A Fermi National Accelerator Laboratory

FERMILAB-Pub-92/182-E

The Dijet Angular Distribution in pfiCollisions at ds = 1.8 TeV

F. Abe et al The CDF Collaboration

Fermi National Accelerator Laboratory, Bataoia, Illinois 60510

July 1992

# Opratad by UniverMties Research Association Inc. under Contract No. DE-ACOZ-76CH03.000 with the United States Department of Energy

Submitted to Physical Reuiew Letters

Disclaimer

This report u~as prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or seruice.by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof: The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof:

CDF/PUB/JET/PUBLIC/1743 FERMILAB-PUB-92/182-E

The Dijet Angular Distribution in pp Collisions at ,,/% = 1.8

TeV

F. Abe,(“) D. Amidei, C. A nway-Wciss,f3) G. Apollinari,tao) M. Ata=,

P. Auchincloss,(r9) A. R. Baden, N. B acchetta,(‘s) W. Badgett,(“) M. W. Bailey,(=)

A. Bamberger,(s+) P. de Barbaro,(rr’) A. Barbara-Galtieri,(‘r) V. E. Barnes,@)

B. A. Barnett,@) G. Bauer,(r3) T. Baumann,(s) F. Bedeschi,(“) S. Behrends,(‘)

S. Belforte,t”) G. Bellettini,(“) J. BeRinger, D. Benjamin,(“) J. Benlloch,ts+)

J. Bensinger, A. Beretvas,@) J. P. Berge,(s) S. Bertolucci,(r) K. Biery,(‘Q)

S. Bhadra,(‘) M. Binkley,(s) D. Bisello,(‘s) R. Blair,(‘) C. Blocker,(r) A. Bodek,(‘a)

V. Bolognesi,(“) A. W. Booth,(s) C. Bos~ell,@~) G. Brandenburg,(s) D. Brown,(s)

E. Buckley-Geer,(sl) H. S. Budd,(‘s) G. Busetto,(‘s) A. Byon-Wagner,(s)

K. L. Byrum, C. Campagnari,(s) M. Campbell,(“) A. Caner,(s) R. Carey,(s)

W. Carithers,(‘s) D. Carlsmith,f2s) J. T. Carroll,@) R. Cashmore,@+) A. Castro,(‘s)

F. CerveRi,(“) K. Chadwick,(s) J. Chapman,(“) G. Chiarelli,(r) W. Chinowsky,(‘r)

S. Cihangir,(s) A. G. Clark,@) M. Cobal, D. Connor, M. Contreras,(‘)

J. Cooper,(s) M. CordeRi, D. Crane,(*) J. D. Cunningham,(*) C. Day,(s)

F. DeJongh,fs) S. Dell’Agnello,(“) M. Dell’Orso,(‘r) L. Demortier,@) B. Denby,

P. F. Derwent,(“) T. Devlin,(rl) D. DiBitonto,@r) M. Dickson,@‘) R. B. Drucker,(‘a)

K. Einsweiler,(“) J. E. Elias, R. Ely,(‘r) S. Eno,(‘) S. Errede,@) A. Etchegoyen,(B+)

B. Farhat,tr3) B. Flaugher,(‘) G. W. Foster,@) M. Franklin,(*) J. Freeman,(s)

