Transcript Annecy-talk
摂動論的ＱＣＤの発展 －Personal View－ E' QCD old boy’s view of development of pQCD E q xp p 植松恒夫 (京大理 ) 「核子構造研究の新展開2011」 @KEK January 7-8, 2011 Plan of the talk “温故知新” 1. 2. 3. 4. 5. Introduction QCD以前 黎明期 第1期1973～1970年代 第2期１９８０年代 第3期1990年～現在 Outlook Introduction QCD以前 黎明期 • 核子の構造の研究 (60年代）deep inelastic scattering • Current Algebra Bjorken scaling 1968 • SLAC-MIT experiment Parton分布関数 q ( x ), q ( x ) (0 x 1) L.W.Mo SLAC-PUB-660 (1969) Parton Model Feynman，Bjorken-Paschos 核子構造関数 Scalingの破れ • • • • Broken scaling inv. くりこみ群 ε-展開 Critical phenomena (物理量） Kogut-Susskind Scale-inv. Parton Model 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. g ) asymptotically free theory logarithmic breaking g) 0 U V lim it g g g fixed point theory g) g g 0 g 0 asymptotically free theory Various Ideas leading to QCD Large PT Bjorken Scaling Large Angle Scattering Current Algebra Adler-Dashen Bjorken Light-cone Fritzsch-Gell-Mann Parton Picture Feynman Brodsky-Farrar, Matveev et al. OPE K.Wilson Renormalization Group Asymptotic freedom Gross-Wilczek, Politzer Perturbative QCD Gell-Mann-Low 第１期 1973－1970年代 勃興期 Color gauge theory (Color octet gluon) Nambu 1966 Fritzsch-Gell-Mann-Leutwyler 1973 QCD Weinberg 1973 Asymtotic freedom Gross-Wilczek, Politzer, ‘t Hooft 1973 ・ short distance ・・・漸近的自由 ・ long distance ・・・閉じ込め QCD Lagrangian : coupling const. No free parameter except for Effective coupling constant Fundamental constant of QCD “dimensional transmutation’’ S.Bethke Leading Order (LO) analysis • OPE+RG analysis of structure function Gross-Wilczek, Politzer,… • DGLAP evolution equation for PDFs Dokshitzer-Diakonov-Troyan, Gribov-Lipatov, Altarelli-Parisi,… • Q2 dep. of fragmentation fn. Georgi-Politzer, Owens, T.U.,… • Polalrized structure functions Ahmed-Ross, Sasaki 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． mass (collinear) singularity • parton描像でhadronのcross section singularな因子は hadron分布関数へ吸収 mass singularity Factorization （因子化） 物理量 Collinear factorization short distance long distance 非摂動論 convolution 摂動論 scheme- dep Structure fn. PDF (Q2dep) OPE Q2 dependence DGLAP equation DGLAP eq. or OPE+RGE クォーク・グルーオン演算子 O O q n 1 D 2 D n traces G n クォーク場 G 1 D 2 D n 1 G n traces グルーオン場 Twist=dim－spin=2 分布関数と演算子 p |O q n ( ) | p | 2 Q 2 Twist ツイスト２ の演算子 Kodaira-TU (1978） scheme- dependence 1 x n 1 2 q ( x , Q ) dx 0 でくりこまれた演算子 p |O G n ( ) | p | 2 Q 2 1 x 0 n 1 2 G ( x, Q )dx Splitting functions “Plus distribution” real emission infrared cancel Kinoshita-Lee-Nauenberg -Nakanishi Theorem virtual correction e+e-hadrons jet production Sterman-Weinberg jet infrared/collinear-safe quantity Event shapes: Thrust etc. 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 Factorization in hadron collisions C fA A a c Dc C high-energy Q C D process: AB C X a d ˆ b fB B Q b 2 R , F , D 4Q 2 4 d 2 2 2 dx a dx b dz c f A ( x a , F ) f B ( x b , F ) a b d ˆ ( x a , x b , z c , R , F , D ) D c ( z c , D ) C 摂動計算可能 DIS, e+ e－→hX, Drell-Yan, hadron-hadron semi-inclusive・・ Higher-twist effects ＋ Twist-3 or 4 twist-2 twist-4 twist-6 twist=dim-spin • Twist-4 4-quark 2-quark&1gluon operators • Anomalous dimensions of 4-quark operators Gottlieb(78) ,Okawa(80) • Polarized structure fn. twist-3 contributes to g2 Kodaira-Tanaka-TU-Yasui • twist-4 effects to g1 Kawamura et al (97) (96) QCD higher-order (NLO) effects Moment of structure fn. LO 1-loop NLO NNLO 2-loop Floratos et al (78) 1-loop anomalous dim. coefficient fn. RG eq. LO 1-loop Bardeen et al (78) Scheme independent anomalous dim. coefficient fn. 1-loop tree NLO 2-loop 1-loop NNLO 3-loop 2-loop Moch et al (04) 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 SLAC DESY • EMC effects Spin Crisis CERN • Polarized structure functions g 1 , g 2 • Twist-2, twists-3 effects mixing complicated renormalization of higher-twist ops. •Small-x behavior BFKLeq. BK eq. Polarized DIS & Structure Functions E' spin E incident lepton spin q nucleon Structure tensor 2 q ( x, Q ) xp p scattered lepton or 2 q ( x, Q ) scattered quark Unpolarized structure fns. polarized structure fns. 