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摂動論的 Ｑ Ｃ Ｄ の発展 － Personal View －

摂動論的 Ｑ Ｃ Ｄ の発展 － Personal View －. QCD old boy’s view of development of pQCD. 植松恒夫 ( 京大理 ). 「核子構造研究の新展開 2011 」. @KEK January 7-8, 2011. 1. Introduction QCD 以前　黎明期 2. 第 1 期 1973 ～ 1970 年代 3. 第 2 期１９８０年代 4. 第 3 期 1990 年～現在 5. Outlook. Plan of the talk. “温故知新”.

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摂動論的 Ｑ Ｃ Ｄ の発展 － Personal View －

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  1. 摂動論的ＱＣＤの発展 －Personal View－ QCD old boy’s view of development of pQCD 植松恒夫 (京大理 ) 「核子構造研究の新展開2011」 @KEKJanuary 7-8, 2011

  2. 1. IntroductionQCD以前　黎明期 2. 第1期1973～1970年代 3. 第2期１９８０年代 4. 第3期1990年～現在 5. Outlook Plan of the talk “温故知新”

  3. IntroductionQCD以前　黎明期 • 核子の構造の研究 (60年代）deep inelastic scattering • Current Algebra Bjorken scaling • SLAC-MIT experiment 1968 Parton分布関数 L.W.MoSLAC-PUB-660 (1969) PartonModelFeynman，Bjorken-Paschos 核子構造関数

  4. Scalingの破れ • Broken scaling inv. くりこみ群　ε-展開 • Critical phenomena (物理量） • スケーリングの破れ • 場の理論でのくりこみ群的解析 fixed point theory power breaking anomalous dim. asymptotically free theory logarithmic breaking Kogut-Susskind Scale-inv. Parton Model fixed point theory asymptotically free theory

  5. VariousIdeas leading to QCD CurrentAlgebra Bjorken Scaling Large PT Adler-Dashen Bjorken Light-cone Large Angle Scattering Fritzsch-Gell-Mann Parton Picture OP E Feynman K.Wilson Brodsky-Farrar, Matveev et al. Asymptotic freedom Renormalization Group Gross-Wilczek, Politzer Perturbative QCD Gell-Mann-Low

  6. 第１期　 1973－1970年代　勃興期 Color gauge theory (Color octet gluon) QCD Asymtotic freedom ・ short distance ・・・漸近的自由 ・ long distance ・・・閉じ込め QCDLagrangian : coupling const. Nambu 1966 1973 Fritzsch-Gell-Mann-Leutwyler Weinberg 1973 Gross-Wilczek, Politzer, ‘t Hooft 1973 No free parameter except for

  7. Fundamental constantof QCD Effective coupling constant “dimensional transmutation’’ S.Bethke

  8. Leading Order (LO) analysis • OPE+RG analysis of structure function • DGLAP evolution equation for PDFs • Q2 dep. of fragmentation fn. • Polalrized structure functions Gross-Wilczek, Politzer,… Dokshitzer-Diakonov-Troyan, Gribov-Lipatov, Altarelli-Parisi,… Georgi-Politzer, Owens, T.U.,… Ahmed-Ross, Sasaki

  9. Mass singularityの因子化（Factorization） • quark-gluonの系を摂動論で扱うと質量0の粒子の4元運動量が0になることから生じる赤外発散（infrared divergence）や質量0のgluonがquarkとcollinearに放出されることによる質量特異性(mass singularity）が現れる． • parton描像でhadronのcross section mass (collinear) singularity singularな因子は hadron分布関数へ吸収 mass singularity

  10. Factorization （因子化） Collinear factorization short distance 物理量 long distance 非摂動論 convolution 摂動論 scheme- dep Structure fn. PDF (Q2dep) OPE Q2 dependence DGLAP eq. or OPE+RGE DGLAP equation

  11. クォーク・グルーオン演算子 Twist ツイスト２の演算子 クォーク場 グルーオン場 Twist=dim－spin=2 分布関数と演算子 Kodaira-TU(1978） scheme- dependence でくりこまれた演算子

  12. Splittingfunctions “Plus distribution” real emission virtual correction infrared cancel Kinoshita-Lee-Nauenberg -Nakanishi Theorem

  13. e+e-hadrons jet production 3-jet event @DESY 1979 半角δのconeに全エネルギーの (1-ε)倍が放出される Sterman-Weinberg jet infrared/collinear-safequantity Event shapes: Thrustetc.

