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Eur. Phys. J. C 50, 435466 (2007) THE EUROPEANPHYSICAL JOURNAL C

DOI 10.1140/epjc/s10052-007-0239-1

Special Article Scientific Note

Prediction for minimum bias and the underlying eventat LHC energies

A. Moraes1,a, C. Buttar2, I. Dawson3

1 Physics Department, Brookhaven National Laboratory, Upton, NY, 11973, USA2 Department of Physics and Astronomy, University of Glasgow, Kelvin Building, Glasgow, G12 8QQ, UK3 Department of Physics and Astronomy, University of Sheffield, The Hicks Building, Sheffield, S3 7RH, UK

Received: 8 September 2006 / Revised version: 23 January 2007 /Published online: 16 February 2007 Springer-Verlag / Societa Italiana di Fisica 2007

Abstract. In this report we investigate the models employed by PYTHIA and PHOJET Monte Carlo event

generators used to describe soft interactions in hadronhadron collisions. The aim of this study is to pre-dict the important properties of minimum bias and the underlying event at the LHC energy scale. Focusingon a wide range of measurements dominated by soft interactions in protonproton and protonanti-protoncollisions, one of the aims of this study is to check the consistency of these models when compared to dataand evaluate the accuracy of their descriptions of low-pt processes. Based on comparisons to a wide rangeof minimum bias and underlying event data we present a tuning for PYTHIA6.214 and compare it to otherPYTHIA tunings. Our proposed tuning for PYTHIA6.214 has been used for the ATLAS Data Challengeproductions.

PACS. 12.40.-y; 13.85.Hd

1 Introduction

At the Large Hadron Collider (LHC) [1], essentially allphysics processes will arise from quark and gluon inter-actions. Probed at high-energy, protons, or indeed anyother hadron, look like clusters of confined partons, i.e.quarks (anti-quarks) and gluons. High-energy proton col-lisions at the LHC can therefore be described in termsof parton interactions [2, 3]. However, our ability to de-scribe parton scatterings through quantum chromodynam-ics (QCD) depends on the amount of transverse momentawith respect to the collision axis (pt) involved in a givenscattering [46].

QCD has been very successful in describing quark, anti-quark and gluon scatterings involving large amounts oftransverse momenta known as hard interactions. How-ever high-energypp andpp collisions are dominated by softpartonic collisions, so-called minimum bias events. Softpartonic interactions also occur in the remains of hard scat-tering events not associated with the hard process and thisis important for many physics analyses such as W bosonand top-quark mass measurements [7], Higgs VBF [8] andSUSY searches.

As in previous hadron colliders, soft interactions willalso be the dominant processes in protonproton collisionsat the LHC. Hence, most of the particles produced at theLHC will originate from soft interactions. This is particu-

a e-mail: [email protected]

larly relevant for predictions of background levels associ-ated to many physics processes and also for understanding

the complex nature of the radiation environment in whichthe LHCs detector systems will operate [9].QCD breaks in the region of soft interactions due to

two effects. At QCD few hundred MeV, s 1 and per-turbative QCD breaks down. At momentum transfer of few GeV, QCD for a 2 2 parton scattering will ex-ceed the pp or pp cross-section. One method of solving thishas been to introduce multiparton interactions for whichthere is an increasing number of supporting experimentalevidence [1014].

Current models of high-energy hadron collisions willtypically combine perturbative QCD to explain parton in-teractions where it is applicable (high-pt scatterings), withan alternative phenomenological approach to describe softprocesses. Examples of these are the dual parton model(DPM) [15 18] and modified versions of QCD in which thedivergences presented by the running coupling constantare phenomenologically corrected to reproduce experimen-tal observations [19].

In this paper we assume that minimum bias eventsand the underlying event, or many aspects of them, canbe described by the same physical model as has beendone, for example, in PYTHIA [2022]. Minimum biasdata have been collected in the energy range 200 GeV1.8 TeV [23 30]. This allows many aspects of the model tobe tuned but especially allows the energy dependence to beinvestigated. The underlying event data from CDF meas-

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436 A. Moraes et al.: Prediction for minimum bias and the underlying event at LHC energies

urements at 1.8 TeV [31] have been used to tune the modeldescription of the underlying event. This method, whichcombines minimum bias and underlying event data-sets,has meant we have been unable to investigate HERWIGwith the JIMMY package [32] as this does not describeminimum bias events since it operates above a pt-cut-offand only describes the underlying event.

In Sect. 2 we investigate two Monte Carlo (MC) eventgenerators, PYTHIA [2022] and PHOJET [33, 34], fo-cusing on their models for soft interactions in hadronhadron collisions. Aiming to check the consistency of thesemodels, in Sects. 3 and 4 we compare their predictionsto wide range of data which demand of them an effi-cient description of low-pt processes. Comparisons to min-imum bias data are shown in Sect. 3 and to the underlyingevent measured by CDF, in Sect. 4. A proposed tuning forPYTHIA6.214 is presented in Sect. 5, where we also com-pare our tuning predictions to those generated with alter-native PYTHIA tunings. Predictions for levels of particleproduction and event activity at the LHC for interactions

dominated by soft processes such as minimum bias interac-tions and the underlying event associated to jet productionare discussed in Sect. 6. Finally, in Sect. 7 we present ourconclusions.

2 MC event generators

2.1 PYTHIA model for hadron collisions

In the PYTHIA model the total rate of parton interactions,Npartonparton , as a function of the transverse momentumscale pt, is assumed to be given by perturbative QCD. At

reasonably large pt values (pt 2 GeV) parton scatteringscan be correctly described by the standard perturbativeQCD, but to extend the partonparton scattering frame-work to the low-pt region a regularisation to correct thedivergence in the cross-section is introduced.

The starting point of this model is provided by theperturbative QCD cross-section for partonparton interac-tions which is given by:

=i,j,k

dx1

dx2

dt ki,j(s, t, u)

fiAx1, Q

2

fjB

x2, Q2

, (1)

where ki,j is the hard-scattering cross-section for the kthsubprocess possible between incoming partons i and j ands, t and u are the Mandelstam variables. For massless par-tons, the three Mandelstam variables are related by

s + t + u = 0 (2)

and

s = x1x2s . (3)

The parton distribution functions fiA

x1, Q2

fjBx2, Q2 give the probability to find a parton i (j)

with a fraction x1 (x2) of the beam energy inside the in-coming hadron A (B), if it is probed at a scale Q2. Finally,the Q2 scale is set to

Q2 =p2t =tu

s. (4)

The differential cross-section as a function ofp2t describ-ing a 2 2 parton scattering is given byd

dp2t=i,j,k

dx1

dx2

d t

fiA

x1, Q2

fjB

x2, Q2 dkij

d t

p2t

tu

s

, (5)

and the interaction cross-section above any chosen ptminlimit is thus written as

int(ptmin) =

s/4p2

tmin

d

dp2t

dp2t . (6)

This introduces two problems that must be solved. Thefirst one is observed at pt 2 GeV. Since QCD 0.2 GeV,perturbative QCD can still be applied at this pt region.However, the interaction cross-section exceeds the totalcross-section. The second problem happens as lower ptvalues are used. Defining the momentum fraction x as theapproximated value x |pt|/

s, low-pt parton scatterings

probe the parton densities at small-x values. As pt 0,the small-x region where parton distribution functions risequite steeply, give the major contribution to the integralin (6) and the differential cross-section diverges roughlylike dp2t /p

4t [19].

The first problem is solved by introducing the conceptof multiple parton interactions [19]. At high-energy, each ofthe incoming hadrons may be viewed as a beam of partonshence there is a possibility of having several partonpartoninteractions when the hadrons collide. Thus, events withint(ptmin) > tot are interpreted as having more than onepartonparton interaction taking place in the event. Ac-cording to this model, the average number of parton scat-terings in the event is defined as

Npartonparton =int(ptmin)

nd, (7)

where nd is the non-diffractive inelastic interaction cross-section [19].The multiple parton scatterings in hadron collisions

have been observed by experiments such as AFS [10],UA2 [11] and most recently has been directly measured bythe CDF Collaboration [12 14].

The second problem, which remains after multipartoninteractions are introduced, is related to the divergenceobserved as pt 0, is solved by introducing a cut-off pa-rameter ptmin given by [19]

ptmin(s) = (1.9 GeV)

s

1 TeV2

0.08. (8)

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A. Moraes et al.: Prediction for minimum bias and the underlying event at LHC energies 437

The cut-off parameter ptmin can be interpreted as theinverse of some colour screening length, d, in the had-ron [19, 35] (see Fig. 1). Equation (8), shows ptmin withthe default energy dependence in the PYTHIA versionsreleased after the version 6.200. The energy dependenceshown in (8), is taken to vary with the power 0.08 follow-ing the same energy dependence as observed in the total

cross-section [36].There are two strategies, or scenarios, proposed by the

Lund model to introduce the cut-off parameter definedby (8).

In the first one, labelled simple scenario, an ef-fective cut-off is established at ptmin, which means thatd/ dp2t = 0 for pt < ptmin . In other words, a sharp cut-offat ptmin is equivalent to establishing a maximum impactparameter, bmax, above which there is no interaction. Thesharp cut-off applied to the probability of partonpartoninteractions may also be interpreted as a consequence ofthe parton confinement. In this framework, valence quarksfrom incoming hadrons carrying a transverse component

of momentum pt < ptmin would not be able to overcomethe partonic binding and interact inelastically. For interac-tions withpt < ptmin there will be an exchange of a very softgluon between the two colliding hadrons which does not af-fect the momentum distribution of partons, but transformshadrons into colour-octet objects (two-string picture) [19].

