Reconstructing jet-jet invariant masses

Volume 178, number 4

PHYSICS LETTERS B

9 October 1986

RECONSTRUCTING J E T - J E T I N V A R I A N T M A S S E S ~" R.D. F I E L D Particle Theory Group, Department of Physics, University of Florida, Gainesville, FL 32611, USA Received 30 June 1986

Limits are placed on the ability to reconstruct, from an examination of jets, the mass of W bosons that are produced in hadron-hadron collisions and decay hadronically, W-~qCl.A QCD patton-shower Monte Carlo model is used to simulate the production and decay of W bosons and it is found that jet-jet mass resolutions are limited not by experimental factors such as calorimetergrid size but by the inherent uncertainty in the true origin of the particles forming the jets. The best one can do on a pure sample of W--.qdl events at CM energies of 540 and 1600 GeV is a jet-jet mass width of 30 GeV. Fictitious heavy narrow W' bosons are generated at 1600GeV and analyzed usingjet and cluster techniques. Both techniques yield a similar mass width of about 50 GeV for the W' (336) --'q~levents.

The idea o f " j e t spectroscopy" is an intriguing one. Instead of determining the mass of an unstable particle by analyzing the individual hadrons into which it decays, one reconstructs its mass by studying the "jets" initiated by the quarks into which it decays. M o m e n t u m and energy conservation guarantees that the invariant mass of all the particles resulting from its decay yield the mass of the unstable particle. Event-by-event variations of this reconstructed mass reflect of the true width of the resonance. However, in analyzing jets there is an intrinsic uncertainty as to the true origin o f the particles included within the jets. This results in an inherent "jet-jet" mass width that is considerably larger than the true width of the decaying particle. In this paper I will examine the jet-jet and cluster-cluster mass distributions resulting from the hadronic decay of W bosons using a Q C D parton-shower Monte Carlo model o f hadr o n - h a d r o n collisions. In a larger and more detailed paper, Gottschalk and I [ 1 ] study the more general question of jets produced in association with W and Z bosons and examine both the hadronic and leptonic decay modes. None of the existing Q C D Monte Carlo models for h a d r o n - h a d r o n collisions should be taken too seriResearch supported in part by the US Department of Energy under Grant No. FG05-86-ER40272 and Contract No. DEAC-02-76ER03069. 0370-2693/86/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

ously. They all contain a little Q C D perturbation theory and a lot of phenomenology and, in fact, they do not give precisely the same predictions for experiment [ 2,3 ]. At the parton level there are theoretical uncertainties and inaccurate approximations being made in all the present Monte Carlo approaches [ 4 ]. However, the parton level is not the weakest link in the chain of theory and phenomenology leading to the simulation of events in h a d r o n - h a d r o n collisions. The most uncertain ingredient in the models is the "hadronization" phase (the algorithm used to turn the outgoing partons into hadrons). I do not believe that anyone knows the correct way to fragment a collection o f partons into hadrons. For this reason none of the predictions of the Q C D model presented here are precise. Nevertheless, the model does exhibit many o f the general features expected from Q C D and it is the physics of these general Q C D features that I will emphasize. The Q C D Monte Carlo model I use includes some important Q C D corrections to the naive patton model. Complicated 2 ~ N subprocesses are estimated by including the noncollinear emission o f gluons off both the initial- and final-state partons in the "leading pole" approximation [ 5-11 ]. Fig. 1 illustrates the production and hadronic decay o f a W boson. Final-state partons have timelike invariant masses with the radiated partons being kinemati423

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PHYSICS LETTERS B

9 October 1986

W-Boson Production and Hadronic Decay

"Type I" Hadrons: All hadrons from initial partons A~,A2,. etc plus hadrons from "hole" ha.

