Statistical errors only

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1 XVIII Physics in Collision Frascati, June 8th-9th, 998 Conference Proceedings, pp JET PHYSICS A. Akopian The Rockefeller University New York NY 002 USA ABSTRACT Recent measurements of the inclusive jet cross section, dijet cross section, dijet invariant mass distributions and strong coupling constant at TEVATRON, HERA and LEP colliders are presented in this paper. The comparisons with NLO perturbative QCD predictions are shown. In general consistency with QCD predictions is observed for a variety of processes and energy ranges. The observed discrepancies can be accommodated by the modications of parton distribution functions. Inclusive Jet Production at TEVATRON, p s = 800 GeV The inclusive jet cross section measured by CDF at p s = 800 GeV in the data agrees with the NLO QCD prediction up to a jet E t of 250 GeV. For E t above 250 GeV the measured cross section is higher than the NLO QCD prediction ). An independent measurement from data conrmed the high E t excess (Fig., Left). The inclusive jet cross section, measured by D experiment in (Fig.,Right) shows no signicant excess above NLO QCD prediction at high E 2) t. For the NLO QCD predictions CDF used EKS 3) with renormalization and factorization scale = E Jet t f, while D used JETRAD 4) Leading Jet with = Et f, where f is a multiplicative factor usually chosen as EKS and JETRAD use dierent approaches in the calculations but provide essentially the same result, since both of them are based on the same NLO matrix element calculations. Both experiments selected central jets, CDF in jj range , D in the range jj <0.5. D also measured the inclusive jet cross section in the CDF range for direct comparison of results.

2 Percentage (DATA-THEORY)/THEORY CDF Preliminary Run B (87 pb - ) with run A results overlayed NLO QCD CTEQ3M scale Et/ Statistical errors only Transverse Energy (GeV) Figure : Left: CDF inclusive jet cross section at p s = 800 GeV. There is agreement with NLO QCD predictions up to 200 GeV, and signicant excess at higher E t. Right: D preliminary result at p s = 800 GeV is consistent with NLO QCD predictions in both D and CDF ranges. D has recently reevaluated the systematic uncertainties and energy scale of the calorimeter. The nal systematic uncertainties are shown in Fig. 2(Left). Fig. 2(Center) shows the change in the cross section due to the dierent choices of: individual jet renormalization and factorization scale (Et is % at E t 420 GeV multiplicative factor for : 5% eect at 420 GeV vs E leading jet t ) dierence parton distribution function: CTEQ3M vs CTEQ4HJ 20 % at E t =450 GeV R sep (eective minimal distance between the jets) is 2:0 R cone for CDF and :3 R cone for D, where R cone is the size of the jet cone (R cone =0.7 for both CDF and D ) The dierence in cross section at jet E t = 450 GeV is about 2%. More than 20% of the discrepancy between theory and experiment can be accommodated by the choice of parton distribution function (pdf) in NLO QCD calculations. The CTEQ4HJ 5) pdf is the result of a global t by CTEQ which includes the CDF high E t inclusive jet data with an increased weight. The photon data were excluded from the t, but the agreement with other data sets which were included in the global t did not change signicantly. This t was obtained by a modication of the gluon distribution

