Multiple interactions at HERA

Multiple interactions at HERA

A. Knutssona (on behalf of the H1 and ZEUS collaborations)

aDESY - Deutsches Elektronensynchrotron, Notkestr. 85,22607 Hamburg, Germany

Presented are recent measurements in ep collisions at HERA, which comprise results that are expected tobe sensitive to multiple interactions and the underlying event. A measurement of 3- and 4-jet event cross-sections in photoproduction, as well as two measurements which target the activity in the soft underlying eventin photoproduction and deep inelastic scattering at low photon virtuality (Q2), respectively, are reviewed. Thedata are compared to various QCD models with and without multiple interactions simulated. The multijet eventcross-sections are in addition compared to a fixed-order O(αα2

s) calculation.

1. Introduction

Neutral current electron-proton collisions atHERA can be divided into interactions with di-rect and resolved photons. In direct photon inter-actions the photon interacts as a point-like parti-cle, while in the resolved photon interaction thephoton fluctuates into a partonic system. Thelatter results in a reaction that resembles hadron-hadron collisions, where interactions between thebeam remnants may occur in addition to the pri-mary ones. This is called multiple interactions(MI).

In photoproduction, where the exchanged pho-ton theoretically is real and experimentally thephoton virtuality, Q2, is close to 0, the partonicfluctuations of the photon can be long lived andthe contribution to the cross section from re-solved photons larger. The life time of the par-tonic fluctuation of the photon typically scaleswith 1/Q. Thus, in photoproduction and inlow Q2 deep inelastic scattering (DIS), additionalremnant-remnant interactions can be expected tocontribute to jet multiplicities and the underlyingevent (UE). The UE is defined as everything ex-cept the studied LO process, which is the hardestinteraction in the event. Already more than 10years ago, H1 and ZEUS have shown [1–3] thatin photoproduction jet cross-sections and the UEcan only be described by theoretical models, if MIare taken into consideration.

The fractional momentum of the exchangedphoton carried by the parton taking part in thehard interaction, xobs

γ , gives an experimental han-dle to select samples enriched in direct or resolvedphoton events. xobs

γ close to one means that pre-dominantly a direct photon takes part in the re-action.

The situation is summarised in Fig. 1, wherethe number of dijet events in photoproduction ismeasured [3] as a function of xobs

γ . The uncor-rected data are compared to predictions from theMonte Carlo generators PYTHIA [4] and HER-WIG [5] with MI, as well as HERWIG withoutMI. Also the direct photon contribution is shownseparately for HERWIG. The Monte Carlo (MC)simulated events have gone through a full detec-tor simulation. One can clearly see that onlymodels with MI simulated are able to account forthe data in the resolved enriched region.

Using a total integrated luminosity of 121 pb−1

ZEUS measures 3- and 4-jet cross-sections in pho-toproduction [6]. This measurement provides agood tool to study higher-order QCD, such asfixed-order calculations and QCD models withparton showers, as well as the contributions fromMI, which are expected to increase the multijetcross-section.

Two measurements from the H1 collabora-tion [7,8] investigate the underlying event by mea-suring the activity in different azimuthal regionswith respect to the hardest jet in the event, re-

Nuclear Physics B (Proc. Suppl.) 191 (2009) 141–150

0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved.

www.elsevierphysics.com

doi:10.1016/j.nuclphysbps.2009.03.121

0

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Figure 1. The number of uncorrected dijet eventsin photoproduction data [3] as a function xobs

γ

compared to Monte Carlo predictions. The linesrepresent: PYTHIA with MI (dashed line), HER-WIG with MI (full line), HERWIG without MI(dotted line). The contribution from direct pho-ton processes in HERWIG is shown as a shadedarea.

ferred to as the leading jet. Similar measurementshave been performed at the TEVATRON [9]. Inthe first measurement, the charged particle mul-tiplicity in dijet events is measured in photopro-duction. In the second one, the production ofjets with low transverse momenta, so called mini-jets, is measured in low Q2 deep inelastic scatter-ing events with at least one hard jet. Althoughthe possibility for remnant-remnant interactionsis smaller in DIS, where the contribution fromresolved photons is smaller, one can expect sec-ondary interactions between the proton remnantand the quarks produced at the photon vertex.The measurement is performed in bins of Q2.This is useful in order to control the contributionfrom resolved photon events which is expected todecrease with increasing Q2.

