Min-Bias Data: Jet Evolution and Event Shapes

Transcription

1 Min-Bias Data: Jet Evolution and Event Shapes Rick Field and David Stuart July 1, 1999 Abstract The Min-Bias data are used to study the transition between soft and hard collisions. We study this transition by plotting a variety of observables versus PTmax (leading charged particle) and PT(jet#1) (leading jet). The data are compared with soft scattering Monte-Carlo models and hard scattering QCD Monte-Carlo models. The data contain a lot of hard scattering and exhibit jet structure even for PT values as small as 1 GeV. We define jets as simple circular regions in η-φ space with R =.7 and watch the growth and development of jets from.5 to 5 GeV. Jets are born somewhere around PT(jet) of about 1 GeV with, on the average, about charged particles and grow to, on the average, about 1 charged particles at 5 GeV. The QCD hard scattering Monte-Carlo models are in qualitative agreement with the properties of jets and agree as well with GeV jets as they do with 5 GeV jets. We also examine carefully the growth and development of the underlying event in hard scattering. None of the QCD Monte-Carlo models describe properly the behavior of the underlying event. Accurate predictions of detector occupancies and physics backgrounds in Run II depend on the correct modeling of min-bias interactions and the underlying event. I. Introduction The total proton-antiproton cross section is the sum of the elastic and inelastic cross sections. The inelastic cross section consists of a single-diffractive, double-diffractive, and hard core component. The hard core component is everything non-diffractive, it is what is left after one removes the single-diffractive and the double-diffractive events. The CDF minimum bias trigger selects predominately the hard core component of the inelastic cross section. Hard core, of course, does not necessarily imply hard scattering. A hard scattering Hard Scattering Outgoing Parton PT(hard) Proton Underlying Event AntiProton Underlying Event Outgoing Parton Fig Illustration of a proton-antiproton collision in which a hard -to- parton scattering with transverse momentum, P T (hard), has occurred. The resulting event contains particles that originate from the two outgoing partons and particles that come Page 1 of 65

2 from the breakup of the proton and antiproton (i.e. beam-beam remnants ) that contribute to the underlying event. collision, such as that illustrated in Fig. 1.1, is one in which a hard (i.e. large transverse momentum, PT(hard)) -to- parton-parton subprocess has occurred. Soft hard core collisions, such as the one shown in Fig. 1., corresponds to events in which no hard interaction has occurred. When there is no large transverse momentum subprocess in the collision one is not probing short distance and it probably does not make any sense to talk about partons. Soft Collision (no hard scattering) Proton AntiProton Fig. 1.. Illustration of a soft proton-antiproton collision in which no hard scattering has occurred. The proton and antiproton ooze through each other and fall apart. The minimum bias data is an excellent place to study the transition between soft and hard collisions. Ultimately, the goal is to find a Monte-Carlo generator that will fit the entire hard core inelastic cross section. To do this one will have to combine a model for the soft collisions with a QCD perturbative Monte-Carlo model for the hard collisions. The QCD perturbative - to- parton-parton differential cross section diverges as PT(hard) goes to zero. One must set a minimum PT(hard) large enough so that the resulting cross section is not larger that the total entire hard core inelastic cross section, and large enough to ensure that QCD perturbation theory is accurate. A non-perturbative soft model would then be used to describe (or parameterize) the remaining hard core inelastic cross section (i.e. all collisions in which PT(hard) is less than the cut-off). We do not attempt such a superposition of soft and hard models here. In this note on the physics of the min-bias data we simply compare the data with the models, soft and hard scattering. We find that at 1.8 TeV that there is a lot of hard scattering in the min-bias data and we will be able to examine the evolution of jets from low to high transverse momentum. Multiple Parton Interactions Outgoing Parton PT(hard) Proton Underlying Event AntiProton Underlying Event Outgoing Parton Page of 65

3 Fig Illustration of a proton-antiproton collision in which a multiple parton interaction has occurred. In addition to the hard -to- parton scattering with transverse momentum, P T (hard), there is a semi-hard parton-parton scattering that contributes particles to the underlying event. A hard scattering event, like that shown in Fig. 1.1 consists of large transverse momentum outgoing hadrons that originate from the large transverse momentum partons (i.e. outgoing jets ) and also hadrons that originate from the break-up of the proton and antiproton (i.e. the beam-beam remnants ). The underlying event is an interesting object that is not very well understood. In addition to hadrons from the break-up of the initial proton and antiproton, it may contain hadrons resulting from initial state gluon radiation. Also, it is possible that the underlying event contains hadrons that originate from multiple parton interactions as illustrated in Fig Pythia, for example, uses multiple parton interactions as a way to enhance the activity of the underlying event. Since we are attempting to describe entire min-bias events, we will be able to examine closely the growth and structure of the underlying event. We find that the underlying hard scattering event is not the same as the soft collision illustrated in Fig. 1.. For the same available energy the underlying event in a hard scattering is considerable more active (i.e. higher charge particle density and more transverse momentum) than a soft collision. This is not surprising since a violent hard scattering has occurred! We find that none of the QCD Monte- Carlo models describe properly the behavior of the underlying event. A good way to watch the transition between hard and soft collisions is to plot observables versus the maximum transverse momentum particle in the event, PTmax. If PTmax is large then clearly a hard scattering has occurred and if PTmax is small there was no hard scattering. After we discuss the data selection and Monte-Carlo models in Section II, we study the overall event structure of the Min-Bias data as a function of PTmax in Section III. We use the TRACK1 data to extend the range of PTmax. Combining the Min-Bias and the TRACK1 allows us to examine events with PTmax from.5 GeV to 5 GeV. We do not define jets in Section III, nevertheless the jet structure in the data is clearly seen, even for PTmax values as low as 1 GeV. Furthermore, we examine carefully the growth and development of the underlying event as a function of PTmax. In Section IV, we define jets as simple circular regions in η-φ space with R =.7 and watch the growth and development of jets from.5 to 5 GeV. We use the JET data to extend the range of P T (jet#1) (leading jet). In addition, we examine carefully the growth and development of the underlying event as a function of P T (jet#1). We reserve Section IV for summary and conclusions. There are many more interesting Min-Bias data plots than we can put in the this note. We plan to write a second CDF note on the physics of the Min-Bias data that examines the differential cross sections in P T, PTmax, PTsum, P T (jet), and P T (jet#1). II. Data Selection and Monte-Carlo Models In this analysis we use the three sets of data listed in Table 1. The minimum bias (min-bias) data were selected by requiring at least two interactions in the beam-beam counters located at high pseudo-rapidity (at least one forward and at least one backward) as illustrated in Fig..1. We Page 3 of 65