3 . (E T jet /2)/(E T max /2) Scale Dependence 0.8 (E T max /4)/(E T max /2) (2.0*E T max )/(E T max /2) Scale Dependence.2. CTEQ4HJ/CTEQ3M R sep =2.0/R sep =.3 pdf fits Clustering Jet E T (GeV) Figure 2: Left: The updated estimates of D systematic uncertainties. The dominant contribution to the overall uncertainty is due to the energy scale uncertainty. Center: Calculated and measured cross sections can be aected by dierent choices of parameters. The most signicant possible change is due to the choice of parton distribution function in QCD calculations. Right: The direct comparison of CDF and D data. Two experiments agree within systematic uncertainties. function at large x. Fig. 2(Right) presents a direct comparison of the CDF and D measurements. Within systematic uncertainties there is overall agreement. The D data is about 0% lower than CDF; about 3% of this dierence is due to the dierent values of total inelastic cross section used by the experiments to estimate the integrated luminosity. 2 Dijet Production 2. Inclusive Dijet Production at TEVATRON The triple dierential cross section for inclusive dijet production presents a measurement of the same process as the inclusive jet production but in terms of dierent parameters. d The cross section 3 de td d 2, measured by the CDF experiment is presented in Fig.3. JE- Leading Jet TRAD with = Et f is used as NLO QCD calculation. One of the jets was required to be in range , the second jet can be in one of the following ranges: , ,.4-2., The dierential dijet cross section shows high E t excess, compatible with the one observed in inclusive jet production. Again CTEQ4HJ 5) pro-

4 Figure 3: Left: Right: Cross section normalized by the E n t, n varies with range of the second jet. vides the best agreement between NLO QCD calculations and the measurement. In the case when both jets are in the central region the agreement with NLO QCD predictions is better than when the second jet is in the forward region. This is because CTEQ4HJ is obtained by modication of the gluon distribution function in order to t better the CDF inclusive jet cross section (central jets). For the forward region, the higher values of correspond to dierent regions of x and Q 2, and pdf, obtained for central high E t jets, might be not as good when evolved to dierent x and Q Dijet Mass Distribution Dijet mass distribution was measured by both CDF and D experiments. q CDF calculated invariant dijet mass using 4?momenta of the two leading jets: M JJ = (E + E 2 ) 2? ( ~P + ~P 2 ) 2. High mass excess is seen in CDF data, Fig.4(Left). A better agreement with QCD predictions was obtained when CTEQ4HJ was used. Systematic uncertainties for this measurement are large. At D the dijet invariant mass was calculated by assuming massless jets: M JJ = p 2E t E t2 [cosh()? cos()]. There is a slight excess in the D invariant mass spectrum, Fig.4(Right), but within statistical and systematic uncertainties it is consistent with QCD predictions 6).

5 DØ Preliminary Jetrad CTEQ4M, µ = 0.5E T max R sep =.3, η <.0 (Data-Theory)/Theory (400) M JJ (GeV/c 2 ) Figure 4: Left: CDF dijet invariant mass distribution (jj < 2:0) shows an excess at the higher masses. Agreement with NLO QCD calculation is better when CTEQ4HJ is used. The systematic uncertainties in this measurement are large. Right: D invariant mass distribution also shows a slight excess but is in agreement with QCD predictions within statistical and systematic uncertainties. 2.3 New Resonance Searches The dijet invariant mass distribution is sensitive to particle resonances. CDF previously searched for particle resonances in dijet invariant mass spectrum without any avor tagging 7). A search for particle resonances decaying to b b pairs was recently performed by CDF. Theories beyond standard model such as TECHNICOLOR and TOPCOLOR assisted TECHNICOLOR 8), that explain the large top quark mass and suggest an alternative to Higgs mechanism of spontaneous electroweak symmetry breaking, introduce a number of new particles, which decay to b b pairs. The dijet invariant mass was measured for events where both leading jets were tagged as b?jets. Fig.5(Left) presents double b?tagged dijet invariant mass spectrum, compared with normalized Monte Carlo calculation of direct b b QCD production. The inset in Fig. 5(Left) shows no evidence for new particle resonances. Fig.5(Right) presents the upper limits of the resonance cross sections as a function of mass for a narrow resonance and for topgluon with dierent widths.