2. Theoretical Models

2.1. Monte Carlo Programs

The different measurements are compared tovarious theoretical predictions. The Monte Carlo

programs RAPGAP 3.1 [10], HERWIG 6.5 [5] andPYTHIA 6.2 [4] are based on leading-order ma-trix elements supplemented with parton showersin the DGLAP scheme, while the ARIADNE [11]program is producing gluon cascades according tothe Color Dipole Model (CDM) [11].

The PYTHIA 6.2 and HERWIG 6.5 programsallow to add contributions from remnant-remnantmultiple interactions. In PYTHIA 6.2 this isdone by using the so called simple model. Inthis model the total partonic interaction cross-section σint(pt,min), integrated from a cut offpt,min, grows with decreasing pt,min such thatit finally exceeds the total non-diffractive cross-section σTot. This is interpreted that the averagenumber of partonic interactions 〈n〉 is larger thanone, i.e. 〈n〉 = σint(pt,min)/σTot [12].

In HERWIG 6.5, two different models forUE/MI are available. The first is based on a phe-nomenological model for the soft underlying eventas introduced by the UA5 collaboration; its maineffect is to distribute additional energy isotropi-cally in the rest frame of the UE. In additional,the JIMMY package can be used to simulate MIwithin the HERWIG framework. JIMMY 4.0 [13]implements an impact parameter dependent MImodel, in which the colliding particles are approx-imated as overlapping discs. In the HERWIG pre-dictions presented here, MI is simulated by usingJIMMY 4.0.

These MI models are so far only implementedfor remnant-remnant interactions, and althoughone can imagine additional scatterings betweenthe proton remnant and the partons produced ina direct photon interaction, where no photon rem-nant is present, there are so far no attempts madeto describe such MI events.

If not stated otherwise, the default parametersof the generators are used in the presented stud-ies.

2.2. O(αα2s) Calculation

The 3-jet cross-sections measured by ZEUSin photoproduction are compared to a next-to-leading order O(α, α2

s) calculation [14,15], whichhere effectively is a leading order calculation,since events with three jets are selected. The cal-culations are corrected for hadronisation and mul-

A. Knutsson / Nuclear Physics B (Proc. Suppl.) 191 (2009) 141–150142

tiple interaction effects using PYTHIA 6.2 andHERWIG 6.5.

3. 3- and 4-jet Final States in Photopro-

duction

The ZEUS collaboration has measured [6] 3-and 4-jet event cross-sections in photoproduction.Analysed were events with the photon virtual-ity Q2 < 1 GeV2 and the photon inelasticity0.2 < y < 0.85. Jets were defined according to theinclusive kt-algorithm and were required to havetransverse energy ET > 6 GeV and pseudora-pidity |ηlab

jet | < 2.4. The events were divided intotwo subsamples with respect to the invariant massMnj of the n-jet system, 25 < Mnj < 50 GeV andMnj > 50 GeV, respectively.

In Fig. 2a) the 3-jet event cross-section is shownas a function of the invariant mass of the 3-jetsystem, M3j. The statistical errors of the dataare represented by the inner error bars, whilethe outer error bars represent the systematic andthe statistical errors added in quadrature. Theshaded band following the data points gives thesystematic error from the calorimeter energy scaleuncertainty. In this figure the cross-section iscompared to the O(αα2

s) calculation [14,15] (de-scribed in 2.2). The theoretical uncertainty onthe calculation is indicated as the dashed band.Fig. 2b) shows the hadronisation and MI correc-tions. While the hadronisation corrections aresmall and constant, the MI corrections are in-creasing with lower invariant mass by up to afactor of 2. The symmetric uncertainties of thecorrections are calculated as half of the differ-ence between the predictions from HERWIG andPYTHIA. As can be seen, the uncertainty ofthe MI corrections are significantly larger thanthe hadronisation corrections, and decreases from20% at low M3j to about 5% at high M3j . InFig. 2c), the ratio of data over theory is shown.The data are described within the fairly large the-oretical uncertainty, but only when the calcula-tion is corrected for MI effects.

