Status of Deeply Inelastic Parton Distributions

Transcription

1 Status of Deeply Inelastic Parton Distributions Johannes Blümlein DESY DIS Theory Status QCD Analysis of Unpolarized Structure Functions Polarized Structure Functions Moments of Parton Densities Λ QCD and α s (M 2 Z ) Outlook J. Blümlein DIS Parton Distributions... Temple University, May 28 p.1

2 Deeply Inelastic Scattering e l l e, ν p Jet space like process : q 2 = (l l ) 2 = Q 2 < W 2 = (p+q) 2 M 2 p x = Q2 2p.q, y = p.q p.l x, y 1 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.2

3 Theory of DIS 69, QCD: Parton Model Light Cone Expansion [f] Twist 2 polarized unpolarized Fixed Order PT: QCD Higher Twist 77 Twist 3 Twist 4... α s Splitting functions Coefficient functions O(α 4 s) O(α 3 s) O(α 3 s) 73, 74, 8, 97 73, 82, 24 82, 92,24 Sum Rules 6ies - now Special Kinematics Domain: Small x Resummations? 75, Diffractive Scattering More General View Non-forw. scattering Angular Momentum: q, G Higher Orders = New Algorithms Novel Mathematics J. Blümlein DIS Parton Distributions... Temple University, May 28 p.3 1

4 Status of Highest Order Calculations Running α s : O(α 4 s) Larin, van Ritbergen, Vermaseren 1997 Unpol. anomalous dimensions and Wilson coefficients: O(α 3 s) Moch, Vermaseren, Vogt 24/5 Unpol. NS anomalous dimension 2nd Moment: O(αs) 4 Baikov, Chetyrkin 26 Pol. anomalous dimension: O(αs); 2 Mertig, van Neerven, 1995; Vogelsang 1995; P qq P qg : O(αs) 3 Moch, Rogal, Vermaseren, Vogt 28 Pol. Wilson coefficients: O(αs); 2 C qq NS, C qg: van Neerven, Zijlstra 1994 Transversity: O(αs), 2 some moments anom. dim.: O(αs), 3 Hayashigaki, Kanazawa, Koike; Kumano, Miyama; Vogelsang; 1997; Gracey 26 Unpol. Heavy Flavor Wilson Coefficients: O(α 2 s) Laenen, van Neerven, Riemersma, Smith, 1993 Fast Mellin Space code: Blümlein & Alekhin, 23 Pol. Heavy Flavor Wilson Coefficients: O(α 1 s) Watson 1982 Q 2 m 2 Unpol. Heavy Flavor Wilson Coefficient F L : O(α 3 s) Blümlein, De Freitas, van Neerven, S. Klein 25 Q 2 m 2 Pol. Heavy Flavor Wilson Coefficient : O(α 2 s) van Neerven, Smith et al. 1996, Bierenbaum, Blümlein & Klein 27 Q 2 m 2 Unpol. Heavy Flavor Wilson Coefficient F 2 : O(α 2 sε): all operators (also polarized), Bierenbaum, Blümlein, Klein, Schneider, 28; O(α 3 s): First contributions to the moments of the operator matrix elements, Bierenbaum, Blümlein, Klein, 28 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.4

5 DIS Structure Twist 2 F j (x, Q 2 ) = ˆf i (x, µ 2 ) σ i j ) (α s, Q2 µ 2, x bare pdf sub system cross sect. ) = ˆf i (x, µ 2 ) Γ i k (α s (R 2 ), M2 µ 2, M2 R }{{ 2 } Move to Mellin space : finite pdf f k ) Cj (α k s (R 2 ), Q2 µ 2, M2 R 2, x }{{} finite Wilson coefficient F j (N) = 1 dxx N 1 F j (x) Diagonalization of the convolutions into ordinary products. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.5

6 Evolution Equations [ M [ M M + β(g) ] g 2γ ψ(g) F i (N) = ] + β(g) + M g γn κ (g) 2γ ψ (g) f k (N) = [ ] M + β(g) M g γn κ (g) Cj k (N) = CALLAN SYMNANZIK equations for mass factorization ALTARELLI PARISI evolution equations x-space : d d log(µ 2 q+ (x, Q 2 ) G(x, Q 2 ) 1 A = α s 2π P(x, α q+ (x, Q 2 ) G(x, Q 2 ) 1 A P(x, α s ) = P () (x) + α s αs 2 2π P(1) (x) + P (2) (x) π J. Blümlein DIS Parton Distributions... Temple University, May 28 p.6

