QCD at high energy. Paolo Nason. INFN, sez. di Milano, and Università di Milano-Bicocca. LP01 Rome July 2001

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1 QCD at high energy Paolo Nason INFN, sez. di Milano, and Università di Milano-Bicocca LP1 Rome July 21

2 QCD at high energy very lively and active field: 6 abstracts submitted to the conference QCD at end of LEP hera: emphasis shifts from testing the theory to pushing its precision Theory Standard: NLO. Tackle the study of power suppressed effects Status of phenomenology Large body of tests in many different areas Overall agreement with theory Some minor discrepancies (need for better calculations) Some major discrepancies (interesting puzzles) LP1 Paolo Nason - QCD at high energy 2

3 PLAN OF THE TALK Few examples of current results in e + e, ep and p p physics Power suppressed effects Towards NNLO Some puzzling results LP1 Paolo Nason - QCD at high energy 3

4 QCD in e + e hadrons: QCD studies at highest available energies 4-jets NLO studies Fits to QCD color factors and α S Charge multiplicity studies Bose-Einstein correlations, color reconnection Power corrections, energy evolution of shape variables distributions Heavy quark mass effects Fragmentation function studies γγ collision studies LP1 Paolo Nason - QCD at high energy 4

5 NLO formulae for 3 jets Theoretical basis α S (µ 2 )A + α 2 S(µ 2 )B(µ 2 /Q 2 ) +... K.Ellis, Ross, Terrano and 4 jets, infrared safe quantities α 2 S(µ 2 )C + α 3 S(µ 2 )D(µ 2 /Q 2 ) +... Signer, Dixon; Nagy, Trocsanyi; Campbell, Cullen, Glover; Weinzierl, Kosower Heavy quark mass effects included in the 3 jets result Bernreuther, Brandenburg, Uwer; Rodrigo, Santamaria, Bilenky; P.N., Oleari LP1 Paolo Nason - QCD at high energy 5

6 Resummation of Sudakov effects at NLL level: needed in the limit of thin jets R(y) = F (α S ) e Lg 1(α S L)+g 2 (α S L) Catani, Dokshitzer, Olsson, Turnock, Webber where R is a jet rate, y the jet thickness, L = log y. Hadronization and power corrections: suppressed as 1/Q, but still important at LEP energies. Estimated using Montecarlo hadronization models. Renormalon inspired models provide an alternative Dokshitzer, Marchesini, Webber LP1 Paolo Nason - QCD at high energy 6

7 L3: thrust, heavy jet mass, total jet broadening, wide jet broadening and C parameter measured at different energies. From fit: Shape variables at highest energy α s Reduced s s =91.2 GeV LEP 1.5 LEP 2 QCD Evolution Constant α s (GeV) α S (M Z ) =.122 ±.11(exp.) ±.61(th.) s LP1 Paolo Nason - QCD at high energy 7

8 Fits to QCD color factors (OPAL, ALEPH) Jet resolution y ij = 2min(Ei 2, E2 j )(1 cos θ ij)/evis 2 Differential 2-jet rate D 2 (y 23 ) = σ 1 dσ tot dy (OPAL) 23 4-jet rate R 4 (y cut ) 4-jet, y cut =.8, E 1 > E 2 > E 3 > E 4 χ BZ = [( p 1 p 2 ), ( p 3 p 4 )] Θ NR = [(( p 1 p 2 ), ( p 3 p 4 )] Φ KSW = [( p 1 p 4 ), ( p 2 p 3 )] 3 4 cos(α 34 ) = cos( [( p 3, p 4 ]) (ALEPH) Color dependence D 2 = α S C F... + α 2 SC F (C F... + C A... + T F n f...) R 4 = α 2 S C F(C F... + C A... + T F n f...) + α 3 S... LP1 Paolo Nason - QCD at high energy 8

9 ALEPH PRELIMINARY Z peak data (1991/1995) hadronization corrections: Montecarlo models (fixed color factors?) T R /C F 1.8 This analysis, 68% CL contour OPAL: C A = 3.2 ±.25 ±.49 C F = 1.34 ±.13 ±.22 α S (M Z ) =.12±.11±.2 ALEPH: C A = 2.93 ±.14 ±.49 C F = 1.35 ±.7 ±.22 α S (M Z ) =.119±.6± SU(4) ALEPH-1997 OPAL LP1 Paolo Nason - QCD at high energy 9 C A /C F

10 Heavy Quark mass effects comparison of light and heavy quark hadronic events exposes the effects of the heavy quark mass. Two kind of analysis: Fit the b quark mass from the ratio of 3-jet rates in b-quark jets and light quark jets B 3 = Rb 3 R dusc 3 (which can be computed at NLO including mass effects) Compare the α S determination in light quark events and b, c quark events (tests of flavour independence of α S ) LP1 Paolo Nason - QCD at high energy 1

