The Hadronic Final State at HERA

60 Pages·2014·2.13 MB·English

The Hadronic Final State at HERA
Paul R. Newman∗
School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK
Matthew Wing†
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK;
DESY, Notkestrasse 85, 22607 Hamburg, Germany
(Dated: March 20, 2014)
Thehadronicfinalstateinelectron–protoncollisionsatHERAhasprovidedarichtestingground
fordevelopmentofthetheoryofthestrongforce,QCD.Inthisreview,over200publicationsfrom
4
the H1 and ZEUS Collaborations are summarised. Short distance physics, the measurement of
1
processesathighenergyscales,hasprovidedrigoroustestsofperturbativeQCDandconstrained
0
the structure of the proton as well as allowing precise determinations of the strong coupling
2
constant to be made. Non-perturbative or low energy processes have also been investigated and

r results on hadronisation interpreted together with those from other experiments. Searches for
a exotic QCD objects, such as pentaquarks, glueballs and instantons have been performed. The
M subject of diffraction has been re-invigorated through its precise measurement, such that it can
now be described by perturbative QCD. After discussionof HERA, the H1and ZEUS detectors

9 andthetechniquesusedtoreconstructdifferinghadronicfinalstates,theabovesubjectareasare
1 elaborated. The major achievements are then condensed further in a final section summarising
whathasbeenlearned.

]
x
e
- Contents 1. Pentaquark States 32
p 2. Instanton Searches 33
e I. Introduction 2 3. SearchforGlueballStates 33
h
4. DeuteronandAnti-DeuteronProduction 34
[ II. Reconstruction of Final States at HERA 3

A. TheH1andZEUSDetectors 3
2 B. ChargedParticles 4 V. Exclusive and Semi-Inclusive Processes 35
v
C. Electrons,PhotonsandMuons 4 A. Introduction 35
8 D. HeavyFlavourIdentification 5 B. ExclusiveProductionof1−− States 37
6 E. HadronicJets 6
1. KinematicsandExperimentalSelection 37
3 F. PhotoproductionandDISandHowtoTellThemApart6
3 G. VeryForwardTaggers 7 2. GeneralCharacteristics ofVectorMeson
. H. Triggering 7 Production 37
8
3. Vector MesonProductioninQCD 39
0
III. Hadronic Final States and Short Distance Physics 8 4. DeeplyVirtualComptonScatteringand
3
A. PerturbativeQCDTheoryoftheHadronicFinalState 9 GeneralisedPartonDensities 40
1
v: B. C1.omJeptarPirsoondsucwtiiothnData 1111 5. SEaxtculurastivioenProcessesinDipoleModelsandLowx 41
2. JetSubstructure 13
i C. InclusiveDiffractiveDissociation 41
X 3. PromptPhotonProduction 14
4. HeavyQuarkProduction 16 1. KinematicsandExperimentalSelectionof
r
a C. ExtractingInformationFromtheData 17 Diffraction 41
D. PushingtheBoundariesofApplicability 19 2. InclusiveDiffractionData 42
1. HigherOrders 20 3. FactorisationStudies 43
2. NewLowxPhenomena 21
4. EnergyDependences andSoftPhenomenology 44
3. VirtualPhotonStructure 23
5. QCDPhenomenology andDiffractiveParton
4. TheUnderlyingEvent 23
Densities 45
5. Discussion 24
E. EventShapes 25 6. ApplicationsofDiffractivePartonDensities 47
7. LimitationsofDiffractivePartonDensities 48
IV. Non-Perturbative Aspects and Hadronisation 27
8. DiffractiveDISinDipoleModels 50
A. ChargedParticleDistributions 27
D. LeadingProtonsandNeutrons BeyondthePomeron
B. Bose–EinsteinCorrelations 28
Region 50
C. CharmFragmentation 29
D. InelasticJ/ψ Production 31 E. VeryHardDiffractionandtheBFKLPomeron 51
E. ExoticandUnusualQCD 32
VI. Summary and Outlook 52
Acknowledgements 54
∗Electronicaddress: [email protected]
†Electronicaddress: [email protected] References 54
2
I. INTRODUCTION } e
e
HERA (the Hadron Elektron Ringanlage) g*(Q2)
(Voss and Wiik, 1994) at the DESY laboratory in
}
Hamburg, Germany is, to date, the only example of a
storage ring devoted to producing collisions between
leptons and hadrons. It was located in a tunnel of (s) (x )
length 6.3km, housing two independent beam-pipes,
the first storing electrons or positrons, here generically (W2)
referred to as electrons, the second protons. In an
initial phase of operation (HERA-I, 1992–2000), the
electron beam energy was predominantly 27.5GeV and
p
the protons were at 820GeV (1992–1997) or 920GeV
(1998–2000). In its second, higher-luminosity phase
(HERA-II, 2002–2007), the electrons remained at the FIG. 1 Schematic illustration of a generic electron–proton
same energy, but were longitudinally polarised, and DIS process, in which an exchanged photon of virtuality Q2
the proton energy also remained at 920GeV except couplestoaquarkcarryingafractionxoftheproton’slongi-
for the last few months, when lower energies (575 and tudinal momentum. The electron–proton centre-of-mass en-
460GeV) were used primarily for a measurement of the ergyisdenoted√sandthephoton–protoncentre-of-massen-
ergy (equivalently the invariant mass of the hadronic final
longitudinal proton structure function. Experiments
state) is denoted W.
were located at up to four points around the ring,
of which this review is concerned with the two, H1
and ZEUS, where the electrons and the protons were
broughttocollision,yieldinganepcentre-of-massenergy
strumentationoftheHERAexperimentswerewellsuited
√s 318GeV.