7 Anomalous Dimensions and Wilson Coefficients.3.25 γ qq (N).6 γ gg (N) LO NLO NNLO.1 ps α S =.2, N f = N N Vermaseren, Moch, Vogt 24 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.7

8 The Basic Functions of massless QCD to w=5: 3 Loops Representative : S 1 (N) = ψ(n + 1) + γ E and its derivatives.» ln(1 + x) Weight w=3 : F 1 (N) = M (N) 1 + x» " Li2 «Li2 (x) (x) F 2 (N) = M (N), F 3 (N) = M 1 + x 1 x + # (N) Yndurain et al., 1981: F 2 (N) Weight w=4 :» S1,2 (x) F 4 (N) = M (N), 1 + x " S1,2 «(x) F 5 (N) := M 1 x + # (N) F 3 (N) F 5 (N): J.B., 23; J.B., V. Ravindran,24 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.8

9 Weight w=5 : " Li4 «(x) F 6,7 (N) = M 1 ± x " S2,2 «(x) F 9,1 (N) = M 1 ± x (+) (+) # (N), # (N),» S1,3 (x) F 8 (N) = M (N), 1 + x» Li 2 F 11 (N) = M 2 (x) (N), 1 + x " ln(x)s1,2 ( x) Li 2 2 F 12,13 (N) := M ( x)/2 «1 ± x (+) # (N) F 6 (N) F 13 (N) : J.B., S. Moch, 24. Weight w=6 : Massless QCD to 3 Loops depends on 14 Functions. Representation for 3 Loop Wilson Coefficients: 35 Functions, J.B., 28. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.9

10 Complex Analysis of these Functions Construct exact analytic continuations to complex N The functions are meromorphic (up to soft corrections, which have a simple structure) Asymptotic Representation Recursion z + 1 z Solve the Evolution Equations fully analytically and form an analytic expression for the Structure functions in Mellin Space at all Q 2 Include the heavy flavor Wilson coefficients in Mellin Space Perform a single fast, numerical Mellin inversion (at high precision) Fastest and most Precise Way of Analysis J. Blümlein DIS Parton Distributions... Temple University, May 28 p.1

11 2. QCD Analysis of Unpolarized Structure Functions DIS range Nucleon structure: 1 5 < x <.9, 1 < Q 2 < 5.GeV 2 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.11

12 ZEUS F 2 2 i x =.5, i = 21 x =.8, i = 2 x =.13, i = 19 x =.2, i = 18 x =.32, i = 17 x =.5, i = 16 x =.8, i = 15 x =.13, i = 14 x =.2, i = 13 x =.32, i = 12 H1 e + p ZEUS e + p BCDMS NMC em F 2 -log1 (x) 5 4 x=6.32e-5 x=.12 x=.161 x=.253 x=.4 x=.5 x=.632 x=.8 x=.13 x=.21 x=.32 ZEUS NLO QCD fit tot. error ZEUS 96/97 BCDMS E665 NMC x =.5, i = 11 x =.8, i = 1 x =.13, i = 9 x =.2, i = 8 x =.32, i = 7 x =.5, i = 6 3 x=.5 x=.8 x= x =.8, i = 5 x =.13, i = 4 x =.18, i = 3 x =.25, i = 2 2 x=.21 x=.32 x= H1 PDF 2 extrapolation 1-3 x =.4, i = 1 x =.65, i = Q 2 / GeV 2 H1 Collaboration x=.8 x=.13 1 x=.18 x=.25 x=.4 x= Q 2 (GeV 2 ) J. Blümlein DIS Parton Distributions... Temple University, May 28 p.12

13 New ZEUS + H1 averaged F 2 (x,q 2 ) HERA I e + p Neutral Current Scattering - H1 and ZEUS NC σ r (x,q 2 ) 1.4 x=.2 HERA I e + p (prel.) 1.2 ZEUS H1 1.8 x= x= Q 2 / GeV 2 DIS8 Joël Feltesse HERA Structure Functions Working Group J. Blümlein DIS Parton Distributions... Temple University, May 28 p.13

