Elementary Particle Physics III (素粒子物理学III) Satoru Yamashita (山下) and Junichi Tanaka (田中) • E-mail – [email protected] for Yamashita – [email protected] for Tanaka • Website for materials (to be uploaded after each lecture) – http://www.icepp.s.u-tokyo.ac.jp/~satoru/lecture/pp3/ – http://www.icepp.s.u-tokyo.ac.jp/~jtanaka/lecture/pp3/ 1 Schedule of the Course (if no cancellation) Monday 14:55-16:40 • • 4/6 Introduction, QCD, Weak and EW unification (1) JT 4/13, 20 QCD, Weak and EW unification (2,3) SY and JT – Short report (I) • • Today’s lecture: QCD and QCD in experiments 4/27 CKM Matrix and CP Violation (4) JT 5/11, 18 Higgs Mechanism, Higgs Search and Measurements (5,6) SY – Short report (II) • • • 6/1 Higgs Measurements and Supersymmetry (7) JT 6/8 Supersymmetry (8) JT 6/15 Neutrino Physics (9) SY – Short report (III) • 6/22, 6/29 New Physics Search at the Energy Frontier Experiments (10,11) JT – Short report (IV) • • 7/6 Grand Unified Theories (12) SY 7/13 Search for LFV and Summary of this Course (13) SY – Final Report 2 Today’s lecture • Quantum Chromodynamics (量子色力学) – Flavor SU(3) and Color SU(3) – Color自由度 (Color freedom) • Confinement – Asymptotic freedom • “QCD” in collider experiments – – – – • How to describe proton-proton collision Deep inelastic scattering -> Parton model PDF Jets Short Report I -> http://www.icepp.s.u-tokyo.ac.jp/~jtanaka/lecture/pp3/ Deadline 27 April (4月27日) 3 http://www.icepp.s.u-tokyo.ac.jp/~jtanaka/lecture/pp3/ 4 http://www.icepp.s.u-tokyo.ac.jp/~jtanaka/lecture/pp3/ 5 Quark model （復習も兼ねて） 6 Isospin • Nucleon(核子): proton (p) and neutron (n) – Proton : 938.3MeV なぜpとnの集合体（原子核）が存在できるか？ – Neutron : 939.6MeV p <-> pは電磁気力で反発するはず – Spin ½ Phenomenology of nucleon (nuclear force、核力) looks like the same between “p” and “n”. It looks NOT to depend on “p” or “n” label. -> SU(2) symmetry = isospin by Heisenberg, This is analogy of “spin”. • Nucleon SU(2) p  p 0 – Triplet and singlet – Triplet is a set of p mesons : p+, p0, p• p+, p- mass : 139.57MeV • p0 mass : 134.98MeV -> Forces between nucleon are carried by these particles. – Singlet : h (547.9MeV) p    p     n   7 新しいタイプの粒子の発見 -> 新しい「保存」則 “Strangeness” • So-called “V events” was observed in a cloud chamber (霧箱) by Rochester and Butler in 1947. V is “Kaon” in the present particle physics. K0(ds) : 497.7MeV This particle has a long lifetime. -> It indicates that there is a kind of “conservation”/”symmetry”. -> “Strangeness” is introduced. This is conserved in the strong interaction but not in the weak interaction. Where is a “V” particle? Typical lifetime ~10-23 (s) for strong ~10-16 (s) for EM ~10-8 (s) for Weak 8 Flavor SU(3) • A “Lambda” particle was also observed in cosmic rays (1947). – Lambda (L0) : 1116 MeV • Hundreds of hadrons are “produced” by accelerators in 1960’s. • Toward establishing “quark model” – Sakata model (坂田モデル) … 1955 What quarks are (p,n,L) made of/from? • (p, n, L) is used to explain mesons. – Gell-Mann - Nishijima formula (ゲルマン・西島の公式) … 1953 BS Y Q  I3   I 3  (or  I3  Y ) 2 2 – Quark model by Gell-Mann … 1964 • (u, d, s) is used to explain hadrons. -> This is I3 … isospin B … Baryon number S … strangeness Y … hyper-charge (“/2” depends on definitions…) “Flavor SU(3)”. 