1. f Don Lincoln f La Thuile 2002 Don Lincoln Fermilab Tevatron Run I QCD Results Don Lincoln f

2. f Don Lincoln f La Thuile 2002 Quantum Chromo Dynamics Topics Today Inclusive Jet Cross-Section (Cone Algorithm) Measurement of  s Inclusive Jet Cross-Section (k T Algorithm) Event shape variables Jet structure/quark-gluon separation Study of the force governing the behavior of quarks and gluons New

3. f Don Lincoln f La Thuile 2002 R=  2 +  2 Cone Definition R=0.7 in  Merging and splitting of jets required if they share energy R sep required to compare theoretical predictions to data (R sep is the minimum separation of 2 partons to be considered distinct jets) Cone Definition of Jets Centroid found with 4-vector addition E jet =  E i E T jet = E jet sin  jet (CDF’s Definition) 2R 1.3R  = -ln[tan(  /2)] Suggests need for more robust algorithm Observable remnant of parton-parton hard scatter

4. f Don Lincoln f La Thuile 2002 State of the Art 1995 (The Controversy) High p T excess is exciting prospect PRL 77 438 (1996)PRL 82 (1999) 2451

5. f Don Lincoln f La Thuile 2002 Controversy Resolved(?) PRD 64 032001 (2001) Erratum-ibid. D65 039903 (2002) PRD 64 032003 (2001) More modern pdf’s (esp. CTEQ4M and CTEQ4HJ) ameliorate the disagreement CDF

6. f Don Lincoln f La Thuile 2002 CDF 1B Result PDF 22 Confidence Level CTEQ4M 63.11% CTEQ4HJ 46.810.1% MRST 49.57% Plots show statistical error only  2 below include systematic error 33 degrees of freedom R sep = 1.3 × R (R = 0.7) PRD 64 032003 (2001)

7. f Don Lincoln f La Thuile 2002  s from Inclusive Jet PRL 88 042001 (2002)  s 2 X (0) is LO prediction  s 3 X (0) k 1 is NLO prediction X (0) and k 1 determined from JETRAD MS scheme used (CTEQ4M) Jet cone algorithm used with R sep = 1.3  s determined in 33 E T bins

8. f Don Lincoln f La Thuile 2002  s from Inclusive Jet  s determined at M Z  50 < E T < 250 GeV  All E T (CTEQ4HJ)  World Average PRL 88 042001 (2002) Consequence of high E t excess Theory errors ~ 5% (  ~  2)

9. f Don Lincoln f La Thuile 2002 K T Definition of Jets K T Definition cells/clusters are combined if their relative k T 2 is “small” (relative transverse momentum) (D=1.0 or 0.5 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 Ellis-Soper PRD 48 3160

10. f Don Lincoln f La Thuile 2002 Inclusive Cross Section Using K T Algorithm Predictions IR and UV safe Merging behavior well-defined for both experiment and theory |  < 0.5 D = 1.0 Phys. Lett. B 525 211 (2002)

11. f Don Lincoln f La Thuile 2002 Comparison with Theory Normalization differs by 20% or more No significant deviations of predictions from data, when correlated systematic errors are included When first 4 data points ignored, probabilities are 60- 80% D  Preliminary PDF  /dof Prob MRST1.12 31 MRSTg  1.3810 MRSTg  1.1725 CTEQ3M1.56 4 CTEQ4M1.3015 CTEQ4HJ1.1329 Phys. Lett. B 525 211 (2002)

12. f Don Lincoln f La Thuile 2002 Transverse ‘Thrust’ at D  Using K T jets Event shapes used at e + e - and ep to test QCD developments like resummation calculations and non- perturbative corrections Non-perturbative corrections: of the order of 1/Q. Related to hadronization effects. Resummations: needed at small values of the shape variable where fixed-order perturbative calculations are expected to fail. Traditional variable (thrust) not suitable for hadron-collider environment. (Lorentz boost invariance) Transverse Thrust: 2 partons in final state 3 partons in final state N partons in final state T=[2/3,1] (LO) T=[1/2,1] (N...NLO) T=1