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Fig. 1. Illustration of the production and hadronic decay of a W boson produced in hadron-hadron collisions using a parton-shower Monte Carlo model which includes in an approximate manner the emission ofgluons offboth the initial- and final-state partons. Hadrons are labeled according to where they originate with type-I hadrons arising from the fragmentation of the initial partons AI, A2,... etc. plus the fragmentation of the "'hole" ha (which is assigned fractional momentum 1-xA). Similarly, type-2 hadrons arise from the fragmentation of the initial patrons B~, B2, ... etc. plus "hole" hB. Type-3 and type-4 hadrons arise from the fragmentation of outgoing partons Ci and D,, respectively, and .fitis the transverse momentum of the subprocess qaClb--~qcqd.

cally constrained to have invariant masses less than their parents with the difference being converted into the transverse momentum of the emitted partons. The radiated partons themselves radiate more partons until all invariant masses have been degraded to some cut-off mass, /~A, thus producing a "parton shower". Initial partons also form a shower, but in this case the partons have spacelike invariant masses. For the initial-state parton showers I use the backwards evolution Monte Carlo model constructed by Gottschalk [ 10]. Perturbative branchings are generated by working backwards from the hard-scattering subsystem to the unevolved structure functions at the reference scale Qo = 2 GeV. Gottschalk's backwards evolution method for the 424

initial-state shower yields similar results to the forward-evolution method that I have used previously [ 12 ]. However, with the backwards method I can select the value of the constituent hard-scattering CM energy squared, g, initially. In the previous method, g is calculated after the event has been generated and one is left with a broad distribution of~ values. With the new method, for example, W bosons are generated according to a Breit-Wigner distribution with a mass of 84 GeV and a width of 3 GeV. In the analysis presented here I do not keep track of the color strings. Instead each parton is allowed to fragment independently into hadrons in the hadron-hadron CM frame according to the Field-Feynman (FF jet) prescription [13]. This is

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the fragmentation scheme adopted by ISAJET [9] and by Odorico [6]. I do not believe that this is a correct fragmentation procedure, however, for the present I have nothing better to suggest. In addition, the "hole" that remains after a parton is knocked out of the beam or target hadron is assigned the full remaining m o m e n t u m and then also allowed to fragment according to the FF-jet prescription. The invariant m a s s c u t - o f f ~ A - - - - 2 GeV and the Q C D perturbative parameter 2 = 0.2 GeV. With this hadronization scheme I can keep track o f where the outgoing hadrons come from. As is illustrated in fig. 1, type-I hadrons are those arising from initial partons A~, A 2 . . . . etc. plus the hadrons arising from the fragmentation of the "hole" hA. Similarly, type-2 hadrons arise from the initial partons BI, B2, ... etc. plus the "hole" ha. Outgoing partons C, and D, fragment into hadrons of type 3 and type 4, respectively. The invariant mass of all the type-3 and type4 hadrons is precisely the generated mass of the W boson. I have been careful not to call, for example, type-3 hadrons a "jet". Type-3 hadrons may form several "jets" or no "jets" or type-3 and type-1 hadrons may conspire to form one "jet". The definition of a "jet" is at the discretion o f the experimenter. In analyzing the produced events 1 will use both "jet" and "cluster" techniques. "UA1 jets" are defined by dividing phase space into a finite number of cells. The energy o f a cell is computed by adding together the energies of all the particles within the cell. Each cell is then considered as a massless "particle" o f energy E(cell) and with a direction given by the position of the center o f the cell. Jets are formed from the cells using the UA 1-j et algorithm [ 14]. Here one first considers the " h o t " cells (those with transverse energy greater than 1.0 GeV). Hot cells are combined to form a "jet" if they lie within a "distance" d = ( A q 2 + A ¢ 2) I/2<1 from each other, with the jet direction being the vector sum of the momenta o f each cell in the jet. Cold cells (those with ET< 1.0 GeV) are added to a jet if d < 1 or if the angle o f the cold cell relative to the jet is less than 45 ° and the relative PT is less than 1 GeV. " C D F clusters" are also examined [ 15 ]. They are formed by including in a "cluster" all cells with a c o m m o n side, but where cells with transverse energy less than some minimum transverse energy, ET(min), are ignored. UAI jets and C D F clusters have an

9 October 1986

energy given by the sum of the energies of all the cells within the jet or cluster and a m o m e n t u m given by the vector sum o f the m o m e n t u m s o f each cell. Finally, jets and clusters are ordered according to the total ET of all the cells in the jet or cluster with the ~1 jet or cluster having the highest transverse energy. The definition of C D F clusters is intimately related to the size o f the cells in the transverse energy grid, Ar/A¢. On the other hand, the UAl-jet algorithm can be applied directly to the outgoing particles themselves without defining a transverse-energy grid at all. This corresponds to the limit in which the number o f cells becomes infinite with the size o f each cell shrinking to zero. As I have shown in a previous paper [ 12], UA1 jets are not the same as C D F clusters. They are different experimental observables, but both provide a way to study event topologies in hadr o n - h a d r o n collisions. Fig. 2 shows the invariant-mass distribution of the leading two UA1 jets resulting from a pure sample o f W~q~l events in lbp collisions at 540 and 1600 GeV. 003 960 celts M=>=71-+20Gev