  14. Factorization in hadron collisions DIS, e+ e－→hX, Drell-Yan, hadron-hadron semi-inclusive・・

  15. Higher-twist effects • Twist-44-quark2-quark&1gluon operators • Anomalous dimensions of 4-quark operators Gottlieb(78) ,Okawa(80) • Polarized structure fn. twist-3 contributes to g2 • twist-4 effects tog1 twist-2 twist-4 twist-6 twist=dim-spin ＋ Kodaira-Tanaka-TU-Yasui(96) Twist-3or4 Kawamura et al(97)

  16. QCD higher-order (NLO) effects Moment of structure fn. LO NLO NNLO 1-loop 2-loop Floratos et al(78) 1-loop anomalous dim. coefficient fn. RG eq. 1-loop Bardeen et al(78) Scheme independent anomalous dim. coefficient fn. 1-loop LO tree 2-loop 1-loop NLO NNLO 3-loop 2-loop Moch et al(04)

  17. 第２期　 1980年代　中間期 • QCDの摂動論および非摂動論での様々な 理論的整備/実験の進歩 • Unpolarized & polarized DIS data SLACDESY • EMC effects Spin Crisis CERN • Polarized structure functions • Twist-2, twists-3 effects • renormalization of higher-twist ops. • Small-x behavior BFKLeq. BK eq. mixing complicated

  18. scattered lepton spin incident lepton or spin scattered quark nucleon Polarized DIS & Structure Functions Structure tensor Unpolarized structure fns. polarized structure fns.

  19. 1988 EMC at CERN “Spin Crisis” “quarks carries only a small fraction of nucleon spin” in contradiction with naïve quark model But this is relativistic quantities ! Altarelli-Ross Phys. Lett B212 (1988) 391 Gluon polarization contributes due to anomaly Parton distribution functions are scheme-dependent J. Kodaira and T. U. Nucl. Phys. B141 (1978) 497

  20. 1st moment sum rule Kodaira et al. 1979 Kyoto Group flavor non-singlet Phys.Rev.D20 (1979) 627; Nucl.Phys. B159 (1979) 99 Now Larin-Vermaseren (1991) Axial anomaly flavor singlet Kodaira Nucl.Phys. B165 (1980)129 QCD correction

  21. Coefficient functions: Transversity Higher-twist twist-3 contributes in leading order to Many structure functions van Neerven-Zijlstra (1994) Chiral-odd structure fn. twist-2 op. 2-loop anomalous dim. Hayashigaki, Kanazawa, Koike;Kumano,Miyama : Collins function Asymmetry in Semi-inclusive DIS :Sivers function Transversity & Collins and Sivers asymmetries

  22. Small-x region physics • Large logs の足し上げ BFKL方程式 • Non-linear evolution equation BK方程式 gluon分布のsaturation color glass condensation (CGC) recombination

  23. Soft-gluon resummation • 2 mass scales: e.g. Q2&m2 orQ2&QT2 large logsappear at kinematical boundaries spoil perturbative expansions e.g. (real and virtual contributions highly unbalanced) Sudakov resummation=resumming the double- logarithmic perturbative contributions

  24. Threshold Resummation と書くと，以下が示される Sterman(’87),Catani&Trendadue(’89, ’91) LL NLL (Trentadue and Kodaira Catani, D’Emilio and Trentadue) NNLL

  25. 第３期　 1990年代－現在 Precisionof QCD:LO→NLO→NNLO 検証から精密化へ • QCDの量子補正をNNLOの精度に高める # of diagrams Splitting functions LO 18 NLO 350 NNLO 9607 1-loop 3-loop 2-loop Gross-Wilczek, Politzer(1974) Floratos-Ross-Sachrajda(1978) Coefficient functions Moch-Vermaseren-Vogt (2004)

  26. Recent topics in QCD Color Glass Condensation Higgs production String-inspired QCD Global PDF analysis Multi-parton amplitudes Perturbative QCD AdS/CFT Heavy quark mass effects Precision QCD

  27. Global PDF Analysis Collaborations • MSTW (MRST) LO NLO NNLO • CTEQ LO NLO Tevatron jet analysis • NNPDFNLO Neural networks • ABKM NNLOheavy quark effects • GRV, AAC NLO polarized PDFs

