manchester UK
23
Institute for Theoretical and Experimental Physics Moscow Russia
24 f
Lebedev Physical Institute Moscow Russia
25
CPPM Universit e d Aix Marseil le II IN P CNRS Marseil le France
26 a
Max Planck Institut fur Physik Munchen Germany
27
LAL Universit e de Paris Sud IN P CNRS Orsay France
28
LPNHE Ecole Polytechnique IN P CNRS Palaiseau France
29
LPNHE Universit es Paris VI and VII IN P CNRS Paris France
30 f h
Institute of Physics Czech Academy of Sciences Praha Czech Republic
31 f h
Nuclear Center Charles University Praha Czech Republic
32
INFN Roma and Dipartimento di Fisica Universita La Sapienza Roma Italy
33
Paul Scherrer Institut Vil ligen Switzerland
34
Fachbereich Physik Bergische Universit at Gesamthochschule Wuppertal Wuppertal
a
Germany
35 a
DESY Institut fur Hochenergiephysik Zeuthen Germany
36 i
Institut fur Teilchenphysik ETH Zurich Switzerland
37 i
Physik Institut der Universit at Zurich Zurich Switzerland
38
Stanford Linear Accelerator Center Stanford California USA
39
Visitor from Yerevan Phys Inst Armenia
40 a
Visitor from Institute of Physics Azerbaijan Academy of Sciences Baku Azerbaijan
Supported by the Bundesministerium fur Forschung und Technologie FRG under contract
numbers AC P AC P DO I HH P HH I HD I HD I KI P
MP I and WT P
b
Supported by the UK Particle Physics and Astronomy Research Council and formerly by
the UK Science and Engineering Research Council
c
Supported by FNRS NFWO IISN IIKW
d
Supported by the Polish State Committee for Scienti c Research grant No
e
Supported in part by USDOE grant DE F ER
f
Supported by the Deutsche Forschungsgemeinschaft
g
Supported by the Swedish Natural Science Research Council
h
Supported by GA CR grant no and by GA AV CR grant no
i
Supported by the Swiss National Science Foundation
Intro duction
The measurement of the inclusive deep inelastic lepton proton scattering cross section has
b een of great imp ortance for the understanding of quark gluon substructure of the proton
Exp eriments at HERA extend the previously accessible kinematic range up to very large
2 4 2 4
squared momentum transfers Q GeV and to very small values of Bjorken x
2
In the rst observation was rep orted of a rise of the proton structure function F x Q
2
2
at low x with decreasing x Such a b ehaviour is qualitatively exp ected in
the double leading log limit of Quantum Chromo dynamics It is however not clari ed
whether the linear QCD evolution equations as the conventional DGLAP evolution in
2
ln Q and or the BFKL evolution in ln x describ e the rise of F or whether there is
2
a signi cant e ect due to nonlinear parton recombination The quantitative investigation
of the quark gluon interaction dynamics at low x is one of the ma jor challenges at HERA
It requires high precision for the F measurement and an investigation of the hadronic nal
2
state
2
The structure function F x Q is derived from the inclusive lepton proton scattering
2
2
cross section It dep ends on the squared four momentum transfer Q and the scaling variable
x These variables are related to the inelasticity parameter y and to the total squared centre
2
of mass energy of the collision s as Q xy s with s E E In the incident electron
e p
energy was E GeV and the proton energy was E GeV A salient feature of
e p
the HERA collider exp eriments is the p ossibility of measuring not only the scattered electron
but also the complete hadronic nal state apart from losses near the b eam pip e This means
2
that the kinematical variables x y and Q can b e determined with complementary metho ds
which exp erimentally are sensitive to di erent systematic e ects The comparison of the
results obtained with di erent metho ds improves the accuracy of the F measurement A
2
convenient combination of the results ensures maximum coverage of the available kinematic
range
In this pap er an analysis is presented of inclusive deep inelastic scattering DIS data
1
taken by the H collab oration in with an integrated luminosity of pb During
its second year of op eration HERA delivered an integrated luminosity of an order of
magnitude larger than in With these increased statistics the accessible kinematic range
has b een extended and the b ehaviour of F has b een investigated at a new level of precision
2
A similar measurement was published recently by the ZEUS collab oration
The structure function results presented here are more precise with a typical systematic
error of than the previous H data The following new information is provided i
analyzing data with shifted vertex p osition along the proton b eam line the rst DIS data for
2 2
Q b etween and GeV at x is obtained in a region where new e ects could b e
observed ii the analysis extends down to y which allows for the rst time to approach
with HERA data the region of the xed target lepton proton scattering exp eriments iii due
2 2
to the increased statistics the rst precise H measurement of F b eyond Q GeV
2
can b e presented An analysis is presented of the dep endence of F on the e ective mass W
2
of the virtual photon proton system which due to the very large energy s at HERA can b e
p erformed in a new kinematic range
A rst measurement is given of the di ractive contribution to F by analyzing the sub
2
sample of ab out of the DIS events which exhibit no activity in the forward detector region
where forward denotes the direction of the proton b eam Characteristics of the events with
a large pseudo rapidity gap in the hadron ow close to the proton remnant direction have
already b een studied at HERA
The pap er is organized as follows After a brief intro duction to the kinematics of the
inclusive ep scattering pro cess sec the H apparatus and the data taking sec
are describ ed Then the event selection including the background rejection sec and the
detector resp onse sec are discussed Section describ es the F analyses and discusses the
2
results In section the di ractive data analysis is presented The pap er is summarized in
section
Kinematics and Analysis Metho ds
The kinematic variables of the inclusive scattering pro cess ep eX can b e reconstructed in
di erent ways using measured quantities from the hadronic nal state and from the scattered
2
electron The choice of the reconstruction metho d for Q and y determines the size of
2
systematic errors acceptance and radiative corrections The basic formulae for Q and y
2
used in the di erent metho ds are summarized b elow x b eing obtained from Q xy s For
the electron E metho d
0
2
0 2
E E sin
e e
2
e e
2
y sin Q
e
e
E y
e e
where the electron p olar angle is de ned with resp ect to the incident proton b eam direction
2
z axis The resolution in Q is while the precision of the y measurement degrades
e
e
as y Thus the electron metho d cannot b e used for y In the low y region it
e e
is however p ossible to use the hadronic metho ds for which it is convenient to de ne the
following variables
X X X
2 2 2 h
p p E p p
x i y i i z i
T
i i i
Here E p p p are the four momentum vector comp onents of each particle and the sum
x y z
mations extend over all hadronic nal state particles The standard de nitions for y
h
and are
h
h
y tan
h
h
E p
e
T
2
The combination of y and Q de nes the mixed metho d which is well suited for medium
h
e
and low y measurements It was used in the previous H analysis of F The double angle
2
DA metho d makes use only of and with
e h
tan cot
h e
2 2
y Q E
DA
DA e
tan tan tan tan
e h e h
The metho d is rather insensitive to the absolute energy calibration of the detector It has
2
go o d resolution at large Q where the jet energies are high but the resolution deteriorates
2