14 New ZEUS + H1 averaged F 2 (x,q 2 ) HERA I e + p Neutral Current Scattering - H1 and ZEUS σ r (x,q 2 ) x 2 i x =.32, i=22 x =.5, i=21 x =.8, i=2 x =.13, i=19 x =.2, i=18 x =.32, i=17 x =.5, i=16 x =.8, i=15 x =.13, i=14 x =.2, i=13 x =.32, i=12 x =.5, i=11 x =.8, i=1 x =.13, i=9 x =.2, i=8 x =.32, i=7 x =.5, i=6 x =.8, i=5 x =.13, i=4 x =.18, i=3 x =.25, i=2 DIS8 Joël Feltesse HERA I (prel.) Fixed Target H1 2 PDF ZEUS-JETS x =.4, i=1 x =.65, i= Q 2 / GeV 2 HERA Structure Functions Working Group J. Blümlein DIS Parton Distributions... Temple University, May 28 p.14

15 Direct F L (x,q 2 ) Measurement at HERA J. Blümlein DIS Parton Distributions... Temple University, May 28 p.15

16 Direct F L (x,q 2 ) Measurement at HERA J. Blümlein DIS Parton Distributions... Temple University, May 28 p.16

17 Parton Distributions: Overview xp(x) xu xu v xu xd xd v xg x H1 xd H1 PDF 2: Q 2 = 4 GeV 2 Fit to H1 data experimental errors model uncertainties Fit to H1 + BCDMS data parton distribution x H1 Collaboration J. Blümlein DIS Parton Distributions... Temple University, May 28 p.17

18 World Data Analysis: Valence Distributions xu v (X) x xu v (X) x World data: NS-analysis W 2 > 12.5 GeV 2, Q 2 > 4 GeV xd v (X).5.4 xd v (X) N 3 LO : α s (M 2 Z) = x x J.B., H. Böttcher, A. Guffanti, [hep-ph/672] J. Blümlein DIS Parton Distributions... Temple University, May 28 p.18

19 Why an O(α 4 s) analysis can be performed? assume an ±1% error on the Pade approximant ±2 MeV in Λ QCD γ approx:3 n 2 = γ(2) n γ n (1) Baikov & Chetyrkin, April 26: γ 3;NS 2 = 32 9 a s + 944» a2 s » ζ 3 a 3 s ζ ζ ζ 5 a 4 s The results agree better than 2%. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.19

20 Valence Distributions xu v (X) x xu v (X) x.5.4 xd v (X).4 xd v (X) x x J. Blümlein DIS Parton Distributions... Temple University, May 28 p.2

21 Valence Distributions Q 2, GeV Q 2, GeV 2 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.21

22 Valence Distributions: higher twist PROTON C HT (x) [GeV 2 ] 12 1 DEUTERON C HT (x) [GeV 2 ] 1 4. GeV 2 < W 2 < 12.5 GeV GeV 2 < W 2 < 12.5 GeV NLO NNLO N3LO N4LO NLO NNLO N3LO N4LO x agreement between p and d analysis, J.B., H. Böttcher, 28 LGT determination of interest x J. Blümlein DIS Parton Distributions... Temple University, May 28 p.22

23 Flavor distributions: light quarks MRST21E ALEKHIN2 E dbar - ubar Q 2 = 54 GeV 2 x J. Stirling, 24 More work needed. HERMES probably could measure s(x, Q 2 ) in an independent way. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.23

24 Flavor distributions: light quarks C6.5M:ū+- d C6.5S:ū+- d C6.5M:s + C6.5S:s + x 5/3 f(x) x CTEQ 27 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.24

25 Charm F cc 2 (x, Q2 ) will be very well measured at HERA. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.25

26 Slope of F 2 at low x df 2 S(x)/dt H1 Collaboration 2 1 H x J.B., A. Guffanti 25 Very likely, that the MS gluon is remains positive! J. Blümlein DIS Parton Distributions... Temple University, May 28 p.26

27 Perturbative or non-perturbative growth? F 2.4 Q 2 =.5 GeV 2 F Q 2 = 2 GeV x x F 2 Q 2 = 7 GeV x H1 QEDC 1997 H H1 SV 1995 ZEUS BPT E665 NMC SLAC ALLM97 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.27

28 Gluon Density H1 Collaboration H1 MRST 2 vs CTEQ 6 More work needed; MS vs scheme-invariant evolution. F L (x, Q 2 ) could be decisive. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.28

29 Gluon Density xg(x,q 2 =5) 4 Not both distributions can be correct. F L (x, Q 2 ) could be decisive x MRST6 vs Alekhin: 26 More work needed! BB Analysis in progress. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.29

