Recent developments on Perturbative QCD (Part I)

Transcription

1 Recent developments on Perturbative QCD (Part I) Jianwei Qiu Iowa State University/Argonne National Laboratory 威海高能物理前沿暑期论坛 (Weihai Summer Topic Seminar On the Frontiers of High Energy Physics) 山东大学 - 威海分校, 威海, 山东, 中国 2007 年 7 月 31 日至 8 月 7 日 1

2 Plan Part I: Success of pqcd and its role in the LHC physics (Collinear factorization formalism) Part II: New pqcd treatment and application (resummation, k T -factorization, quarkonium, etc.) Role of pqcd in heavy flavor physics (Hsiang-nan s talk) Role of pqcd in nuclear scatterings (Xin-Nian s talk) 2

3 Outline Foundation of perturbative QCD Predictive power of pqcd Factorization Global QCD analysis universal parton distributions QCD tests vs QCD applications Prospects for the LHC Update on the high order calculation Summary and outlook 3

4 Quantum Chromodynamics (QCD) Known Fundamental Interactions: AdS/CFT correspondence Strong QCD Weak Electromagnetic - QED Gravity Electro Weak Standard Model QCD stands as a very solid building block of the SM: Unbroken SU(3) color gauge symmetry Asymptotic freedom at high energy Success of QCD perturbation theory Nonperturbative results from Lattice calculations No major areas of discrepancies with data 4

5 Fields: QCD as a field theory ( ) f ψ i x A μ,a ( x) Strong color interactions: Quark fields, Dirac fermions (like electron) Color triplet: i = 1,2,3=N C Flavor: f = u,d,s,c,b,t Gluon fields, spin-1 vector field (like photon) Color octet: a = 1,2,,8 =N C2-1 Quark-gluon interaction Electron-photon interaction Gluon-gluon interaction 5

6 Foundation of perturbative QCD Renormalization QCD is renormalizable Asymptotic freedom weaker interaction at a shorter distance Infrared safety pqcd factorization and calculable short distance dynamics 6

7 Foundation of perturbative QCD Renormalization QCD is renormalizable Asymptotic freedom weaker interaction at a shorter distance Infrared safety pqcd factorization and calculable short distance dynamics PQCD provides a framework for computation of hard processes, and a testing ground for QCD at short-distance 7

8 α s Asymptotic freedom α ( μ ) 4π ( μ ) = 0 as s β 1 μ 2 μ 1 α ( 2 s μ 1 ) n 2 β 1 n 2 4π μ 1 Λ QCD μ μ 2 and μ 1 not independent 8

9 Running quark mass: Infrared Safety μ 2 dλ m( μ2) = m( μ1) exp - [ 1 + γ m( g( λ)) ] 0 as μ2 λ μ1 Perturbation theory becomes a massless theory when μ Infrared safety: 2 2 ( 2 ) 2 2 ( 2 ) κ Q 2 m μ Q 2 m μ σ ˆ phy, α ( ),, ( ) 2 s μ σ α 2 2 s μ + O 2 μ μ μ μ Infrared safe = κ > 0 Asymptotic freedom is useful for quantities that are infrared safe 9

10 Running quark mass: Infrared Safety μ 2 dλ m( μ2) = m( μ1) exp - [ 1 + γ m( g( λ)) ] 0 as μ2 λ μ1 Perturbation theory becomes a massless theory when μ Infrared safety: 2 2 ( 2 ) 2 2 ( 2 ) κ Q 2 m μ Q 2 m μ σ ˆ phy, α ( ),, ( ) 2 s μ σ α 2 2 s μ + O 2 μ μ μ μ Infrared safe = κ > 0 Asymptotic freedom is useful for quantities that are infrared safe QCD perturbation theory (Q>>Λ QCD ) is effectively a massless theory 10