Since each incoming hadron is a composite object, con-sisting of many partons, there should exist the possibil-ity of several parton pairs interacting when two hadronscollide. The model assumes that different pairwise inter-actions take place essentially independent of each other,and that therefore the number of interactions in an event isgiven by a Poissonian distribution. This is the strategy of

the simple scenario [19].Considering that hadrons are not only composite butalso extended objects, partonic interaction probabilitiesare likely to vary for each reaction. In this approach,called the complex scenario, the probability associatedwith each interacting parton depends on the assumed mat-ter distribution inside the colliding hadrons. In the com-plex scenario an impact parameter dependent approachis therefore introduced [19]. A small b value (pt ptmin)corresponds to a large overlap between the two colliding

Fig. 1. Illustration of resolved ( < d) and screened ( > d)colour charges in a hadron

Table 1. Default parameters for ptmin as definedin PYTHIA 6.214

ptmin parameters

PARP(81) = 1.9 simple scenario

PARP(82) = 1.9 complex scenario

PARP(89) = 1 TeV energy scalePARP(90) = 0.16 power which regulatesptmins energy dependence

hadrons, and hence an enhanced probability of multiple in-teractions. On the other hand, a large b (pt < ptmin) meansa large probability that no partonparton interaction willtake place in the event. This causes the so-called pedestaleffect seen by UA1 [19] and also affects charged multiplicitydistributions.

In this scenario, the divergences at pt 0 are cor-rected by multiplying the matrix elements by a factor

p4t /(p

2t +p

2tmin)

2

and replacing the argument p2t in s by

(p2t +p2tmin

). This action removes divergent terms propor-tional to 1/p4t , provides a continuouspt spectrum for calcu-lated interaction properties, and reduces to standard per-turbative QCD for pt ptmin [19].

The parameters defining ptmin as shown in (8) are dis-played in Table 1. The factor 1.9 GeV is defined in thesimple scenario by PARP(81) and by PARP(82) in thecomplex scenario. The energy scale of 1 TeV is defined byPARP(89) and is included in (8) to be a convenient tuningparameter rather than a parameter with physical meaning.PARP(90) gives the power with which ptmin varies withthe centre of mass energy,

s. The default option is set as

PARP(90) = 0.16 [2022].In both scenarios, all the scatterings that occur in an

event must be correlated somehow by momentum andflavour conservation for the partons from each incominghadron, as well as by various quantum-mechanical effects.Finally, after the parton interaction cross-sections are esti-mated by the model, the resulting partons are fragmentedinto colourless hadrons. This introduces a correlation be-tween the final-state hadrons and the number of multipleinteractions.

2.2 PHOJET

The physics model used in the MC event generatorPHOJET combines the ideas of the dual parton model(DPM) [1518] with perturbative QCD [46] to givean almost complete picture of high-energy hadroncollisions [33, 34].

PHOJET is formulated as a two-component model con-taining contributions from both soft and hard interac-tions. The DPM is used to describe the dominant soft pro-cesses and perturbative QCD is applied to generate hardinteractions [33, 34].

Combining non-perturbative topological expansions ofQCD with generally accepted theoretical principles likeduality, unitarity, Regge behaviour and the parton struc-

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ture of hadrons, the DPM provides a complete phenomeno-logical description of soft processes in high-energy hadroncollisions [15 18].

The mechanism of Pomeron exchange is at the heartof the DPM [1518]. According to the DPM, the leadingcontribution to multiparticle production in high-energyhadronhadron collisions stems from the exchange of a sin-

gle Pomeron between the colliding hadrons. SecondaryPomeron exchanges account for the remaining activity inthe event.

Each exchanged Pomeron gives rise to two colour-neutral chains stretching between quarks and diquarks, forbaryons, or quarks and anti-quarks for mesons or pairs ofsea quarks and anti-quarks polarised from the vacuum. Inthe case of the leading Pomeron exchange, these chainsstretch between valence quarks (or anti-quarks) whereasfor the other exchanges the chains will end on valence andsea quarks from the initial hadrons.

As an example, the dominant two-chain diagram de-scribing multiparticle production in high-energy proton

proton (pp) collisions is shown in Fig. 2a and the leadingtwo-chain contribution with a secondary pair of chains cor-responding to the exchange of two Pomerons in Fig. 2b.

The model employed by PHOJET is based on thecalculation of scattering amplitudes, taking into accountthe unitarization principle. Comparisons between the cal-culated results for cross-sections and the available datahave been made to determine the unknown model parame-

Fig. 2. a Dominant two-chain diagram corresponding to a sin-gle Pomeron exchange and b leading two-chain contributionwith a secondary pair of chains corresponding to the exchangeof two Pomerons in high-energy pp collision

ters (couplings, Pomeron intercepts and slope parameters),which are needed to generate multiparticle final states pro-duced in inelastic interactions [33, 34].

2.2.1 The two-component model

In PHOJET, the division of inelastic hadronic interac-tions into soft and hard processes is similar to that usedin PYTHIA and a pcut-offt separating soft and hard interac-tions is also introduced in PHOJET.

The total cross-section, tot, is obtained by adding thesoft, soft, and the hard, hard, cross-section with the cor-rections imposed by unitarity. The soft and hard cross-sections vary for different values ofpcut-offt .

Within the DPM, Pomeron exchanges dominate thesoft processes in high energy hadronhadron interactions.The Pomeron exchange cross-section for pure soft interac-tions can be parametrised as [37]

soft = 37.8s0.076 (mb) . (9)

As shown in (9), the soft cross-section increases withthe centre-of-mass energy as a power ofs. The total cross-section has been observed to grow as (ln s)2 [37, 38] whichmeans that as s , soft becomes bigger than the tot,violating the unitarity bound. The mechanism used topreserve unitarity consists of including multiple Pomeronexchange as an additional component in the hadron in-teraction, a model which agrees with the experimentalevidence [15 18].

The hard cross-section is calculated with a lower trans-verse momentum cut greater than 2 GeV [37]. As for thesoft cross-section, the hard cross-section increases withthe centre-of-mass energy

s approximately as a power

ofs [37]. The expression for hard scattering cross-section isgiven by

h =

i,jk,l

dx1

dx2

d t x1fi

x1, Q

2

x2fj

x2, Q2

1x1x2

M22s (Q

2)

s2, (10)

where fi,j(x, Q2) are the parton distributions, M =Mi,jk,l is the matrix element for the hard partonpartonscattering i, j k, l, and s(Q2) is the strong couplingconstant at the hard scale Q2 [37].

For increasingly higher

s, events with hard > tot willappear, and similarly to the mechanism of multiple softinteractions which explains interactions with soft > tot,a mechanism of multiple hard parton scatterings must beadopted to preserve unitarity. Therefore PHOJET allowsthe possibility of having events with multiple soft inter-actions (multiple Pomeron exchanges) and multiple hardparton scatterings.

In addition to soft and hard interactions as describedabove, PHOJET also allows the possibility of having initialand final state parton showers. These parton showers aregenerated in leading-log approximation [33, 34].

The fragmentation of soft-chains or hard scatteredpartons is done by the Lund model [2022,33,34], i.e.

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PHOJET uses the same fragmentation model adopted byPYTHIA [39].

The soft, soft, and hard, hard, cross-sections are inclu-sive cross-sections and the average multiplicities of soft andhard scatterings in an inelastic event are

ns

=s

inel,

nh = hinel

, (11)

respectively. The hard scatterings are mostly independentof each other, being related only by the sharing of energyand momentum of the incoming protons. These multiplic-ities increase with the colliding centre-of-mass energy. Forpp collisions at

s = 14 TeV a considerable part of inter-

actions is expected to have more than one hard or softscattering.

2.3 PYTHIA vs. PHOJET

The starting point for the event generation in PYTHIAis the description of possible hard interactions in e+e,pp, pp or ep colliders. However, as shown above, it alsocombines sophisticated models dealing with soft hadronicinteractions [2022]. PHOJET, on the other hand, ini-tialises the event generation by describing the soft compon-ent of hadronhadron, photonhadron or photonphotoninteractions at high energies. The hard component, cal-culated by perturbative QCD at the partonic level, isthen introduced to complete the event simulation [33, 34].Due to the different underlying theoretical models usedin the physics simulation by these two event generators,

PYTHIA presents the user with hundreds of settings thatcan be adjusted in order to better reproduce the data whilePHOJET is relatively more tightly restricted.

Throughout the next sections, we will present analysisbased on both MC event generators, however the empha-sis will be in adapting the PYTHIA model to the datawhile using PHOJET as a reference to evaluate uncertain-ties which appear when these event generators, especiallytheir models for soft interactions, are extrapolated to theLHC energies. Note that parameters not mentioned in thetext are kept as default in comparisons shown throughoutthis article. The PHOJET parameters used in our simula-tions are the ones found in [33, 34]. The physical meaning

of the relevant PYTHIA parameters to be investigated issummarized in Appendix A. The program versions used inthis study are PYTHIA version 6.214 (PYTHIA6.214) andPHOJET version 1.12 (PHOJET1.12).

3 Cross-section predictions

The total collision cross-section for hadronhadron scat-terings, tot, can be divided into elastic (elas) and inelas-tic (inel) processes. The inelastic scattering cross-sectionis also usually sub-divided into single (sd) and double(dd) diffractive and non-diffractive inelastic cross-sections

(nd) [40]. The total cross-section, tot, can thus be writtenas

tot(s) = elas(s) + sd(s) + dd(s) + nd(s) , (12)

where s is the square of the total centre of mass energy.As shown in (7) and (11), both models rely on compo-

nents of the hadronic cross-section (nd and inel used byPYTHIA and PHOJET, respectively) to estimate the rateof multi-parton scattering or multi-Pomeron exchanges.In this section we investigate cross-section predictionsfor pp and pp collisions generated by PYTHIA6.214 andPHOJET1.12.

Figure 3 shows a schematic view of elastic (Fig. 3a),single-diffractive (Fig. 3b), double-diffractive (Fig. 3c) andnon-diffractive inelastic hadron interactions (Fig. 3d) inthe phase space, the angle being the azimuthal scat-tering direction and the pseudorapidity.

As schematically shown in Fig. 3a,the hadronseparationin pseudorapidity is maximum for elastic scatterings. Single

and double diffractive events, shown in Fig. 3b and c respec-tively,displayclearseparation,orgaps,betweenthesystemstravelling in the forward and backward regions. However, forparticles produced in a non-diffractive event, as displayedin Fig. 3d, gaps which naturally occur between two systemsmoving in opposite directions (forward and backward) arefilled by particles produced in the central region.