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M,2(GeV) Fig. 2. Distribution of the invariant mass of the top two UA 1jets, M~2, resulting from a pure sample of W--,q¢levents produced in lbp collisions at CM energies of 540 and 1600 GeV by a QCD patton-shower Monte Carlo. The UA 1-jet algorithm was applied to 60 cells of size Ar/A'¢=0.8×60 ° (c, f) or 960 cells of size Ar/A¢=0.2 X 15° (b, e) ot it was applied directly to the particles themselves (exact) (a, d):'The plots are labeled with the resulting average value of M~2 where the + refers not to the error but to the root-mean-squaredeviation from the mean, a, and an arrow marks the input W boson mass of 84 GeV. 425

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The W~q~l events are analyzed in the region I1/I < 4 with 60 cells (A~/A~= 0.8 X 60 ° ) and with 940 cells (Ar/AO= 0.2 X 15 ° ). This is compared with the exact jet-jet invariant mass determined by applying the UAl-jet algorithm directly to the hadrons themselves. In each case the precise energy of every particle is included (i.e. neutrals, neutrinos, etc.). It is clear from the figure that the limiting factor in determining the mass of the W boson in this manner is not the calorimeter cell size. A grid with only 60 cells does almost as well as a grid of 960 cells and 960 cells does as well as an infinite number of cells (exact). The large widths of the jet-jet mass distributions seen in fig. 2 are not due the lack of resolution arising from the size of the transverse-energy grid cells, but instead are a result of the inherent uncertainty in defining a "jet". In a given event one can never be sure that, for example, the top two jets include the particles you would like to incude (i.e. those resulting from the hadronic decay of the W boson) and at the same time exclude background particles. Sometimes one of the top two jets is not a jet resulting from the decay of the W boson, but one that arose from initial-state bremsstrahlung (see fig. 1 ). Sometimes one of the outgoing W--, qCljets fragments into a multitude of jets and thus the mass of the W boson is shared among more jets than the top two. This inherent smearing of the true W mass is seen dramatically in fig. 3 where the true (generated) W mass is compared with the observed jet-jet invariant mass of fig. 2. The roughly 3 GeV W-boson mass width is observed (in the hadronic decay mode) as a jet-jet mass width of about 30 GeV ~1! The areas under the two distributions in fig. 3 are equal. Clearly the width of the jet-jet invariant-mass distributions affects ones ability to see the hadronic decay mode of the W boson. To do so one would have to see a peak in the jet-jet invariant-mass distribution above the smooth background arising from normal QCD two-to-two parton scatterings. It might be possible in certain circumstances to see the true Wmass distribution in fig. 3 above background, howThe numerical values of the mass widths presented in this paper are crudely estimated by drawing a Breit-Wigner curve through the peak in the distribution and reading off the full width at half m a x i m u m . These widths are in general smaller than twice the standard deviations from the mean, tr, presented in table 1.

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9 October 1986

0.20

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Lq~

540 GeV

0.15

~E "b 0

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0.05

°.°°o ~o 4~o'~b' 80 ,&o ,~o ,40 ,oo M (GeV) Fig. 3. Distribution of the invariant mass of the top two UA1 jets, Mj2, resulting from a pure sample of W ~ q ( l events produced in ~p collisions at a CM energy of 540 GeV by a Q C D parton-shower Monte Carlo (same as fig. 1a) compared with the true generated W-boson mass distribution (solid). The area under the two distributions is the same.

ever, it is essentially impossible to see the smeared out jet-jet invariant-mass distribution of the W--,q(l events. In comparing the W bosons produced at a CM energy of 540 GeV with those produced at 1600 GeV one finds slightly more jet activity associated with the W boson at the higher CM energy. This can be seen in fig. 2 in the jet-jet invariant-mass plots. At 540 GeV the mean value of M~2 is 74+ 19 GeV, whereas at 1600 GeV it has risen to 80 + 28 GeV. The effect is not large, but at the larger energy the model predicts that the rapidity plateau under the W boson has a higher density of particles and hence more jet fluctuations. Fig. 4 shows the jet-jet invariant-mass distribu-