for x The formulae for the metho d are constructed requiring Q and y
to b e indep endent of the incident electron energy Replacing in eq the quantity E by
e
0 1
E cos as allowed by the conservation of the total E P of the event and
e z
e
y by y in eq one obtains
e
0
2
2
E sin
e
e
2
y and Q
0
E y cos
e
e
For non radiative events y and y are equivalent at low y However the mo di ed quantity
h
y is less sensitive than y to the imprecise hadronic measurement at high y since the term
h
dominates the E P of the event Therefore the metho d can b e applied over the full
z
kinematic range considered in this pap er
2
All these metho ds were utilized to measure F Resolution values of the x and Q variables
2
reconstructed with the H detector are discussed for all metho ds at the end of section
The H Detector and the Data Taking in
The H Detector
The H detector is a nearly hermetic multi purp ose apparatus built to investigate the
inelastic high energy interactions of electrons and protons at HERA The structure function
measurement relies essentially on the inner tracking chamb er system on the backward elec
tromagnetic calorimeter and on the liquid argon calorimeters which are describ ed brie y
b elow For the luminosity measurement see section
The tracking system includes the central tracking chamb ers the forward tracker mo dules
and a backward prop ortional chamb er These chamb ers are placed around the b eam pip e at
z p ositions b etween m and m A sup erconducting solenoid surrounding b oth the
tracking system and the liquid argon calorimeter provides a uniform magnetic eld of T
The central jet chamb er CJC consists of two concentric drift chamb ers covering a p olar
o
angle of to Tracks crossing the CJC are measured with a transverse momentum
resolution of p p p GeV The CJC is supplemented by two cylindrical drift
T T T
chamb ers at radii of and cm resp ectively to determine the z co ordinate of the tracks
To each of the z drift chamb ers a prop ortional chamb er is attached for triggering The inner
one CIP was used in addition to estimate residual photopro duction background
A tracking chamb er system made of three identical mo dules measures charged particles
o o
emitted in forward direction to This forward tracker FT is used to determine the
vertex for the events which leave no track in the CJC This extends the analysis into the
larger x region
In the backward region a four plane multiwire prop ortional chamb er BPC provides a
space p oint for charged particles with a spatial resolution of ab out mm in the transverse
o o
plane The p olar angle acceptance of the BPC ranges from to The reconstructed
space p oint together with the z vertex p osition de nes the p olar angle of the scattered elec
trons
The BPC is attached to the backward electromagnetic calorimeter BEMC which is made
2
of lead scintillator stacks with a size of cm and a depth of radiation lengths
P
1
de ned as E P E p the sum extending over all particles j of the event
z j z j
j
corresp onding to ab out one hadronic interaction length The angular coverage of the BEMC
o o
is A cm spatial resolution of the lateral shower p osition is achieved
using four photo dio des which detect the wavelength shifted light from each of the scintillator
stacks A scintillator ho doscop e TOF situated b ehind the BEMC is used to veto proton
induced background events based on their early time of arrival compared with nominal ep
collisions
2
Hadronic nal state energies and electrons at high Q are measured in the highly seg
o
mented liquid argon LAr calorimeter which covers an angular region b etween and
o
The LAr calorimeter consists of an electromagnetic e m section with lead absorb er
and a hadronic section with stainless steel absorb er The electromagnetic part has a depth
b etween and radiation lengths The total depth of b oth calorimeters varies b etween
and interaction lengths The most backward part of the LAr calorimeter is a smaller
2 o o
electromagnetic calorimeter BBE which covers the p olar angle range from to
2 o
The DIS events in the backward region low Q data were triggered by an
e
energy cluster in the BEMC E GeV which was not veto ed by an out of time signal in the
2
TOF The high Q events were triggered by requiring an e m energy cluster with E GeV
in the LAr calorimeter For lower energy thresholds GeV the events were also triggered
if there was simultaneously a tracking trigger The trigger e ciency has b een determined
from the data using the redundancy of the H trigger system which relies on calorimetry and
0
tracking In the region of the nal F data presented b elow i e for E GeV the DIS
2
e
electron trigger e ciency is within the errors
Data Samples and Luminosity
In HERA was op erated with colliding electron and proton bunches Sixteen pilot
bunches proton and electron underwent no ep collision From these the b eam induced
background could b e estimated A small part of the data was taken with the nominal inter
2 2
action p osition shifted in z by cm in order to reach Q values as low as GeV The
2
lower Q region was covered also by analyzing events which originated from the so called
early proton satellite bunch which collided with an electron bunch at z cm The
satellite bunch data amount to of the total data Both event samples with shifted z
vertex p ositions were analyzed indep endently and the results combined
To reduce the systematic errors of the F measurement a strict data selection was p er
2
formed based on the b ehaviour of the main detector comp onents In particular data taken
during a p erio d in which there was no magnetic eld due to a failure of the coil were excluded
1
pb The numb er of accepted events p er luminosity was checked to b e constant
within statistical errors during the full data taking p erio d
The luminosity was determined from the measured cross section of the Bethe Heitler
reaction e p e p The nal state electron and the photon are simultaneously detected
2 o
The H detector calorimetry and electron detection is thus split into two parts At large angles
the electron is measured in the BEMC and preceding tracking chamb ers This de nes for the subsequent
2 o
analysis the low Q data sample Electrons at lower p olar angles are detected in the LAr calorimeter
2
and the forward and central chamb ers de ning the high Q event sample For the structure function analysis
2
b oth data samples were combined but the analyses of the low and high Q data required partially sp eci c
techniques and cuts Sp ecial attention had to b e paid to the BEMC BBE transition region where the electron
energy is often shared b etween the two calorimeters
in small electromagnetic calorimeters electron and photon taggers close to the b eam
pip e but at a large distance from the main detector at z m and z m
This coincidence metho d gives the b est on line luminosity estimate but it is sensitive to
variations in the electron b eam optics through the electron tagger acceptance Therefore the
nal luminosity determination was p erformed based on the hard photon bremsstrahlung data
using the photon tagger only The results of these two metho ds di er by This is well
b elow the overall systematic error which is estimated to b e equal to
An indep endent check of the luminosity measurement has b een p erformed by determining
the cross section for QED Compton events which leave a scattered electron and a photon in
the backward part of the apparatus For the data this yields a luminosity value which
is lower than the one from the Bethe Heitler cross section measurement with a combined
systematic and statistical error of
1
The integrated luminosity for the nominal vertex data used in this analysis is pb