4 consider only charged particles with P T >.5 GeV and η < 1 where the CTC efficiency is high. Also, to improve the purity we select events with zero or one vertex and in addition require that the intercept of the charged track with the beam axis, z c, lies within cm of the vertex, z v, which reduces fakes and helps remove secondary interactions. CDF Min-Bias Trigger BBC 5.9 < η < -3. BBC 3. < η < 5.9 Proton AntiProton Fig..1. Illustration of the CDF min-bias trigger in which at least one charge particle must interact with the forward beam-beam counter BBC (3. < η < 5.9) and at least one charge particle must interact with the backward BBC (-5.9 < η < -3.). Table 1. Data sets and selection criterion used in this analysis. CDF Data Set Trigger Events Selection Min-Bias Min-Bias Trigger (Fig..1) 63,8 zero or one vertex in z < 1 cm z c -z v < cm TRACK1 JET Charged particle track in the with P T > 1 GeV (ONE_CFT_NTRK_1) Calorimeter tower cluster with E T > GeV P T >.5 GeV, η < 1 6,88 zero or one vertex z c -z v < cm P T >.5 GeV, η < 1 3,87 zero or one vertex z c -z v < cm P T >.5 GeV, η < 1 The three soft Monte-Carlo models considered in this analysis are listed in Table. There is no theory for soft collisions (perturbation theory is not valid). All the soft models are essentially parameterizations. Isajet s soft min-bias generator [1] uses a model based on a cut Pomeron with Poisson fluctuations. At 1.8 TeV it produces 7.8 charged particles in the range P T > and η < 1, or roughly 3.9 charged particles per unit rapidity with a <P T > of around MeV. Herwig s min-bias generator [] also produces 7.8 charged particles in the range P T > and η < 1 with a <P T > of 3 MeV. Table. Soft theoretical Monte-Carlo models studied in this analysis. Monte-Carlo Model Subprocess Comments Herwig 5.9 Soft collisions: Herwig s soft min-bias generator IPROC = 8 Isajet 7.3 Soft collisions: Isajet s soft min-bias generator MINBIAS MBR hard core component: iproc = 1 Rockefeller s min-bias generator version Page of 65

5 MBR is a soft Monte-Carlo generator written by the Rockefeller group [3], that conserves energy, momentum, and charge. At 1.8 TeV it produces 7.6 charged particles in the range P T > and η < 1, or roughly 3.8 charged particles per unit rapidity with a <P T > of 53 MeV. MBR agrees well with the overall multiplicity and P T distributions of the Min-Bias data. All the soft models have no correlations (except for resonances and momentum conservation) and, as we will see, the data have strong correlations associated with jets and hard scattering. The hard scattering QCD Monte-Carlo models used in this analysis are listed in Table 3. Each of the QCD Monte-Carlo models handle the beam-beam remnants (Fig. 1.1) in a similar fashion. A hard scattering event is basically the superposition of a hard parton-parton interaction on top of a soft min-bias type collision. Herwig [] assumes that the underlying event is a soft collision between the two beam clusters. Isajet [1] uses a model similar to the one it uses for i.e. cut Pomeron ), but with different parameters, to describe the underlying beam-beam remnants. Pythia [] assumes that each incoming beam hadron leaves behind a beam remnant, which do not radiate initial state radiation, and simply sail through unaffected by the hard process. However, unlike Herwig and Isajet, Pythia also uses multiple parton interactions to enhance the activity of the underlying event as illustrated in Fig Table 3. Theoretical QCD hard scattering Monte-Carlo models studied in this analysis. In all cases we take PT(hard) > 3 GeV. Monte-Carlo Model Subprocesses Comments Herwig 5.9 Herwig EN Herwig EN Isajet 7.3 Pythia Pythia 6.15 Pythia No MS Pythia 97 QCD -to- parton scattering: IPROC = 15 QCD -to- parton scattering: IPROC = 15 QCD -to- parton scattering: IPROC = 15 QCD -to- parton scattering: TWOJET QCD -to- parton scattering: MSEL = 1 QCD -to- parton scattering: MSEL = 1 QCD -to- parton scattering: MSEL = 1 QCD -to- parton scattering: MSEL = 1 Default values for all parameters Underlying event multiplicity enhancement factor: ENSOF =. Underlying event multiplicity enhancement factor: ENSOF =. Default values for all parameters Default values for all parameters: PARP(81) = 1. Default values for all parameters: PARP(81) = 1.9 Pythia 6.15 with no multiple parton interactions : MSTP(81) = Pythia with the multiple scattering parameters set according to CDF Note #97: MSTP(81) = 1 MSTP(8) = 3 PARP(81) = 1. PARP(8) = 1.55 PARP(85) = 1. PARP(86) = 1. MSTP(33) = 1 PARP(31) = 1.69 PARJ(1) =.613 In this analysis we examine four versions of Pythia including Pythia and Pythia 6.15 both with the default values for all the parameters. The default values changed in going from version to In particular, the effective minimum transverse momentum for multiple parton interactions, PARP(81), changed from 1. GeV in version to 1.9 GeV in version Increasing this cut-off decreases the multiple parton interaction cross section which reduces the Page 5 of 65