Based on a parametrisation derived from the Pomeronexchange model [36], PYTHIA generates the total pp andpp cross-section (mb) using the following expressions:

pptot(s) = 21.7s0.0808 + 56.1s0.4525, (13)

pptot(s) = 21.7s0.0808 + 98.4s0.4525, (14)

where the first term on the right hand side of both (13)and (14) is the Pomeron contribution and the second onea reggeon exchange [2022].

In PHOJET, the total pp and pp cross-section are gen-erated through the optical theorem and are corrected forhigh energies using the unitarity principle [33, 34]. The dif-ferential elastic cross-section is related to the scatteringamplitude A(s, t) by

delasdt

=1

16s2|A(s, t)|2, (15)

and through the optical theorem relation

elas =2tot

16Belas(16)

the total cross-section tot is estimated, with Belas beingthe elastic slope and elas the elastic cross-section.

The resulting total pp and pp cross-sections are pro-portional to (ln s)2 [37] and will not violate the FroissartMartin bound which postulates that tot < A ln

2 s, wherethe constant A 60 mb [38].

As can be seen in Fig. 4 the total cross-sections for ppand pp are very similar to each other for

s > 10 GeV.

A plausible explanation can be derived from the Pomeronexchange model: as shown in (13) and (14), for

s

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Fig. 3. Schematic view ofa elastic, b single-diffractive,c double-diffractiveand d non-diffractive hadron interactionsin the space

the Pomeron term, which is the same for both pp and pptotal cross-sections, dominates, leading to a high similar-ity between the two cross-sections at high energies. Fig-ure 4 also shows good agreement between the predictionsof the generators and the experimental data for energiesbelow 1 TeV. For energies higher than 800 GeV the pre-dictions start to diverge at the level of 15%. The totalcross-section predictions for pp collisions at 14 TeV aretot =101.5mband tot =119.1 mb for PYTHIA6.214 andPHOJET1.12, respectively. Recent theoretical studies pre-dict tot = 106.35.1syst.2.4stat. mb for pp collisions atthe LHC [41].

Fig. 4. PYTHIA6.214 andPHOJET1.12 total cross-sect-ion for pp (a) and pp (b) in-teractions. Data points takenfrom [42]

Once PYTHIA calculates the total cross-section, thesame expression from the optical theorem used byPHOJET, given in (16), (with different parametrizationsfor the elastic slope Belas in each program), is used to esti-mate the elastic cross-section [2022, 33, 34]. In both eventgenerators, the inelastic part of the interaction is obtainedby subtracting the elastic from the total cross-section.

The inelastic and elastic contributions to the totalpp cross-section generated by PYTHIA6.214 andPHOJET1.12 are displayed in Fig. 5a. As expected [40],inelastic events are the major contributors to the totalcross-section. The pattern of the distributions, tot and

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Fig. 5. PYTHIA6.214 andPHOJET1.12 cross-sectionpredictions for pp collisions:a inelastic and elastic, andb NSD interactions

inel, is the same, with the divergences between the pre-dicted cross-sections starting at roughly the same energy,but being less pronounced in the inel distribution. Theelastic cross-sections on the other hand, present a con-siderable divergence for

s > 1 TeV. This is mostly due

to the differences in tot which are magnified in elas asindicated by (16). At the LHC energy, PYTHIA6.214 pre-dicts elas = 22.5 mb while PHOJET1.12 estimates elas =34.5 mb, 53% greater than the former.

3.1 Minimum bias interactions

It is not unusual to find slightly different definitions forminimum bias events in the literature. Historically, fromthe days of CERN-ISR [23], CERN-SPS UA5 [24] upto the more recent Tevatron experiments CDF [25] andE735 [26, 27], measurements of minimum bias events area close approximation of non-single diffractive inelastic(NSD) interactions, i.e. nsd = totelassd. This in-terpretation is based on the triggering system used in theexperiments mentioned above which favoured the detec-tion of NSD events. On the other hand, with the re-ignitedinterest for theoretical models that could satisfactorilydescribe soft interactions and diffractive processes, somegroups have identified minimum bias events as non-diffractive inelastic interactions [40].

In practical terms, the experimental choice for non-single diffractive inelastic interactions as minimum biasevents does not differ considerably from the more theoret-ical non-diffractive choice, since their cross-sections wouldhardly differ by more than 15% at the current collider en-ergies. Throughout this article, we will associate minimumbias events with NSD inelastic interactions, following theexperimental trend. As shown in Table 2, in the languageof the MC event generators used in this work, subpro-cesses 94 and 95 are switched on in PYTHIA6.214, andprocesses IPRON(1,1), IPRON(4,1) and IPRON(7,1) inPHOJET1.12. Note that in PHOJET we are also includingcentral diffraction (IPRON(4,1)) as part of the processes

generated as minimum bias events as this category of inter-actions also fits in the selection of NSD events.

In Appendix B we verify that the direct selection ofNSD interactions in both PYTHIA6.214 and PHOJET1.12(as indicated in Table 2) agrees reasonably well to thecross-sections and minimum bias distributions predictedby the same event generators with the trigger simulation.

Defining minimum bias events as NSD interactions en-ables us to probe theoretical models by comparing themwith a variety of experimental observables measured overa range of energies in the last quarter of a century.

Diffractive inelastic events (single and double diffrac-tive) are simulated in both programs. Although dif-

ferent parametrizations are used, both PYTHIA andPHOJET consider Pomeron models to describe diffractiveevents [2022, 33, 34]. The NSD cross-section, nsd, is thenobtained by subtracting single diffractive cross-sectionsfrom the inelastic.

Figure 5b shows the estimated nsd for pp collisionsgenerated by PYTHIA6.214 and PHOJET1.12. For thecentre-of-mass energy range displayed in Fig. 5b, PHOJETgenerates higher cross-sections for non-single diffractiveinteractions, or minimum bias events, than PYTHIA.This implies that for pp collisions at the same luminos-ity, PHOJET will generate more minimum bias eventsthan PYTHIA. The non-single diffractive scattering cross-sections obtained for each generator at

s = 14 TeV were:

65.7 mb for PYTHIA6.214, and 73.8 mb for PHOJET1.12,a difference of 12.3%. This shows that minimum bias events

Table 2. Parameters used to generate minimum biasevents (NSD)

PYTHIA6.214 MSUB(94) = 1 double diffractionMSUB(95) = 1 low-pt production

PHOJET1.12 IPRON(1, 1) = 1 non-diffractiveIPRON(4, 1) = 1 central diffractionIPRON(7, 1) = 1 double diffraction

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are expected to contribute significantly (more than 65%) tothe total scattering process at the LHC.

3.2 Charged particle multiplicity distribution

Charged particle multiplicity distributions [28] have been

widely used as important tools for studying multiple par-ticle production in inelastic and NSD events [23, 24, 26, 27].They are particularly useful when displayed in terms ofmultiplicity scaled variables as suggested by Koba, Nielsenand Olesen (KNO variables) [28]. Plotted as a function ofKNO variables, the charged multiplicity distributions pro-vide a clearer display of fluctuations seen for both verylow (less than half of the average multiplicity) or very highmultiplicity (more than the double the average) events.This provides invaluable information on the evolution ofthe event multiplicity with the colliding energy.

When the KNO plots first appeared, it was suggestedthat the probability distributions, Pn, of producing n par-

ticles at a given inelastic or minimum bias hadronhadroncollision should scale with energy as s following therelation

F(z) = nPn = n nn

n, (17)

with n being the average particle multiplicity, z = n/nand Pn alternatively defined in terms of cross-sections as

Fig. 6. Charged multiplicity distributions for pp collisionsat

s = 546 GeV and 1.8 TeV, compared to the fit to ISR

distributions

Pn = n/

n n, where n is the cross-section for interac-tions producing n particles and

n n is the inelastic or

the minimum bias cross-section.KNO scaling was indeed observed up to the highest ISR

energies as shown in [23]. Nevertheless, experiments withcentre of mass energy greater than those achieved at theISR demonstrated the scaling is broken [24, 29].

Figure 6 shows charged multiplicity distributions forNSD pp collisions measured by UA5 at

s = 546 GeV [24]

and by E735 at

s = 1.8 TeV [26, 27]. It also shows the fitto the KNO distributions measured at ISR given in [23].

Comparing the UA5 546 GeV and E735 data to the ISRfit, the KNO violation is clearly visible. The violation oc-curs for z > 2, i.e., for high multiplicity events. The scalingviolation is interpreted as a manifestation of multi-partoninteractions (second, third or a higher number of partonscatterings) [1014] whose effects become measurable asthe colliding energy increases [26, 27].

3.3 Describing charged multiplicity distributionswith PYTHIA

By default PYTHIA is set to use multiple parton interac-tions. Nevertheless, one still has to define how the diver-gency for scatterings with pt < ptmin will be treated by theevent generator. PYTHIA allows two different phenomeno-logical approaches: simple and complex scenarios [19]. Se-lecting the complex scenario one has also the choice ofselecting different matter distributions for the collidinghadrons, which introduces a dependence on the collisionsimpact parameter b .

In this section we compare charged multiplicity dis-tributions generated using the simple scenario

(MSTP(82) = 1) and those obtained using the complexscenario (MSTP(82) = 2, 3 and 4) to the data. Compar-isons between PYTHIAs models and the pp 546 GeV UA5data have been presented in [19]. Here we extend thesecomparisons to UA5 data taken at 900 GeV [24], to recentdata taken at higher energies by E735 [26, 27] and also toone of the latest PYTHIA versions [2022].

For each comparison we calculate the 2/d.o.f. associ-ated to the MC generated distribution as [43]

2/d.o.f. =1

Nd.o.f.

Nd.o.f.i=1

(yii)22i (yi) +

2i (i)

, (18)

where Nd.o.f. is the number of degrees of freedom, yi andi are the MC and measured values for the ith bin respec-tively, and 2(yi) and 2(i) are the errors associated toyi and i . This allows us to compare how well simulationsgenerated with different parameters agree with the data.