11 Results from b-mass fits to B 3, called (improperly?) a test of the running of the b-quark mass, from various experiments. DELPHI has new results: m b (M Z ) (in GeV) = Duhram: 2.67 ±.25(stat.) ±.34(had.) ±.27(th) Cambridge: 2.61 ±.18(stat.) ±.47(had.) ±.18(tag) ±.12(th) m b (Q2 ) [GeV] Measurement of the b mass in high energy processes PDG (Production threshold) this analysis ALEPH Brandenburg et al (SLD) DELPHI OPAL Q= s [GeV] LP1 Paolo Nason - QCD at high energy 11

12 Flavour independence of the strong coupling: α (b/c) S /α (uds) S is much more consistent with 1 if heavy flavour mass effects are included y 23 1-T M H B W C OPAL (a) c massless b massive (b) c massive b massless uds / α s α s Q LP1 Paolo Nason - QCD at high energy 12

13 HERA Structure function studies Jet studies in DIS Jet studies in photoproduction Shape variable and power correction studies Production of Heavy flavours LP1 Paolo Nason - QCD at high energy 13

14 α s.18 α s from R 2+1 Example: α S from jets in DIS a) ZEUS α s PDG α s αsfrom inclusive jet cross section H1 for CTEQ5M1 parton densities 15 < Q 2 < 5 GeV 2 inclusive k algo α s (E T ) α s (M Z ).1 ZEUS µ r = E T α s (ES) α s (Th) b) c) Q (GeV) Zeus: α S (M Z ) =.1166 ±.19(stat.) (exp.) (th.+pdf) E T / GeV H1: α S (M Z ) = ±.7(stat.)±.3(exp.) (th.).23 (pdf) LP1 Paolo Nason - QCD at high energy 14

15 3 jet study from H1 R 3/2 = σ 3jet / σ 2jet Recent NLO Calculation by Nagy and Trocsanyi Jets defined with k T cluster algorithm E T > 5 GeV, M 3jet > 25 GeV H1 data.6.4 M.2 n-jet > 25 GeV hadr QCD: NLO (1+δ ) α s(m Z ) =.118 ±.6 gluon: CTEQ5M1 ±15%.5 < (µ r / E T ) < 2 hadr QCD: LO (1+δ ) Q 2 (GeV 2 ) dσ 3jet /dq 2 (pb/gev 2 ) data / theory M 3jet > 25 GeV H1 data QCD: NLO (1+δ hadr) NLO LO H1 data / NLO (1+δ hadr ) α s(m Z) =.118 ±.6 gluon: CTEQ5M1.5 < (µ ±15% r / E T ) < Q 2 (GeV 2 ) LP1 Paolo Nason - QCD at high energy 15

16 θ 3 1/σ 3jet dσ 3jet /d cos H1 data 15 < Q 2 < 5 GeV 2 QCD NLO QCD LO Phase Space ψ 3 1/σ 3jet dσ 3jet /d H1 data 15 < Q 2 < 5 GeV 2 QCD NLO QCD LO Phase Space cos θ ψ3 LP1 Paolo Nason - QCD at high energy 16

17 TEVATRON Inclusive jet versus E t and pseudorapidities Jets with cluster (k T ) algorithms Jet structure W/Z and γ production LP1 Paolo Nason - QCD at high energy 17

18 DØ Inclusive Jets η < 3, present measurement CDF/DØ Inclusive Jets η <.7 ZEUS 95 BPC+BPT+SVTX & H1 95 SVTX + H1 96 ISR ZEUS & H E665 CCFR BCDMS NMC SLAC η <.5.5 η < η < η < η < 3. "$#&%('*)*+-,-./% ! D jet analysis at large rapidity extends sensitivity to PDF s at small x and large Q 2. Impressive agreement with NLO theoretical calculations LP1 Paolo Nason - QCD at high energy 18

19 D data, JETRAD (O(α 3 S)) "! # $%#'& )( )(*! # $%#'& +, , "! # $%#'& +,)( ,)(*! # $%#'& -' ' "! # $%#'&.' "! # $%#'& )( )(*! # $%#'& +, , "! # $%#'& +,)( ,)(*! # $%#'& -' ' "! # $%#'&.' CTEQ4HJ ( ) and CTEQ4M ( ) MRSTg ( ) and MRST ( ) LP1 Paolo Nason - QCD at high energy 19

20 CDF dijet study: look at E T of one central jet (.1 < η 1 <.7) where the other jet lies in several different pseudorapidity intervals. Sensitivity to PDF at large x enhanced; Qualitatively good description of data, quantitative problems LP1 Paolo Nason - QCD at high energy 2