6 amount of multiple parton scattering. Pythia 97 is Pythia with the multiple parton interaction parameters set according to the tuned fit from CDF Note #97 [5]. In this note, a set of Pythia parameters were tuned to fit the structure of the underlying event in reactions with B candidates. The high statistics B + to lepton D data set was used and a comparison with the W data was also made. Pythia 97 has a tremendous amount of multiple parton scattering and does not agree with the data presented here. For completeness, we also consider a version of Pythia with no multiple scattering (MSTP(81)=). Isajet and Herwig do not include multiple parton interactions. In Isajet and Herwig the underlying event arises solely from the breakup of the beams (i.e. beam-beam remnants) and from initial state radiation. If a QCD Monte-Carlo model does not describe correctly the underlying event, it is very difficult to say if this due to the lack of multiple parton interactions or due to a poor parameterization of the beam-beam remnants. We investigate this a bit by considering three versions of Herwig. The default version of Herwig 5.9, plus a version with ENSOF = and a version with ENSOF =. ENSOF is a Herwig parameter that effects the multiplicity of the underlying event by changing the energy, Wcm, at which the underlying event multiplicity is calculated. The underlying event is assigned the multiplicity of a soft hadron-hadron collision an energy of ENSOF times Wcm. In comparing the Monte-Carlo models with the Min-Bias data, we require that the Monte-Carlo events satisfy the CDF min-bias trigger (see Fig..1) and we apply an 8% correction for the CTC efficiency. The CTC efficiency can vary substantially for very low P T tracks and in dense high P T jets (PT(jet) > 15 GeV). To avoid this we consider only the region P T >.5 GeV and η < 1 where the CTC efficiency is high and stable (assumed to be 9% efficient) and we restrict ourselves to jets less the 5 GeV. Our conclusions are not sensitive to variations in the tracking efficiency. III. Studying the Event Structure as a Function of PTmax It is instructive to examine collider observables as a function of the charged particle with the maximum transverse momentum in the event (called PTmax). There is just one PTmax per event. Here it is not necessary to define jets and PTmax is an excellent probe that distinguishes between hard and soft scattering. Clearly if PTmax is large, a hard scattering has occurred. We will plot observables versus PTmax and examine the transition from soft to hard scattering. Page 6 of 65

7 <Nchg> Produced in Association with PTmax (charged) Associated <Nchg> 1.8 TeV eta <1. PT>.5 GeV 16 Does not include PTmax TRACK1 Data 1 8 Min-Bias Data PTmax (GeV) Fig Average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle). Each point corresponds to the <Nchg> in a.5 GeV bin (not including PTmax). The solid (open) points are the Min-Bias data (TRACK1 data). The data have not been corrected for efficiency. (1) Associated Nchg and Associated PTsum versus PTmax Fig. 3.1 shows the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the Min-Bias and TRACK1 data. Here one plots <Nchg> not including PTmax. It is the number of charged particles that are produced in association with PTmax. The TRACK1 data connect on smoothly to the Min-Bias data and allows us to study observables over the range.5 < PTmax < 5 GeV. There is a small overlap region where the Min-Bias and TRACK1 data agree. The errors are only statistical and the data have not been corrected for efficiency (the true multiplicities are about 9% larger). Fig. 3.1 shows a fast rise in the associated multiplicity at low PTmax and then a flattening out at high PTmax. For events with PTmax around.5 GeV, the associated charge particle multiplicity is about 1 (P T >.5 GeV and η < 1) and for PTmax around GeV it is about 6. Page 7 of 65

8 <Nchg> Produced in Association with PTmax (charged) Associated <Nchg> 1.8 TeV eta <1. PT>.5 GeV 16 Does not include PTmax PTmax (GeV) Herwig Isajet Pythia MBR CDF TRACK1 CDF Min-Bias Fig. 3.. Data on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) from Fig. 3.1 compared with the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and the soft scattering predictions of MBR. Each point corresponds to the <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Fig. 3. compares the theoretical Monte-Carlo predictions of Herwig 5.9, Pythia 6.115, Isajet 7.3, and MBR with the data on the average number of associated charged particles as a function of PTmax from Fig The wiggles in the theoretical curves are due to limited statistics. It is not easy to generate the theoretical predictions over this large range of PTmax. Each theory curve contains,, events corresponding to four 5, event runs with PT(hard) > 3, 5, 1, and GeV, which then are carefully fitted together to form the curves. The hard scattering Monte-Carlo models describe the data qualitatively but not precisely. The soft MBR model does not describe correctly the associated multiplicity. It is interesting to note that the MBR model does fit the overall multiplicity and transverse momentum distribution of the Min-Bias data, however, it does not fit the associated multiplicity shown in Fig. 3.. This is because the MBR model has no hard scattering and thus no jets and, as we will see, there are jets in the Min- Bias data. It will become clear that PTmax is part of a jet of charged particles that accompany it, even for very low PTmax values! Page 8 of 65