≤ to the study of the hadronic final state over a wide
For the bulk of the kinematic region accessible at range of W, Q2 and x values. These favourable kine-
HERA,theelectron–protoncollisionsproceedviatheex- matics allowed, for the first time, a detailed explo-
changeofaphoton,asshowninFig.1. Thepossiblepro- ration of the dynamics of the excitations of a single
cesses are conveniently sub-divided into two categories hadron under a multitude of different circumstances.
according to the photon virtuality, Q2. The region with The vast majority of the processes under study are
Q2 1GeV2 corresponds to the short distance ‘Deep driven by the strong interaction, such that where hard
≫
Inelastic Scattering’ (DIS) regime, where the photon is scalesarepresent,thetheoryofquantumchromodynam-
usually consideredas a structureless t-channelexchange. ics (QCD) (Gross and Wilczek, 1973a,b; Politzer, 1973,
In contrast, in the ‘photoproduction’ regime, Q2 0, 1974)andourunderstandingofprotonandphotonstruc-
→
the photon can be thought of as a distinct object, de- ture were tested with unique precision. This has led to
coupling from the electron well in advance of the proton newinsightsandadeeperunderstandingofQCDingen-
targetandinteractingasaseparateentity,oftenthrough eral, as well as providing the stimulus for ever-more so-
its ownpartonic structure (see SectionIII.A). To a large phisticated calculations.
extent, analyses at HERA have treated these two kine-
HERA hadronic final state data provide a very wide
maticregionsseparately,thoughparticularlywherethere
rangeinthe energyscaleofthe process. The softestpro-
are other hardscales in the problem, this is a largely ar-
cessesaregovernedbyhadronicmassscalesof (1)GeV.
tificial distinction. O
Increasing the scale from this starting point allows the
Conventionally, the term ‘Hadronic Final State’ is closely-controlled study of the transition from a regime
taken to mean the full final state after the removal of which must be described in terms of hadronic objects to
the scattered beam lepton and any electroweak radia- one which can be described perturbatively in terms of
tion clearly associated with it. It therefore includes any partons. At the other extreme, the highest transverse
furtherleptonsorgaugebosonsproducedinthephoton– energy jets provide scales of (100)GeV, resolving the
proton interaction. As illustrated in Fig. 1, the invari- structure of electron–parton inOteractions at the 10−18 m
ant mass of the hadronic final state is denoted W, and level. The correspondingkinematic range inthe Bjorken
is equivalent to the centre-of-mass energy of the γ(∗)p variable is approximately 10−4 < x < 0.5. Together
collision. Expressed in terms of the commonly used ‘in- with a new window on fragmentation and hadronisation
elasticity’ invariant, y, W2 ys Q2. When a hard phenomena, these aspects of HERA data have provided
≈ −
scale is present, the photon couples to a single quark, a laboratory of unprecedented precision and kinematic
which carries a fraction x of the proton’s momentum, range for the elucidation of the QCD dynamics of stan-
where x Q2/(sy) is the Bjorken variable. For a more dard DIS processes, which has led to a vastly improved
≈
formal introduction to deep inelastic scattering, see for understanding of the structure of the proton and im-
example (Devenish and Cooper-Sarkar, 2004). proved measurements of fundamental parameters of the
The asymmetric beam energies and near-hermetic in- Standard Model such as the coupling constant of the
3
strong force.
Beyondthebestunderstooddomain,HERAdatahave
provided access to new kinematic regions and processes
withwhichtotestQCDandextendtherangeofapplica-
bility of existing predictions. Many hadronic final state
problems have contained multiple hard scales, provided
by largetransversemomenta and heavy quarkmasses as
wellasQ2. Understandingthedelicateinterplaybetween
these different scaleshas providedexacting challenges to
theory. In photoproduction, HERA data scan the tran-
sition from the classic ep scattering picture, where the
photon interacts in a point-like manner, to the situation
where the photon interacts via its own distinct partonic
XY View ZR View
structure,morereminiscentofhadron–hadronscattering,
facilitating a controlled study of the differing character-
istics of the two extremes. Diffractive and related pro-
cesses in which the proton stays intact or converts to a
neutronviaacharge-exchangereactionimply morecom-
plex interactions in which no net colour is exchanged.
HERA has provided an explosion of precise and eclectic
measurements of these hard exclusive and semi-inclusive
processeswithcleanlyidentifiedexperimentalsignatures,
leading to a detailed understanding in the framework of
QCD. As discussed and illustrated in considerably more
detail in the following, the multitude of Hadronic Final
StateprocessesstudiedinepcollisionsatHERAhasthus
led to something of a revolution in the development and
testing of QCD.
II. RECONSTRUCTIONOF FINAL STATES AT HERA
A. The H1 and ZEUS Detectors
FIG. 2 Event displays of the (top) ZEUS and (bottom) H1
detectors showing a neutral current and a charged current
To visualise the physics processes and reconstruction
DISevent,respectively.
requirements,displaysofaneutralandachargedcurrent
DISeventareshowninFig.2fortheZEUS(ZEUS,1993)
and H1 (Abt et al., 1997a,b) detectors, respectively. In
a neutralcurrentevent, where a photon, or at high Q2 a
Other than the forward–backward asymmetry in in-
Z0, is exchanged, a deposit of energy in the calorimeter
strumentation, the detectors were similar to other
consistent with an electron, matched to a track, can be
general-purposedetectorsathighenergycolliderssuchas
seen back-to-back in azimuth with a hadronic jet. In a
those at LEP, the Tevatron and the LHC. Both H1 and
charged current event, where a W± is exchanged, there
ZEUSdetectorshadmicrovertexdetectorsformeasuring
is no activity to balance the hadronic jet, indicating the
weak decays, surrounded by a central drift chamber for
presence of an undetected neutrino. The figures also
the precise tracking of charged particles. Forward and
showthekeypartsofthecentraldetectors. Inbothcases,
rear tracking detectors gave additional charged-particle
the electron beam enters the detector from the left and
information with the rear detectors particularly useful
the proton beam from the right; due to the significantly
for measuring low-angle scattered electrons at small Q2
larger energy of the protons there is more instrumenta-
wheretheDIScrosssectionislargest. Beyondthe track-
tion in the direction of the outgoing proton beam1.