Figure 7 shows charged multiplicity distributions forNSD pp collisions at

s = 546 GeV and 1.8 TeV. We

compare distributions generated by PYTHIAs simpleand complex scenarios to UA5 [24] and E735 [26, 27]data. Apart from the mentioned changes in the settingMSTP(82), all other parameters are set to use PYTHIAsdefault options, as described in [2022]. Typically, thenumber of generated events used to plot each MC distri-

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Fig. 7. Charged multiplicitydistributions for NSD pp col-lisions at

s = 546 GeV and

1.8 TeV: a and b simple sce-

nario distributions comparedto data for

s = 546 GeV and

1.8 TeV, respectively; c andd complex scenario distribu-tions compared to data for

s = 546 GeV and 1.8 TeV,respectively

bution is greater than 106 events. This is valid not onlyfor charged particle distributions but also for all minimumbias predictions shown in this note.

Figures 7a and b show that using the simple scen-ario (MSTP(82) = 1), which is the default inPYTHIA6.214 [2022], the generated distributions failto reproduce the data, especially in the region of high z(z > 1.5). This is the region of events with particle mul-tiplicities several times greater than the average multi-plicity. The 2/d.o.f. associated to the MC generateddistributions in Fig. 7a and b are 2/47 d.o.f. = 80.6 and2/128 d.o.f. = 107.2, respectively. Notice that althoughsome points in the MC distributions may be off the curveand look like a systematic effect in the model predictionsthey are actually the result of using the binning of the data(which depends on the measurement of z = n/n) to pro-duce the MC plots. This, however, has no effect on the finalresults.

Distributions generated using the complex scenariovary with the hadronic matter distribution selected foreach case. As shown in Fig. 7c and d, the complex scenariooption which uses a uniform hadronic matter distribution(MSTP(82) = 2) fails to describe the charged multipli-city distributions correctly and gives 2/47 d.o.f. = 86.2and 2/128 d.o.f. = 132.9, for the distributions at 546 GeVand 1.8 TeV, respectively. Notice that for both the sim-ple scenario and the complex scenario with a uniformmatter distribution, the charged multiplicity distribu-tions tend to have a Poissonian behaviour and cannotreproduce the shape of the high-multiplicity tail. The dis-tributions generated using the double Gaussian option(MSTP(82) = 4) also fail to reproduce the data and gener-ate an excess of high multiplicity events, which results in2/47 d.o.f. = 84.3 and 2/128 d.o.f. = 66.9, respectively.The best agreement to the data is observed for the com-plex scenario with the single Gaussian matter distribution

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option (MSTP(82) = 3). The 2/d.o.f. obtained with thisoption are 2/47 d.o.f. = 33.9 and 2/128 d.o.f. = 29.1 forthe comparisons shown in Fig. 7c and d.

The comparisons of charged multiplicity distributionsshown in Fig. 7c and d indicate that the matter distribu-tion used to describe the colliding hadrons does affect theprobability of particle production in minimum bias events.

The simple Poisson distribution of multi-parton events failto fit the data indicating that there is a correlation betweenimpact parameter and number of events. This was also seenas the pedestal effect by UA1 [19].

Although in the comparisons shown in Fig. 7, whereall PYTHIA parameters except MSTP(82) are kept asdefault, the best agreement to the data was obtainedby selecting the complex scenario with the single Gaus-sian matter distribution option, we shall adopt the com-plex scenario with a double Gaussian matter distribution(MSTP(82) = 4) as our preferred choice.

This is done because by choosing the double Gaussianoption, the user is able to control some of the properties

of this matter distribution. The double Gaussian matterdistribution is given by [2022]

(r) 1a31

exp

r

2

a21

+

a32exp

r

2

a22

. (19)

Hadrons described by this distribution have a small coreregion of radius a2 containing a fraction of the totalhadronic matter. This core is embedded in a larger volumeof radius a1 containing the remaining fraction of matter,i.e., (1) of the total hadronic matter. The parameterPARP(83) controls the portion of the total hadronicmatter assigned to the core of the hadron. The ratio a2/a1

is given by the parameter PARP(84). By default, PYTHIAsets PARP(83) = 0.5 and PARP(84) = 0.2 describing anygiven hadron as a body with half of its matter concentratedwithin a core which is limited by a radius a2 = 20% of thehadron radius a1 [2022].

Fig. 8. Charged multiplicitydistributions for NSD pp col-lisions at a

s = 546 GeV and

b

s = 1.8 TeV

Notice that this double Gaussian distribution can eas-ily be reduced to a single Gaussian by selecting specificvalues of PARP(83) or PARP(84) (e.g. PARP(83) = 1 orPARP(84) = 1).

High pt scattering processes are associated with smallimpact parameters. Therefore if a double gaussian modelwith a dense core is used to describe the matter dis-

tribution in the proton, hard scatters will be associatedwith a greater number of multiple interactions and hencea greater activity in the underlying event.

3.3.1 Double Gaussian matter distribution

As noted above, the type of matter distribution describ-ing the colliding hadrons produces considerable changes inthe shape of the charged multiplicity distributions (Fig. 7cand d). The effect produced by variations in the propertiesof the double Gaussian distribution, particularly the effectof variations in the core size to the minimum bias chargedmultiplicity distributions can be seen in Fig. 8.

As shown in Fig. 8 considerable changes in the high- ztail of the charged multiplicity distributions are observedas the core radius varies from 20% to 50% and 80% of theradius of the colliding hadrons. As the core is made harderand denser (smaller core radius) the overlap between twocolliding cores is accompanied by high-pt partonic scatter-ings, and yields higher multiplicity events more often thanwhen two relatively softer cores (larger radius) overlap ina collision.

For the distributions generated at

s = 546 GeV, the2/d.o.f. varies from 2/47 d.o.f. = 84.3 to 30.8 and 34.9as PARP(84) varies from 0.2 to 0.5 and 0.8, respectively.At

s = 1.8 TeV, 2/128 d.o.f. = 66.9, 17.8 and 34.4 for

PARP(84) = 0.2, 0.5 and 0.8, respectively. This indicatesthat the choice of a value for the core size affects con-siderably how well charged multiplicity distributions aredescribed by PYTHIA. Notice that in PYTHIA6.214 thedefault value for PARP(84) is 0.2, which is the parame-

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Fig. 9. Charged multiplicitydistributions for NSD pp col-lisions at a

s = 546 GeV and

b

s = 1.8 TeV

ter giving the worse 2/d.o.f. for the comparisons shownin Fig. 8. The data favour a larger less dense core than thedefault option currently used by PYTHIA6.214.

3.4 Describing charged multiplicity distributionswith PHOJET

As mentioned above, PHOJET describes hadron collisionsusing the multiple Pomeron exchange mechanism proposedby the DPM [1518] complemented by a multiple par-ton scattering picture for high-pt processes [33, 34]. Fig-ure 9 shows charged multiplicity distributions for NSD pp

collisions at s = 546 GeV and 1.8 TeV, comparing dis-tributions generated by PHOJET1.12 to UA5 [24] andE735 [26,27] data.

There is a reasonable agreement between chargedmultiplicity distributions generated by PHOJET1.12and the data. The 2/d.o.f. obtained by comparingPHOJET1.12 to the data shown in Fig. 9a and b are2/47 d.o.f. = 11.8 and 2/128 d.o.f. = 10.6, respectivelyfor

s = 546 GeV and 1.8 TeV.

3.5 Pseudorapidity distribution

The rate of partonparton scattering in a hadronic colli-sion is strongly correlated to the observed particle multi-plicity and the pseudorapidity distribution of producedparticles. This happens because in each parton interactionpart of the collision energy that would otherwise be car-ried by the fast moving system of beam-remnants in theforward regions, is converted into low-pt particles whichpopulate the central region.

Figure 10 displays charged particle densities, dNch/ d,distributed in the pseudorapidity space, , for NSD pp col-lisions at

s = 200 GeV [30], 900 GeV [30] and 1.8 TeV [25].

It shows a central plateau at small and a falling density inthe fragmentation region, i.e. max. As the colliding en-ergy increases, the rate of multiple parton interactions, or

multiple Pomeron exchanges, also increases producing a riseon the central plateau. Therefore, in order to correctly de-scribe dNch/ d, the MC event generators have to generatethe right amount of partonic activity (multiple parton scat-tering or multiple Pomeron exchanges), taking into accountthe expected variation with the colliding energy.

In PYTHIA, one of the main parameters used to reg-ulate the rate of partonparton interactions is ptmin given

Fig. 10. Charged particle density distributions for NSDpp col-lisions at

s = 200 GeV [30], 900 GeV [30] and 1.8 TeV [25]

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Fig. 11. Charged particledensity distributions, dNch/d, for NSD pp collisions com-paring PYTHIA6.214 to thedata at a

s = 900 GeV and

b

s = 1.8 TeV

by (8). Low values of ptmin imply high rates of partonparton scatterings and hence in high levels of particlemultiplicity; for increasing ptmin the opposite is expected.

Figure 11 displays charged particle density distribu-tions, dNch/ d, plotted against pseudorapidity, . Itshows a comparison between UA5 and CDF measurementsof dNch/ d [25, 30] (Fig. 1a and b, respectively) and dis-tributions generated by PYTHIA6.214 with the complexscenario for multiple parton scattering (MSTP(82) = 4)varyingptmin by changing the parameter PARP(82). As ex-pected, increasing PARP(82) from 1.7 to 1.9 and 2.1, i.e.increasing ptmin , dNch/ d decreases.

For the dNch/ d distributions generated byPYTHIA6.214 at s = 900 GeV, 2/19 d.o.f. = 25.2, 1.9and 13.4 for PARP(82) = 1.7, 1.9 and 2.1, respectively. At

s = 1.8 TeV, 2/9d.o.f.=5.6, 0.3 and 1.8 for PARP(82) =1.7, 1.9 and 2.1, respectively. Notice that relatively smallchanges in PARP(82) ( 10%) cause significant variations

Fig. 12. Charged particledensity distributions, dNch/d, for NSD pp collisions com-paring PYTHIA6.214 for dif-ferent core-sizes to the data ata

s = 900 GeV and b

s =1.8 TeV

in 2/d.o.f. showing how sensitive dNch/ d distributionsgenerated by PYTHIA are to changes in ptmin. The defaultvalue of PARP(82) is set to 1.9 in PYTHIA6.214.