9 <PTsum> Produced in Association with PTmax (charged) Associated <PTsum> (GeV) 1.8 TeV eta <1. PT>.5 GeV 3 Does not include PTmax PTmax (GeV) Pythia Isajet CDF Min-Bias CDF TRACK1 Herwig MBR Fig Data on the associated scalar P T sum of charged particles (P T >.5 GeV and η < 1)as a function of PTmax (leading charged particle) compared with the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and soft scattering predictions of MBR. Each point corresponds to the <PTsum> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Fig. 3.3 compares the theoretical Monte-Carlo predictions of Herwig 5.9, Pythia 6.115, Isajet 7.3, and MBR with the data on the average scalar PT sum of the associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax. In each event one constructs the scalar sum of the transverse momentum of all the charged particles produced in association with PTmax (not including PTmax). Again, the TRACK1 data connects on smoothly to the Min-Bias data. The hard scattering Monte-Carlo models describe the data qualitatively but not precisely and the soft MBR model does not correctly describe the data. PTmax Direction φ Correlations in φ Fig. 3.. Illustration of correlations in the azimuthal angle φ relative to the direction of the leading charged particle in the event, PTmax. The angle φ = φ φmax is the relative azimuthal angle between charged particles produced in association with PTmax and the direction of PTmax. Plots of <Nchg> and <PTsum> as a function of φ are referred to as associated multiplicity flow in φ relative to PTmax and associated transverse momentum flow in φ relative to PTmax, respectively. PTmax itself is not included in these plots. Page 9 of 65

10 () Correlations in φ relative to PTmax and Jet Structure To see the jet structure in the data we examine correlations in the azimuthal angle φ relative to the direction of the leading charged particle in the event, PTmax. As illustrated in Fig. 3., the angle φ = φ φmax is the relative azimuthal angle between charged particles produced in association with PTmax and the direction of PTmax. Plots of <Nchg> and <PTsum> as a function of φ are referred to as associated multiplicity flow in φ relative to PTmax and associated transverse momentum flow in φ relative to PTmax, respectively. PTmax itself is not included in these plots. Multiplicity Flow Relative to PTmax Associated <Nchg> in 3.6 o bin.8 PTmax >.5 GeV.7 "Jet" Structure 1.8 TeV PT>.5 GeV eta < "Soft" Physics PHI-PHImax (degrees) CDF Min-Bias MBR Herwig "Soft" MB Isajet "Soft" MB Fig Associated charged particle multiplicity flow in φ relative to PTmax as a function of φ φmax. Each point corresponds to the <Nchg> in a 3.6 o bin (not including PTmax). The solid squares are the Min-Bias data (PTmax >.5 GeV, P T >.5 GeV, η < 1) and the curves correspond to the Monte-Carlo predictions of MBR, Herwig soft min-bias, and Isajet soft min-bias. The Monte-Carlo predictions have been corrected for the CTC efficiency. Fig. 3.5 shows the data on the associated multiplicity flow in φ relative to PTmax for PTmax >.5 GeV. Each point corresponds to the <Nchg> (P T >.5 GeV, η < 1) in a 3.6 o bin (not including PTmax). The solid squares are the Min-Bias data and the curves correspond to the theoretical Monte-Carlo predictions of MBR, Herwig soft min-bias, and Isajet soft min-bias. Clearly, the soft models do not show the structure seen in the data. The data show additional particles in the direction of PTmax (i.e. jet structure). In the data, quite often PTmax is the leading particle within a jet and the enhancement of particles following PTmax correspond to the accompanying particles within the jet. The soft models have no hard scattering and no jets. Any correlations in the soft models come from resonances and momentum conservation. Clearly there is a lot of hard scattering in the Min-Bias data even for PTmax >.5 GeV! It is interesting to note that although the MBR program fits the overall multiplicity and P T distribution of the Min-Bias data, it does not fit the associated multiplicity flow shown in Fig Page 1 of 65

11 Associated <PTsum> in 3.6 o bin.7 "Jet" Structure.6 PT Flow Relative to PTmax 1.8 TeV PT>.5 GeV eta < "Soft" Physics PHI-PHImax (degrees) Herwig "Soft" MB Isajet "Soft" MB MBR CDF Min-Bias Fig Associated transverse momentum flow in φ relative to PTmax, as a function of φ φmax. Each point corresponds to the scalar <PTsum> in a 3.6 o bin (not including PTmax). The solid squares are the Min-Bias data (PTmax >.5 GeV, P T >.5 GeV, η < 1) and the curves correspond to the Monte-Carlo predictions of MBR, Herwig soft minbias, and Isajet soft min-bias. The theoretical predictions have been corrected for the CTC efficiency. Fig. 3.6 shows the data on the associated transverse momentum flow in φ relative to PTmax for PTmax >.5 GeV. Each point corresponds to the <PTsum> (P T >.5 GeV, η < 1) in a 3.6 o bin (not including PTmax). The solid squares are the Min-Bias data and the curves correspond to the theoretical Monte-Carlo predictions of MBR, Herwig soft min-bias, and Isajet soft min-bias. Again, the soft models do not show the structure seen in the data. Multiplicity Flow Relative to PTmax Associated <Nchg> in 3.6 o bin.5 PTmax >. GeV 1.8 TeV PT>.5 GeV eta < "Toward" "Transverse" "Away" PHI-PHImax (degrees) Herwig Isajet Pythia MBR CDF Min-Bias Fig Average number of charged particles (not including PTmax) produced in association with PTmax as a function of φ φmax, where PTmax is the maximum P T charged particle in the event and φ φmax is the relative azimuthal angle between the particle and PTmax. Each point corresponds to the <Nchg> in a 3.6 o bin. The solid squares are the Min-Bias data (PTmax >. GeV, P T >.5 GeV, η < 1) and the curves Page 11 of 65