The same cross-sections, and additionally the4-jet cross-sections, are shown in Fig. 3 as afunction of the invariant mass of the 4-jet sys-tem, M4j, and are compared to HERWIG and

Figure 2. 3-jet cross-sections as a function of theinvariant mass, M3j, of the 3-jet system. Thedata are compared to a fixed-order O(αα2

s) calcu-lation. The middle plot shows the corrections ap-plied to the calculation, and the lower plot showsthe ratio between data and theory. [6]

PYTHIA with and without contributions fromMI. Furthermore for HERWIG the direct photoncontribution are showed separately. Each modelprediction has been area normalised to the datain the high mass region (Mnj > 50 GeV), as in-dicated by the scaling factors given in the legend.The result is a reasonable description of the shape

A. Knutsson / Nuclear Physics B (Proc. Suppl.) 191 (2009) 141–150 143

of the data in the high mass region. However, atlow invariant masses the data cross-sections are

Figure 3. 3- and 4-jet cross-sections as a func-tion of the invariant mass of the jet system. TheQCD models and the errors of the data points aredescribed in the text. [6]

only described by the models, if MI are includedin the simulation. In that case PYTHIA performsslightly better compared to HERWIG. This be-haviour is most significant for the 4-jet final state,where the contribution from resolved photon in-teractions is seen to be much larger, and thus alsothe probability for remnant-remnant interactions.

The data cross-sections as a function of xobsγ

are shown in Fig. 4 for the 3- and the 4-jet finalstate and the low and high invariant mass regions.Due to the area normalisation of the MC only ashape comparison is possible for the high massregion, and as seen the MI flattens out the distri-bution slightly. For the low Mnj region the dataare only described if MI are included in the MC.It is worth noting that this is most relevant at lowxobs

γ , where the photon’s substructure is probed,and remnant-remnant interactions are expectedto be most prominent. At xobs

γ close to one MIhave a comparably small effect on the MC predic-tions. Again, the effect is largest for the four-jetfinal state, which is enriched in higher-order re-actions.

The presented analysis shows that in order todescribe the data MI have to be included in themodels. This is most prominent at low invariantmasses of the jet system, low xobs

γ and for higherjet multiplicity.

4. Charged Particle Multiplicity in Photo-

production

The H1 collaboration has measured the chargedparticle multiplicity in photoproduction dijetevents. The photoproduction events are selectedby tagging the outgoing electron, which putsthe upper limit on the photon virtuality, Q2, to0.01 GeV2. Analysed are events with at least twojets within the pseudorapidity range |ηjet| < 1.5

and with transverse momenta P jett > 5 GeV. Se-

lected are charged particles within the same pseu-dorapidity range as the jets, |ηpart| < 1.5 and withtransverse momenta of Pt > 150 MeV.

The charged particle multiplicity is measuredas a function of the azimuthal difference, Δφ, be-tween the leading jet and the particles, as well asa function of P jet

t of the leading jet in differentregions of φ. This is done at both low and high


Figure 4. 3- and 4-jet cross-sections as a function of the fractional momentum of the photon carried bythe struck quark (xobs

γ ). The QCD models and the errors of the data points are described in the text. [6]

xobsγ . Four different azimuthal regions are defined

(see Fig. 5): The toward region, in which theleading jet axis is always in the center, is definedaccording to 120o < φ < 240o. The away re-

gion corresponds to 300o < φ < 60o and, dueto momentum conservation, usually contains thesubleading jet, although no explicit restriction ismade. The transverse regions 240o < φ < 300o

and 60o < φ < 120o are distinguished by the

scalar sum of the transverse momentum, P sumt ,

of the charged particles in these angular regions.The high activity region is the region with thehigh P sum

t , while the low activity region has thelow P sum

t .In Fig. 6 the charged particle multiplicity is

shown as a function of Δφ, for a resolved enrichedregion, xobs

γ < 0.7 (Fig. 6, upper), and a direct en-

riched region, xobsγ > 0.7 (Fig. 6, lower). These


Toward

Awayo

o

Leading Jeto

φ=240o

φ=300o

φ=120

φ=180

φ=60

Transverse Transverse

Figure 5. Illustration of the azimuthal regionsused in the measurement of the charged particleproduction in photoproduction [7].

distributions are constructed such that the highactivity region is always to the right of the lead-ing jet axis, which is always at Δφ = 180o. Dueto momentum conservation the subleading jet isconsequently typically to the left in the plot in or-der to balance the momentum in the high activitytransverse region.