ingdetectorswerecalorimetersinwhichasingletechnol-
ogy was used for the ZEUS detector with the H1 detec-
tor also including a dedicated higher-precision electron
calorimeter in the rear direction. Finally, large muon
1 Aright-handedCartesiancoordinatesystem isusedthroughout
detectors surrounded the calorimeters. Further, smaller
this review, with the Z axis pointing in the proton beam di-
rection, referred to as the ‘forward’ direction, and the X axis
pointing towards the centre of HERA. The coordinate origin is
atthe nominal interaction point. The pseudorapidity isdefined
asη=−ln tanθ ,wherethe polarangle, θ,ismeasuredwith respecttotheprotonbeamdirection.
(cid:16) 2(cid:17)
4
detectorswithdedicatedpurposes,suchasforelectronor teredelectrons,whichshoulddisplaythesignatureofiso-
protontagging,wereplacedalongthe beam-pipeinboth lated high-energy deposits in the EM calorimeter. Var-
directions. Thesedetectorcomponentsarediscussedfur- ious requirements were made on the EM clusters and
ther in the following subsections. the isolation, usually including a matching of the clus-
ters of energy to a charged particle track, such that
DIS events were selected with high purity and high ef-
B. Charged Particles ficiency (Abramowicz et al., 1995; Glazov, 1998). A typ-
ical minimum energy requirement on the scattered elec-
Tracks from charged particles were primarily re- tron was 10GeV for the H1 LAr and ZEUS calorimeters
constructed by cylindrical drift chambers surrounding and 6.5GeV for the SpaCal. In order to make the best
the interaction point: central jet chambers (CJC1 and measurements of the longitudinal structure function at
CJC2) (Abt et al., 1997a,b; Burger et al., 1989) in H1 highy,theseminimumenergyrequirementswerereduced
and the central tracking detector (CTD) (Foster et al., indedicatedanalysesto 3.4GeV(Aaron et al.,2008c)in
1993, 1994; Harnew et al., 1989) in ZEUS. These were the SpaCal and 6GeV (Chekanov et al., 2009h) in the
supplemented by silicon vertex detectors (Eick et al., ZEUS calorimeter.
1997; Pitzl et al., 2000; Polini et al., 2007) placed be- The variables Q2, x and y can be reconstructed
tween the beam-pipe and the drift chambers and in from the energy and polar angle of the scattered
front of forward and rear tracking devices. The H1 electron only, using the so-called “electron method”,
and ZEUS drift chambers covered polar-angle regions of which arises from simple consideration of the DIS
20◦ < θ < 160◦ and 15◦ < θ < 164◦, respectively, and kinematics. Several other reconstruction methods ex-
were operated in uniform axial magnetic fields of 1.16T ist which make use of combinations of the measure-
and 1.43T. The high magnetic fields ensured excellent ments of the scattered electron and the hadronic fi-
chargeseparationup to about20GeV. The tracking res- nal state (Bassler and Bernardi, 1995; Bentvelsen et al.,
olutions were both σ(p )/p (0.002 0.003)p , with 1992;Hoeger,1992;Jacquet and Blondel,1979). There-
T T T
≈ −
p in GeV. construction method used depends on the analysis and
T
Pulse height measurements from the sense wires were the regions in which particles are measured; e.g. for
also used to calculate the specific energy loss due to charged current events where there is no isolated high-
ionisation, dE/dx. The resolutions of the dE/dx energy electron, the Jacquet–Blondel method was used.
measurements for well-reconstructed tracks were under TypicalrelativeresolutionsinQ2werebetweenabout2%
10% (Bartsch, 2007; Steinhart, 1999). The dE/dx mea- and 10%, depending on the reconstruction method.
surements were used as a method of particle identifica- Photoncandidates,typicallyabove5GeVintransverse
tion, using likelihood tests to distinguish between elec- energy, were identified in the central calorimeters by re-
trons, pions, kaons, protons and deuterons. constructing narrowclusters in the EM calorimeter with
no track pointing to them. Backgrounds from π0 and η
particles were removed by considering the shape of the
C. Electrons, Photons and Muons cluster and of the calorimeter shower; example quanti-
ties were the transverse radius of the cluster and the
Both detectors had large general purpose sampling ratio of the highest energy EM cell to the total clus-
calorimeters which covered most of the solid angle ter energy (Aaron et al., 2010j; Chekanov et al., 2010d).
for the measurement of electromagnetic (EM) ob- Photons of lower energy could be identified in Compton
jects. The H1 Collaboration had a finely segmented scattering processes (ep eγp) in which the final state
→
liquid argon (LAr) (Andrieu et al., 1993) calorime- consists only of the photon, an electron and a lack of
ter with lead or stainless steel absorber, comple- hadronic activity.
mented by a lead–scintillating fibre Spaghetti Calorime- Muons were identified by a combination of tracking,
ter (SpaCal) (Appuhn et al., 1997) which covered polar- calorimetry and the large muon chambers surrounding
angle ranges of 4◦ < θ < 153◦ and 153◦ < θ < the calorimeters. Depending on the given analysis and
177◦, respectively. Under test beam conditions, the kinematic cuts and whether a highly pure or highly effi-
energy resolutions were σ(E)/E 11%/√E and cientsamplewasrequired,differentalgorithmswereused
≈
7%/√E for electrons in the LAr calorimeter and to combine information from the various sub-detectors.