12 correspond to the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and the soft scattering predictions of MBR. The theoretical predictions have been corrected for the CTC efficiency. Associated <PTsum> in 3.6 o bin.5 Transverse Momentum Flow Relative to PTmax PTmax > GeV 1.8 TeV PT>.5 GeV eta < "Toward" "Transverse" "Away" PHI-PHImax (degrees) Herwig Isajet Pythia CDF Min-Bias Fig Average charged particle scalar P T sum (not including PTmax) produced in association with PTmax as a function of φ φmax, where PTmax is the maximum P T charged particle in the event and φ φmax is the relative azimuthal angle between the particle and PTmax. Each point corresponds to the <PTsum> in a 3.6 o bin. The solid squares are the Min-Bias data (PTmax >. GeV, P T >.5 GeV, η < 1) and the curves correspond to the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, and Pythia The theoretical predictions have been corrected for the CTC efficiency. Fig and Fig. 3.8 shows the data on the associated multiplicity flow and transverse momentum flow, respectively, in φ relative to PTmax for PTmax >. GeV. The solid squares are the Min-Bias data and the curves correspond to the theoretical Monte-Carlo hard scattering predictions of Herwig 5.9, Isajet 7.3 and Pythia The hard scattering Monte-Carlo models describe the data qualitatively but not precisely. Below PTmax for around GeV that data is a mixture of hard and soft collisions. Page 1 of 65

13 Multiplicity Flow Relative to PTmax Associated <Nchg> in 3.6 o bin.6 PTmax > 5. GeV 1.8 TeV PT>.5 GeV eta < 1... "Toward" "Transverse" "Away" PHI-PHImax (degrees) Herwig Isajet Pythia CDF Min-Bias Fig Average number of charged particles (not including PTmax) produced in association with PTmax as a function of φ φmax, where PTmax is the maximum P T charged particle in the event and φ φmax is the relative azimuthal angle between the particle and PTmax. Each point corresponds to the <Nchg> in a 3.6 o bin. The solid squares are the Min-Bias data (PTmax > 5. GeV, P T >.5 GeV, η < 1) and the curves correspond to the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, and Pythia The theoretical predictions have been corrected for the CTC efficiency. Associated <PTsum> in 3.6 o bin.8 Transverse Momentum Flow Relative to PTmax PTmax > 5 GeV 1.8 TeV PT>.5 GeV eta < "Toward" "Transverse" "Away" PHI-PHImax (degrees) Herwig Isajet Pythia CDF Min-Bias Fig Average charged particle scalar P T sum (not including PTmax) produced in association with PTmax as a function of φ φmax, where PTmax is the maximum P T charged particle in the event and φ φmax is the relative azimuthal angle between the particle and PTmax. Each point corresponds to the <PTsum> in a 3.6 o bin. The solid squares are the Min-Bias data (PTmax > 5. GeV, P T >.5 GeV, η < 1) and the curves correspond to the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, and Pythia The theoretical predictions have been corrected for the CTC efficiency. Page 13 of 65

14 Multiplicity Flow Relative to PTmax Associated <Nchg> in 3.6 o bin.5 PTmax > 5. GeV 1.8 TeV PT>.5 GeV eta < "Toward" "Transverse" "Away" PHI-PHImax (degrees) Pythia Pythia 6.15 Pythia No MS CDF Min-Bias Fig Average number of charged particles (not including PTmax) produced in association with PTmax as a function of φ φmax, where PTmax is the maximum P T charged particle in the event and φ φmax is the relative azimuthal angle between the particle and PTmax. Each point corresponds to the <Nchg> in a 3.6 o bin. The solid squares are the Min-Bias data (PTmax > 5. GeV, P T >.5 GeV, η < 1) and the curves correspond to the QCD hard scattering Monte-Carlo predictions Pythia 6.115, Pythia 6.15, and Pythia (no multiple scattering). The theoretical predictions have been corrected for the CTC efficiency. Associated <PTsum> in 3.6 o bin.6 Transverse Momentum Flow Relative to PTmax PTmax > 5 GeV 1.8 TeV PT>.5 GeV eta < 1... "Toward" "Transverse" "Away" PHI-PHImax (degrees) Pythia No MS Pythia 6.15 CDF Min-Bias Pythia Fig Average charged particle scalar P T sum (not including PTmax) produced in association with PTmax as a function of φ φmax, where PTmax is the maximum P T charged particle in the event and φ φmax is the relative azimuthal angle between the particle and PTmax. Each point corresponds to the <PTsum> in a 3.6 o bin. The solid squares are the Min-Bias data (PTmax > 5. GeV, P T >.5 GeV, η < 1) and the curves correspond to the QCD hard scattering Monte-Carlo predictions of Pythia 6.115, Pythia 6.15, and Pythia (no multiple scattering). The theoretical predictions have been corrected for the CTC efficiency. Page 1 of 65