H. Frisch,(‘) T. Fuess,fs) Y. Fukui,f”) A. F. Garfinkel,(‘s) A. Gauthier,@) S. Geer,fs)

D. W. Gerdes,(‘) P. Giannetti,t”) N. Giokaris,@‘) P. Giromini,(‘) L. Gladney,t’s)

Submitted to Physical Review Letters June 30, 1992

i

M. Gold,(“) K. Goulianos,(*“l H. Grassmann, G. M. Grieco,(‘? R. Grin&y,@*@)

C. Grosso-Pilcher,(‘l C. Haber,@l S. R. Hahn,(s) R. Handler,(rs) K. Hara,(“sl

B. Harral,(*sl R. M. Harris,(s) S. A. Hauger,@l J. Hauser,t31 C. Hawk,tr’l

T. Hessing,(rrl R. Hollebeek,(‘sl L. H 11 o oway,fsl S. Hong,(“) P. Hu,12*l B. Hubbard,

B. T. Huffman, R. Hughes,(‘sl P. Hurst,(*) J. Huth,@l J. Hylen,(sl M. Incagli,t”71

T. Ino,tz31 H. Iso,(‘sl H. Jensen,@) C. P. Jessop,@l R. P. Johnson,(s) U. Jo&,(s)

R. W. Kadel,(*rl T. Kamon,faal S. Kanda,(r31 D. A. Kardelis,@l I. Karliner,(sl

E. Kearns,@l L. Keeble,(221 R. Kephart,(sl P. Kesten,(“l R. M. Keup,(‘l H. Keutelian,(sl

D. Kim,(e) S. B. Kim,t141 S. II. Kim,f2sl Y. K. Kim,(‘rl L. Kirsch,@l K. Kondo,(‘sl

J. Konigsberg,(sl K. Kordas ,(‘s+l E. Kovacs,(*l M. Krasberg,f”l S. E. Kuhlmann,(‘l

E. Kuns,(“l A. T. Laasanen,f’sl S. Lammel,f31 J. I. Lamoureux,(asl S. Leone,(“)

J. D. Lewis,tsl W. Li,(‘l P. Limon,(sl M. Lindgren,t31 T. M. Liss,@l N. Lockyer,(*s)

M. Loreti,(‘sl E. H. Low,f’sl C. B. Luchini,@l P. Lukens,(sl P. Maas,

K. Maeshima,(sl M. Mangano,I”l J. P. Marriner,(sl M. Mariotti,I*‘) R. Markeloff,(2sl

L. A. Markosky,tasl R. Mattingly, P. McIntyre,fZZl A. Menzione,f”l T. Meyer,tz21

S. Mikamo,f”l M. Miller,(‘) T. M’ lmashi,tz31 S. Miscetti,f7) M. Mishina,(“l

S. Miyashita,(a31 Y. Morita,ta31 S. Moulding,t21 J. Mueller,(“) A. Mukherjee,(s)

T. Muller,t3) L. F. Nakae,t’l I. Nakano,(‘sl C. Nelson,@) C. Newman-Holmes,(sl

J. S. T. Ng,f*l M. Ninomiya,fr’l L. Nodulman,(*l S. Ogawa,(r31 R. Paoletti,(“l

V. Papadimitriou,@l A. Para, E. Pare,@) S. Park,(s) J. Patrick,@) G. Pauletta,(171

L. Pescara,(*sl T. J. Phillips,(s) F. Ptohos,(sl R. Plunkett,(sl L. Pondrom,@l

J. Proudfoot, G. Punzi,t’71 D. Q uarrie,(sl K. Ragan,(‘s+l G. Redlinger,

.I. Rhoades,(rsl M. Roach,tz41 F. Ri mondi,ts*“l L. Ristori,t*‘l W. J. Robertson,(s)