≈
SpaCal,respectively,withE inGeV.TheZEUSdetector Wherever possible, a track matched with a muon signa-
had a uranium–scintillator calorimeter (Andresen et al., ture in another sub-detector was used for the momen-
1991; Bernstein et al., 1993; Caldwell et al., 1992; tum measurement. A minimum ionising particle (mip)
Derrick et al., 1991) which covered a polar-angle range signal in the calorimeters was also used as a high effi-
of 2.5◦ <θ <178.5◦. Under test beam conditions, the ciency, but low purity, signal for a muon. Finally, the
single-particle energy resolution for the ZEUS calorime- clearest signal for a muon was provided by the muon
ter was 18%/√E for electrons, with E in GeV. chambers. Inthe caseofH1,thereturnyokeofthe mag-
One of the primary design considerations of the ex- neticcoilwastheoutermostpartofthedetectorandwas
periments was the accurate reconstruction of the scat- equipped with streamer tubes forming the central muon
5
detector (Abt et al., 1997b) and tail catcher (4◦ < θ < principalwaytoidentifybeautyeventswastoreconstruct
171◦). In the forward region (3◦ < θ < 17◦), a set of leptons and measure their momentum, prel, perpendicu-
T
drift chamber layers formed the forward muon detector lartotheaxisofanassociatedjet. Thisgavealargesam-
(Biddulph et al.,1994),whichallowedamomentummea- ple due to a 10% branching ratio which is much higher
surement, together with an iron toroidal magnet. The than any given meson’s branching fraction to easily us-
ZEUS central and rear muon chambers (Abbiendi et al., able hadronic decays. Due to the quark’s larger mass,
1993)consistedoflimited-streamertubechambersplaced leptons from beauty decays are concentrated at higher
behind the calorimeter, inside and outside a magnetised valuesofprel thanleptonsfromcharmdecaysorinevents
T
iron yoke, covering a polar-angle region of 34◦ < θ < initiated by light quarks. Typical purities achieved for
171◦. Theforwardmuondetector(Abbiendi et al.,1993) beauty events by this method were about 20%.
consisted of six trigger planes of limited-streamer tubes The reconstruction of secondary vertices, using a mi-
and four planes of drift chambers covering the angular crovertexdetector,fromtheweakdecayofheavyquarks,
region 5◦ < θ <32◦. The efficiency of muon reconstruc- provides a method for tagging charm and beauty with
tion depended on the method used, with the detection high efficiency or, by applying stringent requirements,
of a mip signal having almost 100% efficiency and iso- with high purity. The H1 central silicon tracker (CST)
lated muons above 2GeV being detected 90% and 55% (Pitzl et al.,2000)consistedoftwolayersofdouble-sided
of the time in the H1 and ZEUS muon systems, respec- silicon strips, covering an angular range of 30◦ < θ <
tively (Aaron et al., 2009g). 150◦ for tracks passing through both layers. The ZEUS
microvertex detector (MVD) (Polini et al., 2007) con-
sisted of barrel (BMVD) and forward (FMVD) sections
D. Heavy Flavour Identification with, respectively,threecylindricallayersandfourverti-
calplanes. TheBMVDprovidedpolar-anglecoveragefor
As in other high-energy physics experiments, heavy tracks with three measurements from 30◦ to 150◦. The
quarks were identified by several means such as recon- FMVD extended the coverage to 7◦. A commonly used
structing a given meson mass, requiring a large momen- variable is the impact parameter, δ, of a track which is
tumofaleptonperpendiculartotheaxisofanassociated the transverse distance of closest approach of the track
jet,orreconstructingdisplacedverticesusingasiliconde- to the primary vertex, see Fig. 4. If the angle α is less
tector placed close the interaction point. than 90◦, δ is defined as positive, otherwise δ is defined
All ground state charm mesons have been recon- as negative. Negative values arise only due to imperfect
structed by combining tracking information from poten- resolution and hence events initiated by light quarks are
tial decay products. When only considering this infor- symmetric about δ = 0. An asymmetry to high posi-
mationandnofurther particleidentificationormeasure-
ments of secondary vertices, the decay D∗ D0π
s
→ →
Kππ has the purest signal; an example is shown in
s
Fig. 3. No beauty mesons have been fully reconstructed
due to the significantly smaller statistical sample. track
d>0 quark axis
16000
V
Me ZEUS (126 pb-1) f track
14000
5 backgr. wrong charge
s per 0. 1102000000 DN(*±D →*± ) (=K 3p 9)p5s00 ± 310 |d| (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)a f quark
n X
o
ati 8000
n
bi 6000 d<0
m track
o quark axis
C 4000
Gaussmod + backgr.
2000
f
track
0
0.14 0.15 0.16 (cid:0)(cid:1)(cid:0)(cid:1)a f
M(Kpp ) - M(Kp ) (GeV) |(cid:0)(cid:0)(cid:1)(cid:1)d| (cid:0)(cid:0)(cid:1)(cid:1) quark
s (cid:0)(cid:1)(cid:0)(cid:1) X
FIG. 3 The distribution of the mass difference m(D∗)
m(D0) for D∗ candidates and a background estimat−e.
FIG.4 DiagramsofatrackintheXY plane. Thedirectionof
From (Chekanov et al., 2009i).
the struck quark, experimentally approximated as a jet axis,
is used to definetheimpact parameter, δ.