1
and nb for the sp ecial data taking with the shifted vertex p osition The luminosity of
the satellite data was obtained from the measured luminosity for the nominal vertex data
multiplied by the e ciency corrected event ratio in a kinematic region common to b oth data
sets The error of that luminosity determination was estimated to b e
Event Selection and Monte Carlo Simulation
Event Selection
The event selection criteria can b e divided into four categories i electron identi cation
ii event vertex requirement iii kinematical constraints and iv background rejection The
latter is discussed in the subsequent section A summary of the selection cuts is given in
tables and
i For the electron identi cation in the backward region of the H detector for
e
o
the most energetic cluster in the BEMC is selected Its center of gravity is required
to b e at a radial distance CLBP smaller than cm from a reconstructed BPC p oint
The lateral size ECRA of that cluster calculated as the energy weighted radial distance
of the cells from the cluster centre has to b e smaller than cm In the LAr calorimeter
o
for several electron identi cation algorithms have b een develop ed which have
e
the common feature of demanding signi cant electromagnetic energy dep osited in a con ned
region table The E metho d required an isolated electromagnetic cluster with
4
and a minimum relative energy of in the rst e m layer of the LAr calorimeter
3
which amounts to ab out three radiation lengths Here is the energy sum over the four
4
most energetic cells of a cluster divided by its total energy For the analysis an e m cluster
with was considered to b e an electron
4
o o
In the transition region b etween the BEMC and the BBE for ab out a
e
dedicated E and DA analysis was p erformed in which the electron nding was based on
0
top ological criteria only i e without making use of E explicitely For the analysis a
e
ducial cut was applied if the electron cluster was shared b etween the BEMC and the BBE
2
Because of the smearing of the z vertex p osition there is no loss in the x Q coverage only
a reduction in statistics
The electron identi cation e ciency for DIS events as determined from Monte Carlo
simulation is b etter than apart from the BEMC BBE transition region where it amounts
to approximately The scattered electron is considered to b e the cluster with the largest
energy If two electron candidates are present in the same event the one of highest energy
is selected This intro duces a misidenti cation probability of at most at the smallest
electron energy which was considered in the systematic error calculation
ii The event vertex p osition is needed for a precise determination of the kinematics It
was de ned by at least one well measured track in the CJC or in the FT crossing the b eam
axis The z vertex region for the events with interactions in the nominal time intervals was
z cm For the satellite bunch data the requirement was z cm
and for the shifted vertex data z cm The vertex reconstruction e ciency as
determined from the data is at y It decreases smo othly to an average of
in the lowest y bins y since with decreasing y the hadronic particles are emitted at
smaller p olar angles The vertex reconstruction e ciency for the shifted vertex data is only
ab out lower than for the nominal vertex data since z cm is still inside the central
tracking system
o
iii The basic kinematic constraints were a maximum electron scattering angle of
o
for the shifted vertex data and minimum energy requirements in order to ensure
2
high trigger e ciency and a small photopro duction background For the high Q data the
minimum energy requirement was replaced by intro ducing a cut rejecting events at high y
e
2 0
At low Q the minimum electron candidate energy E was GeV for the E analysis and
e
GeV for the analysis That di erence is an example of selection criteria di erences arising
due to the combination of several complete and indep endent analyses The analysis also
required a total missing transverse momentum smaller than GeV and a total E P b etween
z
and GeV In analyzing the BEMC BBE transition region alternative requirements like
0
l og y y were intro duced avoiding the use of E in the selection The latter
DA h
e
conditions rejected photopro duction background events and DIS events with an energetic
photon radiated along the electron b eam direction thus reducing the radiative corrections to
F
2
E metho d metho d DA metho d
o
e
0
E GeV
e
z cm
v er tex
ECRA cm
CLBP cm
E P GeV
z
o
h
selected events
2 o
Table Summary of event selection criteria for the low Q data i e for For the
e
de nitions of abbreviations see the text
E metho d metho d DA metho d
o
e
y
e
z cm track
v er tex
electron ident min R
4 4 cl
0 0
E GeV E GeV
3
e e
h e
p p
T T
E P GeV
z
missing p GeV
T
selected events
2
Table Summary of event selection criteria for the high Q data Further top ological
requirements based on the LAr calorimeter were imp osed to reject background The quantity
R in the DA metho d denotes the average over calorimeter cell energies of the p olar angle
cl
distance b etween a cell and the cluster centre which is a measure of the lateral extension of
the calorimeter energy dep osition For further de nitions see the text
Background Rejection
Non ep Background
2
At low Q the main sources of non ep background are due to proton b eam interactions with
residual gas and b eam line elements upstream of the H detector Beam wall events in the
interaction region were rejected by requiring the reconstructed vertex to b e centered on the
b eam axis An e cient reduction of the remaining background is provided by the minimum
energy and the vertex requirements discussed ab ove In addition two algorithms have b een
develop ed based on the central tracking information An event was rejected either if the
fraction of tracks which did not p oint to the reconstructed vertex was to o high or if at least
two tracks p ointed to the backward direction and crossed the b eam line at z cm Both
algorithms gave similar results They intro duced a loss of a few p er cent of genuine DIS events
which was controlled by eye scanning and corrected for From the study of pilot bunches the
residual background was estimated to represent less than of the total numb er of selected
events
2
At high Q the main background is due to muons travelling o axis parallel to the proton
b eam These are pro duced by proton b eam halo interactions and o ccasionally generate an
electromagnetic shower in the LAr calorimeter Requiring a reconstructed vertex rejects most
of them Further rejection was obtained by requiring more than GeV dep osited outside the
calorimeter region which contains the electron candidate cluster Residual cosmic ray event
candidates were rejected with similar top ological requirements The remaining background
was estimated to b e smaller than by a visual event scan and also by analyzing the pilot
bunch data
Photopro duction Background
The only signi cant background to DIS from ep interactions is due to photopro duction events
2
at Q where the scattered electron escap es the detector along the b eam pip e but in which
an energy cluster from the hadronic nal state fakes an electron Ab out of these events
are identi ed as photopro duction background if the scattered electron is found in the electron tagger
80 120
a) 100 b) c) 70 events events events 100 H1 data 60 80 PYTHIA + VDM 80 50 PYTHIA 60 40 60
30 40 40
20
20 20 10
0 0 0 10 20 10 15 160 165 170 , , θ o
Ee,tagged/GeV Ee,fake/GeV e,fake/
Figure Distributions for tagged photopro duction events a Energy distribution of the
