ÁREA MODULAR ÉTICO-INSTITUCIONAL

In order to study the systematic effects of the jet and event selection requirements, and the various corrections that are applied to the data, a series of systematic studies was per- formed. For each requirement or correction, we measured the effect on the angular distribution by varying the requirement or correction by an appropriate amount.

To determine the systematic uncertainties on the shape of the angular distribution, each distribution is fit with a func- tion:F!A&B0&C/0&D/02_&E/03_{. The effect of varying}

each of the selection criteria or corrections is measured by taking the ratio of the distribution with the nominal selection criteria, and with the adjusted criteria !Fig. 71", giving the size of the systematic uncertainty.

The largest source of uncertainty involves the ' depen- dence of the jet energy scale. Small uncertainties in the rela- tive response as a function of ' have large effects on the TABLE XXVII. Uncertainty correlations in the ratio of cross

sections. ‘‘0’’ indicates no correlation, ‘‘1’’ indicates complete cor- relation.

Uncertainty source Correlation in Comments

!

Luminosity Partial 1

Filter match 0 1 1800 GeV only

Event cuts 0 0 Jet cuts 0 0 Resolution Fits Partial 1 Closure 1 1 Unsmearing fits 0 1 Energy scale Offset Partial 1

Response fit 1 Partial

Response at 630 GeV 0 1

Showering 1 1

FIG. 65. The correlation matrix for the ratio of cross sections. Axes indicate the bin numbers.

TABLE XXVIII. Percentage uncertainties in the ratio of inclusive jet cross sections at

!

xT Statistical Jet selection Trigger match Luminosity Trigger efficiency Unsmearing Energy scale Total

0.07 1.5 1.1 1.7 4.1 2.4 6.6 9.5 12.7 0.08 2.4 1.1 1.7 4.1 0.9 4.2 7.4 9.7 0.09 3.5 1.1 1.7 4.1 0.3 2.7 6.0 8.0 0.11 1.9 1.1 1.1 4.1 0.6 1.9 5.0 7.0 0.12 2.7 1.1 1.1 4.1 0.2 1.3 4.4 6.3 0.13 3.5 1.1 1.1 4.1 0.1 1.0 4.0 6.0 0.14 4.9 1.1 1.1 4.1 0.0 0.8 3.7 5.8 0.15 5.8 1.1 0.0 4.1 0.0 0.7 3.4 5.5 0.16 7.3 1.1 0.0 4.1 0.0 0.7 3.2 5.4 0.17 2.4 1.1 0.0 4.1 1.1 0.7 3.2 5.4 0.18 3.0 1.1 0.0 4.1 0.4 0.7 3.2 5.4 0.19 3.5 1.1 0.0 4.1 0.2 0.7 3.3 5.4 0.21 4.4 1.1 0.0 4.1 0.1 0.8 3.4 5.5 0.22 5.1 1.1 0.0 4.1 0.0 0.8 3.5 5.5 0.23 6.2 1.1 0.0 4.1 0.0 0.8 3.7 5.6 0.24 7.3 1.1 0.0 4.1 0.0 0.8 3.9 5.8 0.25 8.5 1.1 0.0 4.1 0.0 0.9 4.1 5.9 0.27 6.6 1.1 0.0 4.1 0.0 1.0 4.7 6.4 0.32 11.0 1.1 0.0 4.1 0.0 1.1 6.3 7.7 0.43 20.5 1.1 0.0 4.1 0.0 1.3 8.7 9.7

angular distribution. The uncertainties in the jet energy scale are less than 2% up to an!'! of 2.0 and become large near

!'!>3.0. The uncertainty in the showering correction is less than 2% for !'!%2.0 and becomes large at high !'!. The effect of the '-dependent energy scale uncertainties are given in Fig. 72!a".

The resolution of our measurement of the jet energy can also affect the angular distribution. This was determined by measuring the difference between the smeared and un- smeared theory calculations. Since we are not unsmearing the data for the effects of' andETsmearing, we apply this as an uncertainty in the measurement$Fig. 72!b"%.

The effect on the angular distribution due to the' bias in the jet reconstruction algorithm !Sec. III G" was studied by applying a correction for the bias. The difference between the corrected and uncorrected distributions was 1% on aver- age$Fig. 72!c"%.

The overall energy scale does not affect the shape of the distribution, because a shift in the overall energy scale shifts the entire distribution in mass. The angular distribution changes very slowly with mass, so a small shift would not cause a significant change in the shape.

For the Jet_30 and Jet_50 triggers, an onlineMITOOL!see Sec. VII"requirement was used in the trigger for part of the run. To determine if the MITOOL requirement biased the an-

0.122–0.133 0.127 1.59)0.06 6.0 0.133–0.144 0.139 1.48)0.07 5.8 0.144 –0.156 0.150 1.63)0.09 5.5 0.156 –0.167 0.161 1.64)0.12 5.4 0.167–0.178 0.172 1.64)0.04 5.4 0.178 –0.189 0.183 1.62)0.05 5.4 0.189–0.200 0.194 1.67)0.06 5.4 0.200–0.211 0.205 1.60)0.07 5.5 0.211–0.222 0.216 1.74)0.09 5.5 0.222–0.233 0.228 1.69)0.10 5.6 0.233–0.244 0.239 1.78)0.13 5.8 0.244 –0.256 0.250 1.81)0.15 5.9 0.256 –0.300 0.271 1.74)0.11 6.4 0.300–0.356 0.319 1.85)0.20 7.7 0.356 –0.622 0.432 1.83)0.38 9.7

FIG. 66. The ratio of dimensionless cross sections for!'!%0.5 compared with JETRAD predictions with 5!0.5E_Tmax and the

CTEQ3M, CTEQ4M, CTEQ4HJ, and MRST PDFs. The shaded band represents the )14 systematic uncertainty band about the prediction.

