Recent Results on Jet Physics and α s

Recent Results on Jet Physics and α s XXI Physics in Collision Conference Seoul, Korea June 8, Presented by Michael Strauss The University of Oklahoma

Outline Introduction and Experimental Considerations Jet and Event Characteristics Low E T Multijet Studies Subjet Multiplicities Cross Sections Three-to-Two Jet Ratio Ratio at Different Center-of-Mass Energies Inclusive Production DiJet Production

Motivation for Studying Jets Investigates pqcd Compare with current predictions pqcd is a background to new processes Investigates parton distribution functions (PDFs) Initial state for all proton collisions Investigates physics beyond the Standard Model d σ de T dη pdf? Compositeness? Central η region E T

Developments in Jet Physics (with proton initial states) Inclusion of error estimates in the PDFs calculation of virtual corrections Progress toward NNLO predictions covariance matrices More rigorous treatment of experimental errors jet algorithms workshop More consistent E T calculations between experiments at the Tevatron

Cone Definition of Jets Centroid found with 4-vector addition Cone Definition R=.7 in η φ Merging and splitting of jets required if they share energy R= η + ϕ η = -ln[tan(θ/)] R.3R R sep required to compare theoretical predictions to data (R sep is the minimum separation of partons to be considered distinct jets)

k T Definition of Jets d d ij ii = = min( i E T i E T, j E T ) R D ij k T Definition cells/clusters are combined if their relative k T is small (D=. or.5 is a scaling parameter) min(d ii, d ij ) = d ij Merge min(d ii, d ij ) = d ii Jet Infrared Safe Same definition for partons, Monte Carlo and data Allows subjet definitions

k T and Cone Algorithm Use CTEQ4M and Herwig Match k T jets with cone jets Number of matched jet pairs 4 3 DO Preliminary p T (k jet) - E T (cone jet) (GeV) 8 7 6 5 DO Preliminary...3.4 R(k jet, cone jet) 5 5 p T of k jet (GeV) 99.9% of Jets have R<.5 p T of k T algorithm is slightly higher

k T Algorithm and Subjets * For subjets, define large k T * Beam Beam min( i R j ij E T, ET ) > D (y cut = -3 ) y cut E T ( jet) Beam Beam * * Beam Beam * Increasing y cut

Jet Selection Criteria Typical selections on EM fraction, hot cells, missing E T, vertex position, etc. Outer Muon Magnet Inner Muon Hadronic Calorimeter > 97% efficient > 99% pure EM Calorimeter Central Tracking e γ jet µ noise

Jet Energy Corrections d σ de T dη E T Response functions Noise and underlying event Showering no distinction between jets of different kinds d σ de T dη E T Resolutions: Uncertainty on E T Estimated with dijet balancing or simulation Important for cross section measurement Observed Cross Section

Jet and Event Quantities Low E T Multijet Studies Subjet Multiplicity

D Low E T Multijet events At high-e T, NLO QCD does quite well, but the number of jets at low-e T does not match as well. (Comparison with Pythia) Each jet s E T > GeV. Theory normalized to -jet data >4 GeV. DIFFERENTIAL CROSS SECTION (µb/gev) - - -3-4 - - -3 E T of Leading Jet (a) PRELIMINARY (b) PRELIMINARY 5 5 5 5 E T (GeV) ( jet) E T (GeV) ( jet) (c) (d) PRELIMINARY - - -3 - -3 PRELIMINARY Looking also at Jetrad and Herwig -4 5 5 E T (GeV) ( 3 jet) -4 5 5 E T (GeV) ( 4 jet)

D Low E T Multijet events Strong p T ordering in DGLAP shower evolution may suppress spectator jets in Pythia BFKL has diffusion in THREE JETS PRODUCTION log(p T ) SYSTEMATIC (DATA-THEORY)/THEORY UNCERTAINTY 5 4 3 - - 5 4 3 (a) PRELIMINARY E T (GeV) ( jet) (c) PRELIMINARY 5 4 3 - - 5 4 3 (b) PRELIMINARY E T (GeV) ( jet) (d) PRELIMINARY jet-"spectator" - - final state radiation - E T (GeV) ( 3 jet) - E T (GeV) ( 4 jet) (a) (b) (c)