scattered electron energy in the electron tagger b and c energy and angle distributions of
the fake electron candidate in the BEMC The statistical errors of the Monte Carlo simulation
are of the same order of magnitude as the exp erimental ones
To estimate this background photopro duction events were simulated corresp onding to
the luminosity of the data The soft vector meson contribution was simulated using the
RAYVDM program and the hard scattering part using the PYTHIA program
For hard scattering interactions direct and resolved pro cesses and the pro duction of heavy
quarks were included The relative contributions of b oth were adjusted to agree with the total
photopro duction cross section analysis The simulation b oth in shap e and normaliza
tion is in go o d agreement with the tagged photopro duction data This is illustrated
in g showing the scattered electron energy distribution in the tagger and the energy and
angle distributions of the fake electron detected in the BEMC The photopro duction back
ground was subtracted statistically bin by bin The highest contamination is in the lowest
2 0
Q x bin and amounts to for E GeV Only three bins have a contamination
e
larger than
An indep endent analysis made use of the tracking information to identify that part
2
of the photopro duction background which originates from photons in a low Q interaction
These can mimic a DIS electron due to conversion in the CJC end ange Such events were
rejected by requiring a hit in the innermost tracking chamb er which is crossed by the particle
b efore reaching the CJC The remaining background from charged pions and conversions in
the b eampip e was estimated based on a comparison of the tagged photopro duction events
and the Monte Carlo simulation which allowed to subtract this background part statistically
This background estimation gave consistent results with the Monte Carlo metho d describ ed
ab ove
Monte Carlo Simulation
More than half a million Monte Carlo events were generated using DJANGO and di erent
quark distribution parametrizations corresp onding to an integrated luminosity of approxi
1
mately pb The program is based on HERACLES for the electroweak interaction
and on LEPTO to simulate the hadronic nal state HERACLES includes rst or
der radiative corrections the simulation of real bremsstrahlung photons and the longitudinal
structure function The acceptance corrections were p erformed using the MRSH parametriza
tion which is constrained to the HERA F results of LEPTO uses the colour dip ole
2
mo del CDM as implemented in ARIADNE which is in go o d agreement with data on the
energy ow and other characteristics of the nal state as measured by H and ZEUS
For the estimation of systematic errors connected with the top ology of the hadronic nal
state the HERWIG mo del was used in a dedicated analysis Based on the GEANT
program the detector resp onse was simulated in detail After this step the Monte Carlo
events were sub ject to the same reconstruction and analysis chain as the real data
Calibration and Kinematical Distributions
The structure function measurement requires an understanding of the reconstruction of the
energies and angles of the scattered electron and of the hadronic nal state b ecause all are
used to de ne the kinematics of the interaction Figs and display the distributions
0
of the reconstructed energy E and angle of the scattered electron and of the hadronic
e
e
2
variables y and Fig shows the distributions for the high statistics low Q event sample
h
with the electron measured in the BEMC The small contamination due to photopro duction
background is also displayed The Monte Carlo distributions are normalized to the luminosity
measurement Agreement b etween data and Monte Carlo simulation was obtained after
an iteration of the structure function parametrization see b elow The remaining small
discrepancies as visible for example in the distribution of y around have negligible
in uence on the acceptance calculation for F Fig shows the same distributions for the
2
2
smaller sample at large Q with the electron detected in the LAr calorimeter Data and
simulation agree well
A crucial part of the F analysis is the absolute energy calibration The determination
2
of the energy scale of the BEMC is based on the observed shap e of the kinematic p eak see
g a for energies b etween and GeV Taking into account stack to stack variations of
the resp onse and correcting for dead material in front of the BEMC as well as for energy losses
0
b etween the stacks the absolute scale of the E measurement in the BEMC was determined
e
with systematic and statistical accuracy The result was cross checked with
the double angle metho d to reconstruct the electron energy and agreement was found to
2
within the quoted uncertainty For the high Q data the double angle metho d was used to
re ne the energy scale determined by test b eam measurements The resulting systematic
0 o o
uncertainties in E are smaller than for b etween and BBE region and
e
e
o
for electrons in the barrel part of the calorimeter
e
The hadronic energy scale in the liquid argon calorimeter is presently known to as
determined from studies of the transverse momentum balance of DIS events Test b eam
data of pions b etween GeV and GeV showed agreement on the level with the
0 2
Figure Distributions of the kinematical quantities E y and for the low Q data
e h
e
closed circles and the Monte Carlo simulation op en histogram The Monte Carlo cal
culation is normalized to the luminosity The hatched histogram is the estimation of the
background due to photopro duction pro cesses
0 2
Figure Distributions of the kinematical quantities E y and for the high Q data
e h
e
o
closed circles and the Monte Carlo simulation op en histogram using the MRSH
e
2 2
parametrization as input structure function For the energy distribution Q GeV
e
is required For the distribution a cut at y is applied to exclude the region where
h DA
DA
F is not measured
2
Monte Carlo description The calibration parameters were determined from Monte Carlo
simulated jet data The calorimetric energy due to charged particles in the central
detector region was replaced by the more precise momentum measurement of the CJC which
renders y sensitive to charged hadrons of low momentum This improved the resolution
h
2
of y by ab out at low Q and high y
h
An extension to higher y values from as in the previous H analysis to was
h
achieved by using the metho d The b ehaviour of y can b e studied with the high y data
by means of the ratio y y g a using the excellent resolution of y as a reference
e e
As can b e seen b oth the mean value and the measured resolution are well repro duced
h e
by the Monte Carlo simulation Go o d agreement is also achieved in the p p distribution
T T
at high y g b although the hadronic nal state particles are of rather low energy and on
h
average are emitted into the backward direction The resolution of p is wider than
T
e
the p resolution The coverage of the full y range necessitates an understanding of the e ect
T
of the calorimeter noise on F For low y this is sensitive in particular in the backward part of
2
the detector where any energy dep osition of MeV generates an additive contribution to
y of ab out Fig c suggests that y values b elow can b e reconstructed In g c the
y y distribution is shown for y including and excluding the calorimeter
g en
noise contribution for the reconstruction of y The distributions have a maximum near and
the resolution obtained is when the noise is included Note that for low y the quantity
y cannot b e considered as a measure for the true y since its resolution function is distorted