30 Gluon Density Recent Fits based on H1 + ZEUS combined data sets J. Blümlein DIS Parton Distributions... Temple University, May 28 p.3

31 3. Polarized Structure Functions High Luminosity is most important: Various precision measurements. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.31

32 The polarized Structure Function Now & Then July x=.8 ( x 248) x=.15 ( x 124) x=.25 ( x 512) 1 2 x=.35 ( x 256) x=.5 ( x 128) x=.8 ( x 64) 1 x=.125 ( x 32) g 1 p 1 x=.175 ( x 16) x=.25 ( x 8) x=.35 ( x 4) 1-1 x=.5 ( x 2) 1-2 Q 2 [(GeV/c) 2 ] x=.75 ( x 1) E155 E143 SMC HERMES EMC Lower values of x are reached, improving accuracy in the medium and large x region. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.32

33 The polarized Structure Function Now & Then How does g 1 (x, Q 2 ) behave at small x? = Sufficiently wide slopes in ln(q 2 ). J. Blümlein DIS Parton Distributions... Temple University, May 28 p.33

34 Polarized Parton Densities at Present x x x x J.B., H. Böttcher (22) J. Blümlein DIS Parton Distributions... Temple University, May 28 p.34

35 The W-Asymmetry A W and g 5 (x,q 2 ) A W = [2b(y)g W 1 + a(y)g W 5 ]/[a(y)f W 1 + b(y)f W 3 ] g W+,p 5 + g W,p 5 = u v + d v, g W+,p 5 g W,n 5 = [ (u + ū) (d + d)] Measurement of a polarized electro-weak structure function at high Q 2. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.35

36 The Polarized Gluon Distribution at Present AAC3 GRSV BB LSS.2 x g(x) x J.B., H. Böttcher (22) x q(x) Q 2 = 1 GeV x AAC = Currently slight move of G towards lower values J. Blümlein DIS Parton Distributions... Temple University, May 28 p.36

37 The Polarized Gluon Distribution at RHIC g/g(x) 1.5 AAC24 AAC 1-σ limit GRSV std GRSV limit g/g(x) 1.5 AAC24 AAC 1-σ limit GRSV std GRSV limit HERMES di-hadron SMC di-hadron COMPASS di-hadron COMPASS di-hadron projection RHIC Jet projectn. at s=5 GeV HERMES di-hadron SMC di-hadron COMPASS di-hadron COMPASS di-hadron projection -1 RHIC γ projection 65 pb at s=2 GeV -1 RHIC γ projection 39 pb at s=5 GeV x x Accuracies for G, which may be reached at RHIC J. Blümlein DIS Parton Distributions... Temple University, May 28 p.37

38 The Polarized Gluon Distribution at EIC x g(x) fb -1 P e P p =5% x g(x) pb -1 P e P p =5% GS-A GS-C x -.1 GS-A GS-C x Excellent Resolution for G at EIC J. Blümlein DIS Parton Distributions... Temple University, May 28 p.38

39 The Polarized Gluon Distribution at EIC G/G COMPASS, fit with G>, MS, Q =3(GeV/c) 2 2 COMPASS, fit with G<, MS, Q =3(GeV/c) 2 COMPASS, open charm, µ 2 =13(GeV/c), prel., COMPASS, high p, Q <1(GeV/c), prel., 2-4 T 2 2 COMPASS, high p, Q >1(GeV/c), prel., T 2 SMC, high p, Q >1(GeV/c) T 2 HERMES, high p, all Q, published (2) T 2 HERMES, high p, all Q, prel. T x Accuracy for G from Open Charm Production at EIC J. Blümlein DIS Parton Distributions... Temple University, May 28 p.39

40 The Polarized Gluon Distribution at EIC x u.2 x d.4.2 x( u+ u ) x u v x g x u x d Q 2 = 2.5 GeV 2 GRSV2 LO std BB1 LO x( d+ d ) x u x d v x d x s KRE (NLO) KKP (NLO) unpolarized KRE χ 2 min +1 KRE χ 2 min +2% x s x HERMES, x Bj x Bj De Florian & Sassot, x Bj -.6 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.4

41 Unfolding the Sea Quarks.4 x u x d DSSV DNS GRSV DSSV χ 2 =1 DSSV χ 2 /χ 2 =2% x s Q 2 = 1 GeV 2 x g GRSV max. g GRSV min. g x x De Florian, Sassot, Stratmann, Vogelsang, 28 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.41