15 Fig. 3.9 and Fig. 3.1 shows the data on the associated multiplicity flow and transverse momentum flow, respectively, in φ relative to PTmax for PTmax > 5. GeV. The solid squares are the Min-Bias data and the curves correspond to the theoretical Monte-Carlo hard scattering predictions of Herwig 5.9, Isajet 7.3, and Pythia The hard scattering Monte-Carlo models describe the data quite well but not precisely. These plots are sensitive to the entire event structure both the underlying event and the outgoing parton jets. This is seen clearly in Fig and Fig. 3.1 which show the data for PTmax > 5. GeV compared with three versions of Pythia (Pythia 6.115, Pythia 6.15, and Pythia with no multiple scattering). These three version of Pythia differ in the amount of activity in the underlying event. PTmax Direction φ Toward Transverse Transverse Away Fig Illustration of correlations in azimuthal angle φ relative to the direction of the leading charged particle in the event, PTmax. The angle φ = φ φmax is the relative azimuthal angle between charged particles produced in association with PTmax and the direction of PTmax. The region φ φmax < 6 o is referred to as toward PTmax and the region φ φmax > 1 o is called away from PTmax. The transverse to PTmax region is defined by 6 o < φ φmax < 1 o. Each region, toward, transverse, and away covers the range η x φ = x 1 o. (3) Event Shape versus PTmax In Fig. 3.7 Fig. 3.1 we have labeled the region φ φmax < 6 o as toward PTmax and the region φ φmax > 1 o is as away from PTmax. The transverse to PTmax region is defined by 6 o < φ φmax < 1 o. As illustrated in Fig. 3.13, each region, toward, transverse, and η x φ = x 1 o. The toward region contains the jet of particles associated with PTmax. The transverse region is very sensitive to the underlying event. The away region is a mixture of the underlying event and the away-side jet. Fig. 3.1 shows the data on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax for the three regions. Each point corresponds to the toward, transverse, or chg> in a 1 GeV bin (not including PTmax). The solid points are the Min-Bias data and the open points are the TRACK1 data. The data in Fig. 3.1 define the average event shape. Page 15 of 65

16 This is illustrated in Fig which shows an average proton-antiproton collider event at 1.8 TeV with PTmax = 1 GeV. There are, on the average,. charged particles toward PTmax (not including PTmax),. transverse to PTmax, and. away from PTmax. These numbers are not corrected for CTC efficiency (the true multiplicities are about 9% higher). Associated <Nchg> <Nchg> Produced in Association with PTmax (charged) TeV eta <1. PT>.5 GeV Does not include PTmax "Toward" "Away" "Transverse" PTmax (GeV) Fig Average number of associated charged particles with P T >.5 GeV and η < 1as a function of PTmax (leading charged particle) for the three regions defined in Fig Each point corresponds to the toward, transverse, or away <Nchg> in a.5 GeV bin (not including PTmax). The solid (open) points are the Min-Bias data (TRACK1 data). The data have not been corrected for efficiency. <Nchg> =. <Nchg> = 1.1 <Nchg> =. <Nchg> = 1.1 PTmax = 1 GeV Fig Illustration (drawn to scale) of an average proton-antiproton collider event at 1.8 TeV with PTmax = 1 GeV. The data in Fig. 3.1 show that the average number of associated charged particles with P T >.5 GeV and η < 1 for the three regions defined in Fig is. charged particles toward PTmax (not including PTmax),. transverse to PTmax, and. away from PTmax. The data have not been corrected for efficiency (the true multiplicities are about 9% higher). For.5 < PTmax < 5 GeV the associated charged multiplicity in the toward region (not including PTmax) is about the same as in the away region and although there is much more charged multiplicity in the forward and away region (i.e. the event shape is flat ), there is a lot of activity in the transverse region. If we suppose that the transverse multplicity is uniform in azimuthal angle φ and rapidity η, the observed. charged particles translates to 3.6 charged particles per unit rapidity with P T >.5 GeV (multiply by 3 to get 36 o, divide by for the two units of rapidity, multiply by 1.9 to correct for the CTC efficiency). We know that if we include all P T then there are roughly charged particles per unit rapidity which is not much different than the 3.6 we see with P T >.5 GeV! If we further assume that the P T distribution is Page 16 of 65

17 an exponential at small P T with a mean of 5 MeV then the 3.6 charged particles extrapolates to 9.7 charged particles per unit rapidity (multiply by.7), which is about a factor of two larger than the charged particles per unity rapidity seen in soft parton-antiproton collisions at this energy. The underlying event in a hard collision is considerably more active (by at least a factor of two) than a soft collision. Furthermore, the particle density in the underlying event is a function of PTmax and as can be seen in Fig. 3.1 it rises very rapidly as PTmax increases. The transverse charged multiplicity doubles in going from PTmax =.75 GeV to PTmax = 1.5 GeV and forms an approximately constant plateau for PTmax > GeV. Associated <PTsum> (GeV) <PTsum> Produced in Association with PTmax (charged) TeV eta <1. PT>.5 GeV Does not include PTmax "Toward" "Away" "Transverse" PTmax (GeV) Fig Average associated scalar P T sum of charged particles (P T >.5 GeV and η < 1)as a function of PTmax (leading charged particle) for the three regions defined in Fig Each point corresponds to the toward, transverse, or away <PTsum> in a.5 GeV bin (not including PTmax). The solid (open) points are the Min-Bias data (TRACK1 data). The data have not been corrected for efficiency. <PTsum> = 6. GeV <PTsum> = 1. GeV <PTsum> = 7. GeV <PTsum> = 1. GeV PTmax = 1 GeV Fig Illustration (drawn to scale) of an average proton-antiproton collider event at 1.8 TeV with PTmax = 1 GeV. The data in Fig show that the average associated scalar PT sum of charged particles (P T >.5 GeV and η < 1) for the three regions defined in Fig is 7. GeV toward PTmax (not including PTmax),. GeV transverse to PTmax, and 6. GeV away from PTmax. The numbers have not been corrected for efficiency. Fig shows the data on the average scalar P T sum of associated charged particles as a function of PTmax for the three regions. Each point corresponds to the toward, transverse, or sum> in a 1 GeV bin (not including PTmax). The solid points are the Min-Bias data and the open points are the TRACK1 data. The event shape in transverse momentum is illustrated in Fig which shows an average proton-antiproton collider event with PTmax = Page 17 of 65