  28. QCD and HERA data

  29. QCD @ LHC era RHICからLHCへ • CMS@7TeV pp collision ～ RHIC heavy ion collision Ridge structure pseud-rapidty (η） correlation • ALICE heavy ion collision high multiplicities • ATLAS & CMS 　ジェット抑制（Jet quenching) Higgs production ｇluon fusion Diffractive production of Higgs

  30. Heavy quark mass effects • heavy quark coefficient functions deep inelastic lepton-hadron scattering for mass factorization: • low では heavy quarkはradiativeに作られる　　　 highでは light quarkと同等 matching condition： Buza et al. (‘96) heavy quark coeff. fn massive operator matrix element light quark coeff. fn heavy quark

  31. Fixed and variable flavor number schemes • Fixed Flavor Number Scheme (FFNS) u,d,s:massless heavy quarks (H):c,b,s are radiatively generated for large log spoils perturbation • Zero Mass Variable Flavor Number Scheme (ZMVFNS) ZMVFNS shows discontinuity at transition → • General massvariable flavor number (GMVFN)scheme To achieve smooth transition

  32. AdS/CFT対応 String on AdS5×S5～N=4SCFT 5次元AdS時空での弦のsemi-classicalな振る舞いと　boundaryの４次元Yang-Mills理論の対応関係 Polyakov et al AdS/CFT対応（弦／ゲージ双対性）とform factorおよび大角度散乱と強結合領域でのDIS構造関数 Polchinski et al String理論でエネルギーについてベキ的振舞い 5次元方向の寄与によるwarp factor AdS/QCD(Holographic QCD) spectrum, decay width, Pomeron, BFKL anom.dim. QCD and String Theory Maldacena

  33. MHV振幅に対するParke-Taylor公式の拡張（spinor-helicity）MHV振幅に対するParke-Taylor公式の拡張（spinor-helicity） WittenCommun.Math.Phys.252(2004)189N=4超対称理論で運動量空間からFourier変換で得たtwistor spaceにおける散乱振幅を弦理論のインスタントンの寄与に結びつけた Cachazo-Svrcek-Witten (CSW) JHEP09(2004)006 最大にヘリシティーを破る(MHV)振幅をvertexに拡張し，一般のMHVでないhelicity振幅を計算するルールを与えた 任意の1-loopmulti-legamplitudes A～(Box)+(triangle)+(bubble)+(tadpole) multi-partonamplitudes + + － MHV + +

  34. QCDは３０有余年を経て確立 検証から精密化へ Hadron物理にとって必須の理論的枠組み 標準模型の確立とそれを超えたPhysicsの探索には強い相互作用 QCDの効果の精密な評価が必要 pQCDはLHCでのppおよび重イオン衝突における新たな現象の解析に必須 ハドロン物理研究の新たなアイデアの創出 QCDは素粒子論と原子核理論のcommunityを繋ぐ 理論屋と実験家のcollaboration@LHC,J-PARC… Summary and Outlook More efforts needed! Even for old boys!

  35. Backup Slides

  36. Nucleon’s total angular momentum proton spin sum rule gluon orbital angular mom. quark orbital angular mom. at Sizable contributions are from gluon pol. Or from orbital angular mom. and Asymptotic values from evolution eq.

  37. Semi-inclusive Deep Inelastic Scattering (SIDIS) Transverse-spin asymmetry at leading-twist in SIDIS fragmentation function : Collins function Transverse distribution in the initial state Sivers function Earlier claim was that Sivers asymmetry vanish time reversal inv. Final-state interaction important for Sivers fn. not to vanish Wilson lines in the op. def required by gauge inv.

  38. Generalized Parton distribution (GPD) See Wakamatsu’s talk non-forward proton matrix elements Deeply virtual Compton scattering (DVCS) can be measured at null vector skewdness parameter Bjorken variable

  39. : Generalized Parton distribution (GPD) Experimentally known Lattice calculation Not in accordance with exp.

  40. Spin-dependent fragmentation function @BELLE at KEK See Seidl’s talk Chiral-odd fragmentation function e.g. Collins function e+e- collider KEK-B at Tsukuba unpolarized Collins function

  41. Buza-Matiounine-Smith-van Neerven (BMVN) prescription

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