21 No PDF set is found that fits the data satisfactorily. Other problematic areas: Direct photon at low transverse momenta b production In all these cases discrepances could be attributed to unknown higher order effects. (data - QCD)/QCD (data - QCD)/QCD a) 5 c) E T (GeV) E T (GeV) (data - QCD)/QCD (data - QCD)/QCD b) 5 d) E T (GeV) E T (GeV) LP1 Paolo Nason - QCD at high energy 21

22 Power Corrections (Movilla Fernández, Bethke, Biebel, Kluth) S = 14 to 189 GeV several shape variables considered fit to α S and to the parameter α in the power correction model of Dockshitzer, Marchesini and Webber /σ dσ/d(1-t) T OPAL 189 GeV L3 189 GeV OPAL 183 GeV DELPHI 183 GeV L3 183 GeV OPAL 172 GeV DELPHI 172 GeV L3 172 GeV OPAL 161 GeV DELPHI 161 GeV L3 161 GeV OPAL 133 GeV ALEPH 133 GeV DELPHI 133 GeV L3 133 GeV OPAL 91 GeV ALEPH 91 GeV DELPHI 91 GeV L3 91 GeV SLD 91 GeV AMY 55 GeV JADE 44 GeV TASSO 44 GeV JADE 35 GeV TASSO 35 GeV MARK2 29 GeV HRS 29 GeV TASSO 22 GeV TASSO 14 GeV LP1 Paolo Nason - QCD at high energy 22

23 α b) Mean Values average <1-T> <M H 2 > <B T > <B W > <C> α S (M Z ) α S (M Z ) =.1187±.14± α (2 GeV) =.485±.13± (fit + syst. + theo. errors) α a) Distributions average 1-T M H, M H 2 B T B W C α S (M Z ) α S (M Z ) =.1111±.4± α (2 GeV) =.579±.5± (fit + syst. + theo. errors) α S (M Z ) = , α (2 GeV) = LP1 Paolo Nason - QCD at high energy 23

24 Power corrections studies at HERA α _ (µ Ι = 2 GeV) Power Correction Fits (stat. and exp. syst. uncertainties) B H1 τ α s (M Z ) τ C ρ C ρ LP1 Paolo Nason - QCD at high energy 24

25 What we know about power corrections In R e + e, 1/Q 4 (from O.P.E.) (why τ hadronic physics works so well) In DIS, 1/Q 2 (from O.P.E.) (why scaling sets in early in Q 2 ) In Jets, 1/Q (from many points of view...) (why Jet physics is so hard) Can we understand Jets better? LP1 Paolo Nason - QCD at high energy 25

26 Power Correction Model Basic idea: from QED analogy, fluctuations of gluons into virtual and real states cause α S running. Physical quantities written as: F (Q 2 ) = dk 2 F(Q 2, k 2 )α S (k 2 ). (Unknown) low energy behaviour of α S determines power corrections. Power correction law determined by low k 2 behaviour of F(Q 2, k 2 ) F (Q 2 ) 1 k 1/Q correction F(Q 2, k 2 ): physical quantity computed with a gluon of mass k 2. Scheme by Dockshitzer, Marchesini, Webber. Several similar suggestions: Akhoury and Zakharov, Sterman and Korchemsky, etc. LP1 Paolo Nason - QCD at high energy 26

27 Cannot work as is for shape variables (Seymour, P.N.) Shape variables know what is inside the blob. Thrust: decreases for a generic blob, does not change in some kinematic configurations 1 t k /Q 1 t Dokshitzer, Lucenti, Marchesini and Salam have examined these effects at the two-loop level. The effect amounts to a factor of order unity (Milan factor) in front of the 1-loop (naive) formula. This factor has the same value for several common shape variables If 2-loop same as 1-loop, what about higher loops? LP1 Paolo Nason - QCD at high energy 27

28 On the bright side: One parameter model of power corrections Also power suppressed effects depend upon color factors: Kluth etal have used it to fit QCD color factors without relying on Montecarlo hadronization models. Some support from data Alternative model to estimate power corrections: low α S values from distributions. Study using DELPHI data: PMS type of data analysis (RGI) gives very good fit to data without power corrections So: Power corrections or NNLO? Reinhardt, Flagmeyer, Hamaker, Passon and Wicke LP1 Paolo Nason - QCD at high energy 28

29 Had. Correction 1/q Powercorrection RGI+K pure RGI JCEF 11 o -16 o EEC 3 o -15 o B max B sum M 2 s /E2 vis E def. M 2 h /E2 vis E def. C-Parameter Major 1-Thrust α s (M Z ) α s (M Z ) α s (M Z ) α s (M Z ) LP1 Paolo Nason - QCD at high energy 29