The charged particle density dNch/ d is also sensitiveto the parameters chosen for the core-size PARP(84). InFig. 12 dNch/ d distributions generated by PYTHIA6.214with PARP(84) = 0.2, 0.5 and 0.8 are compared to UA5(NSD pp collisions at

s = 900 GeV Fig. 12a) and CDF

data (NSD pp collisions at

s = 1.8 TeV Fig. 12b). InFig. 12a the obtained 2/19 d.o.f. is 1.9, 5.9 and 9.2, forPARP(84) = 0.2, 0.5 and 0.8, respectively. For the com-parisons shown in Fig. 12b, the 2/9 d.o.f. is 0.3, 1.5 and

2.3 for PARP(84) = 0.2, 0.5 and 0.8, respectively. Noticethat although the core radius has been significantly varied( factor of 2 for each subsequent increase), the relativechanges in the 2/d.o.f. are much less dramatic than theones seen for the comparatively smaller changes in ptmin( 10% for each subsequent increase).

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Fig. 13. Charged particledensity distributions, dNch/d, for NSD pp collisions com-paring PHOJET1.12 to thedata at a

s = 900 GeV and

b

s = 1.8 TeV

In PHOJET, multiple Pomeron exchanges are pre-dicted by the DPM. Similarly to PYTHIA, this model alsodepends on a pcut-offt which is used to connect the soft andhard components of a hadronic interaction. PHOJET1.12has its default options tuned for pcut-offt = 2.5 GeV. Fig-ure 13 shows dNch/ d distributions generated by PHO-JET1.12 with its default cuts, compared to UA5 and CDFdata in Fig. 13a and b, respectively. There is a good agree-ment between PHOJET1.12 predictions and the data. The2/d.o.f. are 2/19 d.o.f. = 3.8 and 2/9 d.o.f. = 0.3, re-spectively, for the comparisons shown in Fig. 13a and b.

3.6 PHOJET and the two-component model

The comparisons of multiplicity and particle density dis-tributions shown in the previous sections strongly in-dicate that the number of multiple parton or multiplePomeron interactions can fundamentally change the agree-ment between model predictions and the data. WhilePYTHIA allows the user to tune the rate of multipleparton interactions by changing parameters which arerather independent of each other (e.g. ptmin and thehadronic matter distribution) the same does not apply toPHOJET.

As discussed in Sect. 2.2, PHOJET has been developedas a two-component model, i.e. soft and hard interac-tions are generated using different phenomenological ap-proaches and then combined with the use of unitarity con-siderations: soft hadronic interactions are generated witha model based on DPM whereas hard processes are gen-erated by models based on perturbative QCD [33, 34].The total event activity (hadronic cross-sections, rate ofPomeron and parton interactions, multicity and pt distri-butions) is then obtained by connecting the soft and hardregions at an appropriatepcut-offt .

The choice of pcut-offt = 2.5 GeV as default inPHOJET1.12 also implies that other model parameters,especially those related to the parametrization of Regge

phenomenology for soft processes (Pomeron and reggeoncouplings for example), are tuned based on the choice ofpcut-offt [1518, 33, 34, 37]. Therefore, in order to use differ-ent values of pcut-offt one is required to re-tune the entiremodel.

A clear example of how varying only pcut-offt inPHOJET1.12 affects the physics it describes can be seen inFig. 14. Figure 14 displays the total cross-section for pp in-teractions predicted by PHOJET1.12 with different values

Fig. 14. Total cross-section for pp interactions predicted byPHOJET1.12 with different values of pcut-offt . Data pointstaken from [42]

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ofpcut-offt . Note that varying pcut-offt results in considerable

changes in the total cross-section. This occurs because bychanging pcut-offt the balance between soft and hard inter-actions also changes and the program needs re-tuning.

Thus, the correct procedure to tune PHOJET1.12would include not only changes to pcut-offt but also tothe parametrization associated with the DPM for soft

interactions.

4 The underlying event

In a hadronic event containing jets, the underlying event(UE) consists of all event activity except the high-pt jetsfrom the hard scattering process [31]. The underlyingstructure of hadronic interactions has not been fully un-derstood yet and it is not clear how it should be modelled.As for minimum bias events, soft interactions play an im-portant role in the structure of the underlying event and

ought to be carefully considered by any model attemptingto describe the underlying event.

Analyses developed by the CDF Collaboration indicatethat the underlying event contains soft and hard com-ponents. The soft component is mainly associated withbeambeam remnant interactions. Particles composing thehard component come from the initial and final state radia-tion, from colour strings stretching between the underlyingevent and the highest-pt jet and from secondary parton in-teractions. As for minimum bias studies, multiple partoninteraction plays an important role in describing the eventactivity in the underlying event [31].

To compare to the underlying event data presented

in [31], a set of cuts must be applied to the MC simula-tion: (a) only charged particles are considered in this an-alysis; (b) selected particles must have pt > 0.5 GeV and||< 1 [31]. A 92% track finding efficiency is also applied toaccount for the tracking efficiency in CDF.

Once the particles were selected, the next step is tostart looking for jets. The jet finder algorithm chosen was

Fig. 15. Illustration of a jet produced by a hard partonpartonscattering in a pp collision

the cone jet finder in which jets are defined as circular re-gions in space with radius defined by

R =

()2 + ()2 , (20)

where is the pseudorapidity and is the azimuthalscattering angle. The cone radius used in this analysis

is R = 0.7.The transverse momentum of a charged particle jet is

defined as the scalar sum of the transverse momenta of thecharged particles making up the jet. The jet with highesttransverse momentum is taken to be the leading chargedparticle jet, referred to as the leading jet (jet event illus-trated by Fig. 15).

The leading jet is used to define the event. Three re-gions are defined in terms of the azimuthal angle betweencharged particles and the leading charged jet. This angu-lar difference is given by = particleljet. The region||< 60 is referred to as toward the leading charged jetand the region || > 120 is called away from the lead-ing jet. The region transverse to the leading jet is definedby 60 < || < 120, and is used to study the underly-ing event. The event regions defined by are illustratedin Fig. 16.

In the following sections we compare PYTHIA6.214with its default parameters as well as with the doubleGaussian option for the complex scenario (MSTP(82) = 4),and PHOJET1.12 to the CDF data for charged jet evolu-tion, focusing on the distributions associated to the under-lying event.

Fig. 16. Event regions defined in terms of the azimuthal anglebetween charged particles and the leading charged jet, =particle

ljet

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4.1 Describing the UE with PYTHIA

In PYTHIA the activity in the underlying event is relatedto the number of multiparton interactions.

Figure 17 shows the average charged particle multi-plicity (Fig. 17a) and pt sum (Fig. 17b) in the transverseregion generated with PYTHIA6.214 MSTP(82) = 4 dis-

tributions for different values of PARP(82), i.e. differentptmin , compared to the data.

Increasing ptmin, which corresponds to a decrease inthe rate of semi-hard parton scatterings, results in both

Fig. 17. a Average charged particles multiplicity in the trans-verse region and b average pt sum in the transverse regionvarying PARP(82)

Nchg and ptsum decreasing, as seen in Fig. 17a and b.This effect is similar to the one observed in Fig. 11for minimum bias charged particle density distributionsdNch/ d.

A noticeable feature in the distributions generatedwith PARP(82) = 1.5 and 2.0 is the irregular shape of theplateau which is not as flat as in the CDF distribution

for transverse Nchg nor follows the slow rise in ptsum.It shows the presence of a bump for leading jets with5 GeV < Ptljet < 20 GeV. The underlying event associatedto these low-pt leading jets is dominated by particles pro-

Fig. 18. a Average charged particles multiplicity in the trans-verse region and b average pt sum in the transverse regionvarying PARP(84)

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duced in soft interactions which are particularly enhancedby the lower values of PARP(82).

For events with Ptljet > 20 GeV, a rise in both Nchgand ptsum is also observed when lower PARP(82) valuesare used in the event generation. Though smaller thanthe rise seen for events with low-pt leading jets, in the re-gion of Ptljet > 20 GeV the rise of

Nchg

and

ptsum

is

more sensitive to the hard component of the underlyingevent which stems from initial and final state radiation andfrom a secondary hard scattering falling into the transverseregion [31].

Thus lowering ptmin , the rate of multiple parton inter-actions increases causing the multiplicity and ptsum in theunderlying event to rise. However the rise is more accen-tuated in softer than in harder parton interactions whichleads to the change in the shape of the distributions seenin Fig. 17.

An interesting effect in the underlying event is observedfor the double Gaussian with different core sizes as shownin Fig. 18. It shows the average charged particle multipli-

city (Fig. 18a) and average pt sum (Fig. 18b) in the trans-verse region, comparing PYTHIA6.214 MSTP(82) = 4with different core sizes to the data. ptmin is set to the de-fault value in all cases. For example, changing PARP(84)from 0.2 to 0.5 reduces the plateau of Nchg by nearlya factor of two, while a further increase in PARP(84) from0.5 to 0.8 only reduces the plateau by 15%. In terms of2/d.o.f., comparing PYTHIA 6.214 - MSTP(82)=4 withPARP(84)=0.2, 0.5 and 0.8 to the data for Nchg one gets2/50 d.o.f. = 16.7, 0.7 and 2.2 respectively.

The explanation for the changes in the underlying eventdue to different core sizes is the same as already discussedfor minimum bias events. Jets are likely to be produced

when there is a core overlap in the hadronic collision.Smaller and dense cores imply that events with a coreoverlap have also a large overlap of less dense matter re-gions which surround the core, and when overlapped gen-erate high rates of soft interactions causing the higherplateaus observed in both Nchg and ptsum distribu-tions in Fig. 18. Larger cores also imply smaller soft sur-rounding regions in the colliding hadrons, hence producing

Fig. 19. PHOJET1.12 pre-dictions compared to CDFdata for: a average multipli-city in the transverse regionand b average ptsum in thetransverse region

lower multiplicity andptsum distributions in the underlyingevent.

