QCD. Sean Fleming Carnegie Mellon University. Meeting of the Division of Particles and Fields 2004 University of California, Riverside

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1 QCD Sean Fleming Carnegie Mellon University Meeting of the Division of Particles and Fields 2004 University of California, Riverside L = 1 4 F A µν(x)f µν A (x) + ψ(x)(i/d m)ψ(x)

2 Outline Experimental Review Jets at the Tevatron Inclusive b production at the Tevatron e + e J/ψ + η c as measured by Belle Theoretical Review Quick review of NNLO QCD technique Soft Collinear Effective Theory (SCET)

3 Tevatron: Run II Luminosity CME Run I ( ) Run IIa ( ) Run IIb ( ) 0.1 fb 1 1 fb fb 1 s = 1.8 TeV s = 1.96 TeV

4 Jets at the Tevatron jet p p jet Almost 500 pb 1 written to tape between about 350 pb 1 and 150 pb 1 analyzed

5 Jets at the Tevatron: what s new Detectors Upgraded Increase center-of-mass energy ( TeV) Increased cross section at 400 GeV and 5 at 600 GeV Higher E T 2 New Jet cone algorithm Infrared & Collinear safe

6 CDF Run II

7 CDF Run II Run I data exhibited an excess at large E T which could be explained by an enhanced gluon density at high x: fit by CTEQ6.1

8 kt clustering algorithm

9 DO Data Talk by B. Hirosky Inclusive Jet Cross Section in Different Rapidity Bins Large rapidity put constraints on gluon content of the proton at high x values

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11 Di-Jet Mass Spectrum Greater sensitivity to new phenomena Central region y jet < 0.5, data sample 143 pb 1 Run II midpoint algorithm Agreement within uncertainties with NLO/CTEQ6M Jet Energy Scale ( < 7% ) dominant error on measurement

12 Jets at the Tevatron First results: good agreement between theory and data P T M jj Explore high and regions over wide range of rapidities Constrain high- x gluon contributions Direct searches for new physics Measurements will become increasingly precise Tevatron is essential for Precision measurements & searches for new physics Expectations for LHC

13 b-production at the Tevatron

14 b-quark production at the Tevatron 1993 Measured by CDF (Phys. Rev. Lett. 71, 2396 (1993)) Compared to NLO QCD (P. Nason, S. Dawson and R. K. Ellis, Nucl. Phys. B 303, 607 (1988))...the next-to-leading QCD calculation tends to underestimate the inclusive b-quark cross section.

15 > DO weighs in... By 2000 excess is established Phys. Rev. Lett. 74, 3548 (1995) Phys. Lett. B487, 264 (2000) 10 4 y b < 1.0 y b < 1.0 p T min ) (nb)! b (p T b µ D0 / (1992/93) e µ CDF (1988/89) NLO QCD, MRSD0 Theoretical Uncertainty p T min (GeV/c)

16 DO weighs in.....and a Mystery Phys. Rev. Lett. 85, 5068 (2000) b-jets: hadronic jets carrying b flavor Directly observable Reduces model dependency Get to this in a moment

17 More CDF Results d!/dp T (nb/(gev/c)) CDF (Phys. Rev. D65, (2002)) data/theory 2.9 ± 0.2(stat syst pt ) ± 0.4(syst fc ) does not include theory uncertainty Model dependence Non-pert. Peterson fragmentation func. Information on hadronization b B p T (GeV/c)

18 New Theory Analysis M. Cacciari and P. Nason, Phys. Rev. Lett. 89 (2002) data/theory 1.7 ± 0.5(expt) ± 0.5(th) does include theory uncertainty Change due to fragmentation function!

19 Fragmentation Function Fit fragmentation function to LEP data Use the same theory ingredients as in b-production including NLO and NLL b-production is most sensitive to the N=3,4,5 moments

20 CDF Run II Preliminary Data s = 1.96 TeV p p H b J/ψ σ(p p H b J/ψ; P ψ > 1.25, y < 0.6) σ CDF J/ψ = (stat + syst) nb σ FONLL J/ψ = nb σ(p p H b X; P > 0, y < 0.6) B(H b J/ψ) σ CDF H b = (stat + syst) nb σ FONLL H b = nb σ(p p bx; P > 0, y < 1.0) σ CDF b ( y < 1) = (stat + syst) µb M. Cacciari et al Phys. Rev. Lett. 89, (2002) σ FONLL b ( y < 1) = µb Excellent Agreement!