D Subjet Multiplicity Using K T Algorithm Monte Carlo! Perturbative and resummed calculations predict that gluon jets have higher subjet multiplicity than quark jets, on average.! Linear Combination: Mean Jet Multiplicity <M> = f g M g + (-f g ) M Q Gluon fraction f.8.7.6.5.4 DO Preliminary 8 GeV 63 GeV Gluon Jet Fraction Quark Jet Fraction.3 5 54 56 58 Minimum parton p T (GeV)

D Subjet Multiplicity Using K T Algorithm! Assume M g, M Q independent of s! Measure M at two s energies and extract the g and Q components Normalized number of jets.4.3...3.. DO Preliminary HERWIG + full detector simulation (a) Gluon jets Extracted Tagged, 8 GeV Tagged, 63 GeV (b) Quark jets 4 6 8 Subjet multiplicity M

D Subjet Multiplicity Using K T Algorithm Raw Subjet Multiplicities Extracted Quark and Gluon Mutiplicities Normalized number of jets.4.3.. 55 < p T (jet) < GeV η(jet) <.5 M 8 =.74 ±. M 63 =.54 ±.3 8 GeV 63 GeV Normalized number of jets.6.4. 55 < p T (jet) < GeV η(jet) <.5 DO/ data Gluon jets Quark jets DO Preliminary DO Preliminary 4 6 8 Subjet multiplicity M 4 6 8 Subjet multiplicity M Higher M more gluon jets at 8 GeV

D Subjet Multiplicity Using K T Algorithm R R =.84 ± M M HERWIG prediction =.9±.6(stat) Coming soon as a PRD g Q.5 (stat). - +.6 Largest uncertainty comes from the gluon fractions in the PDFs (syst) Normalized number of jets: Theory-DO/..5 -.5 -...5 -.5 -. DO/ Preliminary 55 < p T (jet) < GeV η(jet) <.5 Gluon jets Quark jets DO/ data MC data Forshaw & Seymour 3 4 5 Subjet multiplicity M

ZEUS Subjet Multiplicity Comparison at hadron level Unfolded using Ariadne MC n sbj = N jet N jet k = ( n sbj ) k <n sbj > (y cut ) 5 4.5 4 3.5 ZEUS Parton/Hadron corr < 5 % <n sbj > (E T,jet ).9.8.7.6 ZEUS Parton/Hadron corr < 5 % 3.5.5.5.4.3. -3 - - y cut 5 5 3 35 4 45 5 E T,jet (GeV) NLO QCD describes data Sensitive to α s

α s from ZEUS Subjets n sub - ZEUS Proportional to α s Major Systematic Errors "Model dependence (-3%) "Jet energy scale (-%) Major Theoretical Errors "Variation of renormalization scale α s M z ( ) =.85 ±.6 (stat) +.67 -.48 (syst) +.89 -.7 (th)

Cross Sections Inclusive cross sections Rapidity dependence K T central inclusive R 3 63/8 ratio of jet cross sections Di-Jets α s Conclusions

Jet Cross Sections P P ( x ) f µ a / A, F ( x ) f µ b / B, F x P x P (, ) ˆ σ α s µ R jet X How well are pdf s known? Are quarks composite particles? What are appropriate scales? What is the value of α s? σ ( pp jet + X ) = Is NLO (α s3 ) sufficient? abcx dx dx fa A fb B σ ˆ( ab cx )

CTEQ Gluon Distribution Studies Momentum fraction carried by quarks is very well known from DIS data Fairly tight constraints on the gluon distribution except at high x Important for high E T jet production at the Tevatron and direct photon production

Experimental Differential Cross Section 3 E d σ d ˆ σ = xf ( x) xf( x) ( ab cx ) 3 dp dtˆ = = = 3 d σ d cosθ dx d de 3 T π E σ = dη T E T dx π E T N η ε d de T Ldt σ dη Theoretical cross section Physics variables are θ and x Detector measures E T and η Counting experiment with detector inefficiencies