If increased to its maximum, the core radius in the dou-ble Gaussian matter distribution will actually become thehadronic radius, reproducing the single Gaussian distri-bution. There is therefore a saturation point in the effectobtained by increasing (or reducing) the core size which

can be seen in Fig. 18 when the variation in the underlyingevent for PARP(84) going from 0.2 to 0.5 is larger than thevariation caused by changing PARP(84) from 0.5 to 0.8.

4.2 Describing the UE with PHOJET

As shown in the previous section, PHOJET1.12 withits default options gives a fairly good description of thecharged multiplicity and dNch/ d distributions in min-imum bias events. Here, we compare PHOJET1.12, againwith its default options, to the CDF data for charged jetevolution and the underlying event [31].

Figure 19 shows PHOJET1.12 predictions compared todata for: a average multiplicity in the transverse region andb averageptsum in the transverse region.

The MC predictions agree reasonably well to the datafor the UE multiplicity distribution, as shown in Fig. 19a.The 2/d.o.f. for the comparisons shown in Fig. 19a is2/50 d.o.f. = 5.3.

Although PHOJET1.12 predicts a multiplicity distri-bution for the underlying event which agrees fairly wellwith the data, the same cannot be said for the averageptsum distribution (Fig. 19b). The measured ptsum distri-bution is underestimated by PHOJET1.12 by 20%, andthe comparison between MC and data gives a 2/50 d.o.f.of 9.4.

4.3 UE vs. minimum bias

The CDF measurement shows that the underlying eventmultiplicity forms a plateau for events with Ptljet 5 GeVat Nchg 2.3. Supposing that the transverse region inevents with Ptljet 5 GeV is uniform in azimuthal angle ,

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for the full 2 range this corresponds to 6.9 particles. As-suming also that the transverse region is uniform in pseu-dorapidity , one obtains 3.45 particle per unit pseudora-pidity, which in fact, after multiplying by 1.09 to correct forthe detector effects, corresponds to 3.8 charged particlesper unit pseudorapidity with pt > 0.5 GeV. Extrapolatingto low-pt using the form e2pt [31] implies that there are

roughly 10 charged particles per pseudorapidity unit withpt > 0 GeV in the underlying event.

We can now compare the particle density obtained forthe plateau in the underlying event distribution to the oneshown for minimum bias events in pp collision at 1.8 TeVin Fig. 10. The minimum bias density, which has also beenmeasured by CDF, gives dNch/ d 4 for || < 1 [25],while the equivalent density for the underlying event is atleast a factor of two larger. Although this comparison is anapproximation due to the uncertainties in estimating theparticle density for the underlying event (i.e. extrapolationto low-pt and several assumptions made on the particledistribution in and ), it clearly shows that the underly-

ing event in hard scattering processes (Ptljet 5 GeV) hasmuch more activity than an average minimum bias event.

5 Describing minimum bias and the UE

In the previous two sections, we have comparedPYTHIA6.214 and PHOJET1.12 to minimum bias and theunderlying event data. The comparisons made show thatPHOJET1.12 with its default options is reasonably suc-cessful in describing the data while PYTHIA6.214 requiresa tuning in order to be able to describe either minimum

bias or underlying event measurements.Based on the knowledge of how variations in keyPYTHIA parameters affect minimum bias and underlyingevent distributions we are able to tune PYTHIA6.214 tobetter reproduce the data.

In this section we present a PYTHIA6.214 tuning whichis based on comparisons to a wide range of experimentaldistributions for both minimum bias and the underlyingevent. The data we used to tune PYTHIA6.214 is listedin Table 3.

The predictions of our PYTHIA6.214 tuned model willalso be compared to PHOJET1.12, to a previous ATLAS

Table 3. Minimum bias [2327, 29, 30] and underlying event data [31] used to tune PYTHIA6.214

Experiment Colliding beams Comments

CERN ISR [23] pp at

s = 30.4, 44.5, 52.6 charged mult. distributions,and 62.2 GeV nch and pt at = 0

UA5 SPS [24, 29,30] pp at

s = 200, 546 and 900 GeV dNch/ d and charged mult. distributions,nch, dNch/ d and pt at = 0

E735 Tevatron [26, 27] pp at

s = 1.8 TeV charged mult. distributions

CDF Tevatron [25, 31] pp at

s = 1.8 TeV dNch/d distribution,nch, dNch/ d and pt at = 0,

and Nch and ptsum in the UE

tuning which was used to generate minimum bias distri-butions for the ATLAS-TDR [4446], and to the PYTHIAtuning proposed by the CDF Collaboration [47].

5.1 PYTHIA6.214 tuned model

PYTHIA6.214 allows the user to select a variety of modelsto generate soft particle interactions. Based on results ofthe comparisons presented previously, we opted for thecomplex scenario with a double Gaussian matter distribu-tion MSTP(82) = 4 which proved to be a model capableof describing complex features in particle production, par-ticularly the high-multiplicity tails in charged multiplicitydistributions.

A tuned set of parameters which allows PYTHIA6.214 MSTP(82) = 4 to reproduce the data can be achieved byregulating the event activity generated by multiple partonscatterings. Combining the effects of variations inptmin andin the core-size we obtained a set of PYTHIA6.214 param-

eters which considerably improves PYTHIAs descriptionof minimum bias and underlying event distributions. OurPYTHIA6.214 tuned parameters are displayed in Table 4.

The fundamental difference between our tuned setof parameters and PYTHIA6.214 default settings is ourchoice for the more sophisticated model of hadron interac-tions switched on by MSTP(82) = 4.

Another significant difference is the increase of the core-radius from the default setting of 20% of the hadron ra-dius (PARP(84) = 0.2) to a larger core of 50% of the totalhadron radius (PARP(84) = 0.5). We have also changedptmin slightly by reducing the parameter PARP(82) fromits original 1.9 to 1.8.

To compare with published data, the

0

, Ksand 0 decays are suppressed in our PYTHIA6.214 tunedmodel [25,30]. This will also be applied to thePHOJET1.12 distributions, but not to the events gener-ated by other models.

Figures 2022 show predictions generated byPYTHIA6.214-tuned and default, and PHOJET1.12 com-pared to various minimum bias and underlying event distri-butions. The combined 2 for the minimum bias distribu-tions shown in Figs. 20 and 21 (2min-bias/307 d.o.f.) is 68.0,11.6 and 8.2 for PYTHIA6.214-default, PYTHIA6.214-tuned and PHOJET1.12, respectively (Table 5). Similarly,

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Table 4. PYTHIA6.214 tuned parameters for minimum biasand the underlying event

PYTHIA6.214 tuned

ISUB: 11,12,13,28,53, QCD 2 2 partonic scattering68,94,95,96 +non-diffractive + double diffractive

MSTP(51) = 7 CTEQ5L selected p.d.f. (default)

MSTP(81) = 1 multiple interactions (default)

MSTP(82) = 4 complex scenario+double Gaussian matter distribution

PARP(82) = 1.8 ptmin parameter

PARP(84) = 0.5 core radius: 50% of thehadronic radius

PARP(89) = 1.0 energy scale (TeV) usedto calculate ptmin (default)

PARP(90) = 0.16 power of the energy dependenceofptmin (default)

Fig. 20. Charged multipli-city distributions for NSD ppcollisions at a

s = 200 GeV;

b 546 GeV; c 900 GeV andd 1.8 TeV. It shows compar-isons between PYTHIA6.214-tuned, PYTHIA6.214-default,PHOJET1.12 predictions, andthe data

for the underlying event distributions displayed in Fig. 22aand b, the combined 2 (2UE/100 d.o.f.) is 22.7, 2.1 and7.4, again for PYTHIA6.214-default and tuned, and PHO-JET1.12, respectively (Table 5).

The description of both minimum bias and under-lying event distributions is clearly improved by usingPYTHIA6.214-tuned compared to the predictions gen-

erated by the default settings. As already indicated incomparisons presented in previous sections, PHOJET1.12is also considerably more accurate in describing the datathan PYTHIA6.214-default.

The distributions in Figs. 2022 and the combined 2

derived from both minimum bias and underlying eventdistributions show that PYTHIA6.214-tuned andPHOJET1.12 are compatible to the data. With 2min-bias =8.2, PHOJET1.12 generates slightly better predictions forminimum bias event distributions than PYTHIA6.214-

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Fig. 21. Charged particledensity distributions, dNch/d, for NSD pp collisions ata

s = 200 GeV; b 900 GeVand c 1.8 TeV. In d dNch/ dat = 0 for a wide range of

s

is shown

Fig. 22. PYTHIA6.214-tuned and default, andPHOJET1.12 predictionscompared to CDF data for:a average multiplicity in theunderlying event and b aver-age ptsum in the underlyingevent

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Table 5. 2/d.o.f. for PYTHIA6.214-tuned, PYTHIA6.214-default andPHOJET1.12

PYTHIA6.214- PYTHIA6.214- PHOJET1.12tuned default

Charged multiplicitydistributions (Fig. 20) 13.1 79.7 9.1

2/260 d.o.f.

dNch/ d (Fig. 21) 3.6 3.3 2.9

2/47 d.o.f.

Nchg in the UE (Fig. 22a) 1.3 15.7 5.32/50 d.o.f.

ptsum in the UE (Fig. 22b) 2.8 29.7 9.42/50 d.o.f.

2min-bias/307 d.o.f. 11.62 68.0 8.2

2UE/100 d.o.f. 2.07 22.7 7.4

2global/407 d.o.f. 9.27 56.9 7.9

tuned, which has 2min-bias = 11.6. The opposite hap-pens for underlying event distributions which are bet-ter described by PYTHIA6.214-tuned (2UE = 2.1) thanby PHOJET1.12 (2UE = 7.4). The global

2, combin-ing 307 minimum bias degrees of freedom and 100 fromthe underlying event distributions, is 2global/407 d.o.f. =7.9 for PHOJET1.12 and 2global/407 d.o.f. = 9.3 forPYTHIA6.214-tuned. PYTHIA6.214-default compared tothe data gives 2global/407d.o.f. = 56.9.