21 Why is agreement so good? Improved determination of fragmentation function from LEP data New pdf determinations from data increase theory cross section Run II CDF data is about 30% lower than Run I data Phenomenological input extremely important

22 Run II analysis in progress Both CDF and DO have b-jet analysis in progress CDF and DO also looking at di-jet production with b-tagging study b-jet production mechanism and di-jet mass A lot more data coming: summer 2006 expect 400 pb fb 1 collected and by Can theory keep up?!?!

23 Double Charmonium Production in e + e collisions measured by Belle Talk by T. Ziegler e γ J/ψ e + η c 140 fb 1 on-resonance 15 fb 1 off-resonance 155 fb 1 total

24 * Masses fixed at PDG value set * to set * to 90% C.L. upper limits State M recoil N evt σ

25 Comparison to Theory E. Braaten & J. Lee, Phys. Rev. D67, (2003) (c c) res Belle Data σ Born B(c c) res > 2 charged [fb] J/ψ ψ(2s) Factor of 10discrepancy!! Extra th. errors 60% Relativistic corrections not under control

26 Double Charmonium Production Exclusive double charmonium exhibits a remarkable factor of 10 discrepancy between Belle data and theory Data is quality is very good with errors on at 15% e + e J/ψ + η c Theoretical errors need to be brought under control Understand relativistic corrections Belle has more data Angular analysis Inclusive data: e + e J/ψ + c c

27 Theory Overview New Techniques For higher order QCD calculations Soft Collinear Effective Theory L = 1 4 F A µν(x)f µν A (x) + ψ(x)(i/d m)ψ(x)

28 QCD at NNLO C. Anastasiou et al Phys. Rev. D69, (2004)...the Tevatron and LHC physics programs require NNLO calculations for differential distributions in kinematic variables; knowledge of inclusive rates is insufficient. Process considered: V : vector boson ( W, Z, γ ) X: any number of additional hadrons Differential CS dσ V dy Calculated to NNLO: h 1 + h 2 V + X = ab 1 τe Y dσ V ab dy 1 τe Y = 1 2s Requires a new calculation technique dx 1 dx 2 f (h 1) a (x 1 )f (h 2) b (x 2 ) dσv ab dy (x 1, x 2 ) ( ) pv dπ f M ab V +X 2 p 1 δ u p V p 2

29 Run I Result Comparison to Run I CDF data 3.9% 4 5% normalization error to data difference between different PDFs Approximate NNLO running of PDFs

30 Run II prediction Scale uncertainty at NNLO %!!!! Approximate NNLO running of PDFs Full NNLO running now available S. Moch, Vermaseren & A. Vogt, hep-ph/

31 QCD at higher orders New Technique allows for the calculation of NNLO differential distributions in hadronic collisions: Unprecedented! Precision calculations with errors O(1%) Compare to precision data from Tevatron Run II and LHC Interest from string theory community: Perturbative gaug! theory as a string theory in twistor space, E. Witten hep-th/

32 Soft Collinear Effective Theory

33 Soft-Collinear Effective Theory: An Overview Bauer, Fleming, Luke, Pirjol, Stewart SCET is: Effective theory of a highly energetic, approximately massless particle interacting with a soft background p µ = Qn µ + k µ Brown Muck Energetic: Light-like: Q Λ QCD n µ = (1, 0, 0, 1) Residual Momentum: k Λ QCD Expansion in a small parameter Make an Analogy with HQET p µ = Mv µ + k µ Λ Expansion in: QCD M b λ Λ QCD Q Heavy: Static: M Λ QCD v µ = (1, 0, 0, 0) Residual Momentum: k Λ QCD

34 Soft-Collinear Effective Theory Analogy with HQET breaks down: HQET Not Allowed!!! p µ = mv µ p µ = mzv µ q µ = m(1 z)v µ q 2 = m 2 (1 z) 2 SCET O.K. p µ = 1 2 Qnµ p µ = 1 2 zqnµ q µ = 1 2 (1 z)qnµ q 2 = 0