T. Rodrigo,(‘l T. Rohaly,(*sl A. Roodman,f4) W. K. Sakumoto,(*s) A. Sansoni,(‘l

R. D. Sard,tsl A. Savoy-Navarro,(sl V. s carpine,@) P. Schlabach,(sl E. E. Schmidt,(s)

0. Schneider,@) M. H. Schub,(‘sl R. Schwitters,(*l A. Scribano,(*‘l S. Segler,(sl

Y. Seiya,Iz31 G. Sganos,t*s+l M. Sh apiro,(“l N. M. Shaw,I**l M. Sheaff,(rsl

M. Shochet,(‘l J. Siegrist,(“l P. Sinervo,(‘Ql J. Skarha,(‘s) K. Sliwa,t”‘l A. Spies,(*c)

D. A. Smith,(“) F. D. Snider,(*ol L. Song, tsl T. Song,(“) M. Spahn,(‘rl

P. Sphicas,1131 R. St. Denis, A. Stefanini,f”l G. Sullivan,(‘) K. Sumorok,(‘sl

R. L. Swartz, Jr.,@‘) M. Takano,cz31 K. Takikawa,fa31 S. Tarem,@) F. Tartarelli,(‘71

S. Tether,(131 D. Theriot, M. Timko,@‘l P. T’ t *p on,f181 S. Tkaczyk,(sl A. Tollestrup,tsl

J. Tonnison,Ilsl W. Trischuk,@l J. Tseng,(‘s) N. Turini, Y. Tsay,(‘l F. Ukegawa,tr’sl

D. Underwood,(‘) S. Vejcik, III,(‘“l R. Vidal,(sl R. G. Wagner,(‘) R. L. Wagner,(s)

N. Wainer,(sl J. Walsh,@‘) T. Watts,@‘) R. Webb,trsl C. Wendt,tasl H. Wenzel,(l’l

W. C. Wester, III,f’21 T. Westhusing, (‘1 S. N. White,(r”l A. B. Wicklund,

E. Wicklund,@ H. H. Williams,(‘61 B. L. Winer,f191 D. Wu,(141 J. Wyss,(‘sl A. Yagil,tsl

K. Yasuoka,@l Y. Ye,(*s*nl G. P. Yeh,(s) J. Yoh,(s) M. Yokoyama,@l J. C. Yun,(sl

A. Zanetti,(“) F. Zetti,(“l S. Zhang, (I41 S. Zucchelli,Is~“l

The CDF Collaboration

(1) A?gonnr Ndionol Laborotow, Argonne, IUinoia (IO4JP

0) Bmndria Unitwaitt), Walthmn, Murlrehwrtlr orrrd

(3) Universilv of Cafifomio at Lo, Anpdcr, Lor An&+ California DOOld

(4) Unierrnit~ of Chieap, Chicago, ~~inoir 80637

(6) Duke Unimnity, Durham, North Cwolina 17701

(61 Fe-i Ndional Accrlerdor Laboratory, Beta&, nlinoir (IOIIO

(‘I Lcrboraiori Nazimali di Fmacati, Ialifuto Nerionore di Fi&s Nuclcwc, Rsomli, Italy

@I Hmmrd Univemily, Cambridge, Ma~r~chwrtt~ OtlSB

(91 Uniwroily of IUinsir, [irbonq IUinoio dlSDI

PI The John, Hopkiw Unisbraily, Baltimore, Maryland fit118

(11) Ndiond Laboratory fo? High Energy Pkyaica (KEX), Jspm

WI Lmmencc Bwkrlry Labornlory, Berkeley, CaGfoifDmia 947tO

031 M.,rashlrrctt, In,rituk of Technolopy, C.mbridgr, Mmrrachwrtt, 01139

(14) Unincrrily of Michigan, Ann Arbor, Michigan ddlO0

(151 Univrraih di Padova. Inatituto No&n& di Firica Nualrere, Ssrionr di Padova, 1.56151 Padova, Italy

(4 Vniverrily of Pmnryhanio, Philadelphia, PennayAmis 19104

071 I~tilulo N&on& di Fiaim Nuclears, Unioersiip and Seaale Norm& Suprriore of Piea. I-68100 Pire, It&

(181 Purdue Vniw&g. Weat La,cwrlte, Indian. ,790,

(1~1 Dhimrdl~ of Boehrrtrr, Rochralrr, New York ICII7

PO1 Rockefdlr~ Uniwrril~, New York, New York 1DDLl

011 Brigerr U~i~srrit~, Piacatawry, New JIWLY 08854

WI Teaan ASM Unimrritv, Collrp SWion, Tews 77U3

(=I U&r+& of Tarkubo, Taukuba, Ibwaki 306. Japan

(34) Tuft8 Unioe+aity. Medford, Ma~~~chu~rtt~ OIldd

(=I Lmi~~rdu of Wirrmks, Mediaon, Wiarondn TS?O*

ABSTRACT

The dijet angular distribution is measured in the CDF detector at the Fer-

milab Tevatron Collider. This measurement covers higher mass ranges and

larger scattering angles than previously possible. Good agreement is observed

between the data and both leading order (O(al)) and next-to-leading (O(ai))

order QCD calculations. A limit on quark compositeness of A, > 1.0 TeV is

obtained.