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 1st moment sum rule Kyoto Group Kodaira et al. 1979 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 • Coefficient functions: van Neerven-Zijlstra (1994) • Transversity Chiral-odd structure fn. twist-2 op. 2-loop anomalous dim. Hayashigaki, Kanazawa, Koike;Kumano,Miyama • Higher-twist twist-3 contributes in leading order to • Many structure functions : Collins function Asymmetry in Semi-inclusive DIS Transversity & Collins and Sivers asymmetries : Sivers function Small-x region physics Q F2 x x1 P k0 dk 2 k 2 F2 ( x , Q ) '2 '2 '2 2 '2 K (k ; k ) f ( x, k ) • Non-linear evolution equation BK方程式 gluon分布のsaturation color glass condensation (CGC) recombination kT 1 x BFKL方程式 2 xn P kT 2 • Large logs ( s ln 1x ) n の足し上げ f ( x, k ) 1 ln x 2 x kTn Soft-gluon resummation • 2 mass scales: e.g. Q2&m2 or Q2&QT2 large logs appear at kinematical boundaries C nm s n ln (1 x ) m (m 2n) x1 spoil perturbative expansions e.g. 2 T hreshold z M H / sˆ n S ln 2 n 1 (1 z ) (1 z ) 1 0 dz 1 z N 1 n S ln 2 n 1 (1 z ) (1 z ) n S ln 2n N (real and virtual contributions highly unbalanced) Sudakov resummation=resumming the doublelogarithmic perturbative contributions 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 第３期 1990年代－現在 Precision of 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 LO 18 NLO 350 Splitting functions 1-loop 2-loop 3-loop NNLO 9607 Gross-Wilczek, Politzer(1974) Coefficient functionsFloratos-Ross-Sachrajda(1978) Moch-Vermaseren-Vogt (2004) Recent topics in QCD Higgs production String-inspired QCD Multi-parton amplitudes Color Glass Condensation Global PDF analysis Perturbative QCD AdS/CFT Heavy quark mass effects Precision QCD Global PDF Analysis Collaborations • MSTW (MRST) LO NLO NNLO • CTEQ LO NLO Tevatron jet analysis • NNPDF NLO Neural networks • ABKM NNLO heavy quark effects • GRV, AAC NLO polarized PDFs QCD and HERA data 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 Heavy quark mass effects • heavy quark coefficient functions deep inelastic lepton-hadron scattering for mass factorization: Buza et al. (‘96) • low Q 2 では Q 2 m 2 heavy quark massive operator light quark coeff. fn matrix element coeff. fn heavy quarkはradiativeに作られる 2 high Q では light quarkと同等 matching condition： heavy quark 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 mass variable flavor number (GMVFN)scheme To achieve smooth transition QCD and String Theory • AdS/CFT対応 String on AdS5×S5～N=4SCFT Maldacena • 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. multi-parton amplitudes + + MHV － + + • MHV振幅に対するParke-Taylor公式の拡張（spinor-helicity） • Witten Commun.Math.Phys.252(2004)189 N=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-loop multi-leg amplitudes A～(Box)+(triangle)+(bubble)+(tadpole) Summary and Outlook • 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… More efforts needed! Even for old boys! Backup Slides 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. Asymptotic values from evolution eq. and 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. Generalized Parton distribution (GPD) See Wakamatsu’s talk non-forward proton matrix elements can be measured at Deeply virtual Compton scattering (DVCS) null vector skewdness parameter Bjorken variable : Generalized Parton distribution (GPD) Experimentally known Lattice calculation Not in accordance with exp. Spin-dependent fragmentation function See Seidl’s talk @BELLE at KEK Chiral-odd fragmentation function e.g. Collins function e+e- collider KEK-B at Tsukuba unpolarized Collins function Buza-Matiounine-Smith-van Neerven (BMVN) prescription