CDF Inclusive Jet Cross Section. < η <.7 Complete χ calculation Inclusive Jet cross section (D-T)/T 5 Inclusive Jet Cross Section (CDF Preliminary) CTEQ4M nb/gev - CDF Preliminary 994-95 99-93 NLO QCD prediction (EKS) cteq4m µ=e t / R sep =.3-5 5 Statistical Errors only 5 5 5 3 35 4 CTEQ4HJ - -3-5 5 5 5 3 35 4-4 -5 Statistical Errors Only 5 MRST -6 5 5 5 3 35 4 Transverse Energy (GeV) PRD 64, 3 () -5 5 5 5 3 35 4 GeV

x-q Measured Parameter Space From D Inclusive Cross Section Measurement Q (GeV ) 6 5 4 3 DØ Inclusive Jets η < 3, present measurement CDF/DØ Inclusive Jets η <.7 ZEUS 95 BPC+BPT+SVTX & H 95 SVTX + H 96 ISR ZEUS 96-97 & H 94-97 E665 CCFR BCDMS NMC SLAC - -6-5 -4-3 - - x

D Inclusive Jet Cross Section 7 Five rapidity regions Largest systematic uncertainty due to jet energy scale Curves are CTEQ4M d σ/ de T dη (fb/gev) 6 5 4 3. η <.5.5 η <.. η <.5.5 η <.. η < 3. PRL 86, 77 () 5 5 5 3 35 4 45 5 E T (GeV)

(Data - Theory)/Theory E T (Data - Theory)/Theory E T.6. : jj :5 <.8.4 -.4.6 : :5. < jj.8.4 -.4.6 jj : <. :5.8.4 -.4.6 :5 <. : jj.8.4 -.4.6 jj < 3: :..8.4 -.4 -.8 5 5 5 3 35 4 45 5 D Inclusive Jet Cross Section.6. : jj :5 <.8.4 -.4.6 : :5. < jj.8.4 -.4.6 jj : <. :5.8.4 -.4.6 :5 <. : jj.8.4 -.4.6 jj < 3: :..8.4 -.4 -.8 5 5 5 3 35 4 45 5 CTEQ4HJ CTEQ4M MRSTg! MRST (GeV) (GeV)

Gluon PDF Conclusions PDF χ χ/dof Prob CTEQ3M.56.35. CTEQ4M 9.46.3.4 CTEQ4HJ 59.38.66.99 MRST 3.78.6.5 MRSTgD 55.5.73 <. MRSTgU 85.9.95.63 χ determined from complete covariance matrix Best constraint on gluon PDF at high x Currently being incorporated in new global PDF fits

Inclusive Cross Section Using K T Algorithm -.5 < η <.5 D =. D Preliminary Predictions IR and UV safe Merging behavior well-defined for both experiment and theory

Normalization differs by % or more No statistically significant deviations of predictions from data When first 4 data points ignored, probabilities are 6-8% Comparison with Theory PDF χ/dof Prob MRST. 3 MRSTg#.38 MRSTg$.7 5 CTEQ3M.56 4 CTEQ4M.3 5 CTEQ4HJ.3 9 D Preliminary

Further k T Developments (since PIC ) Detected Particles Hadronization Jet Parton Single parton With hadronization correction PDF χ/dof Prob MRST.86 7 CTEQ4M.6 44 Correction for hadronization explains low E T behavior

dσ de T CDF α s from Inclusive Cross Section s () Strong Coupling Constant α s (E T /).8.7.6.5.4.3... CDF Preliminary. Strong coupling constant as a function of E T measured using CTEQ4M parton distribu- FIG. tions for R = E T =. The curved line corresponds to the NLO QCD predictions for running of s PIC Michael Strauss The University of Oklahoma [ + α ( µ ) k ( µ, µ )] = α ( µ R ) X ( µ R, µ F ) s R α s X () is LO prediction α s3 X () k is NLO prediction X () and k determined from JETRAD MS scheme used Jet cone algorithm used with R sep =.3 α s determined in 33 E T bins α s (M Z ).6.4...8 R 5 5 5 3 35 4 45 Systematic uncertainties 5 5 5 3 35 4 45 E T (GeV) F with (M ) equal to the experimental average value of.9. The shaded area corresponds to

CDF α s from Inclusive Cross Section CDF Preliminary Experimental systematic uncertainty Largest at low E T is underlying event Largest at high E T is fragmentation and pion response Percentage change in α s (E T /) High P T Pions Response - Energy Scale - Underlying Event - Resolution - Low P T Pions Response - Electron Response - Fragmentation - Normalization - 4 3 3 4 4 3 3 4 Transverse Energy (GeV) FIG.. Experimental systematic uncertainties for s measurement with CTEQ4M as input PDF PIC Michael Strauss The University of Oklahoma and R = E T =.