Before the use of silicon microvertex detectors, the
6
tive values occurs due to heavy quark decays. A more calorimeter information in order to optimise the resolu-
powerful discriminator is the significance, S , at which tion. In a typical jet at HERA, the amount of track-
L
the transverse distance between the primary and sec- ing information used, and hence the improvementin the
ondary vertices, L is non-zero. Thus S is defined as jet energyresolutionwhenincluding tracks,is about10–
xy L
L /σ(L ),whereσ(L )istheuncertaintyonL . An 20%. In certain situations, when several tracks are ex-
xy xy xy xy
example distribution is shown in Fig. 5, where a strong plicitly reconstructed in a jet, such as a heavy-flavour
asymmetry is observed. meson (Chekanov et al., 2009g), the fraction of tracking
informationusedintheEFOinputtoajetreachesabout
50%andleadstoasignificantreductioninthesystematic
tststs111000666 H1 Data uncertaintiessuchasthatduetothecalorimeterhadronic
nnn
eee Total MC energy scale.
vvv
uds
EEE The single-hadron energy resolutions, as measured in
c
testbeams, are σ(E)/E 50%/√E 2%and35%/√E,
b ≈ ⊕
111000444 N ‡ 3 with E in GeV, for the H1 and ZEUS calorimeters, re-
track spectively. A detailed parametrisation of the jet en-
ergy resolution has not been performed. However, a
transverse-energy resolution of 9% has been achieved at
H1 for Ejet > 25GeV (Caron, 2002) and at ZEUS for
111000222 T
Ejet >14GeV (Chekanov et al., 2002a).
T
The precision of initial measurements of jet cross sec-
tions was limited by the uncertainty in the relative jet
energy scale between data and Monte Carlo. Due to the
111
crosssection rapidly falling with increasing energy,a 1%
---111000 000 111000 222000 333000
uncertaintyinthedeterminationofthescaleledtoabout
SSSVVV dddiiissstttaaannnccceee sssiiigggnnniiifffiiicccaaannnccceee SSS
a5%uncertaintyinthecrosssection. Therefore,areduc-
LLL
tionintheenergyscaleuncertaintyfrominitialestimates
FIG.5 Distributionofthesignificanceatwhichthetransverse of about 5% (25% uncertainty in the cross section) was
distance between the primary and secondary vertices is non- necessarytobeabletofully exploitthedataforexample
zero. Included in the figure is a decomposition of the data in precise extractions of parton densities or the strong
by fitting Monte Carlo templates for light, c and b quarks.
coupling constant (see Section III.C).
From (Aaron et al., 2010i).
In order to precisely determine the hadronic jet en-
ergyscale,variousmethods were employed,by e.g.using
tracking information in a jet or cross-calibrating jets re-
To achieve the most precise measurements for beauty constructed in different parts of the calorimeters. How-
and also charm production, the above and other dis- ever, the use of neutral current DIS events provided
criminating variables were combined in a neural net- the most powerful calibration tool based on the momen-
work (Aaron et al., 2010i) or a discriminating test func- tum balance between an outgoing jet and the scattered
tion (Chekanov et al., 2008a). electron. This relied on an accurate reconstruction of
the electron and a precise determination of the EM en-
ergy scale uncertainty. For the most precise calibra-
E. Hadronic Jets tions,closelyrelatedtechniquesexploitingthedoublean-
gle kinematic reconstruction method (Bentvelsen et al.,
In the first results on jet production from H1 and 1992; Hoeger, 1992) were employed. The difference be-
ZEUS, jets were reconstructed from the calorimeter tween the jet and electron transverse energies for data
cells using the JADE clustering (Bartel et al., 1986; and Monte Carlo simulations are shown for the ZEUS
Bethke et al., 1988) or cone algorithms. Due to the the- data in Fig. 6 versus the pseudorapidity and transverse
oretical problems with cone algorithms, such as ambi- energy of the jet. This demonstrates that the uncer-
guity in the seed finding and overlapping jets, both col- tainty on the determination of the jet energy scale is
laborations switched to the inclusive k clustering algo- 1% (Chekanov et al., 2002a,d; Wing, 2002). H1 fol-
T
rithm(Catani et al.,1993;Ellis and Soper,1993)forthe lowed similar procedures and achieved an uncertainty of
vast majority of their publications. 1.5% (Aktas et al., 2006h).
Calorimeter cells alone have continued to be used for
some publications, due to the finer granularity achieved
in the forward parts of the detector compared with the F. Photoproduction and DIS and How to Tell Them Apart
results of using some pre-clustering before the jet find-
ing. However,energyflowobjects(EFOs)havealsobeen Results from HERA are often (somewhat arbitrarily)
in common use by both collaborations. These objects classifiedaspertainingtoeitherphotoproductionorDIS.
are based on an algorithm which combines tracking and In a DIS event, the exchanged photon is virtual, with
7
the interaction point, see Fig. 7. These were used to tag
0.03 the electrons in photoproduction events over a narrower
range in Q2 and y. For example, in the case of the H1
DATA-HERWIG
(a) calorimeter at Z = 33m, values of Q2 were smaller
0.02 −
DATA-ARIADNE than 0.01GeV2 and the acceptance range was approx-
imately 0.3 < y < 0.7. This naturally led to smaller
0.01 samples compared with those obtained via the anti-tag
ofanelectroninthemaincalorimeters,butimprovedthe
reconstruction resolution.
0
-0.01 G. Very Forward Taggers
Bothexperimentshadvery-forwardparticletaggersto
-0.02
detect low-angle protons and neutrons, particularly for
measurements of diffractive production (see Section V).