The production of jets is one of the fundamental processes observed at pp colliders.

The properties of jet events are typically predicted at the parton level with leading

order QCD. The lowest-order QCD description of jet events refers to the case in

which a parton in each of the incoming hadrons participates in a collision and results

in two final state partons. The cross section for dijet events can be factorized, at

lowest order, into two terms, one of which depends on the structure functions and the

other on the center-of-mass scattering angle (0’). The structure function dependence

can be determined via the Feynman I calculated from the dijet mass (MJJ) and the

longitudinal boost of the dijet system (qbawrt). With the CDF jet data sample of 4.2

pb-‘, measurements of these quantities have been extended to higher masses and

larger angular regions than previously possible[l].

The description of events with more than two jets requires higher order calcula-

tions and the treatment of these events, bot,h experimentally and theoretically, is a

subject of ongoing development. Recently, O(of) calculations[2] have become avail-

able. These begin to account, at the parton level, for the radiation which can occur

from the scattered partons. This paper discusses the measurement of the dijet angu-

3

lar distribution, the comparison to O(a:) and O(a:) QCD predictions and & test for

quark substructure.

The CDF detector has been described in detail elsewhere[3]. For this analysis, the

relevant detector elements are the electromagnetic and hadronic calorimeters. The

calorimeters use a projective tower geometry, and they are divided into three regions

of pseudorapidity (q) with respect to the beam line: Central (0 5 171 5 1.3), Plug

(1.1 5 171 5 2.4), and Forward (2.2 5 171 5 4.2). The segmentation is z 0.1 units

of pseudorapidity throughout the calorimeter. In the azimuthal angle 4, the central

calorimeter has a segmentation of 1.5” while the plug and forward calorimeters have

a segmentation of 5O . An online cluster finder triggered the detector for events with

at least one jet above a transverse energy (ET E E sin 8, where 6’ is the polar angle.)

of 20 or 60 GeV. For the 60 GeV threshold, all events were written to tape. For the

20 GeV triggers, l/300 of the events passing the requirement were kept.

Jets are identified by the CDF clustering algorithm which has been described in

detail elsewhere[4]. This algorithm defines a cone in 7 - 4 space which has, for this

analysis, a radius of 0.7. For each calorimeter tower with ET >O.l GeV, we calculate

the four-momentum, treating the energy in the tower as if it were deposited by a

single massless particle. The towers which fall within the cone are then summed to

give a single four-vector for each jet. For this analysis, we only consider events which

have two or more jets with ET > 15 GeV. A similar algorithm is used for the O(a:)

calculations[2] where three partons exist in the final state. If two of the partons fall

within a cone, they are summed into one jet.

In both the measurement and the theoretical calculations, the dijet mass of an

event is defined in terms of the four-vectors of the two leading (highest ET ) jets. The

center-of-mass scattering angle and the longitudinal boost of the dijet system are

related to the pseudorapidities of these two jets (w and q1 ) by the equations Q-,* =

j(vl + ~a), and cos0’ = tanhT*, where q’ = ( f 71 - 711). The angular distribution

is plotted in terms of the variable[5] x = e’l”‘1. For pure Rutherford scattering of

massless psrtons (spin-l t-channel exchange), the dN/dx spectrum is flat.

At a given MJJ, the trigger threshold in single jet PT results in a IOSS of efficiency

at high x. This can be illustrated by the case in which there is no transverse boost

to the dijet system. The two jet PT ‘s would be equal and the dijet IIHLBB would be

related to the variable x by the equation MJJ = PT(& + l/A). To ensure an

efficient trigger (> 90%) over a large angular range, we require I~b,~l < 0.75 and

divide the data into mass bins of 240 < MJJ < 475 GeV (using the 20 GeV trigger),

475 < MJJ < 550 GeV and 550 GeV < MJJ (both using the 60 GeV trigger). We

restrict the analysis to 1~’ / <1.6 (x < 24) for the 240 c MJJ < 475 GeV and 550

GeV < MJJ bins, and 17’ 1 <1.5 (x < 20) for the 475 < MJJ < 550 Ge? bin. In

addition, we require that the event vertex along the beam axis be within 60 cm of

the nominal interaction point. After these cuts, we are left with 411, 903, and 541

events in the low, middle and high mass bins respectively.