18 1 GeV. There are, on the average, 7. GeV toward PTmax (not including PTmax),. GeV transverse to PTmax, and 6. GeV away from PTmax. As was the case with the charged multiplicity, the associated <PTsum> in the toward region (not including PTmax) is about the same as in the away region. The transverse <PTsum> also rises rapidity as a function of PTmax and forms an approximately constant plateau for PTmax > GeV. Associated <Nchg> <Nchg> Produced in Association with PTmax (charged) TeV eta <1. PT>.5 GeV Does not include PTmax MBR "Hard Core" "Toward" "Away" "Transverse" PTmax (GeV) Fig Data from Fig. 3.1 on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the three regions defined in Fig compared with the theoretical Monte-Carlo predictions of MBR (solid = toward, dashed = transverse, circles = away ). Each point corresponds to the toward, transverse, or away <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. In Fig data on the average number of associated charged particles as a function of PTmax for the three regions is compared with the Monte-Carlo predictions of the soft MBR model. We have already seen in Fig. 3. that the model does not produce sufficient associated charge particle multiplicity. Here we see that the behavior of the toward, transverse and away multiplicity is opposite to that seen in the data. In the MBR model the toward charged multiplicity is the smallest of the three regions and the transverse multiplicity is larger than the toward multiplicity. The away multiplicity is the largest of the three due to the way the model conserves momentum. Page 18 of 65

19 <Nchg> Produced in Association with PTmax (charged) Associated <Nchg> TeV eta <1. PT>.5 GeV Does not include PTmax 6 Herwig 5.9 "Toward" "Away" "Transverse" PTmax (GeV) Fig Data from Fig. 3.1 on the average number of associated charged particles (P T >.5 GeV and η < 1as a function of PTmax (leading charged particle) for the three regions defined in Fig compared with the theoretical Monte-Carlo predictions of Herwig 5.9. Each point corresponds to the toward, transverse, or away <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Associated <PTsum> (GeV) <PTsum> Produced in Association with PTmax (charged) TeV eta <1. PT>.5 GeV Does not include PTmax Herwig "Toward" "Away" "Transverse" PTmax (GeV) Fig. 3.. Data from Fig on the average associated scalar P T sum of charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the three regions defined in Fig compared with the theoretical Monte-Carlo predictions of Herwig 5.9. Each point corresponds to the toward, transverse, or sum> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Page 19 of 65

20 <Nchg> Produced in Association with PTmax (charged) Associated <Nchg> TeV eta <1. PT>.5 GeV Does not include PTmax Isajet 7.3 "Toward" "Away" "Transverse" PTmax (GeV) Fig Data from Fig. 3.1 on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the three regions defined in Fig compared with the theoretical Monte-Carlo predictions of Iasjet. Each point corresponds to the toward, transverse, or away <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Associated <PTsum> (GeV) <PTsum> Produced in Association with PTmax (charged) TeV eta <1. PT>.5 GeV Does not include PTmax Isajet "Toward" "Away" 3 "Transverse" PTmax (GeV) Fig. 3.. Data from Fig on the average associated scalar P T sum of charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the three regions defined in Fig compared with the theoretical Monte-Carlo predictions of Isajet 7.3. Each point corresponds to the toward, transverse, or sum> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Page of 65

21 <Nchg> Produced in Association with PTmax (charged) Associated <Nchg> TeV eta <1. PT>.5 GeV Does not include PTmax Pythia "Toward" "Away" "Transverse" PTmax (GeV) Fig Data from Fig. 3.1 on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the three regions defined in Fig compared with the theoretical Monte-Carlo predictions of Pythia Each point corresponds to the toward, transverse, or away <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Associated <PTsum> (GeV) <PTsum> Produced in Association with PTmax (charged) TeV eta <1. PT>.5 GeV Does not include PTmax Pythia "Toward" "Away" "Transverse" PTmax (GeV) Fig. 3.. Data from Fig. 3.1 on the average associated scalar P T sum of charged particles (P T >.5 GeV and η < 1)as a function of PTmax (leading charged particle) for the three regions defined in Fig compared with the theoretical Monte-Carlo predictions of Pythia Each point corresponds to the toward, transverse, or sum> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. In Fig and Fig. 3. data on the associated <Nchg> and <PTsum>, respectively, as a function of PTmax for the three regions is compared with the hard scattering Monte-Carlo predictions of Herwig 5.9. Fig. 3.1 and Fig. 3. show the same comparison for Isajet 7.3, while Fig. 3.3 and Fig. 3. show the predictions of Pythis Page 1 of 65

22 The hard scattering Monte-Carlo models shown in Fig Fig. 3. agree qualitatively but not precisely with the data. You can see that Herwig does not have enough activity in the underlying event. Pythia has more activity in the underlying event but as a result of this produces too much toward <Nchg> and <PTsum>. Isajet has a lot of activity in the underlying event but the dependence on PTmax is not quite right. The transverse <Nchg> rises with PTmax rather than forming the constant plateau seen in the data. "Toward" <Nchg> versus PTmax (charged) <Nchg> toward PTmax TeV eta <1. PT>.5 GeV 6 Does not include PTmax PTmax (GeV) Isajet Pythia MBR Herwig CDF TRACK1 CDF Min-Bias Fig Data from Fig.3.1 on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the toward region defined in Fig compared with the QCD hard scattering Monte- Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and the soft scattering predictions of MBR. Each point corresponds to the toward <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. "Toward" <PTsum> versus PTmax (charged) <PTsum> (GeV) toward PTmax TeV eta <1. PT>.5 GeV 1 9 Does not include PTmax PTmax (GeV) Herwig Isajet Pythia MBR CDF Min-Bias CDF TRACK1 Fig Data from Fig on the average associated scalar P T sum of charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for Page of 65