-0.03 The H1 forward proton spectrometer
-1 -0.5 0 0.5 1 1.5 2 2.5 (FPS) (Adloff et al., 1999d; Van Esch et al., 2000) and
ZEUSleadingprotonspectrometer(LPS)(Derrick et al.,
1997) detected positively charged particles carrying a
substantial fraction of the incoming proton energy. The
(b)
particle trajectories were measured using a system of
detectors that could be inserted very close (typically a
few mm) to the proton beam, positioned between 64m
and 80m and 24m and 90m from the interaction point
for the FPS and LPS, respectively. The leading proton
detectors approached the beam in both the horizontal
andtheverticalplanes,withcomplementaryacceptances
in scattered proton energy. Despite providing a pure
sample of protons, the acceptance was only around
2%. The effective transverse-momentum resolution was
dominatedbythe intrinsictransverse-momentumspread
of the proton beam at the interaction point, which was
about 40–45MeV in the horizontal plane and about
! #$%&&’($)*&& 100MeV in the vertical plane.
"
Both H1 and ZEUS had forward neutron calorime-
FIG.6 ZEUSjetenergyscaleuncertaintyasafunctionof(a) ters (Adloff et al., 1999d; Bhadra et al., 1995, 1997a,b)
ηjet and (b) Ejet, showing that the scale is known to 1%. In installed in the HERA tunnel at θ =0 and at
T
(a),therelativedifferencebetweenthehadronicjettransverse Z =106m from the interaction point in the proton-
energy, Ejet, and the transverse momentum of the scattered beam direction. Both devices consisted of a
T
electron, calculated using the double-angle method, pDTA, is main calorimeter, with hadronic energy resolution of
shownasafunctionofthejetpseudorapidity,ηjet. In(b),the σ(E)/E (60 70)%/√E, with E in GeV, supple-
relativedifferencebetweenthedataandMonteCarlosimula- ≈ −
mented by a pre-shower calorimeter in the case of H1
tion is shown for the quantity hrejeti as a function of the jet and a scintillator hodoscope in the case of ZEUS. The
transverse energy, where rejet is the ratio of jet to electron
forward neutron calorimeters had a limited angular cov-
transverse energies.
erage,beingsensitivetoneutronsoflessthanabout0.05◦
or 0.8mrad. Both devices achievedspatial resolutions of
a squared four-momentum typically larger than about about 2mm.
1GeV2, and a high-energy scattered electron observed Figure 7 shows an illustration, for the example of the
inthe maincalorimeters. Photoproductionisusuallyde- H1 experiment, of the layout of the additional compo-
finedbytheabsenceofthescatteredelectroninthemain nents along the beamline in both directions away from
calorimeters, implying a virtuality Q2 < 1GeV2 and a the main detector.
median value of 10−4 10−3GeV2. The value of 1GeV2
−
is operational and depends on the exact coverage of the
calorimeter. Inphotoproduction,thephotonisquasi-real H. Triggering
and the concept of a photon structure is introduced.
Small calorimeters were placed along the direction of Both H1 (Baird et al., 2001; Nicholls et al., 1998;
the outgoingelectronbeam atdistances upto 40m from Sefkow et al., 1995) and ZEUS (Allfrey et al., 2007;
8
Forward Proton
Photon
Neutron Dissociation
Tagger
Calorimeter Taggers
Z (m)
220 106 80 61 24-28 6 40 103
Very Forward Forward Electron
Proton Proton Taggers
Spectrometer Spectrometer
FIG.7 SchematicillustrationofthebeamlineinstrumentationfortheexampleoftheH1experiment. Thedetectorcomponents
shownarealldescribedinthetextwiththeexceptionofthe103mphotontaggerwhichwasusedforluminositydetermination
via the Bethe–Heitler ep epγ process and the proton dissociation taggers which were used to identify forward rapidity gaps
→
(see Section V).
Smith et al.,1992)experimentsmainlyusedathree-level III. HADRONIC FINAL STATES AND SHORT
triggersystemofprogressivesophisticationinordertose- DISTANCE PHYSICS
lectthemostinterestingeventson-lineandremoveback-
groundfrombeam-gasinteractionsandlowenergyepcol-
In this section, measurements are presented of the
lisions in which additional statistics would not improve
hadronic final state in the presence of a hard scale,
anymeasurement. The H1triggerconsistedoftwohard- typically the virtuality, Q2, of the exchanged boson,
warelevelsandasoftwarefilterfarm,whereasZEUShad
the transverse energy of a jet or the mass of a heavy
one hardware level and two software filters. The first
quark in the event. A high or hard scale implies that
two levels often considered simple energy sums in the
the reaction occurs at short distance and hence allows
calorimeter or the reconstructed vertex position. At the
perturbative calculations to be performed. Almost all
third level, a simplified and fast version of much of the
processes and cross sections at HERA, both DIS and
offlinereconstructioncode,suchasjetandtrackingalgo-
photoproduction, involving a jet of high transverse en-
rithms,wasused. FromanominalHERAbunchcrossing
ergy or a heavy quark have been calculated in the
rate of 10MHz, the triggersystem reducedthe rate such
DGLAP (Altarelli and Parisi, 1977; Dokshitzer, 1977;
that data were written to storage at a rate of 10Hz.