11 PQCD Factorization Can pqcd calculate cross sections with identified hadrons? Typical hadronic scale: 1/R ~ 1 fm -1 ~ Λ QCD Energy exchange in hard collisions: Q >> Λ QCD pqcd works at α s (Q), but not at α s (1/R) 11

12 PQCD Factorization Can pqcd calculate cross sections with identified hadrons? Typical hadronic scale: 1/R ~ 1 fm -1 ~ Λ QCD Energy exchange in hard collisions: Q >> Λ QCD pqcd works at α s (Q), but not at α s (1/R) PQCD can be useful iff quantum interference between perturbative and nonperturbative scales can be neglected Short-distance 2 σ phy( Q,1/ R) M PS σ( Q) ϕ(1/ R) + O(1/ QR) Power corrections Measured Long-distance 12

13 PQCD Factorization Can pqcd calculate cross sections with identified hadrons? Typical hadronic scale: 1/R ~ 1 fm -1 ~ Λ QCD Energy exchange in hard collisions: Q >> Λ QCD pqcd works at α s (Q), but not at α s (1/R) PQCD can be useful iff quantum interference between perturbative and nonperturbative scales can be neglected Short-distance 2 σ phy( Q,1/ R) M PS σ( Q) ϕ(1/ R) + O(1/ QR) Power corrections Measured Long-distance Factorization long-lived parton state 13

14 Time evolution: Picture of factorization in DIS Long-lived parton state Time: Past Now Future 14

15 Time evolution: Picture of factorization in DIS Long-lived parton state Time: Past Now Future Unitarity summing over all hard jets: σ DIS tot Im t 1 Q t R Not IR safe 15

16 Time evolution: Picture of factorization in DIS Long-lived parton state Time: Past Now Future Unitarity summing over all hard jets: σ DIS tot Im t 1 Q t R Not IR safe Interaction between the past and now are suppressed! 16

17 Long-lived parton states Feynman diagram representation of the scattering: W μν Perturbative pinched poles: dkh( Q, k) T( k, ) perturbatively 2 2 k + iε k iε r Dominated by a region where k 2 ~0 long-lived parton state 0 17

18 Long-lived parton states Feynman diagram representation of the scattering: W μν Perturbative pinched poles: dkh( Q, k) T( k, ) perturbatively 2 2 k + iε k iε r Perturbative factorization: Dominated by a region where k 2 ~0 long-lived parton state k 2 2 μ μ T μ μ = xp + n + kt dx d k k + k 2xp n H( Q, k = 0) dk T 2 2 x k iε k iε Short-distance 18 0 Nonperturbative matrix element T ( k, ) r 0

19 Collinear factorization Collinear approximation: 2 μ μ kt μ μ k xp + n + kt xp 2xp n γ * q k~xp if Q xp n k, k p T 2 Hadron is approximated by a beam of partons of momentum fraction x i Parton s transverse motion is integrated into ϕ x parton distributions: ( ) 19

20 Collinear factorization Collinear approximation: 2 μ μ kt μ μ k xp + n + kt xp 2xp n γ * q k~xp if Q xp n k, k p T 2 Hadron is approximated by a beam of partons of momentum fraction x i Parton s transverse motion is integrated into ϕ x parton distributions: ( ) Parton distributions are process independent, and QCD collinear factorization has been very successful 20

21 k T factorization Momentum of the long-lived parton is not necessary collinear to the hadron momentum k μ kt x p μ k T 2xp n n μ k μ + + For cross sections with a single hard scale Q, 2 2 dk T leads to power corrections: ( k T Q ) N 21

22 k T factorization Momentum of the long-lived parton is not necessary collinear to the hadron momentum k μ kt x p μ k T 2xp n n μ k μ + + For cross sections with a single hard scale Q, 2 2 dk T leads to power corrections: ( k T Q ) Physical processes with two observed scales: Q and q with a large Q to ensure QCD factorization, while q ~ k T probes a parton s transverse momentum γ * q k p ϕ p Both p and p are observed p probes the parton s k T Effect of k T is not suppressed by Q ( ) ( 2 x ϕ xk, ) T = TMD parton distributions 22 N

