30 Years of QCD From High Energy Physics

30 Years of QCD - From High Energy Physics Point of View - JPS Meeting at Noda TUS, 2005 　シンポジウム 　量子色力学 (QCD) の３０年：現状と展望 J. Kodaira 2005 March 25 J. Kodaira

30(+2) Years of QCD - From High Energy Physics Point of View - Theory Developments 　　　　　 with ● High Energy Experiments Last 30 Years J. Kodaira The “most” beautiful Eqs. in 20 th Century Einstein Eq. for Gravity × Non-abelin Gauge Theory　(QCD)

Asymptotic Freedom and Quantum Chromo Dynamics Symanzik, Fritzsch, Gell-Mann, Weinberg, Callan, Adler, Bjorken, ………. 1972 © Univ. of Chicago ? 1965 1973 © The Nobel Foundation 2005 March 25 J. Kodaira

Advanced information on the Nobel Prize in Physics, 5 October 2004 Says In 1965 he proposed with Moo-Young Han that the field theory should be a non-abelian gauge theory, ………. . , Nambu’s field theory had all the relevant details of the correct theory, but it was perhaps too early and ………. it (QCD) was essentially the same model that Nambu had proposed many years earlier. ………… 2005 March 25 J. Kodaira

Typical examples of success of QCD 1. R (Drell) - Ratio (Discovery of “Color”) ● 1974 ● 1977 2005 March 25 J/Ψ　　　 ● 1984 W (Z) Υ ● 1995 t J. Kodaira

2. Jets (Discovery of “Gluon”) © L 3 at LEP First discovery of 3 jet was at PETRA in 1979 2005 March 25 J. Kodaira

3. (F 2) Structure function in DIS (Discovery of “Scaling Violation”) 　↑ Scaling 2005 March 25 J. Kodaira

4. Strong coupling constant (Discovery of “Asymptotic Freedom”) 2005 March 25 J. Kodaira

30 years of QCD I 1970 II 1980 III 1990 QCD 3 Jet Spin Physics (EMC) 2000 Small-x, Pomeron (HERA) I. Rise of QCD and Start of (p) QCD II. QCD as Field Theory III. Present Status of QCD 2005 March 25 J. Kodaira B Physics

30 years of QCD I 1970 II 1980 1990 QCD 3 Jet Spin Physics (EMC) 物理学論文選集 206 by M and U CSS Review ed. by Mueller Basics of p. QCD by D, K, M and T III Small-x, Pomeron (HERA) 「QCD の新しい局面」 学会特別講演 by J. K. “Pink Book” By E, S and W 「QCD 20 Years Later」 at Aachen 2005 March 25 2000 J. Kodaira B Physics Heavy Quark Phys. by M and W QCD and Pomeron by F and R 「QCD Sympo. 」 at Hiroshima

Development of Experimental Facilities Livingston plot? I III II III © Yokoya at ICHEP 2004 2005 March 25 J. Kodaira

I. Rise of QCD and Start of (p) QCD Basics of p. QCD Renormalization Group Equation Asymptotic Freedom → Small → Large ⇒ Perturbative Calculation to Quark-Gluon System 2005 March 25 J. Kodaira

Consider “Observable” in Quark-Gluon System ： Hadronic Scale ： Hard Scale Formal Answer So Expand Breaks Down of Perturbation Theory 2005 March 25 J. Kodaira

Two Cases to Overcome This Problem ● Singularity Free Case Ex. R-Ratio, Jets (Sterman-Weinberg), Energy-Energy Correlation, Shape Parameter (Thrust, C-parameter, …) …. Kinoshita-Lee-Nauenberg (KLN) Theorem 2005 March 25 J. Kodaira

● Factorization Theorem　(Note: Process Dependent) : Factorization Scale Process for which Factorization holds : PDF , 2005 March 25 : PFF Only their μF, D Dependence Cal. (DGLAP) Contain Non-Perturbative Info. J. Kodaira

☆　Theoretical Ambiguities 　≧ 20 ～ 30% ● Scale （Scheme） Dependence X-Sections do not Depend on μ（R, F, …) Truncation Does Induce Scale Dep. !! BUT → LO (Nonsense) → NLO → NNLO → … ● Edge of Phase Space Perturbative Parts: Free From Singularity BUT In Edge Region of Phase Space Large Log Corrections → ? ? ? ? →　Pessimism (QCD Does Not Give Quantitative Prediction) 2005 March 25 J. Kodaira

Summary of First 10 Years 2005 March 25 J. Kodaira

II. QCD as Field Theory ● Resummation (Infrared Sensitive Quantity) Summation of LARGE LOGs to All Orders Mass Singularity LOG ← Renormalization G. E. DGRAP Infra LOG ←　Difficult ● Renormalon ● Basic Integrals for NNLO Calculations ● Gauge Theory Amplitude (ex. Parke and Taylor) ● Start of Effective Theory (NRQCD, HQET, …) ● …… 2005 March 25 J. Kodaira

Experimental Developments ● Spin (EMC, 1988) →　SMC, SLAC, HERMES, Compass, RHIC, … ● Small-x (HERA, 1992) Hadron Spin Physics II ⇒ III → Goto Rise of F(x) at Small x Rapidity Gap BFKL, Pomeron (Regge) Low x (Saturation) III ● Tevatron Large p. T Jet, B-meson Production, …. . 2005 March 25 J. Kodaira