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PHYSICS LETTERS B

4

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1600GeV

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Fig. 4. Distribution of the invariant mass of the top two UA 1jets, M~2, resulting from a pure sample of W~qdl events produced in f~p collisions at a CM energy of 1600 GeV by a QCD partonshower Monte Carlo (same as fig. l d). Also shown are the jet-jet invariant-mass, M,2, distributions resulting from pure samples of three fictitious narrow high-mass W' bosons (168, 252, and 336 GeV) each produced in f~p collisions at 1600 GeV and each decaying hadronically, W'--,qdl. In all cases the UAl-jet algorithm is applied directly to the particles (exact). The resulting mean values and the root-mean-square deviations, M~2-+a, are shown along the top and arrows mark the input W and W' masses.

tion for the W boson and for three narrow fictitious bosonS,~lth masses 168, 252, and 336 GeV produced in pp collisions at 1600 GeV. In each case a pure sample of W~qCl and W' --*qq events were analyzed and the invariant mass of the top two UA1 jets was constructed on an event-by-event basis using the actual particles themselves (exact). The three W' bosons were generated with the same width as the W boson, namely 3 GeV. As can be seen in the figure, the observed jet-jet mass widths increase as the W' mass increases, although not as rapidly as does the mass itself. The observed jet-jet invariant-mass width of the W' (336) is about 50 GeV! This increasing jet-jet mass width with increasing W' mass is a feature of QCD. Larger W' mass means larger Q2 which means more gluon bremsstrahlung. The higher the mass of the boson produced the more the associated multijet activity and thus the larger the observed jet-jet mass width. The top row of fig. 5 indicates that at the W ' ( 3 3 6 ) much of the low jet-jet mass region arises because of multiple jets being initiated by the W'--,qdl decay. This low-mass tail is removed if one plots the invar-

9 October 1986

iant mass of the top three UAI jets. Plotting the invariant mass of the top four UA1 jets results in a large tail on the high-mass side. Unfortunately, the observed widths of all three distributions M~ 2, M~ 23, and MI234 are large. The best one can do using the UA 1-jet algorithm on a pure sample of W' (336) --. qcl events with no additional cuts is a width of about 40 GeV for the M~23 distribution. Selecting only a portion of the W' (336) --,qdl events to analyze sharpens up the mass distribution somewhat but at the expense of lowering the production rate. The shaded regions in the top row of fig. 5 result from including only those W' (336) ~qcl events in which the leading two UA1 jets contain more than 80% of the total global transverse energy of the event ( I t / l < 4 ) . Table 1 shows that 34% of the W' (336) ~qdl events satisfy this cut which improves somewhat the widths of the two- and three-jet invariant-mass distributions. Table 1 shows several other cuts that slightly improve the observed two- and three-jet invariantmass widths. For example, demanding that there be only two jets with Ex(each) > 10 GeV works fairly well but leaves only 19% of the W' (336) --,qdl events. Demanding that the top two jets have nearly the same transverse energy (R~2>0.95) does not improve things much. The best I could obtain and still keep a reasonable number of events is a width of about 35 GeV for the Ml23 distribution with the h~2> 0.8 cut. The inherent broadening of the jet-jet mass distribution is not simply a feature the chosen jet definition. Any jet definition will exhibit the same features. You can never guarantee that the particles that you want are included and the ones you do not want are excluded. The bottom row of fig. 5 shows the invariant-mass distributions of the top two, three and, four CDF clusters resulting from a pure sample of W' (336)--,qCl events. Here I have defined a transverse energy grid with 960 cells in the range I r/I < 4 of size At/A¢~=0.2×15 ° and have chosen E r ( m i n ) = 0 . 6 GeV. CDF clusters defined in this manner are not as "fat" as UAI jets as the resulting lower Ml 2 distribution indicates. The mean value of M~2 for CDF clustbrs and UA1 jets is 251 _ 6 3 GeV and 282_+63 GeV, ~espectively. However, there is little difference in the widths of the UA l-jet and CDFcluster invariant-mass distributions. As in the UA 1jet case including more clusters in the construction 427

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, . . . . . =282+_63Ge V 4' (319 + 25GeV) 336 UA1- Jets Exact