6 dσ/dm [pb/(gev/c 2 )] pb - CDF Preliminary Double tagged data (Data-N MC)/ N MC dσ/dm = A(-m/ s+cm 2 /s) N /m p 2 0 Statistical Errors Only Corrected for B-tag efficiency χ 2 /DF = Two Jet Mass (GeV/c 2 ) Two Jet Mass (GeV/c 2 ) σ Br{X bb - } (pb) σ Br{g T bb - } (pb) Limits on bb - Resonances CDF PRELIMINARY, 87.3 pb - 95% CL Upper Limit With Systematics Before Systematics Technirho Topcolor Z / Standard Z / Vector Gluinonium New Particle Mass (GeV/c 2 ) % CL Upper Limit With Systematics Before Systematics Γ/M=0.5 Excluded: 340 < M < M(g T ) (GeV/c 2 ) σ Br{g T bb - } (pb) σ Br{g T bb - } (pb) % CL Upper Limit With Systematics Before Systematics Γ/M=0.3 Excluded: 280 < M < M(g T ) (GeV/c 2 ) % CL Upper Limit With Systematics Before Systematics Γ/M=0.7 Excluded: 375 < M < M(g T ) (GeV/c 2 ) Figure 5: Left: The double b-tagged dijet cross section is compared with normalized MC model of the background QCD double b production. The inset shows no evidence for particle resonances. Right: Upper limits on new resonances are set for dierent mass ranges and width values. 2.4 Dijet Photoproduction at HERA At both H and ZEUS, the photoproduction processes were selected by requiring low 4?momentum transfer squared of the process (Q 2 <4 GeV 2 at H and Q 2 < GeV 2 at ZEUS). This requirement decreases the virtuality of the photon in e + p interaction. The photoproduction process can be divided in two subprocesses: direct process, where a quasi real photon directly interacts as a whole with a constituent parton in the proton. resolved process, where a quasi real photon constituent parton interacts with proton constituent parton. The photon parton distribution functions (AFG 0), GRV-HO ), GS96 2) ) combine both subprocesses in single pdf. Both experiments used these photon pdfs and CTE- Q4M 5) as proton pdf in their analyses. The jets were reconstructed with the xed cone algorithm. Fig.6 presents the dierential dijet cross section measured by ZEUS collaboration 9) as a function of jet. Predictions using a variety of photon pdfs and dierent values of R sep are shown by curves. The cross sections for the jets reconstructed with cone size 0.7 agree with the measured cross section and NLO QCD calculations, while for

7 cone size.0 a discrepancy with QCD predictions is observed in forward directions for jet E t thresholds 7 GeV. Two eects can contribute to the observed dierences: rst, the jets become broader as jet increases and E jet t decreases, second, the height of the pedestal is larger for forward jets with R =.0. Use of R =0.7 selects more collimated jets and suppresses the underlying event contribution. The H measurement (Fig.7) shows Figure 6: Dijet photoproduction measured by ZEUS. Curves correspond to dierent choices of photon pdfs, tiny error bars are statistical errors, bold bars are statistical and systematic uncertainties added in quadrature. Absolute energy scale uncertainty is shown separately as a band and is not included in error bars. For the jet cone size 0.7 agreement between NLO QCD calculations and measured dierential cross section is observed. Discrepancy with QCD predictions is observed for cone size.0 consistency with NLO QCD predictions for cone size 0.7 in the dierent bins of x jets, dened as the fraction of parent quasi photon energy carried by the jet 3). These data are used by the H collaboration to extract the eective photon pdf. 3 Inclusive Jet Production at p s =630 GeV The inclusive jet cross section had been measured by CDF and D collaborations at p s =630 GeV. According to the Naive Parton Model the dimensionless invariant cross section, E 3 t d 2 =de t d versus jet transverse momentum fraction, x T = 2E t = p s, is independent of center of mass energy p s. So, the ratio of the cross sections measured at two dierent p s as a function of x T is predicted to be unity. This statement is known as

