QCD Precision Tests in Deeply Inelastic Scattering

Transcription

1 QCD Precision Tests in Deeply Inelastic Scattering Johannes Blümlein DESY Introduction and Method QCD Analysis of Unpolarized Structure Functions Λ QCD and α s (M 2 Z ) What would we like to know? J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.1

2 Meeting with Jiro LL2 Bastei: Germany, PANIC 2, Nara He visited DESY Zeuthen first in 1997 and then very regularly. We had a very good time with him, always interesting scientific discussions and good private conversations, which promoted many long-term ties between Japan & Germany. We have lost a very good friend. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.2

3 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.3

4 DIS: Microscopy of the Nucleon determination of all quark densities and the gluon distribution determination of all polarized parton densities DIS: Fundamental Tests of QCD precision measurement of Λ QCD and α s (M 2 Z ) Thorough verification of the prediction of the light cone expansion: to higher twist Test of linear and non-linear resummations Challenges for Theory: perturbative and non-perturbative higher order precision calculations and data analysis Lattice gauge theory results for Λ QCD and hadronic ME J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.4

5 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.5 1

6 Highest order corrections of HO QCD in DIS 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(α 4 s) Baikov, Chetyrkin 26 Pol. anomalous dimension: O(α 2 s); P qq NS, P qg: O(α 3 s) Mertig, van Neerven, 1995; Vogelsang 1995; Moch, Vermaseren, Vogt Pol. Wilson coefficients: O(α 2 s); C qq NS, C qg: van Neerven, Zijlstra 1994 O(α 3 s) to come Transversity: O(α 2 s), some moments anom. dim.: O(α 3 s), 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(αs), 1 Watson 1982 Q 2 m 2 Pol. Heavy Flavor Wilson Coefficient : O(αs) 2 van Neerven, Smith et al. 1996, Blümlein & Klein 27 Q 2 m 2 Unpol. Heavy Flavor Wilson Coefficient F L : O(α 3 s) Blümlein, De Freitas, van Neerven, S. Klein 25 J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.6

7 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 ), M 2 µ 2, M 2 ) R }{{ 2 } Move to Mellin space : finite pdf f k Cj (α k s (R 2 ), Q2 µ 2, M 2 ) 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.7

8 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 SYMANNZIK 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 2π P (1) αs 2 (x) + P (2) (x) π J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.8

9 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.9

10 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 (x) Li2 (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., S. Moch, 23; J.B., V. Ravindran,24 J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.1

11 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 " S2,2 ( 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. Massless QCD to 3 Loops depends on 14 Functions. Representation for 3 Loop Wilson Coefficients under way. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.11

12 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.12

13 2. QCD Analysis of Unpolarized Parton Distributions DIS range Nucleon structure: 1 5 < x <.9, 1 < Q 2 < 5.GeV 2 J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.13

14 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.14

15 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.15

16 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.16

17 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.17

18 Valence Distributions xu v (X) x xu v (X) x.5.4 xd v (X).4 xd v (X) x x J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.18

19 Valence Distributions Q 2, GeV Q 2, GeV 2 J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.19

20 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 6 4 NLO NNLO N3LO agreement between p and d analysis LGT determination of interest x x J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.2

21 Flavor distributions: light quarks More work needed. J. Stirling, 24 HERMES probably could measure s(x, Q 2 ) in an independent way. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.21

22 Charm F cc 2 (x, Q2 ) will be very well measured at HERA. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.22

23 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.23

24 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.24

25 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.25

26 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! BBG Analysis in progress. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.26

27 "! $ % % ' % &% + ( ( (- $& ', Moments of PDF s: PT + data Moment BB, NLO uv ± ±.6 # # $ $ # " " " & dv.341 (! ( ( $ % 1.47 ±.21 #% #% ) # 2.15 ±.9 ( * uv dv * * 1.21 ±.25 ) & & & & ) & & 2.7 ±.11 $ )% % J.B., H. Böttcher, 22 J.B., H. Böttcher, A. Guffanti, 26 Lattice Results : developing; different fermion-types studied. Low values of mπ crucial; values approach 27 MeV now. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.27

28 3. 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.28

29 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.29

30 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 J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.3

31 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.31

32 4. The Needs : What would we like to know? HERA: Collect high luminosity for F 2 (x, Q 2 ), F cc 2 (x, Q2 ), g cc 2 (x, Q2 ), and measure h 1 (x, Q 2 ). Measure : F L (x, Q 2 ). This is a key-question for HERA. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.32

33 F L (x, Q 2 ) M. Klein, 24: Projection for a possible measurement at HERA = of central importance to study the small x behaviour of the gluon distribution J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.33

34 4. Future Avenues : What would we like to know? HERA: Collect high luminosity for F 2 (x, Q 2 ), F cc 2 (x, Q2 ), g cc 2 (x, Q2 ), and measure h 1 (x, Q 2 ). Measure : F L (x, Q 2 ). This is a key-question for HERA. RHIC & LHC: Improve constraints on gluon and sea quarks: polarized and unpolarized. DIS PDF s Collider PDF s JLAB: High precision measurements in the large x domain at unpolarized and polarized targets; supplements HERA s high precision measurements at small x. J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.34

35 1 % $ 9 = H % G C " < = = ; E = ; = Lq from DVCS HERA and JLAB : Improve DVCS data Theory widely developed, cf. rev. Belitsky & Radyushkin, 25 J u =.4 E= J u =.2 J u = 4<sin(Φ-ΦS )cosφ> J u =.4 E= J u =.2 J u = <sin(Φ-ΦS )cosφ> 4. '.(/ #"! 2(3.(/.(/ +-, * ' % ) #&(' % " > ' 7 4 ; 7 "!: 1@!?> = < 7 4 ; 7 < 1; : : "!87..(/ % +65! A = > = 7. FE 7 ;; <DC! 7I B!87 : A! 7 A Q P O < =!! N = " M KL " < = 7! = J C! " E 7!! = 7 =!! " M E 7 " = F. Ellinghaus et al. 25 The measurement of Lq off data is model dependent at the moment. Lattice calculations at low pion masses are needed to complete the picture J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.35

36 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.36

37 New DIS Machines Where to go? High energies : small x, large Q 2 desirable. High luminosities : ELIC: 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.37

38 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 arrival 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 Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.38

39 Enhancing Precision Further... Calculation of more hard scattering reactions at the 3 loop level: LHC Further perfection of the mathematical tools: = Algorithmic simplification of Perturbation theory in higher orders. Even higher order corrections needed? J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.39

40 Jiro will be commemorated by a large community J. Blümlein Dedicated to the memory of Jiro Kodaira KEK Symposium, March 27 p.4