30 Remarkable progress in NNLO calculations Current goal: jet production in hadronic collisions. Double soft limit (Berends and Giele, 1989) Double collinear and soft-collinear (Campbell and Glover, 1998; Catani and Grazzini, 1999; Del Duca, Frizzo and Maltoni, 2) 2 3 amplitude at one loop level (Bern, Dixon and Kosower, 1993; Kunszt, Signer and Trócsányi, 1994). Collinear limit of one loop amplitudes (Bern, Dixon, Dunbar and Kosower, 1994; Kosower, 1999; Kosower and Uwer, 1999) Soft limit of one loop amplitudes (Bern, Del Duca, Schmidt, 1998; Bern, Del Duca, Kilgore and Schmidt 1999; Catani and Grazzini, 2) Some analytic phase space integrals (Gehrman, Glover; Catani, de Florian, Grazzini) LP1 Paolo Nason - QCD at high energy 3

31 The two loop 2 2 contribution recently computed (Anastasiou, Glover, Oleari, Tejeda-Yeomans; 21). Recursion relations among feynman integrals reduce the problem to the computation of a small number of master integrals. The hardest of those (double box, planar and crossed) only recently solved (Smirnov, 1999; Tausk, 1999). All ingredients needed for a full NLO computation of jet cross sections in hadronic collisions are in place now. The implementation into a useful result is still a formidable task. But it does not look far... LP1 Paolo Nason - QCD at high energy 31

32 Puzzle in b production LP1 Paolo Nason - QCD at high energy 32

33 e + e e + e b b At LEP, direct and single resolved comparable L3 uses the electrons or muons from semileptonic b decays. the P t of the lepton (relative to closest jet) fitted to extract the c, b and light quark fraction: σ(e + e e + e b bx)µ = 14.9 ± 2.8 ± 2.6pb, σ(e + e e + e b bx)e = 1.9 ± 2.9 ± 2.pb OPAL (µ only) gets comparable results c cross section in agreement with calculations, excess of b production LP1 Paolo Nason - QCD at high energy 33

34 σ(e + e e + e cc,bb X) (pb) L3 m c =1.3 GeV m c =1.7 GeV e + e e + e cc X e + e e + e bb X NLO QCD Direct m b m b =4.5 GeV =5. GeV σ(e + e - e + e - bb - ) [pb] OPAL preliminary bands: OPAL (µ, s = GeV, prel.) L3 (µ,e, s = GeV, prel.) NLO (direct+resolved, GRV) NLO (direct only) m b m b =4.5 GeV, µ=m b /2 =5.2 GeV, µ=2m b s (GeV) s [GeV] ee LP1 Paolo Nason - QCD at high energy 34

35 b excess at HERA New H1 results confirm previous findings: σ(b) from impact parameter fit in photoproduction σ(b) in DIS both in excess over QCD calculations. Data / Theory σ vis (ep b X) H1 µ p T rel H1 µ impact param. (prel.) ZEUS e - p T rel NLO QCD Q 2 (GeV 2 ) Theoretical uncertainties are small. In DIS production, no resolved contribution. Similarities with γγ result. Very difficult to justify! LP1 Paolo Nason - QCD at high energy 35

36 Conclusions and outlook Convincing tests of PQCD Few problematic areas, some serious puzzles NLO calculations are the standard now True progress can only come going from NLO to NNLO Hadron colliders are the near future: we need a quality jump in QCD. LP1 Paolo Nason - QCD at high energy 36

37 EXTRA SLIDES LP1 Paolo Nason - QCD at high energy 37

38 D OPAL data R-matched lnr-matched fitted lnr-matched fit range C tot ln(y 23 ) LP1 Paolo Nason - QCD at high energy 38

39 R fit range OPAL data NLO R-matched fitted R-matched C tot log(y cut ) LP1 Paolo Nason - QCD at high energy 39

40 D, jet cross sections with k T cluster algorithm. Resolution parameter: d ij = min(p t 2 i, p t 2 j ) R2 ij D 2, R 2 ij = Φ 2 ij + η2 ij. Merge ij if d ij is the smallest of all p t 2 k and d kl. Choosing D = 1 roughly corresponds to R =.7 in standard jet definition LP1 Paolo Nason - QCD at high energy 4

41 LP1 Paolo Nason - QCD at high energy 41

42 Running of b mass Running of α S : a 3-jet rate goes like α S goes like R 3 = C α S (µ 2 ) [ 1 + α S π α S (Q 2 ) = α S (µ 2 ) 1 + α S π You measure R 3, you prove the running. [ ( A + b log µ2 Q 2 ( b log µ2 Q 2 For the running mass, the commonly used quantity goes like R3 bd 1 = 18.62m2 b Q α S π while the running mass goes like [ ( )] )] log m2 b Q 2 m 2 (Q 2 ) = m [1 2 + α S 8 π log m2 b Q 2 Thus: find a quantity that runs like a mass to prove the running. ( )] )] LP1 Paolo Nason - QCD at high energy 42