µ scale is the major source of theoretical uncertainty E T / < µ < E T PDF affects α s CTEQ4M minimizes χ CDF α s from Inclusive Cross Section Theoretical uncertainties each ~ 5% Strong Coupling Constant α s (M Z ).8.6.4...8.6.4.. 3 α s in CTEQ4A.. χ CDF Preliminary α s (M Z ) as function of E T for µ=e T Uncertainties due to the µ scale ( a) α s (M Z ) as function of E T for CTEQ4M Uncertainties due to the PDF choice ( b) 5 5 5 3 35 4 45 Transverse Energy (GeV) α s ( M Z ) =.9 ±.(stat) FIG. 3. Uncertainties due to the renormalization scale (a) and parton distribution functions (b). The inset shows the variation of for the CTEQ4A PDF family, with minimal value corresponding to CTEQ4M PDF set (input s =.6)..78 - +.89 (exp. syst) 3

ZEUS ZEUS Inclusive Jet Production ZEUS - - - -3-4 - 8 9 3 4 5 6-5 3 4.5.4.3...9.8.7.6.5 3 4.5.4.3...9.8.7.6.5 8 9 3 4 5 6

ZEUS Inclusive Jet Production 8 ZEUS 6 4 8 6 Measured cross section slightly above NLP pqcd in forward section 4.5.4.3...9.8.7.6.5 -.5 - -.5.5.5 -.5 - -.5.5.5

ZEUS Inclusive Jet Production α s Results: Uses various fits of dσ/dq and dσ/de T Full phase-space α s ( M Z ) =.4±.9 (stat) High-Q region (Q >5 GeV ) α s ( M Z ) =.9 ±.7 (stat) High-E T region (>4 GeV) α s ( M Z ) =.6 ±.5(stat) +.43 -.38 +.49 -.3 +.58 -.45 (exp) (exp) (exp) +.53 -.36 +.6 -.6 +.4 -.3 (th) (th) (th)

R 3 : Motivation and Method Study the rate of soft jet emission (-4 GeV) QCD multijet production - background to interesting processes Predict rates at future colliders Improve understanding of the limitations of pqcd Identify renormalization sensitivity Does the introduction of additional scales improve agreement with data? Measure the Ratio σ 3 ( p p 3 + jets) R 3 = vs. H σ with H T H T = jets ( p E p T jets) for all jets with E T >, 3, 4 GeV for η<3 and E T > GeV for η< + T

Inclusive R 3 Features: Rapid rise H T <GeV Levels off at high H T Interesting: 7% of high E T jet events have a third jet above GeV 5% have a third jet above 4 GeV

R 3 Sensitivity to Renormalization Scale E T > GeV, η< show greatest sensitivity to scale

Jet emission best modeled using the same scale i.e. the hard scale for all jets Best scale is that which minimizes χ for all criteria µ R =.6E T max, for GeV thresholds µ R =λ H T, λ.3 for all criteria Introduction of additional scales unnecessary. R 3 Results E T > GeV, η< PRL 86, 955 ()

D Cross Section Ratio: σ(63)/σ(8) vs x T Ratio of the scale invariant cross sections : σ s = (E T3 /π) (d σ/de T dη) vs X T = E T / ( s / ) at different cm energies ( 63 and 8 GeV) σ σ s E T Ratio allows substantial reduction in uncertainties (in theory and experiment). May reveal: Scaling behavior Terms beyond LO ( α s ). x T σ(63)/σ(8) QCD Naive Parton model.4 X T