e
The contribution of the noise which has b een obtained from exp erimental data is apparently
small The tail of the distribution at large y y is related to the nite granularity of the
g en
calorimeter Go o d agreement b etween data and Monte Carlo in the low y region has
h e
b een achieved This can b e seen for example in the distribution of the ratio p p g d
T T
Therefore the F measurement could b e extended to y and for the rst time the
2
x region measured at HERA reaches the domain of larger x values covered in xed target
exp eriments
2
The electron angle has b een determined for the lower Q data from the vertex p osition
e
reconstructed with the central and forward chamb ers and the hit in the BPC closest to
the p osition of the electromagnetic cluster in the BEMC The precision of the z vertex
measurement for most of the events is ab out cm The measurement in part of the
e
kinematic range could b e validated and cross calibrated with the innermost tracking chamb er
and the cluster p osition Potential shifts of the values are estimated to b e smaller than
e
2
mrad and a resolution of mrad is achieved For the high Q data the vertex p osition and
the cluster centre de ne within mrad accuracy and mrad resolution as cross checked
e
2
with the central jet chamb er For the intermediate Q analysis the measurement is made
e
with the CJC and the z drift chamb ers
The hadronic angle is reconstructed according to eq from the energy dep osited in
h
the calorimeter cells The Monte Carlo distribution dep ends crucially on the shap e of
h
the input structure function Agreement b etween data and Monte Carlo was obtained after
iteration of the input by starting with the MRSH distribution extracting and tting F and
2
reweighting the Monte Carlo event distributions by the ratio of the tted F to the MRSH
2
parametrization The weights applied deviate from by less than While this pro cedure
signi cantly improved the description of the event distributions shown in g it had less
than in uence on the structure function derivation b ecause the dep endence of the F
2
analysis on the assumed shap e of F is due only to smearing corrections which are less than
2
in the kinematic range and for the binning used here
h e
Figure Exp erimental and Monte Carlo distributions of a y y and b p p in the high
e
T T
2 2
y range for Q GeV Monte Carlo distributions of c y y with and without w o
g en
h e
the calorimeter noise included and d exp erimental and Monte Carlo distributions of p p
T T
at very low y The p ratio distributions at low y d p eak at ab out due to losses of
T
hadrons in the b eam pip e b oth in the data and in the Monte Carlo simulation
Detailed studies were p erformed of the resolution and systematic shifts of the recon
2
structed x and Q values In table the average resolution values are quoted for the three
2 2 2
x x x Q Q Q
E DA
E DA
2
y low Q
2
high Q
2
y low Q
2
high Q
Table Relative resolution values in p er cent for the three metho ds used to reconstruct x
2
and Q
2
metho ds used to determine F The x Q binning was adapted to the resolution in x and
2
2 2
to the statistics in Q A rather ne grid is obtained at low Q with bins p er order of
2 2
magnitude for Q b etween and GeV Statistics allowed for four more bins equidis
2 2 2
tant in log Q b etween and GeV Indep endently of Q the binning in x was
3
bins p er order of magnitude for x The F measurement is based on kinematic
2
2
variables which in the full x Q range are reconstructed with systematic shifts smaller than
and relative resolutions b etter than apart from three edge bins at very low y with
a resolution b etter than
Structure Function Measurement
Comparison of F Analyses
2
2
The structure function F x Q was derived after radiative corrections from the one photon
2
exchange cross section
2 2 2
d y
2
y F x Q F
2 2
2 4
dxdQ Q x R
2
E ects due to Z b oson exchange are smaller than and were corrected for at high Q
The structure function ratio R F xF has not b een measured yet at HERA and was
2 1
calculated using the QCD relation and the MRSH structure function parametrization
2
At lowest x and Q the assumed R values are ab out all values b eing quoted in the F data
2
summary table see b elow Compared to the previous H analysis the F measurement
2
2 2 2
has b een extended to lower and higher Q from GeV to GeV and also
to larger x
The determination of the structure function requires the measured event numb ers to b e
converted to the bin averaged cross section based on the Monte Carlo acceptance calcula
3
tion The mean acceptance was All detector e ciencies were determined from the
data utilizing the redundancy of the apparatus Apart from very small extra corrections all
e ciencies are correctly repro duced by the Monte Carlo simulation The bin averaged cross
3
The data sample contains a fraction of of large rapidity gap events With a sp ecial rapidity gap
Monte Carlo program acceptances were calculated and they agree within statistical errors with those
calculated using the standard DIS simulation Thus only the DIS Monte Carlo simulation has b een used for
the calculation of the acceptance corrections
section was corrected for higher order QED radiative contributions and a bin size correction
was p erformed This determined the one photon exchange cross section which according to
2
eq led to the values for F x Q
2
Several metho ds were used to derive F each with di erent advantages i the E metho d
2
2
which has the b est resolutions on x and Q at large y and is indep endent of the hadron
reconstruction apart from the vertex requirement ii the metho d which has small radiative
corrections and extends from very low to large y values iii the DA metho d which is less
sensitive to the energy scales A complete analysis has b een p erformed based on the mixed
metho d which agrees very well with the other structure function determinations presented in
this pap er The application of di erent metho ds was imp ortant to check that the systematic
errors were correctly evaluated
The F analyses for the shifted vertex and the satellite bunch data were p erformed with
2
only the E metho d The results were found to b e in go o d agreement with each other and with
the F obtained from the nominal vertex data in the region of overlap Taking into account
2
correlations b etween the systematic errors the two data sets were combined Thus the rst
2 2 4
structure function data for Q GeV and x are presented here
All structure function values are shown in g As can b e seen the agreement b etween
E
was chosen for the nal result and and F the analyses is very go o d A combination of F
2 2
DA
F displayed to demonstrate consistency
2
Systematic Errors
The systematic errors considered are
A p otential miscalibration of the electron energy by in the BEMC by in the
BBE and by in the central calorimeter region
A scale error for the hadronic energy in the LAr calorimeter the e ect of which is
reduced due to the joint consideration of tracks and calorimeter cells for the analysis
A scale error was assigned to the energy of the hadronic nal state measured in the
BEMC These numb ers include uncertainties due to the noise treatment for the LAr
calorimeter and the BEMC
A shift of up to mrad for the electron p olar angle in the BEMC region and of at most
mrad in the LAr calorimeter Errors of the energy and angular resolutions are taken
into account in addition to p ossible shifts of mean values
Apart from the electron identi cation all e ciencies were determined from the data and
compared with the Monte Carlo simulation Agreement b etween the exp erimental and