≈ Gribov and Lipatov,1972;Lipatov,1975)approximation
tonext-to-leadingorder(NLO)inQCDperturbationthe-
ory. In many cases, several different approaches to the
Triggerfilterswhichselectedeventswithahigh-energy NLO QCD calculations are available for a given process
electron candidate were very efficient selectors of DIS and input parameters such as the strong coupling con-
events. Due to bandwidth restrictions, these were of- stant can also be varied. Comparisons between the cal-
ten pre-scaledor werecombined with additionalrequire- culations andwith data have ledto improvementsin the
ments, such as a jet or a reconstructed meson in the predictions. Various other approximations to QCD are
event,dependingonthephysicsmotivation. Severalhun- also available which emphasise different aspects of par-
dreddifferentcombinationsoftriggersexistedto tryand ton cascade dynamics and evolution. These include the
cover all interesting physics channels, whilst remaining BFKL (Balitsky and Lipatov, 1978; Kuraev et al., 1976,
withinthelimitsdictatedbydatatransferratesandpro- 1977)andCCFM(Catani et al.,1990a,b;Ciafaloni,1988;
cessing speeds. Marchesini,1995)approaches. Athoroughreviewofnon-
DGLAP predictionsofstandardshortdistance processes
isnotcarriedoutheresinceNLOcorrectionsarenotusu-
ally available. However,these approaches are considered
The principal trigger chains in the H1 and ZEUS ex-
later in the context of low x physics (Section III.D) and
periments, both in terms of bandwidth and frequency
diffraction (Section V).
of use in physics analyses, were designed to select inclu-
sive DIS and jet events. The information to select an Measurements of jet and heavy flavourproduction are
electron or jet candidate was often supplemented in the directly sensitive to the gluon density in the proton and
trigger with tracking information and, in the case of the havehencebeenusedinQCDfitstoconstraintheparton
photoproductionselection at H1, with an electron tag in densitiesintheproton. HeavyquarkdatainDISarealso
the beam-pipe calorimeters. used to extract the beauty, Fb¯b, and charm, Fcc¯, contri-
2 2
9
bution to the proton structure, F . These results are relatedtothequarkdensityintheproton. Measurements
2
reviewed in detail elsewhere (Klein and Yoshida, 2008; of jet cross sections are therefore sensitive to the strong
Perez and Rizvi, 2013). Measurements of photoproduc- coupling constant, α . When combined with inclusive
s
tion arealso sensitive to the structure ofthe photon and DIS cross-section measurements, they allow its precise
the data can in principle be used in fits to constrain the extraction simultaneously with the parton densities in
partondensitiesinthephoton. Amoredetailedreviewof the proton, as discussed in Section III.C. This can be
photoproductionandits constraintsonphotonstructure seen from a general schematic formula for perturbative
can also be found elsewhere (Butterworth and Wing, QCD calculations of DIS jet processes:
2005); however, new results since that review are dis-
cussed here. 1
dσ = dσˆ (x,α (µ ),µ ,µ )
ep→e+jets+X ea→cd s R F R
Z
Xa 0
A. Perturbative QCD Theory of the Hadronic Final State f (x,µ )dx, (1)
a/P F
A brief description of perturbative QCD related to wherethe sumisoverthepossiblepartons,a,inthepro-
the hadronic final state is given in this section. Fuller ton given by the parton density function (PDF), f .
a/P
accounts can be found elsewhere (Brock et al., 1995; The factorisationandrenormalisationscalesaredenoted
Dissertori et al., 2003; Ellis et al., 1996). by µ and µ and may be given by √Q2, the jet trans-
F R
Given that the lowest-order DIS process, a quark- verse energy, or a combination of the two. The short-
parton model (QPM) event (see Fig. 1), contains a scat- distancecrosssection,dσˆ ,dependsonx,thestrong
ea→cd
tered electron recoiling against a jet, it may seem trivial coupling, α , µ and µ .
s F R
to describe jet cross sections in DIS. However, once the
In photoproduction, where the electron escapes detec-
sizeablephasespaceforpartonradiationis consideredin
tion and continues down the beam-pipe, the virtuality,
the context of the wide range of possible jet algorithms, Q2, is low and the hard scale is given instead by the
the situationbecomes far more subtle. Jetcrosssections
transverse energy of the jets. The diagrams shown in
are generally presented in the Breit frame (Feynman,
Fig. 8 also apply to the LO direct jet photoproduction
1972; Streng et al., 1979) in which the exchanged vir-
processwheredirect-photoneventsareclassifiedasthose
tual boson is purely space-like, with 3-momentum q =
inwhichallofthephoton’smomentumparticipatesinthe
(0,0,Q), and is collinear with the incoming parton, such
hard interaction. Equation 1 is modified to the general
that QPM events do not contribute at large transverse
formula:
energies. Therefore leading-order (LO) QCD processes,
Fig. 8, dominate jet cross sections in DIS. 1
dσ = dσˆ (x,α (µ ),µ ,µ )
e+ e+ ep→e+jets+X Xa Z0 γa→cd s R F R
f f (x,µ )dx, (2)
γ/e a/P F
g g
wherethetermf representstheprobabilityoftheelec-
γ/e
tron radiating a photon and is given by the Weizs¨acker-
Williams formula (Frixione et al., 1993; von Weizsacker,
1934;Williams, 1934). Another class ofevents,resolved-
photon processes, also contribute to the photoproduc-
p p tioncrosssection. AtLO,suchprocessesareclassifiedas
thoseinwhichonlyafractionofthephoton’smomentum
(a) (b)
participatesinthe hardinteraction. Forsuchevents,the
FIG. 8 Illustrations of the (a) boson–gluon-fusion and (b)
photon can be considered as developing a structure, the
u-channel QCD Compton processes. Along with s-channel
parton densities of which are probed by the hard scale
QCDComptonscattering,thesearetheLOQCDprocessesin
DISanddirectphotoproduction,i.e.thelowest-orderprocess of the interaction. This means that the ep collision can
involving at least one power (or vertex) of α . be viewedas a hadron–hadroncollisionin whichpartons
s
from both the photon and the proton participate in the
hardprocess. Thereforemanyextradiagramscontribute
From the diagrams, it can be seen that the boson– in LO QCD to the photoproductioncrosssection; an ex-
gluon-fusionprocessisrelatedtothegluondensityinthe ample is shown in Fig. 9, in which a quark from the
proton. ThisisdominantatlowQ2,wherelow-xpartons photon collides with a gluon from the proton.