23 Factorization for hadronic collisions Picture in collinear factorization: Soft interaction p ' p ' ( ') φ f x x ' p ' x p φ f ( x ) ( ) ( ) d ( x Q)[ ] dσ dxϕ x dx' ϕ x' σˆ x, ', AB a/ A b/ B ab ab, 23

24 Factorization for hadronic collisions Picture in collinear factorization: Soft interaction p ' p ' ( ') φ f x x ' p ' φ f ( x ) Long-range soft interactions before the hard collision could break the PDF s universality loss of prediction x p ( ) ( ) d ( x Q)[ ] dσ dxϕ x dx' ϕ x' σˆ x, ', AB a/ A b/ B ab ab, 24

25 Factorization for hadronic collisions Picture in collinear factorization: Soft interaction p ' p ' ( ') φ f x x ' p ' φ f ( x ) Long-range soft interactions before the hard collision could break the PDF s universality loss of prediction Proof of the factorization to show the soft interaction does not alter the PDFs and the factorized formula x p ( ) ( ) d ( x Q)[ ] dσ dxϕ x dx' ϕ x' σˆ x, ', AB a/ A b/ B ab ab, 25

26 Predictive power of pqcd Short-distance and long-distance are separately gauge invariant Short-distance part is infrared-safe, and calculable LO NLO NNLO Factorized long-distance part (e.g., PDF) is Universal DGLAP: x μ ϕ ( x, μ ) = P, α ϕ ( x', μ ) F i F i/ j s j F μf j x ' LO NLO NNLO 26

27 Predictive power of pqcd Short-distance and long-distance are separately gauge invariant Short-distance part is infrared-safe, and calculable LO NLO NNLO Factorized long-distance part (e.g., PDF) is Universal DGLAP: x μ ϕ ( x, μ ) = P, α ϕ ( x', μ ) F i F i/ j s j F μf j x ' LO NLO NNLO Test of pqcd = Global QCD analysis Universal α s and a set of universal PDFs 27

28 Strong coupling constant: Global QCD analysis ee + : + h : h, γ, J/ ψ,... h+ h': h,j/ ψ, B,... γ, W, Z, H,... 28

29 Global fitting of PDFs Over 20 years effort of QCD Global fits: 29

30 PDFs of a spin-averaged proton Modern sets of PDFs with uncertainties: xf(x,q 2 ) NLO Q 2 =10 GeV 2 Q 2 =10 GeV 2 xu xg(x0.05) xd xs(x0.05) x 30

31 PDFs of a spin-averaged proton Modern sets of PDFs with uncertainties: xf(x,q 2 ) NLO Q 2 =10 GeV 2 Q 2 =10 GeV 2 xu xg(x0.05) xd xs(x0.05) x Consistently fit almost all data with Q > 2GeV 31

32 Comparison with DIS data 32

33 Charm quark distributions Large gluon at small-x large charm quark distribution 33

34 Prediction vs CDF Run II data 34

35 Rapidity dependence of jet data Run 2 Run 1b CDF Results 35

36 Uncertainties of gluon distribution MRST2001 CTEQ5M 36

37 Uncertainties of quark distribution 37

38 PDF uncertainty for observables CTEQ6 PDFs 38

39 PDF uncertainty for observables CTEQ6 PDFs % uncertainty for strong interaction 39

40 NNLO parton evolution A. Vogt, et al. Nucl. Phys. B691, 2004 at μ = 30 GeV

41 NNLO contribution to physical x-section A. Vogt, arxiv: [hep-ph] Uncertainty is from the scale dependence from 1 μ = M W to μ = 2M W 2 41