The data in Fig. 6 are also compared to MCpredictions from PYTHIA 6.2. Both the resolvedand direct photon enriched regions are only de-scribed, if the average charged particle multiplic-ity in the MC is increased by including MI inthe simulation. This effect is significantly moreprominent in the resolved enriched region. Ineach region the MI increase the activity in theMC by roughly an equal amount of charged par-ticles over the full Δφ range, except in the regionof the subleading jet, where the contribution fromMI is smaller.

In Figs. 7 and 8 the average charged particlemultiplicity is shown as a function of the trans-verse momentum of the leading jet, P jet

t , for thedifferent azimuthal regions. Again the measure-ments are separated into a direct and a resolvedenriched region. Looking at the data one can con-clude that in the toward and away regions thecharged particle multiplicity increases with P jet

t ,but the opposite is seen in the transverse regions.Again, the data are only described by the MC ifMI are included in the simulation. The contribu-

]° [±, h1JetφΔ

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Figure 6. Charged particle multiplicity as a func-tion of the azimuthal difference between the lead-ing jet and the charged particles. The figures areconstructed such that the leading jet is centred atΔφ = 180o, and the high activity region is alwaysto the right. The data are compared to PYTHIAwith and without multiple interactions [7].

tion from the MI is not constant in the MC butincreases slightly with lower P jet

t and lower xobsγ .

The description of the data by the MC was im-proved by tuning of the MI model in PYTHIA.The parameters1 which determine the length ofthe color strings in case of MI were varied. Atthe TEVATRON such tunes have been performedextensively to different data, e.g. [16]. While theTEVATRON data suggest MI with short colorstrings, the description of the HERA data pre-

1PARP(85) and PARP(86)


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< 0.7obsγx

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> 0.7obsγx

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Figure 7. The multiplicity of charged particles in photoproduction in the toward and the away azimuthalregions, as a function of the transverse momentum of the leading jet in the toward region. [7]

[GeV]T1JetP10

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arge

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Figure 8. The multiplicity of charged particles in photoproduction in the high and low activity transverseazimuthal regions, as a function of the transverse momentum of the leading jet in the toward region. [7]


sented here is improved when the long color stringscenario is used.

An attempt to describe the average chargedparticle multiplicity, without including multipleinteractions in the MC, was made by increasingthe maximum allowed virtuality2 of the final stateradiation by a factor of 4 (not shown). The re-sult was only a relatively small increase of thecharged particle multiplicity in the MC predic-tions. Furthermore, the description of the shapeas a function of P jet

t did not improve significantly.The presented analysis shows that the charged

particle multiplicity in dijet events in photopro-duction is only described by the MC, if MI is in-cluded in the MC generated events. This is mostprominent at low xobs

γ and for low transverse mo-mentum of the leading jet.

5. Minijet Multiplicities in DIS

H1 analysed DIS events within the kinematicalrange 5 < Q2 < 100 GeV2, 0.1 < y < 0.7 andW > 200 GeV, where the requirement on theinvariant mass of the hadronic final state, W , en-hances the production of soft jets and events withlow xBj. The results are presented for an inclusivejet sample, containing at least one jet, and a dijetsample in which the subleading jet (sj ) is requiredto be roughly back-to-back to the leading jet (lj )according to |Δφ∗| = |φ∗

lj− φ∗

sj| > 140o, where φ∗

denotes the azimuthal angle in the hadronic cen-ter of mass system. The jets are required to fulfilET > 5 GeV and 0.5 < ηlab

jet < 2.79. The ET re-quirement is applied in both the laboratory andthe hadronic center of mass frame.