5.2 Alternative PYTHIA tunings

In this section we compare our PYTHIA6.214 tuned modelto two other PYTHIA tunings for soft hadronic interac-tions, namely, the ATLAS-TDR model used to generateminimum bias events and the underlying structure of jetanalysis at ATLAS [44, 45] and the tuning proposed by theCDF Collaboration [47].

The ATLAS Technical Design Report (ATLAS-TDR)shows minimum bias predictions for the LHC which havebeen based on an early study of minimum bias MC modelspresented in [46]. The parameters used in the generationof minimum bias events for the ATLAS-TDR are shownin Table 6. These parameters were obtained as a result ofcomparisons between PYTHIA5.724 and UA5 and CDFminimum bias data for dNch/ d and CDF measurementsfor one-particle inclusive pt spectra in the central rapidityregion. Though [46] has not used underlying event distri-butions to tune the MC model for soft particle production,the PYTHIA parameters in Table 6 were also used to gen-erate the underlying event in jet studies throughout theATLAS-TDR.

The PYTHIA parameters proposed as the CDF tun-ing (also known as PYTHIA tune A) are shown inTable 7 [47]. This tuning was obtained by comparingPYTHIA6.206 to minimum bias dNch/ d distributions(at

s = 630 GeV and 1.8 TeV) and underlying event data

(at

s = 1.8 TeV) [31] measured by the CDF collabora-

Table 6. ATLAS-TDR parameters for minimum biasevents

ATLAS-TDR parameters for minimum bias

PYTHIA5.724 PYTHIA version

ISUB: 11,12,13,28, QCD 2 2 partonic scattering53,68,95,96 +non-diffractive

MSTP(51) = 9 CTEQ2L selected p.d.f.

MSTP(81) = 1 multiple interactions

MSTP(82) = 4 complex scenario+ double Gaussian matter distrib.

MSTP(2) = 2 NLO formula for sin 2 2 matrix elements

MSTP(33) = 3 inclusion of K factorsin hard 2 2 cross-sections



tion. One of the interesting aspects of the CDF tuning, isthat PARP(67) [2022] is changed from its default valueof 1 to 4, effectively increasing the maximum parton vir-tuality allowed in parton showers. This is done to explainthe pt spectrum of particles in the underlying event. Thiswas not done for the current study, but will be looked at infuture.

Figures 2325 compare PYTHIA predictions generatedwith PYTHIA6.214-tuned, ATLAS-TDR and CDF tuningparameters to data for both minimum bias and the under-lying event. The combined 2min-bias for the distributionsshown in Figs. 23 and 24 is 38.9 and 26.7 for the ATLAS-TDR and CDF tuning models, respectively (Table 8). Sim-ilarly, for the underlying event distributions displayed inFig. 25, the combined 2UE is 15.0 and 1.3, again for the dis-tributions generated with the ATLAS-TDR and the CDFtuning, respectively (Table 8).

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Table 7. CDF tuning for minimum bias and the underlyingevent

CDF tuning for minimum bias and the UE

PYTHIA6.206 PYTHIA version

ISUB: 11,12,13,28,53, QCD 2 2 partonic scattering68,(94),95,96 +non-diffractive + double diffractive

MSTP(51) = 7 CTEQ5L selected p.d.f.

MSTP(81) = 1 multiple interactions

MSTP(82) = 4 complex scenario+double Gaussian matter distribution

PARP(67) = 4 parameter regulatinginitial state radiation



PARP(85) = 0.9 probability that gluons will becolour connected to nearest neighbours

PARP(86) = 0.95 probability to produce gluons eitheras in PARP(85) or as a closed gluon loop

PARP(89) = 1.8 energy scale (TeV) usedto calculate ptmin

PARP(90) = 0.25 power of the energy dependenceofptmin

The 2min-bias from both ATLAS-TDR and CDF tun-ing models are worse than the 2min-bias = 11.6 obtained forPYTHIA6.214-tuned. This reflects the fact that we haveused a wider set of experimental distributions than theother tunings to guide our choice of parameters. In particu-

lar, we have used charged multiplicity distributions meas-ured at different colliding energies to better understandthe effects of multiple parton interactions, which the othermodels have not.

Although the minimum bias data shown in Figs. 23and 24 represents non-single diffractive inelastic interac-tions (i.e. non-diffractive inelastic and double diffractiveevents), the ATLAS-TDR model does not include doublediffraction in its description of minimum bias events. Thisis a particular disadvantage of this model in its attempt todescribe minimum bias events as defined in this work, andsource of considerable disagreements between the modelpredictions and the data for low-multiplicity events (z < 1)as can be seen in Fig. 23. The CDF tuning was obtainedby simulating the CDF min-bias trigger requirements,which picks up some double diffractive events. The sub-process 94 is therefore included in Table 7 to give a goodapproximation of the CDFs trigger requirements for min-imum bias events selection.

Comparing the underlying event distributions gen-erated with ATLAS-TDR, CDF tuning and ourPYTHIA6.214-tuned parameters, the best 2UE is obtainedwith the CDF tuning parameters. On the other hand,predictions generated with the ATLAS-TDR parametersconsiderably overestimate the data with 2UE = 15.0.

There are two fundamental problems limiting theagreement between the ATLAS-TDR distributions and

Table 8. 2/d.o.f. for the CDF tuning and ATLAS-TDRmodels

CDF tuning ATLAS-TDR

Charged multiplicitydistributions (Fig. 23) 29.9 44.2

2/260 d.o.f.

dNch/ d (Fig. 24) 8.4 10.2

2/47 d.o.f.

Nchg in the UE (Fig. 25a) 1.0 20.62/50 d.o.f.

ptsum in the UE (Fig. 25b) 1.6 9.52/50 d.o.f.

2min-bias/307 d.o.f. 26.7 38.9

2UE/100 d.o.f. 1.3 15.0

2global/407 d.o.f. 20.4 33.1

the data and its predictive power for both minimum biasand the underlying event: the hadronic core size and theptmin used in this model. Firstly, with a core radius cor-responding to 20% of the hadrons radius, too much eventactivity accompanies the hard partonic scatterings caus-ing it to overestimate the underlying event multiplicity andaverage ptsum as well as overestimating most of the high-multiplicity tails of charged multiplicity distributions. Thesecond problem is the absence of an energy dependencecorrection for ptmin , this was introduced for PYTHIA ver-sions later than PYTHIA6.1 [2022].

Combining the minimum bias and underlying event2s, one has 2global = 20.4 for the predictions generated

with the CDF tuning and 2

global = 33.1 for the distribu-tions generated with the ATLAS-TDR parameters. The2global for the CDF tuning is greater than the

2global = 9.3

obtained for PYTHIA6.214-tuned.

5.3 Summary of MC model comparisons

Table 9 summarises the 2min-bias , 2UE and

2global obtained

by comparisons between data and prediction from PHO-JET1.12, PYTHIA6.214-tuned and default, CDF tuningand ATLAS-TDR parameters.

The minimum bias and underlying event distributionspresented in this article are satisfactorily described by bothPHOJET1.12 and PYTHIA6.214 appropriately tuned.

The tuning we propose, PYTHIA6.214-tuned(Table 4), is a good example of a successful PYTHIA tun-ing for predicting minimum bias and the underlying event.It is undoubtedly a significant improvement compared tothe predictions generated with the default PYTHIA6.214parameters and also to the distributions generated withthe parameters used in the ATLAS-TDR and in the CDFtuning. The differences between these models exposes thedifferent procedures used to find each particular tuning.For example, the fact that the CDF tuning was primar-ily derived based on UE data makes it the best model forthis particular set of distributions however, it does not nec-

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Fig. 23. Charged multipli-city distributions for NSD ppcollisions at a

s = 200 GeV;

b 546 GeV; c 900 GeV andd 1.8 TeV. It shows compar-isons between PYTHIA pre-dictions generated with ourtuned model, ATLAS-TDRparameters and the CDF tun-ing to the data

essarily succeed in reproducing the minimum bias datashown here.

Due to the fact that information from a wider range ofcomparisons to data was used in our tuning we believe it tobe a more robust model than any of the other competingPYTHIA tunings discussed in this study.

5.4 Extrapolating predictions to higher energies

One of the aims of this study is to verify how well min-imum bias and the underlying event are reproduced byMC models. Once we identify models which appropriatelydescribe the data, these will then be used to generate pre-dictions for the pp collisions at LHC.

Figure 26 shows the average charged particle multi-plicity (Fig. 26a) and the average transverse momentumof charged particles

pt

at = 0 (Fig. 26b) for NSD pp

collisions for a wide range of colliding energies. It com-pares predictions generated with the models which hadthe best two 2global in the comparisons presented above,i.e. PHOJET1.12 and PYTHIA6.214-tuned, and the CDFtuning.

Table 9. 2min-bias, 2UE and

2global for PHOJET1.12,

PYTHIA6.214-tuned and default, CDF tuning andATLAS-TDR parameters

Models 2min-bias 2UE

2global

PHOJET1.12 8.2 7.4 7.9PYTHIA6.214-tuned 11.6 2.1 9.3CDF tuning 26.7 1.3 20.4ATLAS-TDR 38.9 15.0 33.1PYTHIA6.214-default 68.0 22.7 56.9

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Fig. 24. Charged particledensity distributions, dNch/d, for NSD pp collisions ata

s = 200 GeV; b 900 GeV

and c 1.8 TeV. In d dNch/ dat = 0 for a wide rangeof

s is shown. MC dis-

tributions were generatedwith PYTHIA6.214-tuned,ATLAS-TDR and CDF tun-ing parameters

Fig. 25. PYTHIA6.214-tuned, ATLAS-TDR and CDFtuning predictions comparedto CDF data for: a averagemultiplicity in the underlyingevent and b average ptsum inthe underlying event

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The average charged particle multiplicity distributionsin Fig. 26a show small differences between the three modelpredictions for energies up to the Tevatron (

s = 1.8 TeV).