9 October 1986

'M, ')=340 '+ - 5 ; Ge'V ~'' ' z3 (348+31 GeV)356

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Fig. 5. (Top row) Distribution of the invariant mass of the top two UA1 jets, M~ 2; top three UA1 jets, M~ 23; and top four UAI jets, MI234 , resulting from a pure sample of W' (336)--* q(t events produced in lbp collisions at a CM energy of 1600 GeV by a QCD parton-shower Monte Carlo. The Mt z distribution is the same as that shown in fig. 4. In all cases the UA 1-jet algorithm is applied directly to the particles (exact). The resulting mean values and the root-mean-square deviations, M + a, are shown and arrows mark the input W' (336) mass. The shaded region corresponds to only those W' (336)~qcl events in which the top two UA1 jets carry at least 80% of the total global ET ( 34% of the events). The mean values and the root-mean-square deviations, M + a, resulting from this cut sample are enclosed in parentheses. (Bottom row) Distribution of the invariant mass of the top two CDF clusters, Mt 2; top three CDF clusters, M~23; and top four CDF clusters, M1234, resulting from a pure sample o f W ' (336)--,qq events produced in lbp collisions at a CM energy of 1600 GeV. A transverse energy grid with 960 cells of size AqA~= 0.2 X 15 ° ( I~/I < 4) is used and cells with transverse energies less than ET(min) = 0.6 GeV are ignored. The shaded region corresponds to only those W' (336) --*q(Tlevents in which the top two CDF clusters carry at least 80% of the total ET of all cells with ET > E r ( m i n ) (47% of the events). The mean values and the root-mean-square deviations, M + tr, resulting from this cut sample are enclosed in parentheses.

of the invariant mass removes the low-mass tail. For the CDF-cluster definition I have chosen, including the top four clusters works best but still results in an observed width of about 50 GeV. As for the UAl-jet case, selecting only a portion of the W'(336)--,q(:l events sharpens up the mass distributions slightly. The shaded region in the bottom row of fig. 5 arises from events in which the top two clusters carry at least 80% of the total ET of all cells with E T > E r ( m i n ) . Table 1 shows that this corresponds to 47% of the events and gives the results of several other cuts. This cut results in an observed width of the M1234 distribution of about 30 GeV which is the best I could achieve. The best case 428

obtained for the CDF-cluster method is comparable with the best case achieved using UA 1 jets. One may hope to discover other jet or cluster algorithms that improve the sharpness of the hadronic mass distributions, however, I think it unlikely that one can improve the situation dramatically. Because of the inherent nature of jets, an analysis of any particle produced in hadron-hadron collisions and decaying hadronically into a quark and an antiquark (or two quarks) will have an observed jet-jet mass width of at least 30 or 40 GeV regardless of how narrow the true mass width may be. Firstly, you can never be sure that the top two jets (or clusters) actually originate from the decaying particle. Some-

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Table I Mean values of the top two, top three, and top four UA1 jets and CDF clusters resulting from a pure (total) sample and from various selected (cut) subsets of the W' (336) -, q¢t events produced with a 3 GeV mass width in I~P collisions at 1600 GeV using a QCD partonshower Monte Carlo model. The _+ sign refers, not to the errors, but to the root-mean-square deviations from the mean, a. CDF clusters are defined using a transverse energy grid with 960 cells of size At/AO= 0.2 × 15 ° ( I~[ < 4). The UA 1-jet algorithm is applied directly to the particles themselves in the region It/I < 4 (exact). For the UA 1-jet case h~2= [ Ex (jet $1 ) + Ex (jet ~2 ) ]/Ex(tot), while for the CDFcluster case h~2= [ET(Cl ~1 ) +ET(Cl #2 ) ]/Ex( cut ), where Ev(cut) is the total Ex of all of the cells with Ex>ET(min). In both cases R~2= Ev (f~2)/Ex (t$1 ) and N(Ex > 10 GeV ) is the number of jets ( or clusters) in the event with ET > 10 GeV. ( All the masses are in units of GeV. )

UAI jets (exact)

CDF clusters, ET(min) =0.6 GeV

Event selection

Fraction

(Ml2)

(M123)

(M1234)

all W' (336)--.q£1 h~2>~0.80 RL2>~0.95 Njc,(ET> 10 GeV) -= 2 all W' (336) ~q~t h~2>~0.80 R~2>~0.95 Nc~(ET > 10 GeV) ~ 2