42 Higgs production at the LHC S =14 TeV Moch and Vogt,

43 Higgs production at the LHC S =14 TeV Moch and Vogt, 2005 Theory uncertainty: ~ 15% at NNLO, ~ 5% at N 3 LO 43

44 Perspects for the LHC Focus is shifting from QCD tests to QCD applications Many effort are on the production of multiple jets background for potential new physics calculation of multiple parton matrix elements perturbative loop correction MC program to perform this kind of calculating LO has no control on the scale dependence Numerical programs for the loop corrections Numerical integration over the sensitive regions 44

45 Calculation of LO matrix elements Many available programs can do automatic evaluation of the LO matrix elements, and corresponding cross sections General purpose ME generators: e.g., Madgraph, any tree subprocess in SM and MSSM, but not very fast Limited, but, very fast generators: Maltoni and Stelzer e.g., ALPGEN, capable of adding several gluons to given states Mangano et al. 45

46 Calculation of LO matrix elements Many available programs can do automatic evaluation of the LO matrix elements, and corresponding cross sections General purpose ME generators: e.g., Madgraph, any tree subprocess in SM and MSSM, but not very fast Limited, but, very fast generators: Maltoni and Stelzer e.g., ALPGEN, capable of adding several gluons to given states Mangano et al. 46

47 Difficulties with loop diagrams Reliable pqcd prediction requires at least NLO: 2 ( 1, 2,..., ) αs ( ) NLO: Real + virtual corrections to the Born process real: One more light parton emitted virtual: One light parton loop n 2 tree tree 2 dσ A n μ More jets (large n), worse the scale dependence NLO ~ % of LO in hadronic collisions Integrating out massless final-state partons leads IR and CO divergences dσ dσ + dσ NLO tree one-loop c.c. For normal people, a full one-loop 2 3 process takes 1-2 years 47

48 Calculation of NLO contribution Teach computer to calculate the loop diagram and the subtraction A lot progress has been made. Computer is able to calculate full one-loop diagrams of 2 4 process e.g. G. Salam, hep-ph/ Available NLO calculation: 48

49 A wish list for NLO calculation Les Houches wish list for NLO calculation: No principle difficulty, but, technically complicate Key: one loop diagrams with at least 4 parton final-states Several ideas for calculating the virtual contribution e.g., The on shell method: Bern, Dixon, Dunbar, Kosower loop constructed from trees, trees from the twistor technique 49

50 New technique for high orders Express tree amplitudes in terms of color ordered amplitudes: ( 1, 2,..., ) A n = g tree n 2 p Tr(t t...t ) A tree color structure ( 1, 2,..., n) color ordered 1 n G. Salam, hep-ph/

51 New technique for high orders Express tree amplitudes in terms of color ordered amplitudes: tree n 2 3 A ( 1, 2,..., n) = g Tr(t1t 2...t 3) color structure 4 p 2 tree A 1 n ( 1, 2,..., n) Calculate helicity amplitudes A tree i 12 (...) ++ = n1 color ordered Kunszt, 85 Parke, Taylor, 85 Many others G. Salam, hep-ph/

52 New technique for high orders Express tree amplitudes in terms of color ordered amplitudes: tree n 2 3 A ( 1, 2,..., n) = g Tr(t1t 2...t 3) color structure 4 p 2 tree A 1 n G. Salam, hep-ph/ n ( 1, 2,..., n) Calculate helicity amplitudes A tree i 12 (...) ++ = 1 zi n1 color ordered Recursion relations (Twistors): 2 (Britto,Cachazo,Feng, PRL 2005) zi + + Kunszt, 85 Parke, Taylor, 85 Many others = i 1 n i 1 i +1 i Sub-amplitudes made on-shell by analytic continuation of ±z i

53 Calculation of NNLO contribution ee NNLO: is completed! + 3 Jets A.~Gehrmann-De Ridder, et al. arxiv: [hep-ph] 53

54 Calculation of NNLO contribution ee 3 Jets NNLO: is completed! + A.~Gehrmann-De Ridder, et al. arxiv: [hep-ph] Many shape variables at LEP depend on the 3-parton final-state, e.g., the thrust distribution 2 α s α s α s 1( ) 2( ) 3 ( ) 1 dσ (1 T) = C T C T C T σ dt + + 2π 2π 2π Ellis, Rose, Terrano, 1980 New, NNLO ~ 5-15% effect 54