23 the toward region defined in Fig compared with the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and the soft scattering predictions of MBR. Each point corresponds to the toward <PTsum> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. "Transverse" <Nchg> versus PTmax (charged) <Nchg> transverse to PTmax 1.8 TeV eta <1. PT>.5 GeV PTmax (GeV) Isajet Pythia MBR Herwig CDF TRACK1 CDF Min-Bias Fig Data from Fig.3.1 on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the transverse region defined in Fig compared with the QCD hard scattering Monte- Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and soft scattering predictions of MBR. Each point corresponds to the transverse <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. "Transverse" <PTsum> versus PTmax (charged) <PTsum> (GeV) transverse to PTmax 1.8 TeV eta <1. PT>.5 GeV PTmax (GeV) Herwig Isajet Pythia MBR CDF Min-Bias CDF TRACK1 Fig Data from Fig on the average associated scalar P T sum of charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the transverse region defined in Fig compared with the QCD hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and soft scattering Page 3 of 65

24 predictions of MBR. Each point corresponds to the transverse <PTsum> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. "Away" <Nchg> versus PTmax (charged) <Nchg> away from PTmax TeV eta <1. PT>.5 GeV PTmax (GeV) Isajet Pythia MBR Herwig CDF TRACK1 CDF Min-Bias Fig Data from Fig.3.1 on the average number of associated charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the away region defined in Fig compared with the QCD hard scattering Monte- Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and soft scattering predictions of MBR. Each point corresponds to the away <Nchg> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. <PTsum> (GeV) away from PTmax 15 "Away" <PTsum> versus PTmax (charged) TeV eta <1. PT>.5 GeV PTmax (GeV) Isajet CDF Min-Bias Pythia CDF TRACK1 Herwig MBR Fig Data from Fig on the average associated scalar P T sum of charged particles (P T >.5 GeV and η < 1) as a function of PTmax (leading charged particle) for the away region defined in Fig compared with the QCD hard scattering Monte- Carlo predictions of Herwig 5.9, Isajet 7.3, Pythia 6.115, and the soft scattering predictions of MBR. Each point corresponds to the away <PTsum> in a.5 GeV bin (not including PTmax). The theoretical predictions have been corrected for the CTC efficiency. Page of 65

25 Fig. 3.5 and Fig..6 compare the toward <Nchg> and <PTsum>, respectively, with the theoretical hard scattering Monte-Carlo predictions of Herwig 5.9, Isajet 7.3, and Pythia 6.115, and the soft MBR predication with the data. Fig. 3.7 and Fig. 3.8 compare the chg> and <PTsum>, respectively, with the theoretical hard scattering Monte- Carlo predictions of Herwig 5.9, Isajet 7.3, and Pythia 6.115, and the soft MBR prediction with the data. Finally, Fig. 3.9 and Fig. 3.3 compare the away <Nchg> and <PTsum>, respectively, with the theoretical hard scattering Monte-Carlo predictions of Herwig, Isajet, and Pythia 6.115, and the soft MBR prediction with the data. The data show clear jet structure even at quite low PTmax values (see Fig. 3.5). In this section, we define jets and examine the evolution of these jets from P T (jet) =.5 to 5 GeV. We will also examine the event shape as a function of the P T (jet#1) (leading jet). As illustrated if Fig..1, jets are defined as circular regions (R =.7) in η-φ space and contain charged particles from the underlying event as well as particles which originate from the fragmentation of high P T outgoing partons (see Fig 1.1). Also every charged particle in the event is assigned to a jet, with the possibility that some jets might consist of just one charged particle. π φ η Fig..1. Illustration of an event with six charged particles (P T >.5 GeV and η < 1) and five jets (circular regions in η-φ space with R =.7). (1) Jet Definition We define jets as circular regions in η-φ space with distance defined by d = ( η ) + ( φ ). Page 5 of 65

26 Our jet algorithm is as follows: Order all charged particles according to their P T. Start with the highest P T particle and include in the jet all particles within the distance R =.7. Go to the next highest P T particle (not already included in a jet) and include in the jet all particles (not already included in a jet) within the distance R =.7. Continue until all particles are in a jet. We consider all charged particles (P T >.5 GeV and η < 1) and allow the jet radius to extend outside η < 1. Fig..1 illustrates an event with six charged particles and five jets. Jets have a vector momentum given by the vector sum of all the particles within the jet and a transverse momentum given by P T ( jet ) = ( Px ( jet )) + ( Py ( jet )). The maximum number of jets is related to the geometrical size of jets compared to the size of the region considered and is given approximately by ( )( π ) N jet (max) 16. π (.7 ) The additional factor of two is to allow for the overlap of jet radii as shown in Fig..1. <Nchg> in 1 GeV bin Nchg versus PT (Jet#1) (charged) Min-Bias Data 16 JET Data 1 8 Overlap 1.8 TeV eta <1. PT>.5 GeV R= Fig... Average number of charged particles (P T >.5 GeV and η < 1) as a function of P T (jet#1) (leading jet). Each point corresponds to <Nchg> in a 1 GeV bin. The solid (open) points are the Min-Bias data (JET data). The data have not been corrected for efficiency. Page 6 of 65