8 Figure 7: Dijet photoproduction measured by H. Jets are reconstructed with xed cone algorithm, cone size 0.7. Data are presented for dierent range of x jets - energy of the jet as a fraction of parent photon energy. These data are used for extraction of the eective parton distribution function of the photon. the scaling hypothesis. In QCD, the parton distribution functions and coupling constant ( s ) evolve with the energy scale of the interaction. The evolution of pdf and s leads to violation of the scaling hypothesis. In 993 CDF published the ratio 4) (Fig. 8, Left) of the inclusive jet cross sections measured at p s =546 and 800 GeV. With 95% CL the scaling hypothesis was ruled out, however a discrepancy with NLO QCD prediction was observed. In 995 both CDF and D measured inclusive jet cross section at p s =630 GeV. The preliminary result from CDF (Fig. 8,Right) is consistent with CDF's published result. Comparison of inclusive jet cross section measured at p s = 800 GeV and p s = 630 GeV with NLO QCD predictions show (Fig. 9) that the 630 GeV data are the source of the discrepancy in the ratio for both CDF and D experiments. Here again, CDF uses E t (with multiplicative factor) of each individual jet as renormalization and factorization scale, while D uses the highest jet E t in the event. The combined plot (Fig. 9,Right) shows preliminary results from CDF and D. Both experiments are consistent within statistical uncertainties and systematic uncertainty of D. CDF is evaluating its systematic uncertainty. Both experiments are expected to produce the nal result soon.

9 CDF Data (PRL 70 (993)) Ratio of scaled cross-sections Ratio of Scaled Cross-Sections: 630 and 546 over Jet Xt Figure 8: Left: Ratio of cross sections at p s =546 over 800 GeV, scaling hypothesis is ruled out, however discrepancy with NLO QCD predictions are observed. Right: CDF preliminary result at p s =630 Gev over 800 GeV is consistent with the previous measurement. Discrepancy with NLO QCD at low x T is conrmed. 4 Measurement of the Ratio R 0 = (W + Jet)=(W Inclusive) CDF recently measured the ratio R 0 = (W + Jet)=(W Inclusive) as function of threshold on jet E t 5). Fixed cone algorithm with Rcone =0.4 was used for jet reconstruction. Jets were selected with jj <2.4, the threshold on jet E t was incremented from 5 to 95 GeV in steps of 5 GeV. The NLO QCD calculations were performed by DYRAD Monte Carlo. Results are presented in Fig. 0. Agreement between the measured ratio and NLO QCD predictions was observed for the dierent choices of pdf (Fig. 0,Left) and multiplicative factor in expression for renormalization and factorization scale = M W f, f = (Fig. 0, Center). Since the \W + Inclusive Jet" process has an additional strong vertex with respect to \W Inclusive" process, the ratio of the cross sections is expected to be proportional to s. Fig. 0(Right) shows that the measured ratio is insensitive to s. This is explained by the compensation of the contributions from hard scattering matrix element and pdf evolution at p s = 800 GeV 6).

10 .2 CDF: 630 GeV vs 800 GeV Ratio of Scaled Cross-Sections: CDF and DZero 3 DO/ CDF Jet Xt Figure 9: Both CDF (Left ) and D (Center ) show that data at p s =630 GeV are source of the discrepancy with NLO QCD predictions. Right: The ratio of the scaled cross sections. Renormalization and factorization scale is E t =2 for CDF and E lead:jet t =2 for D The experiments are consistent within statistical uncertainties and systematic uncertainty of D. 5 Measurement of s 5. Inclusive Jet Cross Section at p s =800 GeV The inclusive jet cross section measured by CDF at p s = 800 GeV was used for the extraction of s in the range of E t from 40 to 250 GeV. The inclusive jet cross section at NLO level was expanded in powers of s : d(e t ) de t = 2 s()a(e t ) + 3 s()b(e t ) where d(et) de t is the measured cross section, A and B are coecients obtained from JE- TRAD NLO QCD calculations. By solving this equation at each E t value, s (E t ) was extracted. Fig. presents the extracted values of s (E t ) and recalculated s (MZ); 2 CTE- Q4M was used for the calculation of coecients A and B. Only experimental systematic uncertainties are shown on Fig. (Left). Since the evaluation of pdf itself depends on s, this measurement is a consistency check. The extracted s value versus input s, presented on Fig. (Right), gives an estimate of theoretical uncertainty of this method. The extracted values of s are: CTEQ4M : s (M 2 Z) = 0:52 0:000(stat:) +0:0083?0:0093(syst:)