55 Calculation of NNLO contribution ee 3 Jets NNLO: is completed! + A.~Gehrmann-De Ridder, et al. arxiv: [hep-ph] Many shape variables at LEP depend on the 3-parton final-state, e.g., the thrust distribution 2 α s α s α s 1( ) 2( ) 3 ( ) 1 dσ (1 T) = C T C T C T σ dt + + 2π 2π 2π Ellis, Rose, Terrano, 1980 New, NNLO ~ 5-15% effect First chance to test QCD at NNLO beyond inclusive DIS 55

56 Shower Monte Carlo Tools to simulate the full event use available hard QCD partonic cross section dress hard events with QCD radiation (the shower) model the hadron fragmentation model for multi-parton collision, and underlying event use known decays of unstable particles 56

57 Shower Monte Carlo Tools to simulate the full event use available hard QCD partonic cross section dress hard events with QCD radiation (the shower) model the hadron fragmentation model for multi-parton collision, and underlying event use known decays of unstable particles New development CKKW matrix element and parton shower matching NLO improvement Catani, Krauss, Kuhn, Webber, 2001 Frixinoe, Webber, 2002; Kramer, Soper, 2003, Nason

58 Summary The collinear factorization formalism in pqcd has been very successful in interpreting the data from high energy collisions QCD global analysis has produced consistent sets of NLO PDFs, and on the way to NNLO accuracy The first full NNLO pqcd calculation is available for ee 3 Jets + Test QCD at NNLO Many advances have been made for calculating high order QCD partonic diagrams, and NLO contributions 58

59 Summary The collinear factorization formalism in pqcd has been very successful in interpreting the data from high energy collisions QCD global analysis has produced consistent sets of NLO PDFs, and on the way to NNLO accuracy The first full NNLO pqcd calculation is available for ee 3 Jets + Test QCD at NNLO Many advances have been made for calculating high order QCD partonic diagrams, and NLO contributions Ready for the LHC, and new physics? 59

60 Backup slices 60

61 Hadronic matter nuclei hadrons partons QCD dynamics for a scale 1 ~200 MeV Q < fm Question: How to understand hadron properties and structure in terms of partonic dynamics? How to see the partonic dynamics? snap shot of a hadron - seen by a hard probe at a short-distance 61

62 Time evolution: Picture of factorization in DIS Long-lived parton state Time: Past Now Future Unitarity summing over all hard jets: σ DIS tot Im t 1 Q t R Not IR safe Interaction between the past and now are suppressed! 62

63 63

64 64

65 Parton distribution functions (PDFs) μ 2 -dependence determined by DGLAP equations 2 2 x 2 μf ϕ (, ) 2 i x μf = Pi/ j, αs ϕ j( x', μf) μ j x ' F F Boundary condition extracted from physical x-sections Λ = xb Q 2 QCD 2 h( xb, Q ) Cq/ f,, α 2 s ϕ f / h( x, μf) O 2 q x μ F Q extracted parton distributions depend on the perturbatively calculated C q and power corrections Leading order (tree-level) C q Next-to-Leading order C q LO PDF s NLO PDF s Calculation of C q at NLO and beyond depends on the UVCT the scheme dependence of C q the scheme dependence of PDFs 65

66 Error analysis for PDFs 66

67 Gluon distribution over 20 years 67

68 NNLO non-singlet contributions 3 3 α s -splitting function α s 68 -coefficient function to F 2

69 NNLO gluon splitting 69

70 Limits on new physics from jet data D0 Run-I data 70

71 Comparison with hadronic jet data Run 1b results CDF Results 0.1< η <0.7 71

72 DO Run-2 photon + jet data 72