13. f Don Lincoln f La Thuile 2002 Dijet Transverse Thrust cross section K T algorithm (parameter D = 1) Event Selection: Vertex cut (| z | < 50 cm, e ~ 90 %) Jet quality cuts (e ~ 99.5 % ) ( 0.05 < EMF < 0.95, CHF < 0.4 ) Trigger-specific leading jet p T cuts Cut on missing E T (E T /p T lj < 0.7) |  1 | < 1, |  2 | < 1, |  3 | < 3 (if present) Bin in Non-Traditional Aspects Use only leading two jets to calculate T 2 T Bin in HT 3 Compromise on measuring hard scale and insensitivity to noise. Jet production rate  s 3 is NLO Event shape observables  s 3 is LO

14. f Don Lincoln f La Thuile 2002 Dijet Transverse Thrust cross section Only statistical errors included CTEQ4HJ, DØ preliminary Preprint forthcoming Deviations at High (1-T)  higher order Low (1-T)  resummation Systematic error work underway

15. f Don Lincoln f La Thuile 2002 K T Algorithm and Subjets For subjets, define “large” K T (y cut = 10 -3, D = 0.5) Increasing y cut PRD 65 052008 (2002)

16. f Don Lincoln f La Thuile 2002 Quark/Gluon Separation Quark/gluon separation interesting –QCD/fragmentation studies –Useful for enhancing quark-only final states (c.f. t t  all jets) –Find quark (gluon) enhanced samples. Parton Level Use 55 < pt < 100 GeV x 630 ~ 0.09 – 0.16 x 1800 ~ 0.03 – 0.055

17. f Don Lincoln f La Thuile 2002 D  Subjet Multiplicity Using K T Algorithm Assume M g, M Q independent of  s PRD 65 052008 (2002) Uncorrected = f g M g + (1-f g ) M Q Mean Jet MultiplicityQuark Jet FractionGluon Jet Fraction After fragmentation

18. f Don Lincoln f La Thuile 2002 D  Subjet Multiplicity Using K T Algorithm Raw Subjet MultiplicitiesExtracted Quark and Gluon Multiplicities Higher M  more gluon jets at 1800 GeV PRD 65 052008 (2002)

19. f Don Lincoln f La Thuile 2002 HERWIG prediction = 1.91 ± 0.16 (stat) D  Subjet Multiplicity Using K T Algorithm Largest uncertainty comes from the gluon fractions in the PDFs PRD 65 052008 (2002) Amount of radiation

20. f Don Lincoln f La Thuile 2002 Summary #1 CDF’s new inclusive jet analysis does not show the dramatic high p T excess of earlier analyses and highlights need for better high-x gluon pdfs CDF has recently published a nice analysis measuring  s from 50-250 GeV and evolved it to M z, where it agrees nicely with the world average –Analysis does show sensitivity to the high p  excess described above

21. f Don Lincoln f La Thuile 2002 Summary #2 DØ has recently completed an extensive program using the k T jet-finding algorithm –Inclusive jet cross-section Reasonable agreement with NLO calculations Prefers CTEQ4HJ and MRST pdfs k  jets contain more energy than similar cone jets –Event shape analysis (using transverse thrust) Very preliminary results shown here. Preprint available soon. –Jet structure analysis Good agreement with HERWIG Approximately twice as much radiation from gluon jets as from quark jets.

22. f Don Lincoln f La Thuile 2002 www-d0.fnal.gov/~lucifer/PowerPoint/LaThuile2002.ppt

23. f Don Lincoln f La Thuile 2002 D  Subjet Multiplicity Using K T Algorithm Perturbative and resummed calculations predict that gluon jets have higher subjet multiplicity than quark jets, on average. Linear Combination: = f g M g + (1-f g ) M Q Mean Jet Multiplicity Quark Jet FractionGluon Jet Fraction After fragmentation PRD 65 052008 (2002) Monte Carlo

24. f Don Lincoln f La Thuile 2002 D  Subjet Multiplicity Using K T Algorithm Assume M g, M Q independent of  s PRD 65 052008 (2002) Uncorrected