35 SCET Lagrangian Collinear QCD Soft ψ(x) ψ s (x) + ξ n (x) A µ (x) A µ s (x) + A µ n(x) L c = ξ n {in D c + i/d c L s = ψ s i/d s ψ s 1 i n D c i/d c + gn A s } / n 2 ξ n Collinear sector: QCD in boosted frame Soft sector: QCD Coupled through a single term

36 Symmetries Separate collinear and soft gauge symmetries Powerful restriction on the form of operators allowed Soft fields act as a background field to collinear fields Any gauge symmetry connecting soft to collinear introduces a large scale Global U(1) helicity spin symmetry Reparameterization invariance which is a consequence of Lorentz invariance of QCD Relates operators

37 Two important points: Currents 1. Introduce a collinear Wilson line: W = P exp ( ig x W ξ n (x) W ξ n (x) under collinear gauge transformations 2. Wilson coefficients are a function of the large light-cone component of the collinear momentum C( n P ) Hard-Collinear Factorization in SCET ) ds n A n (s n) Example: Energetic up quark produced in (leading order in λ ) b ulν decays ū(p u )Γu(p b ) C i (M) ξ n,p Γ i h v ū(p u )Γu(p b ) i ξ n,p W C i ( n P op )Γ i h v i

38 Leading order in Heavy-Light Current: b u Origin of the collinear Wilson line α s u(p s ) ξ n u(p b )! h v Higher orders u(p b ) u(p s ) q 1 q 2 q m + perms! q 1 q 2 h v ξ n q m n A n } W

39 Decoupling Collinear & Soft Decouple Soft from Collinear in the Lagrangian 1) Soft Wilson Line ( Y (x) = Pexp ig x ) ds n A s (ns) 2) Field Redefinition ξ n (x) = Y (x)ξ n (0) (x) eikonal phase L c ξ n {in D c + i/d c 1 i n D c i/d c } / n 2 ξ n Complicates vertex: For our Heavy-Light example ξ n W Γh v (0) ξ n W (0) ΓY h v Origin of Soft-Collinear Factorization in SCET

40 Soft-Collinear Effective Theory: What have we learned: SCET: EFT of collinear d.o.f. coupled to soft d.o.f. Powerful gauge symmetries constrain operators Decoupling via field redefinition What is it good for? SCET is useful for understanding: Factorization: Obtained from field redefinition and simple algebraic manipulations Summation of Logarithms at the edges of phase space: Obtained from Renormalization Group Equations (RGEs) Systematic Power Corrections in λ : Turn the crank

41 An Example: Factorization in DIS OPE: integrate out final state below the scale onto SCET µ ν µ q q Q 2 by matching ν p P 2 X Q2 x (1 x) p p O p Match onto SCET operators Fix T eff µν C µν (ω 1, ω 2 ) by forcing O(ω 1, ω 2 ) = [ χ / n n,ω1 2 χ ] n,ω 2 χ n,ω = [δ( n P op ω)w ξ n ] Wilson coefficient depends on large light-cone momentum in hard scattering: Standard Convolution form of cross section dω 1 dω 2 C µν (ω 1, ω 2 ) O(ω 1, ω 2 ) T µν = T eff µν

42 Factorization in DIS Decouple soft from Collinear χ n,ω Y χ (0) n,ω / n [ χn,ω1 2 χ ] n,ω 2 (0) / n [ χ n,ω 1 2 Y Y χ (0) ] n,ω 2 1 KLN Theorem 1 4 Parton distributions in SCET 1 pn χn,ω / n χ n,ω pn = dξ δ(ω )δ spin 0 ( ) ω+ 2 n p ξ f i/p (ξ) Factored form dσ ( ) dξ ξ ξ H x ; µ f i/p (ξ; µ)

43 Operator Evolution Equations Operator running +... γ RGE µ d dµ O(ω 1, ω 2 ; µ) = dxdy γ(ω 1, ω 2, x, y; µ)o(x, y; µ) Different momentum constraints give different running: ω 1 = ω 2 DGLAP or ω 1 + ω 2 = Const. BL

44 Some More Applications Color Suppressed B Dπ Decays J/ψ Production at Belle & Babar

45 Mantry, Pirjol, Stewart N 0 c 1 1 N c N c

46 Color- Suppressed decays are indeed suppressed But Large is N c not very predictive How about using SCET & HQET?

47 Color Suppressed Decays in SCET Possible to derive a factorization formula in SCET Complicated because SCET operators are suppressed λ Λ QCD E π 0.2 New non-perturbative function: S (i) (k + 1, k+ 2 )