TABLE XXX. The calculated02_{for the ratio of cross sections} !20 degrees of freedom".

PDF Renormalization scale 02 _Prob.

2E_Tmax 17.9 60% ETmax 21.6 36% CTEQ3M 0.75ETmax 23.1 28% 0.5ETmax 20.5 43% 0.25E_Tmax 15.1 77% CTEQ4M 0.5E_Tmax 22.4 32% CTEQ4HJ 0.5E_Tmax 21.0 40% MRST 0.5E_Tmax _{22.2 33%} MRST(g_↑) 0.5ETmax 19.5 49% MRST(g↓) 0.5ETmax 24.1 24%

FIG. 67. The ratio of dimensionless cross sections for!'!%0.5 compared withJETRADpredictions with various values of5and the

CTEQ3M PDF. The shaded band represents the )14 systematic uncertainty band about the prediction.

gular distribution, runs with no MITOOL requirement were compared to runs with the requirement. A small shape differ- ence was seen and an uncertainty equal to the difference between the two measurements was assigned.

The effects of multiple interactions on the distributions were studied. A secondary interaction adds approximately 0.6 GeV ofETper unit+'#+,!Fig. 20". Since the angular distribution is measured in regions in which theET’s of the two leading jets are in excess of 50 GeV and are often above 100 GeV, the effect of this additional energy on the two leading jets is minimal. It is possible that a second interac- tion may produce a vertex which is incorrectly used as in the primary vertex for the leading two jets. This would cause an error in the measured ' positions of the jets as well as the measured ETof the jets. We studied the effect of not select- ing the primary vertex by minimizing the ST in the event

!Sec. VII". This has a negligible effect on the angular distri- bution.

It is possible that the vertex produced by a second inter- action is the only vertex found in the event. This would also cause an error in the measured' andET values of the jets. We studied the possibility of multiple interactions affecting the angular distribution in this manner by the following

method. For a determined percentage of events, we switched the vertex to a randomly chosen vertex. The new vertex was based on the measured vertex distribution, which has an ap- proximate mean ofz!0 and a4>30 cm. We then recalcu- lated the ' andET of the two leading jets in the event and measured the angular distribution. The percentage of events with a new vertex was determined based on the efficiency of vertex reconstruction for events with largeETjets (>70%), and the percentage of multiple interactions in the data used for this analysis (>60%). The number of vertices switched was 20%, which is an estimate of the number of times that the vertex reconstruction is incorrect. The size of the effect is less than 2% and is dependent on the value of 0 $see Fig. 72!d"%.

The jet quality requirements and their corresponding effi- ciency corrections are necessary to remove noise from the event sample. Their effect on the shape of the angular distri- bution is minimal.

The DØ jet algorithm allows for the splitting and merging of jets. This can cause a shift in the ' of the jet, and there- fore affect the angular distribution. The effect on the shape of the distribution of removing those events in which either of the leading two jets were split or merged is minimal. Since the theoretical predictions are expected to properly address TABLE XXXI. 02 _{comparisons for the ratio of cross sections}

for !'!%0.5 where the renormalization scale is mismatched be- tween c.m. energies.

PDF Renormalization scale

630 GeV 1800 GeV 02 _Prob.

2E_Tmax _0.5E

T

max _{14.9 78%}

CTEQ3M ETmax 0.5ETmax 17.2 64%

0.25ETmax 0.5ETmax 23.1 28%

FIG. 68. The ratio of dimensionless cross sections for!'!%0.5 compared with JETRADpredictions with 5!0.5E_Tmax at

!

GeV, 5!(0.25,1.0,2.0)E_Tmax _at

!

PDF. The shaded band represents the)14 systematic uncertainty band about the prediction.

TABLE XXXII. Normalization-only predictions for the ratio of cross sections and the02_{comparison with the data (1.60)0.08 for}

one degree of freedom".

PDF Renormalization scale Theory

normalization 02 _Prob. 2E_Tmax 1.75 3.3 6.8% E_Tmax _{1.82 7.1 0.8%} CTEQ3M 0.75ETmax 1.87 10.7 0.1% 0.5ETmax 1.85 9.5 0.2% 0.25E_Tmax 1.70 1.5 22.9% CTEQ4M 0.5ETmax 1.90 13.2 0.03% CTEQ4HJ 0.5E_Tmax 1.87 10.7 0.1% MRST 0.5E_Tmax 1.89 12.6 0.04% MRST(g_↑) 0.5ETmax 1.87 11.1 0.09% MRST(g_↓) 0.5ETmax 1.90 12.9 0.03% 630 GeV 1800 GeV 2ETmax 0.5ETmax 1.46 2.7 10.2%

CTEQ3M E_Tmax 0.5E_Tmax 1.71 1.8 18.1%

0.25E_Tmax 0.5E_Tmax 1.44 3.7 5.4%

TABLE XXXIII. The cut on theETof the leading jet to ensure

that the trigger is 100% efficient.

Trigger CorrectedETlimit on leading jet!GeV"

Jet_30 55.0

Jet_50 90.0

Jet_85 120.0

merging and splitting, no uncertainty was assigned due to this effect.