D Inclusive Cross Section s = 8 GeV s = 63 GeV DØ Data η jet <.5 3 DØ Data /( η E T ) d σ/(de T dη)de T dη (fb/gev) 6 5 4 3 JETRAD max CTEQ3M, µ =.5E T /( η E T ) d σ/(de T dη)de T dη (nb/gev) - - -3 JETRAD max CTEQ3M, µ =.5E T s = 63 GeV η jet <.5 3 4 5 E T (GeV) -4 5 5 E T (GeV)

Cross Section Ratio σ(63)/σ(8) is -5% below NLO QCD predictions Top plot: varying choice of pdf has little effect Bottom plot: varying µ R scale is more significant Better agreement where µ R different at 63 and 8 (unattractive alternative!) Higher order terms will provide more predictive power! Ratio of Scaled Cross Sections (63 GeV / 8 GeV).5.5 DØ Data CTEQ4HJ µ=e T / CTEQ4M µ=e T / CTEQ3M µ=e T / MRST µ=e T / CTEQ3M µ=e T CTEQ3M µ=e T / CTEQ3M µ=e T CTEQ3M µ=e T /4...3.4 Jet XT Published in PRL 86, 53 ()

CDF DiJet Provides precise information about initial state partons Cone of R=.7 Both Jets: E T > GeV Jet :.< η <.7 Jet : Four η regions.< η <.7.7< η <.4.4< η <..< η <3.

CDF DiJet Cross Section PDF χ /dof MRST.68 MRST# 3.63 MRST$ 4.49 CTEQ4M.88 CTEQ4HJ.43 All < % Probability (data - QCD)/QCD (data - QCD)/QCD.8.6.4. -..6.4..8.6.4. -. -.4 a) 5 5 5 3 35 4 E T (GeV) c) 5 5 5 E T (GeV) (data - QCD)/QCD (data - QCD)/QCD.5.5.75.5.5.75.5.5 -.5.5.5.75.5.5.75.5.5 -.5 -.5 b) 5 5 5 3 35 4 E T (GeV) d) 5 5 E T (GeV)

k T algorithm used R + = d σ + dσ tot / dq / dq C had dσ/dq (pb/gev ).3. - ZEUS DiJet ZEUS 96-97 DISENT Had DISENT MBFITM µ R =µ F =Q a) ZEUS R +.4.. ZEUS 96-97 DISENT Had MBFIT (α s =.3) MBFIT (α s =.8) MBFIT (α s =.3) µ R =µ F =Q b).8.6.4 E T > 8 GeV (leading) E T > 5 GeV (other) -<η< (leading) 47<Q < GeV Phys Lett B57, 7 () Rel. diff. - -3-4.5 -.5.5 -.5 Q (GeV ) dσ tot dσ + dσ tot 3 4 dσ + Rel. diff....8.6.4.5 -.5 3 4 Q (GeV )

ZEUS DiJet ZEUS R + parameterized as: R + (M Z ) = A α s (M Z ) + A α s (M Z ) α s.8.6.4 α s from R + a) ZEUS 96-97 α s PDG.. α s (ES) α s (Th). -.. -. 4 6 8 b) c) Q (GeV) α s ( M Z ) =.66 ±.9 (stat) +.4 -.33 (exp) +.57 -.44 (th)

Dijets has lowest total error of all Zeus measurements. All measurements consistent with PDG value of.85± ZEUS α s Summary ZEUS

Tevatron Run II Run II: E cm =.96 TeV, fb - expect: ~ events E T > 49 GeV and ~K events E T > 4 GeV 3 Run II fb - Run I pb - Run I: E cm =.8 TeV,.fb - yielded 6 Events E T > 4 GeV Great reach at high x and Q, A great place to look for new physics! Number Events > Jet E T 4 45 5 55 6 Jet E T (GeV)

Conclusions from Jet Physics!Growing sophistication in jet physics analysis %Error matrices %New jet algorithms %Better corrections %PDF refinements!results generally agree with NLO QCD and PDF s %Cross section measurements will continue to refine PDF s % α s measurements agree with PDG %Low E T physics still require theoretical refinements!jet physics should continue to provide fruitful developments %High E T region can reveal compositeness and other new physics %Low E T region reveals soft parton distributions in proton %NNLO and other theoretical refinements needed %Results needed for discovery measurements