are mostimportant, whereasthe QCDCompton process AgeneralschematicformulaforperturbativeQCDcal-
becomes more important with increasing Q2 since it is culations of photoproduction processes is given by:
10
1 1
dσ = dx dx f f (x ,µ )f (x ,µ )dσˆ (x ,x ,α (µ ),µ ,µ ,µ ), (3)
ep→e+jets+X γ p γ/e b/γ γ Fγ a/p p Fp ab→cd γ p s R Fγ Fp R
Z Z
Xa,b 0 0
where x and x are the longitudinal momentum frac- hadron and parton levels in the Monte Carlo simula-
p γ
tions of the parton a in the proton and the parton b tion. As the simulations are only based on LO matrix
in the photon, respectively. The term f (f ) repre- elements with parton showering, their applicability is
a/p b/γ
sentsthePDFsofpartonswithflavoura(b)intheproton questionable. However, some level of control over the
(photon). Thefactorisationscalefortheproton(photon) procedure can be assured by checking the compatibility
is denoted by µ (µ ), and µ is the renormalisation of the dependences on important variables such as jet
Fp Fγ R
scale. The factorisation and renormalisation scales are transverse energy and angle between the NLO calcula-
often assumed to have the same value in calculations, tion and the parton level Monte Carlo simulation. For
although this is not necessarily the case and hence for some event properties and kinematic configurations, the
generality, they are here treated separately. The term NLO QCD calculations are not very reliable, due to the
dσˆ is the hard (partonic) cross section. In the fact that they only allow at most one parton to be radi-
ab→cd
case where parton b is the entire photon, f (x ,µ ) ated in addition to the primary jet pair. Calculations at
b/γ γ Fγ
is δ(1 x ) and Eq. 3 describes direct photoproduction the next order,next-to-next-to-leadingorder(NNLO) in
γ
−
and reduces to Eq. 2. QCD (Alekhin et al., 2010; Jimenez-Delgado and Reya,
2009; Martin et al., 2009), have been performed for in-
clusive DIS but not with final-state objects such as jets
g
e or heavy quarks present.
In DIS, NLO QCD calculations are avail-
able for the production of jets in neu-
tral current (Catani and Seymour, 1997;
Graudenz, 1997; Mirkes and Zeppenfeld, 1996;
g
Nagy and Trocsanyi, 2001; Potter, 1999) and charged
current (Mirkes and Zeppenfeld, 1996) processes.
p The NLO corrections have also been calculated for
2 3 scattering (i.e. three-jet cross sections) in
→
DIS (Nagy and Trocsanyi, 2001) and can in principle be
FIG. 9 An example of a LO resolved jet photoproduction
extended to photoproduction. Inclusive hadron produc-
process, containing a hard scattering between a quark from
tionhasalsobeencalculatedtoNLO(Albino et al.,2005,
thephoton and a gluon from the proton.
2008; de Florian et al., 2007a,b; Kniehl et al., 2000;
Kretzer, 2000), whereas prompt photon production has
been calculated to (α3) (Gehrmann-De Ridder et al.,
The separation between resolved and direct processes
O
2006a,b, 2000).
hasmoretodowiththelimitationsofourabilitytocalcu-
late QCD cross sections than with fundamental physics. In photoproduction, NLO QCD calculations are avail-
The separations are not unique beyond LO. For exam- able for the production of jets (Aurenche et al.,
ple the LO resolved-photon process in Fig. 9 can also 2000; Frixione, 1997; Frixione et al., 1996;
be considered as a direct-photon process in NLO QCD. Frixione and Ridolfi, 1997; Gordon and Storrow,
Nevertheless, the labels ‘direct’ and ‘resolved’ are useful 1992; Harris and Owens, 1997; Klasen and Kramer,
tools for exploring the world of photon physics. 1997), hadrons(Binnewies et al.,1995; Fontannaz et al.,
The NLO corrections for the production of two hard 2002), and prompt photons (Fontannaz et al., 2001;
partons at HERA, both in photoproduction and DIS, Fontannaz and Heinrich, 2004; Gordon and Storrow,
were calculated in the 1990s (see below), thereby al- 1994; Krawczyk and Zembrzuski, 2001;
lowingcomparisonswith inclusive-jetanddijet measure- Zembrzuski and Krawczyk, 2003).
ments, by applying a jet algorithm to the partons in The above perturbative calculations all require some
the final state of an NLO parton-level event generator. choicesofinputparameters,andalsoneedtobecorrected
These NLO QCDcalculations generallygive anaccurate forhadronisation,which leadto uncertainties inthe pre-
prediction of the normalisation and the shapes of basic dictions. The renormalisation and factorisation scales,
kinematic distributions. However, in order to compare theprotonandphotonPDFs,thevalueofα and,where
s
with observables measurable from the data, corrections appropriate, fragmentation functions all need to be cho-
for hadronisation using Monte Carlo models are neces- sen. The uncertainties areusually dominated by varying
sary. A multiplicative hadronisation correction factor is the renormalisation scale by a factor of two. However
determined from the ratio of the cross sections at the theyvarydepending onthephasespaceanddistribution