the simulated values for the individual e ciencies trigger TOF vertex CJC track
BPC hit BEMC and LAr calorimeter cluster reconstruction was found to b e b etter
than An overall error of was assigned due to the imp erfect description of the
various e ciencies A larger error of at most was added to account for the vertex
reconstruction e ciency variation at large x
2
Figure Measurement of the structure function F x Q with the electron closed circles
2
the op en circles and the double angle metho d op en squares The inner error bar is
the statistical error The full error represents the statistical and systematic errors added in
quadrature not taking into account the systematic error of the luminosity measurement
2
Figure Measurement of the proton structure function F x Q The inner error bar is
2
the statistical error The full error represents the statistical and systematic errors added in
quadrature not taking into account the systematic error on the luminosity measure
ment Op en circles and triangles represent NMC and BCDMS measurements resp ectively
A smo oth transition b ecomes apparent from the NMC and BCDMS data op en circles and
triangles resp ectively to the H data The curves represent a phenomenological t to all
data see text
An error of up to in the radiative correction due to uncertainties from the hadronic
2
corrections the cross section extrap olation towards Q second order corrections
and the absence of the soft photon exp onentiation in the HERACLES Monte Carlo
The accuracy was cross checked by comparing the Monte Carlo estimate with
TERAD and also with TERAD supplemented by a leading log higher order cal
culation A direct estimate has b een made comparing in their overlap region the
cross sections derived from the E and the metho ds Note that most of the Compton
events do not contribute here due to the vertex requirement
The structure function dep endence of the acceptance and bin size corrections which was
controlled to b etter than The comparison of the di erent simulation mo dels of the
hadronic nal state mentioned ab ove was used to assign an additional systematic
error to the hadronic metho ds
The uncertainty due to photopro duction background was assumed to b e smaller than
half the correction applied i e smaller than This a ects only the highest y bins
2
at lower Q
Statistical errors in the Monte Carlo acceptance and e ciency calculations were com
puted and added quadratically to the systematic error
The shifted vertex data sample required to assign a error for the vertex e ciency
correction due to lack of exp erimental statistics For the higher statistics satellite data
the additional luminosity uncertainty implies that b oth data samples with shifted z
2
vertex p osition contribute with ab out the same systematic errors to the nal low Q
structure function measurement
2
The Structure Function F (x Q )
2
The combination of di erent metho ds meant that the largest kinematic range could b e covered
2
in an optimum way for the measurement of F x Q Fig presents the combined structure
2
2
function data Data at lower x in the full Q range are obtained with the E metho d For
y the metho d was used Double counting of the events was reduced to the level of a
2 2
few p er cent by intro ducing to the analysis in each Q bin an x cut near to y Q sx
e
The results are in go o d agreement with the previous H publication
The structure function values are given in table with their statistical and systematic
2
errors For low Q values apart from the lower statistics shifted vertex data the systematic
2
error of F is ab out and twice as large as the statistical error while for the larger Q
2
data the statistical error dominates
4
Fig shows that the structure function F rises steeply with x decreasing to x
2
2
As can b e seen in g the dep endence of F on Q at xed x is weak The violation of
2
scaling app ears to b e stronger for smaller values of x a trend already observed in xed
target exp eriments for x Compared to the recent data from the ZEUS exp eriment an
2
extension of the kinematic range is achieved towards low x and low Q see g
2
The x and Q b ehaviour of F can b e describ ed by a phenomenological ansatz of the typ e
2
p
2
2 b d 2 2 g
F x Q a x c x e x ln Q f ln Q x
2
2 2
Q x F R Q x F R
2 stat sy st 2 stat sy st
2
Table Proton structure function F x Q with statistical and systematic errors All p oints
2
2
have an additional scale uncertainty of due to the luminosity determination Q is given
2
in GeV The values of R result from a calculation based on the QCD prescription using the
MRSH parton distribution parametrization
2
Figure Measurement of the proton structure function F x Q The H data closed
2
p oints is consistent with the ZEUS result op en squares but extends further towards low
2
x and also to lower Q in di erent x bins With a small correction the ZEUS F data was
2
shifted to the H x values by using the parametrization given in The curves represent a
phenomenological t to the H NMC and BCDMS data see text The F values are plotted
2
with all but normalization errors in a linear scale adding a term c x i to F
x 2
where i is the bin numb er starting at i for x
x x
The dep endence of that parametrization re ects the following observations i it is constructed
to describ e the F data from BCDMS NMC and H which together cover a range of orders
2
2 g
of magnitude in x and Q ii for large x F is known to vanish like x with the parameter
2
g close to as determined by quark counting rules iii due to momentum conservation the
2 2
integral over F is nearly indep endent of Q Thus the rise of F with Q at low x must
2 2
2
b e comp ensated by a decrease of F with Q at large x As a consequence at x x F
2 o 2
2
is indep endent of Q This demands that a p olynomial term b e included in front of the
p
2
Q dep endent part which has b een chosen to b e e x Since x in the xed target
o
exp eriments has b een determined to b e around the parameter e should b e close to
2 2
iv the Q dep endence of F is exp ected to b e logarithmic The attempt to describ e the Q
2
2 2 2 2
evolution over almost four orders of magnitude from Q GeV to Q GeV
2
requires a quadratic term in ln Q Fits were p erformed with and without that term present
2
v nally the intro duction of a term in eq is required which is indep endent of Q
a b c d e f g
Table Parameters of a phenomenological t to the proton structure function data from
p
this exp eriment combined with F from the NMC and the BCDMS exp eriments The
2
2 2 2 4 2 5 2
parametrization is valid for GeV Q GeV x and Q x GeV
The result of the t to the H NMC and BCDMS data is shown as functions of x and
2
Q in gs and The parameter values are quoted in table In the t the statistical
and systematic errors of all quoted F values were added in quadrature and the relative
2
normalizations were not allowed to vary The t provides a valid description of all data
2
from the exp eriments considered here with a dof of For the H data alone the
2
parametrization gives a dof of The parameters g and e come out as exp ected to b e
2
close to From the result e one nds that the slop e of F with ln Q changes
2
2
2
sign at x The obtained parameter f of eq is small i e the ln Q term amounts
o
2 2
to ab out a correction to the linear b ehaviour at Q values b etween and GeV If
2
2 2
the ln Q term in eq is neglected the dof increases from to An interesting
result of the parametrization is the interplay b etween the rst and the second term with an
exp onential x dep endence The second term dominates at low x The value of the p ower d
2
2
is found to b e correlated with the presence of the ln Q term If the latter is neglected the