42 Unfolding the Sea Quarks q/q 1..5 RHIC pp s = 5 GeV 1 L dt = 8 pb A L (W ) _ A (W ) L + u/u d/d u/u 2 2 Q = M W GS95LO(A) BS( g=) 1 1 d/d RHIC, G. Bunce et al. 2 x EIC J. Blümlein DIS Parton Distributions... Temple University, May 28 p.42

43 Unfolding the Sea Quarks Comparison of the Sensitivity at HERMES and at EIC J. Blümlein DIS Parton Distributions... Temple University, May 28 p.43

44 Charm Contributions xg 1 QQ(x,Q 2 ) xg 2 QQ(x,Q 2 ) x x x JB, Ravindran, van Neerven (23): g cc 1,2 (x, Q2 ) = to be measured at EIC J. Blümlein DIS Parton Distributions... Temple University, May 28 p.44

45 g 2 (x,q 2 ) - a Window to Higher Twist xg 2 p(x,q 2 ).6.4 [12] x JLAB Hall A, 24 g τ=2 2 (x, Q 2 ) (light partons) Accurate measurement highly desired. How big is the τ = 3 contribution? J. Blümlein DIS Parton Distributions... Temple University, May 28 p.45

46 4. Moments of PDF s: PT + data Ò Ì Ø ÅÊË̼ ¼¾ Æ ÄÇ ÆÆÄÇ ÆÆÄÇ ÙÚ ¾ ¼ ¼¼ ¼ ¼¼ ½ ¼º¾ ¼º ¼ ¼ ¼ ¼ ¼¼½¾ ¼ ¼ ¾ ¼ ¼ ¼ ¼ ¼ ¼¼¼ ¼º¼ ¾ ¼º¼ Ú ¾ ¼ ½¾ ¾ ¼ ¼¼¾ ¼º½½ ¼º½¾¼ ¼ ¼ ½ ¼ ¼¼¼ ¼ ¼¾ ¼ ¼¾ ¼ ¼½¼ ¼ ¼¼¼ ¼º¼¼ ¼º¼½¼ ÙÚ Ú ¾ ¼ ½ ¼ ¼¼ ½ ¼º½ ½ ¼º½ ¼ ¼ ¼ ¼¼½ ¼ ¼ ¼ ¼ ¼ ¼¾¾ ¼ ¼¼¼ ¼º¼¾¾ ¼º¼¾ J.B., H. Böttcher, A. Guffanti, 26 Moment BB, NLO u v ± ±.6 d v ± ±.9 u v d v ± ±.11 J.B., H. Böttcher, 22 Lattice Results : developping; different fermion-types studied. Low values of m π crucial; values approach 27 MeV now. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.46

47 5. Λ QCD and α s (M 2 Z ) δα em () α em () δα weak α weak δα s (M 2 Z ) α s (M 2 Z ) > P. Zerwas, 24 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.47

48 Overview of the Analyses Various NLO analyses; Precision requires NNLO analysis and higher! Mixed S- and NS-NNLO analyses S- and NS-NNLO moment analyses NS-N 3 LO analysis e(µ)n world data νn world data e(µ)n world data NLO analyses polarized e(µ)n world data Lattice measurements J. Blümlein DIS Parton Distributions... Temple University, May 28 p.48

49 α s (M 2 Z ) NLO α s (MZ 2 ) expt theory Ref. CTEQ ±.65 [1] MRST ±.2 ±.3 [2] A ±.15 ±.33 [3] ZEUS.1166 ±.49 [4] H1.115 ±.17 ±.5 [5] BCDMS.11 ±.6 [6] GRS.112 [1] BBG.1148 ±.19 [9] +.9 BB (pol).113 ±.4.6 [7] NLO NNLO α s (MZ 2 ) expt theory Ref. MRST ±.2 ±.3 [2] A ±.14 ±.9 [3] SY1(ep).1166 ±.13 [8] SY1(νN).1153 ±.63 [8] GRS.111 [1] A ±.15 [11] BBG /.21 [9] N 3 LO α s (MZ 2 ) expt theory Ref. BBG /.22 [9] NNLO and N 3 LO BBG: N f = 4: non-singlet data-analysis at O(α 4 s): Λ = 234 ± 26 MeV Lattice results : Alpha Collab: N f = 2 Lattice; non-pert. renormalization Λ = 245 ± 16 ± 16 MeV QCDSF Collab: N f = 2 Lattice, pert. reno. Λ = 261 ± 17 ± 26 MeV Lepage et al.: Larger Values, to be discussed. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.49