11 R 0 = σ(w + jets)/σ(w + 0 jets) CDF PRELIMINARY MRSA / CTEQ4M CDF Data (08 pb - ) 0.4 Jet Cones, η d < 2.4 DYRAD NLO QCD Predictions with jet smearing Q 2 r = Q2 f = M 2 W Jet E T min (GeV) (R 0 (Data) R 0 (QCD)) / R 0 (QCD) CDF PRELIMINARY Q r = Q f = 0.5 M W Q r = Q f = M W Q r = Q f = 2.0 M W CDF Data (08 pb - ) 0.4 Jet Cones, η d < 2.4 DYRAD NLO QCD Predictions with jet smearing MRSA /, Q r = Q f = M W Jet E T min (GeV) R 0 R CDF Preliminary CDF Data (08 pb - ) 0.4 Jet Cones Stat. only Stat. + Syst. DYRAD NLO QCD Predictions (Q r = Q f = M W ) MRSA Family CTEQ4 Family Jet E T min = 30 GeV Jet E T min = 60 GeV α s (M Z ) Figure 0: The R 0 measured at CDF is compared with NLO QCD predictions. Left: R 0 versus jet E min t is consistent with QCD calculations with dierent choices of pdf. Errors are correlated since the plot is integrated over jet E t : R 0 ( E t ). Center: Fractional dierence between R 0 ( E t ) and NLO QCD predictions for dierent values of multiplicative factor in renormalization and factorization scale: = (0:5? 2:0) M W. The measurement is in good agreement with QCD predictions over entire range of E min t. Right: R 0 ( E min t ) at E min t =30 GeV and 60 GeV are calculated for dierent pdfs(dots and squares) and for dierent values of s (M Z ). The bands show CDF measurements at the corresponding E min t. This result shows that R 0 is insensitive to s at p s = 800 GeV. (See explanation in the text.) 5.2 DIS processes at HERA CTEQ4HJ : s (M 2 Z) = 0:59 0:000(stat:) +0:0084?0:0099(syst:) The rate of dijet events was measured at HERA. The ratio R dijet =R total was expanded in powers of s in the NLO QCD calculations, and the equation was solved for dierent values of jet E t. The jets were reconstructed using a modied JADE algorithm. The value of s measured by H is s (MZ) 2 = 0:5 0:003(stat:) +0:008?0:0(sys:). This result is consistent with world average value. About 4% variation in measured s was observed depending on the cluster merging scheme: E-scheme (4-momentum of resulting cluster is the sum of 4-momenta of the two clusters) and P-scheme (momentum of resulting cluster is the sum of momenta of the cluster, and the energy is the sum of the weighted energies of the two clusters).

12 CDF Preliminary CDF Preliminary α s (M Z ) = / (exp.stat) weighted average over E T region GeV MRSA CTEQ4A MRS R CTEQ4HJ α s α s (E T ) as function of E T α s (M Z ) as function of E T output α s (M Z ) CTEQ4M parton distributions, µ=e T /2 Input α s (M Z ) = Total Systematic Uncertainty (GeV) Transverse Energy input α s (M Z ) Figure : Left: Extracted value of s, CTEQ4M is used in JETRAD for calculation of A and B. Stars show the running behavior of s, the dots represent the s (MZ) 2 as function of jet E t. Only experimental uncertainties are shown (band). Right: JETRAD uses \input" value of s (MZ) 2 for calculation of coecients A and B. The extracted, \output" value of s is shown versus \input" value of s (MZ). 2 This plot gives an estimate of the order of theoretical uncertainty of the method. 5.3 e? e + scattering at LEP, p s = 83 GeV Experiments at LEP use Power Correction 7) technique for extraction of s. Theoretical calculations of event shape variables were improved by incorporating the analytical calculations of the non-perturbative hadronization corrections. The mean value of event shape variable was presented in the form: <F >=<F > pert + <F > power. The perturbative part was expanded in the series of s : < F > pert = A s (Q) + B 2 s(q). The non-perturbative part, the power correction, was calculated by introducing a single non-perturbative parameter, which was measured from experiment: < F > power = f( 0 ( I ); 2 s(q)), where 0 ( I ) is a non-perturbative parameter, which can be interpreted as an eective strong coupling below an \infrared safe" scale I, QCD I Q. Fig. 2(Left) presents the comparison of the averages of measured Thrust, T = max( P h jp hnj= P h jp hj) and jet mass (as a fraction of visible energy, M 2 h=e 2 vis) with theoretical predictions for dierent center of mass energies. For both variables the measurements are in good agreement with the calculations including power correction. The perturbative part depends on the value of s. The extracted value of s is the one which provides the best t of perturbative calculation (with power correction) to the experimental data. The extracted s for dierent values of renormalization and factorization scale Q is shown on the Fig. 2(Right) 8).