t suggests an x dep endence at low x which is somewhat steep er namely d instead
of d
2
In g the F b ehaviour is illustrated for di erent Q values as a function of W which is
2
the invariant mass of the virtual photon proton p system
q
q
2 2 2
W Q x M Q x
p
2
at low x Here M is the proton mass Since Q x sy the HERA exp eriments reach much
p
larger W values than the previous DIS or real photopro duction exp eriments F is displayed
2
2 3
for the high statistics nominal vertex data and only for those Q bins where x b elow
2 2
was reached i e from GeV to GeV The rise of F at low x corresp onds directly to
2
a rise of F with W This can b e interpreted as a strong rise of the p total cross section
2
o
since for x and in the region where e ects due to Z b oson exchange can b e neglected
2
2
F W Q p
2 tot
2
Q
2
Figure Low Q structure function data of H plotted as functions of the invariant mass W
2
of the p system The straight line is a t F W Q W GeV for x
2
2
which extends up to W GeV where F scales for the Q range considered Data for
2
2 2 2
Q GeV have a similar slop e versus W but are b elow the lower Q data
Three observations are made i the rise of F with W is stronger than the one observed
2
for W b etween and GeV of the total photopro duction cross section in which
the photon is real This b ehaviour for the total cross section of o shell particle scattering
was exp ected and discussed for previous DIS exp eriments in ii for W values b elow
3
GeV corresp onding to x all the measured p oints cluster in a narrow band
2 2
which is well repro duced by a straight line t i e F W Q scales in the Q range considered
2
This observation is consistent with the recent ZEUS measurement iii the extrap olation of
the straight line t dashed line in g into the higher W region W GeV repro duces
2 2 2 3
the data at Q GeV but the F data at lower Q and x app ear to deviate
2
systematically from this linear b ehaviour This trend is con rmed though with less precision
2
by the lowest Q measurements obtained with the shifted vertex data
The b ehaviour of F at very low x requires still more precision data and extended coverage
2
than were available to this analysis A more theoretical discussion of the F data presented
2
in this pap er is deferred to a forthcoming analysis in the framework of p erturbative Quantum
Chromo dynamics 140 H1 Data 180 H1 Data 160 Events 120 MC All Events MC All MC Non-Diff 140 MC Non-Diff 100 120 80 100 60 80 60 40 40 20 20 0 0 10 15 20 25 155 160 165 170 175 ′ θ o Ee / GeV e /
160 10 4
140 H1 Data H1 Data
Events MC All Events MC All 120 10 3 MC Non-Diff MC Non-Diff 100
80 10 2
60
40 10
20
0 1 -2 -1.5 -1 -0.5 0 -2 0 2 4 η
log10(yΣ) max
0
Figure E and y distributions for DIS events with and the distribution
e max max
e
for all DIS selected events The Monte Carlo simulations are describ ed in the text
Di ractive Contribution to F x Q
2
In the previous H measurement of F x Q it has b een observed that for ab out of
2
the deep inelastic events there was no signi cant energy dep osition in the forward region The
o
angular acceptance of the LAr calorimeter is limited to p olar angles corresp onding
to a maximum measurable pseudo rapidity ln tan of The value of the
2
most forward cluster with energy greater than MeV is de ned to b e The
max
2
events with amount to of the low Q data A rst H analysis of the
max
rapidity gap events collected in has b een rep orted in There it was shown that measuremen system sample requiring where Figure circles luminosit tistical and systematic errors added in quadrature not including these prob es a colourless comp onen di ractiv gap and F 2 ollo and ev M con en wing D x The X e The y measuremen
F I di eren
0.05 0.15 0.25 0.05 0.15 0.25 2 ts P p max scattering 0.1 0.2 0.1 0.2 tains is Measuremen t with the additional ev 0 0 ma the momen analysis the 10 inner -4 y the di ractiv b oth t in b e in Q v error pr oton arian 2 describ ed leads uses in tro duces a limit of v t of t alues teractions bar of t tum fraction of the proton carried b 10 8.5 GeV 25 GeV the to mass -3 the max t of the proton the P with is a e con same b relationship 2 the di ractiv y 2 of di ractiv with the l n en tribution the statistical data sample t selection x 10 E I P p -2 a x e metho d I scattered I P P p con e 10 system F scattering -4 tribution 2 error D with of b et x Q and closed omeron on the data w proton max 2 een The This selection to pro cesses F x 10 50 GeV 12 GeV 2 I the circles D P p -3 full F relation The kinematics of deep inelastic 2 and x Q y the P minim x Q error 2 2 criteria x 2 the systematic error of the with and where 2 for to implies um bar omeron suc 10 F a -2 the The di ractiv as 2 size x proton represen the M Q x Q I P p for x X 2 2 that of virtual metho d 2 the the disso ciativ for h that a ts can b e F selection rapidit the 2 x e ev photon I x Q P p op en sta en 2 y e t
de ned as
2
Z Z
10 1 4 D
d
D 2
F x Q dt dx
IP p
2
2
dx dQ dx dt
x t
IP p
min
D
with the di ractive cross section and the kinematic factor de ned as in eq setting
R Here t is the momentum transfer squared b etween the incident and scattered proton
or proton disso ciative system To correct for the acceptance and for e ects due to nite
resolution the RAPGAP Monte Carlo program was used assuming a hard structure
function for the Pomeron x x with the same amount of quark and gluon induced
i IP i IP
events Here x is the fraction of the Pomeron momentum carried by the parton i which
i IP
is assumed to interact with the virtual photon A contribution from the elastic pro duction
of light vector mesons consistent with that observed in was
added to the RAPGAP Monte Carlo events amounting to of the selected rapidity
0
gap sample This simulation describ es the data well as shown in g Here the E y
e
e
distributions for DIS events with and the distribution for all DIS events are
max max
shown for b oth data and Monte Carlo simulation
D
The F contributions derived from the electron metho d and from the metho d are
2
shown in g Both measurements agree well within the errors in the regions of overlap
As for the measurement of F the metho d was taken for y and the electron metho d
2
D
for larger y The resulting values for F are given in table The systematic errors were
2
2
calculated as for the inclusive F x Q measurement taking into account the uncertainties
2
sp eci c to the rapidity gap event analysis
2 2 D
Q GeV x F
stat sy st
2
D 2 2
Table Di ractive contribution F x Q to F x Q for x All p oints have an
2 IP p
2
additional scale error of due to the uncertainty of the luminosity measurement
D 2 D 2
By construction F decreases to zero at x Comparison of the values of F x Q
2 2
2 3
with F x Q for x shows that the former contributes ab out to the proton
2
2
structure function Therefore di raction with x cannot account for the steep
IP p
2 D 2
increase of F with decreasing x The Q dep endence of F x Q at xed x is at and
2
2
2 2
not signi cantly di erent from the Q dep endence of the F x Q An analysis of di ractive
2
events in terms of structure functions will b e given in more detail in a forthcoming publication
of H
Summary
2
A measurement has b een presented of the proton structure function F x Q in deep inelastic
2
electron proton scattering at HERA with data taken in the running p erio d of The
1
integrated luminosity is pb which represents a tenfold increase in statistics compared
to the rst F publication of H The structure function measurement includes data from
2
2
di erent detector comp onents and running con gurations Low Q values are reached using
data with the ep interaction vertex shifted in z from the nominal p osition The data cover a