50 αs(m 2 Z ) CTEQ6 MRST3 A2 ZEUS H1 BCDMS SY1(ep) SY1(νN) BBG MRST3 A6 SY1(ep) SY1(νN) BBG BBG BB SMC ABFR αs (M Z 2 ) J.B., H. Böttcher, A. Guffanti, 26 J. Blümlein DIS Parton Distributions... Temple University, May 28 p.5

51 More Global Analyses α s (MZ 2 ) for different data sets included are too different! applies also to HERA: IS vs FS; and also DIS vs TEVATRON-jet 2 min - χ 2 total χ ZEUS fit with jet data without jet data world average (Bethke 24) ZEUS M. Cooper-Sarkar, 25 α s (M Z ) J. Blümlein DIS Parton Distributions... Temple University, May 28 p.51

52 6. What would we like to know? HERA: Analyze complete collected luminosity for F 2 (x,q 2 ), F2 cc(x,q2 ), g2 cc(x,q2 ), and measure h 1 (x,q 2 ). RHIC & LHC: JLAB: Improve constraints on gluon and sea quarks: polarized and unpolarized. DIS PDF s Collider PDF s High precision measurements in the large x domain at unpolarized and polarized targets; supplements HERA s high precision measurements at small x. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.52

53 Ò ÝÑÑ ØÖÝ Ë µ Ó Í Ì Î Ë ÜÔ Ø Â ¼ ¼ Ò Ø Ê Ð Ø Ô Ò Ðµ Ò ØÓÖ Þ Ö Ø Ô Ò Ðµ Ò ØÞ Ø Ø Ò Ñ Ø Ó Ø ÙÐÐ Ñ ÙÖ Ñ Òغ ¼ ÒÓØ Þ ÖÓ «Ø Ú ÓÒ¹ Ú Ö ÖÓÑ Ø È º Ì ÔÖÓ Ø Ø Ø Ø Ð ÖÖÓÖ ÓÖ Å ÁË Ú ÒØ ØÖ ÙØ ÓÒ Ì Ý Ø Ñ Ø ÖÖÓÖ ÜÔ Ø ØÓ ÒÓØ Ü Ø Ø Ø Ø Ð ÓÒ º ÓÛÒº L q from DVCS HERA and JLAB : Improve DVCS data Theory widely developed, cf. rev. Belitsky & Radyushkin, 25 4<sin(Φ-Φ S )cosφ> E= J u =.4 J u =.2 J u = 4<sin(Φ-Φ S )cosφ> E= J u =.4 J u =.2 J u = Û Ø Ú ½ ½  ٠¼ ¼ ¾ ¼ ¼µ F. Ellinghaus et al. 25 The measurement of L q off data is model dependent at the moment. Lattice calculations at low pion masses are needed to complete the picture J. Blümlein DIS Parton Distributions... Temple University, May 28 p.53

54 Graph Resummation and Saturation Further study of proposed mechanisms needed: RHIC, LHC for nucleus-nucleus collisions. ep scattering: partly different mechanisms more studies would be welcome; link to higher twist contributions in gluon dynamics How do the non-perturbative and perturbative parts factorize? Conservation laws and interplay between the small x and medium x range behaviour J. Blümlein DIS Parton Distributions... Temple University, May 28 p.54

55 New DIS Machines Where to go? High energies : small x, large Q 2 desirable. High luminosities : ELIC/EIC: s between CERN and HERA energies R. Ent,24 high precision physics polarized and unpolarized Would be an important extension of the present programmes in many respects. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.55

56 Enhancing Precision Further... What is the correct value of α s (M 2 z )? MS-analysis vs. scheme-invariant evolution helps. Compare non singlet and singlet analysis; careful treatment of heavy flavor. [Theory & Experiment] Flavor Structure of Sea-Quarks: More studies needed.[all Experiments] Revisit polarized data upon completion of the 3-loop anomalous dimensions; NLO heavy flavor contributions needed. [Theory] QCD at Twist 3: g 2 (x, Q 2 ), semi exclusive Reactions, Transversity, diffraction in polarized scattering [HERMES, High Precision polarized experiments, JLAB, ELIC] Comparison with Lattice Results: α s, Moments of Parton Distributions, Angular Momentum. J. Blümlein DIS Parton Distributions... Temple University, May 28 p.56