13 Observable (arbitrarily normalised) f pert. +f pow. f pert. DELPHI ALEPH OPAL L3 SLD TOPAZ AMY TASSO PLUTO CELLO MK II HRS α s (E cm ) DELPHI α s determined with Dokshitzer Webber ansatz (statistical errors only) World average (PDG 996) 4 <-T> <M 2 h /E 2 vis> DELPHI DELPHI E cm /GeV E cm /GeV Figure 2: Left: The average values of <? T c > and < Mh=E 2 2 vis > are compared with perturbative QCD predictions and the best t of pqcd plus power corrections at dierent values of renormalization and factorization scale. Right: The extracted s follows the QCD predictions. At p s = 83 GeV the s (83GeV) = 0:06 0:0082 0:0025 0:0033 which translates to the s (M Z ) = 0:227 0:00 0:0030 0:004. The event variables measured in DIS processes at HERA by H 9) also showed better agreement with QCD calculations when power corrections were included, but higher orders of QCD calculations are needed for precise measurements of s. 6 Direct Photons Direct photon production processes, gq! q and qq! q, have the advantage of being free of fragmentation ambiguities. The dominance of the gq! q process provides an opportunity to extract the gluon distribution function, G p (x; Q 2 ). Recently D analyzed the data with improved acceptance estimate, recalibrated calorimeter response and improved background suppression. Previous data 20), taken in agree with the recent result when analyzed in a consistent manner. Fig. 3 presents the comparison of D and CDF measurements 2) of the dierential direct photon cross section for jj <0.9. D data are consistent with NLO QCD predictions and CDF measurement over entire D range of photon E t. CDF, however, has data at lower E t (< 25 GeV), which are

14 d 2 σ/de T dη (pb/gev) (Data - Theory) / Theory E T (GeV) Figure 3: D result agrees with NLO QCD predictions and CDF measurement for the entire E t range of D. CDF measurements for E t below 25 GeV indicate systematic oset above NLO QCD. systematically above the QCD predictions. 7 Conclusion Measurements of inclusive jet cross sections, dijet distributions, extraction of strong coupling constant from dierent experiments at dierent center of mass energies show good agreement with Next to Leading Order QCD predictions. In some cases the discrepancies could be accommodated by modications of pdf. The theoretical uncertainties are of the order of 20%. In general higher orders of perturbative calculations and corrections for non-perturbative eects are needed to confront the precise measurements. References. CDF Collaboration, F.Abe et al., Phys. Rev. Lett (996) 2. D Collaboration, S.Abbott et al., submitted to Phys. Rev. Lett., hep-ex/ S. Ellis. Z. Kunszt, and D. Soper, Phys. Rev. Lett (989), Phys. Rev. Lett (990) 4. W. T. Giele, E.W.N. Glover and D.A. Kosower, Nucl. Phys. B (993) 5. H.L.Lai et al., Phys. Rev. D (997)

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