● Structure Function at Small-x -- finite -- : two-scales : three-scales Resum not only but also (Mass Singularity) (Infrared Singularity) BFKL and CCFM Eq. (LL) Resum ⇒ (NLL) QCD (HARD) Pomeron !? !? !!! 2005 March 25 J. Kodaira

★ Gluon Saturation III DGLAP and BFKL : Linear Evolution ⇒ High Gluon Densities at Low x ⇒ Non-linear Effects ↓ Gluon Saturation -- Saturation Model Golec-Biernat and Wüsthoff (’ 99) -- Balitsky-Kovchegov Equation (’ 99) -- CGC (Color Grass Condensation) Iancu, Leodinov, Mc. Lerran, … (～ ’ 00) 2005 March 25 J. Kodaira

Phenomenological Implication Emergence of “Saturation Scale” “Geometric Scaling” X-section should be Function of Staśto, Golec-Biernat and Kwieciński (’ 01) 2005 March 25 J. Kodaira

Summary of Second 10 Years 2005 March 25 J. Kodaira

III. Present Status of QCD ● Precision QCD Reduce Ambiguities (aim : Error ≦ 10%) ¶ Scale （Scheme） Dependence Scale Dep. Induced by Truncation → LO (Nonsense) → NLO → NNLO → … Physically would be a Good Choice →　Look Stability with ¶ Edge of Phase Space　(Infrared Logs) Large Log Corrections → Resummation ¶ PDF , PFF Fitting (Non-Pert. Object) Data (HERA + TEVATRON + LEP) + Theory Used 2005 March 25 J. Kodaira

Example of Higher Order Cal. (gg → H) Higgs Production at LHC (NNLO) ● LO (Georgi, Glashow, Machacek and Nanopoulos ’ 78) II Dawson ’ 91 Spira et al. ’ 95 I ● NLO ( Mt → ∞ ) 　　　　　 ( Exact ) NLO Correction 　～ 100 % !!!!! ● NNLO III Harlander ’ 00 ( Virtual ) Catani et al. ’ 01 Harlander and Kilgore ’ 01 ( Soft ) Harlander and Kilgore ’ 02 ( Numerical ) Anastasiou and Melnikov ’ 02 Ravindran et. al ’ 03 ( Exact ) NNLO Correction 2005 March 25 ～　Moderate J. Kodaira

2005 March 25 J. Kodaira

PDF 1. Status until ‘ 04 NLO = 1 -loop Hard part + 2 -loop (DGLAP) To Determine PDF, Two Errors Enter Data + Theory　(μR 2 = μF 2 = Q 2 : fixed ) 2005 March 25 J. Kodaira

2. Present Status NNLO = 2 -loop Hard Part + 3 -loop DGLAP Available !! Moch, Vermaseren and Vogt (’ 04) Theoretical Error: NLO (10 -20%) to NNLO (a few – 10%) 2005 March 25 J. Kodaira

Resummation Program : Finite in Distribution Sense !! →　Does Not Mean Good Perturbation In Edge Region of Phase Space Two Scale Problem vs. One Scale Problem Ex. 1 Structure Function Small x ( s >> Q 2) , Large x ( s << Q 2) Ex. 2 Drell – Yan Type Process Threshold Logs 　 Recoil or QT Logs Large αS ln 2 ( Ratio of Two Scales) 2005 March 25 J. Kodaira Appear

Structure of PT with Two Different Scales Putting → truncate at a fixed Order → resum Terms Rearrange Perturbative Series such that Leading Log (LL) Next to Leading Log (NLL) (NNLL) 2005 March 25 J. Kodaira

- Threshold Resummation - QT Resummation Sterman(’ 87) Catani and Trentadue (’ 89) Collins and Soper (’ 81) Kodaira and Trentadue (’ 82) Higgs Production with Error Band 　　　　　　　 (NNLO vs. NNLL) Higgs QT Distribution with Error Band (NNLO vs. NNLL) Catani, de Florian, Grazzini and Nason (’ 03) 2005 March 25 Bozzi, Catani , de Florian and Grazzini (’ 03) J. Kodaira

● Effective Theories -- NRQCD(QED) Nonrelativistic System (Heavy Quarkonium Decay and Prod. ) Weakly Couple and/or Fewer Channels: Simple Many Energy Scales: Difficult → Introduce Cut-off and Construct Effective Theory Caswell and Lepage (’ 86) Bodwin, Braaten and Lepage (’ 95) Boundary between Rela. And Nonrela. Relativistic Phys. 　→　Effective Local Int. 2005 March 25 J. Kodaira

-- HQET Hadron with “Heavy Quark” → Effective Theory in Power Series of 1 / MQ Eichten, Grinstein, Hill, Georgi, Isugar, Wise, … ( ～ ’ 90) QCD Factorization in B Decay Beneke, Buchalla, Neubert and Sachrajda (’ 99) 2005 March 25 J. Kodaira

-- SCET (Soft Collinear Effective Theory) Idea: Fast Moving Light Hadrons Contain ONLY SOFT COLLINEAR MODES Make Effective Theory Containing Only Such Modes Bauer, Fleming, Luke, Pirjol, Stewart, … (’ 01 ～) Beneke, Neubert, … ・ Complete Proof of Factorization ・ Phenomenological Developments ・ ………. Originally in the Context of B, but Can Apply Any Hard Process 2005 March 25 J. Kodaira

Summary ● QCD is the Fundamental Theory of Strong Interaction ● Theory Developments ⇒ Uematsu ● QCD as Tools for LHC ● ……… D C 50 2005 March 25 J. Kodaira f o rs a Ye D C Q 23 20