2 2 4
kinematic range for Q b etween and GeV and x b etween and
The F values presented are obtained using di erent metho ds to reconstruct the inclusive
2
scattering kinematics At high values of the scaling variable y due to its sup erior
resolution the electron metho d is used which is based on the scattered electron energy and
angle Lower y values are covered with the metho d which combines electron and hadronic
information to reduce radiative corrections and calibration errors For comparison and cross
checks F data obtained with the double angle metho d are also presented
2
The measured structure function has statistical and systematic errors considerably smaller
than the previous result For the rst time the HERA structure function measurement
extends to the kinematical region of the high precision xed target exp eriments revealing a
smo oth transition b etween the BCDMS NMC and H results
2
A distinct rise is observed of the structure function with decreasing x at xed Q Around
3
x the decrease of x by an order of magnitude amounts to a rise of F of ab out a factor
2
two This rise cannot b e explained by the rapidity gap events b ecause they contribute only
D
ab out of F They are used to measure for the rst time the di ractive contribution F
2
2
2
to the proton structure function for x smaller than This contribution exhibits no
IP p
2
signi cant Q dep endence
2
The observed Q b ehaviour is consistent with the exp ected scaling violations i e a weak
2
rise of F with increasing Q for x A parametrization is given of the proton structure
2
function data from this exp eriment combined with the data from the NMC and BCDMS
2 2
exp eriment describing F x Q over almost four orders of magnitude in x and Q If F at
2 2
2
low Q is analyzed as a function of the virtual photon proton mass W deviations from a
linear b ehaviour b ecome visible for W GeV which deserve a more precise analysis with
forthcoming data
Acknowledgements
We are very grateful to the HERA machine group whose outstanding e orts made this ex
p eriment p ossible We acknowledge the supp ort of the DESY technical sta We appreciate
the big e ort of the engineers and technicians who constructed and maintained the detector
We thank the funding agencies for nancial supp ort of this exp eriment We wish to thank
the DESY directorate for the supp ort and hospitality extended to the non DESY memb ers
of the collab oration
References
for a recent review see J Feltesse DAPNIA SPP Invited talk at the
International Conference on High Energy Physics Glasgow Scotland
H Collab I Abt et al Nucl Phys B
ZEUS Collab M Derrick et al Phys Lett B
A De Rujula et al Phys Rev D
Yu L Dokshitzer Sov Phys JETP
V N Grib ov and L N Lipatov Sov J Nucl Phys and
G Altarelli and G Parisi Nucl Phys B
E A Kuraev L N Lipatov and V S Fadin Sov Phys JETP
Y Y Balitsky and L N Lipatov Sov J Nucl Phys
L V Grib ov E M Levin and M G Ryskin Phys Rep
A H Mueller and N Quiu Nucl Phys B
ZEUS Collab M Derrick et al DESY submitted to Z Phys C
ZEUS Collab M Derrick et al Phys Lett B
Phys Lett B and Phys Lett B
H Collab T Ahmed et al Nucl Phys B
A Blondel and F Jacquet Pro ceedings of the study of an ep facility for Europ e ed
U Amaldi DESY p
J Blumlein and M Klein Pro ceedings of the Snowmass Workshop The Physics of the
Next Decade ed R Craven p
S Bentvelsen et al Pro ceedings of the Workshop Physics at HERA Vol eds W
Buchmuller and G Ingelman DESY p
C Ho eger ibid p
U Bassler and G Bernardi DESY subm to Nucl Instr and Meth
H Collab I Abt et al DESY
H Calorimeter Group B Andrieu et al Nucl Instr and Meth A
H Collab T Ahmed et al to b e published
H Collab I Abt et al Phys Lett B
C Leverenz Ph D Thesis University of Hamburg in litt
E Pepp el Ph D Thesis University of Hamburg
N H Bro ok A De Ro eck and A T Doyle RAYPHOTON Pro ceedings of the
Workshop Physics at HERA vol eds W Buchmuller G Ingelman DESY
p
H U Bengtsson and T Sj ostrand Computer Phys Comm
H Collab T Ahmed et al Phys Lett B
M Erdmann et al DESY
S Levonian Pro c of the th Rencontre De Moriond Les Arcs France p
H Collab I Abt et al Phys Lett B
S Reinshagen Ph D Thesis University of Hamburg in litt
D Neyret Ph D Thesis University VI of Paris in litt
K Muller Ph D Thesis University of Zurich
G A Schuler and H Spiesb erger Pro ceedings of the Workshop Physics at HERA vol
eds W Buchmuller G Ingelman DESY p
A Kwiatkowski H Spiesb erger and H J M ohring Computer Phys Comm
G Ingelman Pro ceedings of the Workshop Physics at HERA vol eds W Buchmuller
G Ingelman DESY p
A D Martin W J Stirling and R G Rob erts Pro ceedings of the Workshop on Quan
tum Field Theory Theoretical Asp ects of High Energy Physics eds B Geyer and E M
Ilgenfritz
L L onnblad Computer Phys Comm
H Collab I Abt et al Z Phys C
ZEUS Collab M Derrick et al Z Phys C
G Marchesini et al Computer Phys Comm
R Brun et al GEANT User s Guide CERN DD EE Geneva
C Brune Ph D Thesis University of Heidelb erg in litt
H Calorimeter Group B Andrieu et al Nucl Instr and Meth A
H Calorimeter Group B Andrieu et al Nucl Instr and Meth A
H P Wellisch et al MPI PhE
U Bassler Ph D Thesis University VI of Paris
G Bernardi and W Hildesheim Pro ceedings of the Workshop Physics at HERA vol
eds W Buchmuller G Ingelman DESY p
NMC Collab P Amaudruz et al Phys Lett B
BCDMS Collab A C Benvenuti et al Phys Lett B
G Altarelli and G Martinelli Phys Lett B
H Jung DESY submitted to Comput Phys Commun
U St o lein Ph D Thesis Humb oldt University of Berlin in litt
U Obro ck Ph D Thesis University of Dortmund
A Akhundov et al DESY
J Blumlein Pro ceedings of the Workshop Physics at HERA vol eds W Buchmuller
G Ingelman DESY p and DESY Z Phys C in press
ZEUS Collab M Derrick et al Phys Lett B
DESY to b e published in Z Phys C
C L op ez and F J Yndur ain Phys Rev Lett
A Levy and U Maor Phys Lett B
E L Berger et al Nucl Phys B
J P Phillips Ph D Thesis University of Manchester in litt
G Ingelman and K Prytz Z Phys C
B List Diploma Thesis Techn Univ Berlin unpublished
H Collab T Ahmed et al to b e published ) 2000
max H1 data H1 data
η 1
CDM Events CDM 1500 MEPS MEPS -1 10
1/N(dN/d 1000 -2 10 500 -3 10 0 -2 0 2 0 10 20 30 η max
1500 0.015 -1 H1 data H1 data (RG selection no background subtraction)
Events CDM
1000 MEPS ) / GeV 0.01 CDM (RG selection) X MEPS (RG selection)
500 0.005 1/N(dN/dM
0 0 0 5 10 15 20 0 10 20 30
EPLUG / GeV MX )
max H1 data H1 data (RG selection after
η 0.4 1 H1 data (RG selection after background subtraction) background subtraction) DIFF (RG selection) -1 0.3 10 DIFF (RG selection) 1/N(dN/dy) 1/N(dN/d 0.2 -2 10 0.1 -3 10 0 -2 0 2 0 0.2 0.4 0.6 0.8 η max
0.1 ) β ))) ))) 0.3 P
I H1 data (RG selection after H1 data (RG selection after
(x 0.08 background subtraction) background subtraction) 10 DIFF (RG selection) DIFF (RG selection) 0.2 0.06 1/N(dN/d
0.04 0.1 1/N(dN/d(log 0.02
0 0 -4 -3 -2 -1 0 0 0.2 0.4 0.6 0.8
log10(xIP ) D
10 1 10 10 10 1 10 10 10 1 10 10 10 1 10 10 F2 -1 2 -1 2 -1 2 -1 2 10 -3 Q Q Q Q 10 2 2 2 2 =8.5 GeV =8.5 GeV =8.5 GeV =8.5 GeV -2 β β β β =0.375 =0.175 =0.065 =0.65 10 -1 x 2 2 2 2 I P 10 -3 Q Q Q Q 10 2 2 2 2 =12 GeV =12 GeV =12 GeV =12 GeV -2 β β β β =0.065 =0.375 =0.175 =0.65 10 -1 x 2 2 2 2 I P 10 -3 Q Q Q Q 10 2 2 2 2 =25 GeV =25 GeV =25 GeV =25 GeV -2 β β β β =0.065 =0.375 =0.175 =0.65 10 -1 x 2 2 2 2 I P 10 -3 H1 data Q Q Q 10 2 2 2 =50 GeV =50 GeV =50 GeV -2
β β β
=0.65 =0.375 =0.175 10 ~ FD 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 2 0 0 0 0 H1 data 10 β β β β =0.65 035Q Q =0.375 =0.175 =0.065 Q 2 /GeV 10 2
2 ~ FD 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 2 0 0 0 0 . . . . 1 0.8 0.6 0.4 0.2 0 Q Q 2 2 2 2 =50 GeV =8.5 GeV =25 GeV =12 GeV 2 2 2 2 β