48 Color Suppressed Decays in SCET S (i) (k 1 +, k+ 2 ) = D ( ) O s B is the lightcone distribution function for the spectator quarks in the B and D It is universal for a particular set of directions {v, v, n} Will be the same for D and D It is a complex function: large strong phases are natural

49 Comparison to Date Universality for D and Branching ratio D Strong Phase Predict Explain naturally SCET Predicts Natural sized parameter fits the data:

50 One More Application J/ψ Production at Belle & Babar

51 J/ψ Production at Belle & Babar Fleming, Leibovich, Mehen e + e J/ψ + X ( s = 10.6 GeV) Angular distribution dσ dp dcosθ = S(p)(1 + A(p)cos2 θ) A(p) Babar σ tot (pb) 2.52 ± 0.21 ± 0.21 p < 3.5 GeV p > 3.5 GeV 0.05 ± ± 0.6 Belle 1.47 ± 0.10 ± ± Belle σ(e + e J/ψc c) σ(e + e J/ψX) = ± 0.12

52 NRQCD Color Singlet J/ψ c c Color Octet J/ψ c σ = 0.73 pb c σ = 0.79 pb c J/ψ c c c σ = 0.20 pb c c cj/ψ c σ = 0.08 pb σ (1) tot = 0.93 pb + σ (8) tot = 0.87 pb σ tot = 1.8 pb σ(e + e J/ψ c c) σ(e + e J/ψ X) = 0.1

53 Differential Distribution dσ δ(1 z p ) z p = p/p max 1 Theory Babar d " /dz[pb] e + e J/! +gg e e J/! + e + e J/! + cc e + e J/! + qq Entries / 500 MeV/c p* (GeV/c) z

54 SCET & NRQCD In the Endpoint region: use SCET for the fast & soft d.o.f. use NRQCD for the heavy quark-antiquark c c + cr ossed diagr am collinear gluon

55 Factorization New factorization formula in the endpoint region: dσ dz 1 z Nonperturbative shape function dξ S(ξ; µ)j(ξ z; µ) Jet function Jet function: perturbatively calculable in Shape function is universal α s ( s m c Λ QCD ) Used a simple model with 2 parameters: require moments to scale appropriately Overall normalization includes color-octet matrix element Not well determined Sum logs using RGEs (Similar to B X s γ )

56 Comparison to Babar Data B. Aubert et al. Phys. Rev. Lett. 87: (2001) 1000 Endpoint z > 0.7 p > 2.57 GeV N p

57 Comparison to Belle Data K. Abe et al. Phys. Rev. Lett. 88: (2002) Different Normalization N p

58 Angular Distribution 2 A(p! ) 1 Belle Babar p!

59 SCET Summary Flavor of Soft Collinear Effective Theory Theory of light-like particles interacting with a soft background Derive factorization Sum logarithms Systematically treat power corrections Scope of applications is large B decays, sub-leading pion form factor, event shapes, Quarkonium production and decay A very active field: more to come... Watch for collider physics applications

60 Summary Experiment Jets at the Tevatron: Precision Physics Tevatron b-production: resolved Double charmonium at Belle???? Theory New methods for high order QCD perturbation theory Soft Collinear Effective Theory

61 Di-Jet Azimuthal Decorrelations Di-Jets produced at LO in perturbation theory φ dijet = π Soft radiations results in small decorrelations φ dijet π Talk by M. Begel Sensitive to higher-order QCD radiation without explicitly measuring 3rd and 4th jets k Hard radiation ( large) leads to large decorrelations 2π 3 φ dijet < π

62 Di-Jet Azimuthal Decorrelations LO: QCD calculation of three jet production O(αs) 3 NLO: QCD calculation of four jet production O(αs) 4

63 An Example: Factorization in DIS k k q = k k p P X Kinematics: Breit frame q µ = Q( n µ n µ )/2 Q2 x = 2p q p µ = n µ Q ( 2x + nµ x m2 p m 2 2Q + O p Q 2 P µ X = pµ + q µ with with q 2 = n n 2 Q2 = Q 2 ) P 2 X = Q2 x (1 x) + m2 p