The measured distribution, dN/dx , and the corresponding theoretical distribu-

tion, are each normalized to unit area and then a chi-square comparison is performed.

With this approach we are sensitive to the shape of the dN/dx distribution. Since

the relative energy scales of the calorimeters affect the shape of the acceptance, the

11 dependence of energy scale is the dominant source of systematic uncertainty.

To measure the relative response of the detectors at large pseudorapidity, jet PT

balancing is used. Events are selected by requiring that there be two and only two

jets with PT >15 GeV. To avoid trigger biases, the average jet transverse momentum,

PT , must be at least 5 GeV above the trigger threshold. Each jet in an event is then

labeled either “trigger”, meaning it is contained in the central region (0.2< 171 <0.7),

or “probe”, meaning it can be anywhere in n. With these cuts the central jet is

well contained in the central calorimeter where the absolute energy scale has been

extensively studied[6, 41. If both jets fall in the central region, a random assignment

of trigger and probe is made. Events with no jet in the central region are excluded

from this study.

The balancing is performed using the Missing & Projection Fraction (MPF),

MPF =gT. fiy” 14,

where fig” is a unit vector along the direction of the probe jet, and J&r, is defined

as the vector sum over calorimeter towers with ET > 0.1 GeV:

&=-BE&“,, i = calorimeter tower number with 1~1 < 3.6. (1) i

The unit vector 61 is perpendicular to the beam axis and points at the ith calorimeter

tower.

The component of & along the probe jet is measured by MPF, and should be

zero if the correct relative energy scale is used. By using the & of the event, rather

than the PT imbalance of the jets, the effects of any transverse boosts of the system

are minimized. The MPF is measured as a function of the 71 of the probe jet for five

bins of 4 . From this we derive a function which corrects the energy of each jet

based on the n and the PT of the jet. Figure 1 shows the MPF as a function of n

before and after the relative jet energy correction function has been applied for five

bins of PT . After the jet energy corrections, the relative energy scales are equal at

the l-2% level.

The absolute energy response for all jets is derived[4] from Monte Carlo jets gener-

ated in the central region and passed through a detector simulation. We determined

a correction which accounts for losses in jet energy in cracks between the calorimeter

towers and nonlinear response at low energy in the hadronic calorimeters. The effects

on the measured jet energy from the underlying event and from fragmentation parti-

cles falling outside the cone are model-dependent. We do not attempt to correct for

these effects.

To estimate the acceptance and its systematic uncertainties, a fast jet-detector

simulation was constructed by using the inverse of the relative energy scale correc-

tions, smearing the jet response with the resolution of the detector and adding an

estimate of the underlying event and transverse momentum of the system. The jet

directions are smeared in 7 and 4 with resolutions which are determined using a more

detailed Monte Carlo. The resolution in n leads to a resolution in x of ox/x * 5%,

however the flatness of the expected distribution at high x makes us insensitive to

the exact value of this smearing. After jet corrections were applied, Monte Carlo

studies indicated that the acceptance is flat in x and thus does not influence the

comparisons to theoretical calculations. Varying the relative energy scales in differ-

ent detector regions by zt2%, resulted in acceptance curves that deviated from flat at

the ~-IO% level. The resolutions in the different detector regions were independently

varied by *ZO% yielding no change in the shape of the acceptance. Systematic uncer-

tainties due to these changes were included in the chi-square comparison, along with

the bin-to-bin correlations. The statistical correlations induced by the normalization

condition were also included.