1.00 0.34 0.26 0.19 1.00 0.47 0.26 0.34

282+63 319+25 308+46 328+29 251_+63 291_+35 287_+52 282+55

340+59 348+31 346+45 344_+32 293_+57 313_+34 311_+49 297_+48

372+63 367+39 369+49

times one or both of the top two jets arises from bremsstrahlung off the initial quarks or gluons (type 1 and type 2 in fig. 1). Secondly, quite often the outgoing quark or antiquark splits into multiple jets and thus the top two jets reconstruct only a portion of the decaying-particles' invariant mass. Finally, even if there is no final-state splitting and you have captured the two jets associated with the decaying particle, there is an ambiguity as to the origin of the soft hadrons. There is no way to know which jet the soft hadrons belong to nor if they belong to either jet. Furthermore, the soft hadrons are important in reconstructing the true invariant mass of the decaying particle. I am still optimistic about doing "jet spectroscopy", however, one must realize that the reconstructed jet-jet (or cluster-cluster) mass distributions are going to be broad and the backgrounds from ordinary QCD parton-parton scattering large. This greatly restricts the production rates of the particles that will be able to be studied in this manner. I would like to thank T. Gottschalk for providing me with his initial state parton shower algorithm and for many useful discussions. In addition, I gratefully acknowledge helpful conversations with H. Frisch.

309_+55 320_+34 321_+48 306+44

References [ 1 ] R.D. Field and T. Gottschalk, paper in preparation. [2] M. Derrick and T. Gottschalk, Proc. 1984 DPF Snowmass Summer Study on the Design and utilization of the Superconducting Super Collider. [ 3 ] J. Huston, A comparison of the predictions of ISAJET and FIELDAJET for jet production and the SSC, Proc. 1984 DPF Snowmass Summer Study on the Design and utilization of the Superconducting Super Collider. [4] R.K. Ellis and J.F. Owens, Proc. 1984 DPF Snowmass Summer Study on the Design and utilization of the Superconducting Super Collider. [5] G.C. Fox and S. Wolfram, Nucl. Phys. B 168 (1980) 285; A gallimaufry of e+e - annihilation shapes, Caltech preprint CALT-68-723 (1979), unpublished; G.C. Fox, lectures 1981 SLAC Summer School, Caltech preprint CALT-68-863; G.C. Fox and R.L. Kelly, Caltech preprint CALT-68-890; and Proton-Antiproton collider physics, AIP Conf. Proc. No. 85 (1981); R.D. Field, G.C. Fox and R.L. Kelly, Phys. Lett: B 119 (1982) 439; M.P. Shatz, Caltech preprint CALT-68-1145 (1984), unpublished. [6] R. Odorico, Nucl. Phys. B 199 (1982) 189; Phys. Lett. B 118 (1982) 151; Nucl. Phys. B 228 (1983) 381. [ 7 ] R.D. Field, The production of patrons and hadrons in e+e annihilations - Quark and gluon jet models, preprint UFTP81-12; and Proc. Conf. on Perturbative QCD (Florida State University, 1981), AIP Conf. Proc. No. 74, Particle and Fields Subseries No. 24; Jet formation in QCD, invited talk XIII Intern. Symp. on Multiparticle dynamics (Volendam, The Netherlands, June 1982); UFTP-82-28 (1982).

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[8] G. Marchesini and B.R. Webber, Nucl. Phys. B 238 (1984) 1; B.R. Webber, Nucl. Phys. B 238 (1984) 492. [9] F.E. Paige and S.D. Protopropescu, preprint BNL 29777 (1980). [ 10 ] T. Gottschalk, A backwards evolution Monte Carlo model for initial state parton showers, Caltech preprint CALT-681241 (1985). [11] T. Sjostrand, Phys. Lett. B 157 (1985) 321.

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[ 12] R.D. Field, Nucl. Phys. B 264 (1986) 687. [ 13 ] R.D. Field and R.P. Feynman, Phys. Rev. D 15 (1977 ) 2590; Nucl. Phys. B 138 (1978) 1. [14] UAI Collab., G. Arnison et al., Phys. Lett, B 132 (1983) 214; UA 1 CoUab., J. Rohlf, contributions 1984 DPF Snowmass Summer Study on the Design and utilization of the Superconducting Super Collider. [ 15 ] H. Frisch and M. Schocket, CDF trigger notes, unpublished.