The average multiplicity of jets with ET >3 GeV, referred to as minijets, is measured indifferent azimuthal regions relative to the lead-ing jet. These regions are sketched in Fig. 9 andare defined for each event in the same way asdescribed for the photoproduction measurementfrom H1. Although with the difference that 20o

buffer regions are used between the away regionand the transverse regions in order not to con-taminate the latter ones with particles belongingto the subleading jet.

2PARP(67) was increased from 1.0 to 4.0

The Leading Jet

Δφ∗ = 60

Δφ∗ = 120

Δφ∗ = 140

High active Region Region

Low active

TransverseRegion Region

Transverse

Toward Region

Away Region

(b)

The Subleading Jet

Figure 9. Illustration of the transverse regionsused for the measurement of the minijet multi-plicity in DIS. [8]

In Fig. 10 the average minijet multiplicity as afunction of the transverse momentum of the lead-ing jet is presented for the inclusive jet sample.This is done in bins of Q2 and for the differentazimuthal regions.

The Fig. 10 (left) shows comparisons to RAP-GAP and CDM. The predictions from RAPGAPcontain contributions from both direct and re-solved photon events. Neither RAPGAP norCDM have any MI implemented, and in the trans-verse regions, where MI signals are expected to beimportant, these models predict too low a minijetmultiplicity. This failure is most significant at lowQ2, where the contribution from resolved photonsis large, and thus remnant-remnant interactionsare expected to be relevant. In the toward andthe away region, where hard physics dominates,the data are reasonably well described.

Fig. 10 (right) shows the same data comparedto PYTHIA 6.2, with and without MI. In the lowQ2 bins, where the resolved component is large,the inclusion of MI events provides a clear im-provement of the description of the data in thetransverse regions, while at high Q2 the MI makeonly a very small difference. It should be kept inmind that in PYTHIA 6.2, only remnant-remnantinteractions are simulated. This means that for


HERA I(Preliminary) HERA I(Preliminary) CDM Rapgap (dir+res)

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< 2.79ljlabηMini Jet Production. Inclusive Sample. 0.5 <

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(j)

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(k)

10 20

(l)

Figure 10. Average minijet multiplicity in bins of Q2 in different azimuthal regions with respect to theleading jet, as a function of the transverse momentum of the leading jet in the inclusive jet sample. Thedata are compared to QCD models which are described in the text. [8]

the direct contribution MI are missing in the sim-ulation. Thus the fact that PYTHIA 6.2 with andwithout MI give about the same prediction in thehighest Q2 bin reflects the fact that there is verylittle contribution from resolved photons in thiskinematic region.

6. Conclusion

Measurements from the ZEUS and H1 experi-ments on 3- and 4-jet cross-sections [6], chargedparticle multiplicity in photoproduction [7] andminijet multiplicity in DIS [8] provide some in-dication that MI have to be considered in or-der to describe the data. In the multijet anal-ysis in photoproduction this is most significantfor low invariant masses of the jet system, andwhen the event contains 4 hard jets rather than3. It is also observed that the fixed-order cal-culation only describes the photoproduction data

after the large corrections for MI have been ap-plied. The charged particle multiplicity analysisin photoproduction shows that the activity in theUE depends on the transverse momentum of theleading jet.

In the analysis of minijet production in DIS thecontribution from remnant-remnant MI is largestat low Q2 and shows up in the azimuthal re-gions transverse to the leading jet. At high Q2

where the contribution from the resolved photonis small, and remnant-remnant interactions arethus strongly suppressed, the data description isnot improved when the available MI model is in-cluded in the MC. This may reflect the fact thata theoretical model for MI in direct photon inter-actions is currently not implemented in the MCgenerators used.

The analyses presented here comprise severalmore results. The 3- and 4-jet cross-sections inphotoproduction have been measured as a func-


tion of several additional variables. For the mini-jet production in DIS results exist also for moreinclusive rapidity regions as well as a dijet sample.

The overall message is that the activity in theevents, in terms of jet multiplicity and the soft un-derlying event, needs to be increased in the mod-els by adding MI. It is however not clear, if thedata presented cannot be described in other ways,e.g. by parton showers based on other evolutionequations than DGLAP.

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Multiple interactions at HERA