Figure 2 shows the data compared to O(a:) and O(af) calculations[‘l] for HMRSB[B)

structure functions with renormalization scale Q’ = (PT/~)‘. The error bars represent

the statistical uncertainty in the data. Table 1 contains the data with the statistical

uncertainty for the three mass bins. The absolute size of the systematic uncertainty

is small (S-10%), but the bin-to-bin correlations make them of roughly equal impor-

tance as the statistical uncertainties in the comparisons to theory. Table 2 sumrna-

rises the results of fits to the O(ai) and O(az) p d t re ic ions with renormalization scales

Q2 = (PT/2)’ and Qr = @. The renormalization scale is seen to make very little

difference in the confidence levels. Four sets of Morfin-Tung structure functions[9]

were also tested (S, Bl, B2 and E); they gave the same confidence levels as HMRSB

to within 2%.

In addition, a test for possible quark substructure has been done by comparing the

angular distribution to a model[lO] which adds a contact term to the leading order

QCD Lagrangian. This model predicts that, if quarks are composite structures, an

excess of events in the dN/dx distribution at low x and high MJJ would be observed.

We calculate the ratio R(7,24) of events with x < 7 to those ,with 7 < x < 24.

In the sample with MJJ > 550 GeV we find R(7,24) = ,374 f 0.036 f 0.040, or

R(7,24) < 0.46 at the 95% confidence level. The compositeness is characterized in

terms of the variable A,. Leading order calculations of compositeness with A. < 1.0

TeV would predict R(7,24) > 0.50, which is above our 95% confidence level upper

limit. To be exact, R(7,24) > 0.50 is excluded at the 99% confidence level. Figure 3

shows the data compared to the O(at) and O(aj) QCD curves and to the curve with

A. = 1.0 TeV. This result is less stringent than the A. > 1.4 TeV limit obtained from

the CDF inclusive jet cross section[6] however, it is an independent method with

different systematic uncertainties. Our result can be compared directly to previous

limits obtained from the dijet angular distribution[l] of A, > 0.33 TeV from an earlier

CDF data set, or A. > 0.41 TeV from the UAl collaboration at 4 = 630 GeV.

In summary, the dijet angular distribution has been measured over a large angular

region. Both O(af) and O(a3) al 1 t’ c cu a ions provide adequate representations of the

data. The agreement between the O(aj) calculation and the data is slightly better.

A limit on quark compositeness of A. >l.O TeV has been obtained.

We thank the Fermilab staff and the technical staffs of the participating insti-

tutions for their vital contributions. This work was supported in part by the U.S.

Department of Energy and National Science Foundation, the Italian Istituo Nazionale

di Fisica Nucleare, the Ministry of Science, Culture and Education of Japan, and the

Alfred P. Sloan Foundation. We also wish to thank D. Soper, S. Ellis and Z. Kunszt

for useful discussions and for providing the results of their calculations.

References

[l] P. Bagnaia et al.,(UA2 Collaboration) Phys. Lett. m, 283 (1984). G. Arnison

et al.,(UAl Collaboration) Phys. Lett. m, 494 (1985). G. Arnison et al.,(UAl

Collaboration) Phys. Lett. m, 244 (1986). F.Abe et al.,(CDF Collaboration)

Phys. Rev. Lett. 62, 3020 (1989).

[2] S. Ellis, Z. Kunszt and D. Soper, Phys. Rev, D @ 2188 (1989); Phys. Rev. Lett.

64,212l (1990).

[3] F. Abe et al (CDF Collaboration), Nucl. Inst. and Meth. A271 (1988) 387.

[4] F.Abe et aI.,(CDF Collaboration) Phys. Rev. D 45 1448 (1992).

[5] B. L. Cambridge and C. J. Maxwell, Nucl. Phys. m, 428 (1984).

[6] F.Abe et al.,(CDF Collaboration) Phys. Rev. Lett. 68:1104,1992.

[7] S.D. Ellis, Z. Kunsst and D.E. Soper; preprint OITS 495; to be submitted to

Phys. Rev. Lett.