However, as

s the rise of nch has a different be-haviour for each model: PYTHIA6.214-tuned gives thesteeper rise following a strong ln2(s) dependence, whilePHOJET1.12 predicts the slower rise with a dominating

ln(s) behaviour and the CDF tuning distribution sits inbetween the other two predictions. At the LHC energy,

s = 14 TeV, the models predict 70 nch 95.In Fig. 26b, the pt at = 0 distributions gener-

ated with the CDF tuning and PHOJET1.12 modelspredict higher pt than PYTHIA6.214-tuned for nearlyall

s range. All distributions rise as ln2(s) and at the

LHC energy the predictions vary from pt = 0.55 GeVto 0.64 GeV.

As shown in Fig. 26, models which are reasonably suc-cessful in describing the wide range of data shown above,give considerably different predictions at higher energies.In the next section, the two models with best global agree-

ment to the data, PHOJET1.12 and PYTHIA6.214-tuned,

Fig. 26. a Average charged particle multiplicity in NSDpp col-lisions; b Average transverse momentum of charged particles

pt

at = 0, for NSD pp collisions

will be used to generate minimum bias and the underlyingevent predictions for the LHC.

6 LHC predictions for minimum bias

and the UE

The LHC will collide protons at centre-of-mass energiesmany times greater than any hadron collision ever per-formed in laboratory.

Models capable of reproducing the available minimumbias and underlying event data for lower colliding energiesare extremely important for predicting background levelsassociated to many physics processes and also for under-standing the complex nature of the radiation environmentin which the LHCs detector systems will operate.

The study presented in previous sections indicates thatthe models PHOJET1.12 and PYTHIA6.214-tuned givethe best agreement to the data for both minimum bias andunderlying event distributions. Here we present the LHC

predictions generated by both models.

6.1 Minimum bias distributions

For LHC collisions (pp collisions at

s = 14 TeV) theminimum bias cross-section estimated by PYTHIA6.214-tuned is nsd = 65.7 mb while PHOJET1.12 predicts nsd =73.8mb, 12.3% greater than the former. Hence, for thesame luminosity PHOJET1.12 generates more minimumbiaspp collisions than PYTHIA6.214-tuned. We shall how-ever, focus on the general properties per pp collision notweighted by cross-sections. The results per pp collision can

later be easily scaled by the cross-section and luminosity.Figure 27 shows charged particle density distributionsin pseudorapidity for minimum bias pp collisions at

s =

14 TeV generated by PHOJET1.12 and PYTHIA6.214-tuned. The charged particle density generated byPHOJET1.12 and PYTHIA6.214-tuned at = 0 is 5.1and 6.8, respectively. In the central region (|| < 2.5)dNch/ d is 5.5 and 7, respectively for PHOJET1.12and PYTHIA6.214-tuned. Contrasting to the agreementshown for pp collisions at

s = 1.8 TeV in Fig. 21c, at the

LHC PYTHIA6.214-tuned generates 27% more chargedparticle density in the central region than PHOJET1.12.

Compared to the charged particle density dNch/ dmeasured by CDF at 1.8 TeV (Fig. 21c), PYTHIA6.214-tuned indicates a plateau rise of 70% at the LHC in thecentral region while PHOJET1.12 suggests a smaller riseof 35%.

The average charged particle multiplicity in LHC min-imum bias collisions, nch, is 69.62 and 91.04 chargedparticles as predicted by PHOJET1.12 and PYTHIA6.214-tuned, respectively. For centre-of-mass energies greaterthan 1 TeV, the multiple parton interaction model em-ployed by PYTHIA and the DPM used by PHOJET leadto multiplicity distributions with different rates of in-crease with the energy. PYTHIA giving a steeper risethan PHOJET (Figs. 21d and 26a). At

s = 14 TeV,

the activity generated in minimum bias collisions by

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Fig. 27. Charged particle density distributions, dNch/ d, forNSD pp collisions at

s = 14 TeV. Predictions generated by

PYTHIA6.214-tuned and PHOJET1.12

both PHOJET1.12 and PYTHIA6.214-tuned is 2530%greater in the later.

The charged multiplicity distributions for LHC min-imum bias events are shown in Fig. 28. Predictions gen-erated by PYTHIA6.214-tuned and PHOJET1.12 are sig-nificantly different. At low z (low multiplicity events)PYTHIAs prediction reveals a double-peak which is notpresent in PHOJETs distribution. Not seen in the Teva-tron charged multiplicity distribution, the double-peakin PYTHIAs prediction for the LHC reflects a differ-ence between the string drawings for protonproton andprotonanti-proton collisions [48]. For increasingly higherz, the shoulder structure of the distributions indicate thatPYTHIA6.214-tuned generates higher multiplicity eventsthan PHOJET1.12, reflecting the fact that the event ac-tivity generated by multiple parton scattering in PYTHIArises faster with the energy than the corresponding effectdue to the increase of Pomeron exchanges generated byPHOJET1.12.

A close comparison between the E735 charged multi-plicity data presented in Fig. 20d and the LHC predic-tions in Fig. 28 shows that PHOJET1.12 does not predicta LHC charged multiplicity distribution much different ofthe one measured at the Tevatron, while PYTHIA6.214-tuned indicates a sizable extension of the high z tail of thedistribution.

The pt at = 0 for charged particles in LHC min-imum bias collisions predicted by PHOJET1.12 andPYTHIA6.214-tuned models is 0.64 GeV and 0.55 GeV,

Fig. 28. Charged multiplicity distribution for NSD pp colli-sions at

s = 14 TeV. Predictions generated by PYTHIA6.214-

tuned and PHOJET1.12

respectively. The difference of 16% in this case is pro-portionally smaller compared to the differences seen for

particle densities in pseudorapidity and multiplicity, whichare of the order of 30%. Generating less particles in anaverage minimum bias collision at the LHC, PHOJET1.12predicts that the average pt per particle at = 0 isgreater (or harder) than the corresponding prediction fromPYTHIA6.214-tuned.

The pt spectrum of charged particles produced in LHCminimum bias events is displayed in Fig. 29. Once again, itcompares PHOJET1.12 and PYTHIA6.214-tuned. At verylow momenta, pt 0.5 GeV, the particle density predictedby PYTHIA6.214-tuned is 40% greater than the corres-ponding PHOJET1.12 prediction. The difference is muchsmaller for higher pt, and in fact both spectra become vir-tually undistinguishable. The low pt bins account for mostof the multiplicity, but looking at the pt detection capabil-ities at ATLAS [44, 45] and CMS [49] for example, the de-tection of particles with good pt resolution will be limitedto particles with pt > 0.5 GeV [44, 45, 49], both models sug-gest very similar detected pt spectra per pp event.

6.2 The UE at the LHC

Figure 30 displays PYTHIA6.214-tuned andPHOJET1.12 predictions for the average particle multipli-city (Fig. 30a) and average ptsum in the underlying event(Fig. 30b) for pp collisions at the LHC (charged particles

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Fig. 29. Charged particle pt spectrum for NSD pp collisions ats = 14 TeV

withpt > 0.5 GeV and ||< 1). The distributions generatedby the two models are fundamentally different. Exceptfor the events with Ptljet 3 GeV, PYTHIA6.214-tunedgenerates greater activity than PHOJET1.12 in both dis-

tributions shown in Fig. 30.A close inspection of predictions for the underlyingevent given in Fig. 30, shows that the average multiplicityin the underlying event for Ptljet > 10 GeV reaches a plateauat 6.5 charged particles according to PYTHIA6.214-tuned and 3.0 according to PHOJET1.12. Similarlyfor the average ptsum in the underlying event for Ptljet >10 GeV, the plateaus are formed at 7.5 GeV and

Fig. 30. PYTHIA6.214-tuned and PHOJET1.12 pre-dictions for: a average multi-plicity in the underlying eventand b average ptsum in the un-derlying event

3.5 GeV according to PYTHIA6.214-tuned and PHO-JET1.12, respectively. Compared to the underlying eventdistributions measured by CDF at 1.8 TeV (Fig. 22a and b),PYTHIA6.214-tuned indicates a plateau rise of 200% atthe LHC while PHOJET1.12 suggests a much smaller riseof 40%.

As shown in the previous section, the minimum bias

predictions generated by PYTHIA6.214-tuned andPHOJET1.12 for the central plateau of dNch/ d, indi-cate a rise of 70% and 35%, respectively. These aresmaller than the predicted increase for the underlyingevent suggested by both models. As discussed previously,at the Tevatron, for events with Ptljet > 10 GeV the par-ticle density in the underlying event is at least a factor oftwo larger than the equivalent minimum bias prediction.Using similar assumptions as those adopted in the analysisfor the CDF data, LHC events with Ptljet > 10 GeV are pre-dicted to have a charged particle density d Nch/ d of 29charged particles per pseudorapidity unit according toPYTHIA6.214-tuned and

13 according to PHOJET1.12.

In other words, for Ptljet > 10 GeV the underlying eventat the LHC is predicted to have a particle density 4times larger than its equivalent minimum bias predictionaccording to PYTHIA6.214-tuned, and 2 times largeraccording to PHOJET1.12.

Therefore PYTHIA6.214-tuned predicts not only thatthe underlying event particle density will increase at theLHC, but it will also increase its activity compared to theequivalent minimum bias distribution. On the other hand,PHOJET1.12 estimates that the increase in charged par-ticle density in the underlying event at the LHC will followthe same rate to the minimum bias density measured atthe Tevatron. In both cases however, the underlying event

density is greater than its equivalent minimum bias coun-terpart. Contradicting a widespread misconception thatsimulations involving high-pt jets (Ptljet > 10 GeV) and itsaccompanying underlying event can be made by simplyoverlaying minimum bias events on top of jet events.

Further studies are currently being conducted by theCDF Collaboration aiming at a deeper understanding ofthe composite nature of the underlying event and minimum

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bias data. As indicated by the analysis shown in [50] thesoft and hard components of minimum bias data behave dif-ferently with the increase of the colliding energy. The softcomponent of minimum bias events appears to follow theKNO scaling and has a pt distribut

min-bias

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