[8] P. Harriman, A. Martin, R. Roberts and W. Stirling, Phys. Rev. D 42 798 (1990);

Phys. Lett. w, 421 (1990).

[9] J. Morfin and W.K. Tung, Z. Phys. C 52, 13 (1991).

[lo] E.Eichten, K. Lane and M. Peskin, Phys. Rev. Lett. 50,811 (1983).

0.3

.g 0.0

-g -0.3

L= 0.3

.z 0.0 Ti Q) -0.3 *- $ 0.3

J& 0.0

-0.3

0.3

0.0

-0.3

UNCORRECTED CORRECTED

25 < F, < 50 GeV

b I I I I I I -1 I I I I I I

:85<R<lOOGeV :85<&<100GeV f . . . . - - ..a &.0.+* +- _ -$4+.-w-+- ?

I I I I , 1 I -1 I I I I I I %,> 100 GeV F, >lOO GeV

. ’ - .-c’ry. f ‘.-*, f.0 *.%++b+.-

I I I I I 9 8 -1 I t I I I I -3-2-l fj 1 2 3 -3-2-l $j 1 ~2 3

Figure 1: The jet balancing variable, ,& projection fraction (MPF, see text), is plotted

as a function of I) before and after the jet energy corrections for 5 bins of PT . The 11 ‘s of

the structures in the uncorrected plot correspond to the boundaries between the different

calorimeters.

240<M,,<475 GeV

475<M,,<550 GeV

t 1 I I I t I I I I I I I , I I I , , 0 6 10 15 20

x Figure 2: CDF dijet angular distribution compared to O(af) and O(a:) QCD c&u-

laths.

- .

_ : 550 GeV<MJJ . ~1 ***a A,=l.O TeV J -o(4)

0.00 “““““““““‘I ’ ” 0 6 10 15 20

x

Figure 3: CDF dijet angular distribution compared to O(ai) QCD with and without

the addition of a contact term, Ae = 1.0 TeV, to represent quark substructure. The

O(a:) curve is also shown.

Table 1: Data and statistical uncertainties for the CDF dijet angular distribution, where columns A, B and C refer to Mass Bins: 240 < MJ, < 475, 475 < &f,, < 550 and 550 < MJJ Ge\ ively.

di A

5.3 f 1.1 3.1 i 0.8 3.9 f 0.9 5.1 f 1.1 3.6 f 0.9 4.3 IL 1.0 3.1 f 0.8 5.5 f 1.1 5.8 xk 1.1 4.1 f 1.0 2.9 f 0.8 4.6 II= 1.0 3.4 i 0.9 3.2 f 0.9 3.9 f 0.9 5.8 dz 1.1 4.1 f 0.9 5.4 f 1.1 4.4 f 1.0 5.1 f 1.1 3.9 * 1.0 3.7 i 0.9 5.5 f 1.1

,J 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5

Ndx (xl B

5.7 f 0.8 4.7 i 0.7 4.8 f 0.7 5.7 f 0.8 5.0 5 0.7 4.6 f 0.7 3.9 z!c 0.6 4.8 f 0.7 5.6 f 0.8 4.5 f 0.7 6.0 zt 0.8 5.8 zt 0.8 5.0 * 0.7 5.7 f 0.8 4.3 zk 0.7 6.1 & 0.8 5.6 i 0.8 5.6 f 0.8 6.5 f 0.8

-a 1

C 6.9 & 1.1 4.0 f 0.8 3.1 & 0.7 4.6 f 0.9 3.8 i 0.8 4.8 f 0.9 5.2 & 1.0 2.7 f 0.7 3.8 f 0.8 3.4 Ifr 0.8 5.7 f 1.0 3.9 h 0.8 3.7 f 0.8 4.8 f 0.9 3.8 If: 0.8 4.8 + 0.9 4.9 f 0.9 2.9 f 0.7 3.1 h 0.7 t.1 f 0.8 5.5 * 1.1 1.1 f 0.8 5.3 rt 1.c

Table 2: Confidence levels (%) for O(ai)and O(af) theory compared to the CDF dijet angular distribution.