9 Mesons • Mesons (u,d,s) x (u,d,s) -> 3 x 3* = 8 + 1 octet + singlet Spin 0 uu  dd p  2 uu  dd  2 s s h8  6 uu  dd  s s h1  3 0 We have spin 1 case and also if we’ll consider charm…, we can have 4x4* etc. 10 Color SU(3)ではこいつがポイント 3 x 3 x 3 = 1A + 8MS + 8MA + 10S Baryons S … “S”ymmetry, A … “A”symmetry M … “M”ixed Spin 1/2 So far we observe JP=½+ mesons (spin=1/2 and parity=+). 11 Baryons 3 x 3 x 3 = 1A + 8MS + 8MA + 10S Spin 3/2 Mesons/Baryonsの説明 -> Quark modelの成功 -> クォークは実在するのか？ “uuu, ddd, sss” is impossible in term of Fermi statistics. -> hint of “color” freedom？カラーという新しい自由度？ 12 1974 November revolution A “charm meson” was discovered in 1974. SLAC, SPEAR Mark I detector e+e- → hadrons e+e- → m+mBurton Richter (Right) e+e- → e+e- 13 BNL, AGS p + Be -> e+ + e- + X Samuel C.C. Ting GIM mechanism (1970) -> will explain later in this lecture 丁肇中 B.Richter and S.Ting received the Nobel Prize in 1976. 14 Bottom quark Fermi lab p + Be, Cu, Pt -> m+ + m- + anything Narrow resonances around 9.5-10.5GeV were observed in 1977. Upsilon bb states Υ(1S) Υ(2S) Υ(3S) Υ(4S) Mass (MeV) 9460 10023 10355 10579 Width (MeV) 0.054 0.032 0.020 OZI rule 20 CELO@CESR e+e- colliders DORIS@Hamburg CESR@Cornell (~1980) 15 Color freedom • Evidence of this new freedom – Theoretical viewpoint • Success of the quark model … – Experimental results • R-ratios （->先週習った） • Branching ratios of W boson … 16 BR(W->ff’) • W bosons decay into ene, mnm, tnt, ud and cs. – The coupling between fermions and W boson is the same among them. e, m, t, u, c W± ne, nm, nt, d, s 1 ÷ 5 = 0.2 -> 20% for each?  WRONG 1 ÷ (3+3x2) = 0.11 -> 11% for each -> GOOD! 17 QCD: Color SU(3) • Mesons and Baryons including J/Ψ and Υ are made of quarks but we never have results of quark itself, for example, mass distributions of quarks. -> Only color-”neutral” particles are observed/observable. • New 3 charges for “color freedom” are introduced and their interaction is invariant under SU(3). R, G, B •  Analogy of the “three primary colors” (色の3原色) There is singlet from 3x3* and 3x3x3. (See Flavor SU(3).) – Our observable must be singlet, that is, colorless/color-neutral (無色). • RR, GG, BB • RGB, RGB • SU(3) has 8 different generators (生成子) like “pions in isospin SU(2)”. -> We have 8 different gauge bosons, that is, gluons. Gluons are exchanged between colored particles. -> “Strong” force -> QCD = Quantum Chromodynamics (量子色力学), SU(3) gauge theory 18 QCD Lagrangian The last 2 terms -> See ex “QCD and Collider Physics” (Cambridge University Press) LQCD  Lclassical  Lgauge  fixing  Lghost   1 a mn   q j i Dm  m j q j  Gmn Ga 4 j Lclassical m a Gmn   m Ana  n Ama  gf bca Amb Anc Dm   m  igt a Ama 1 a t   2 a This Lclassical is invariant under the following gauge transformation. qe i aTa q 1 Am  Am   m a  f bca b Amc g g2 g … QCD coupling  S  , Ta … SU(3) generators 4p a a 19 Gluon “Discovery” in 1979 gluon /Z 3-jets events (JADE, PETRA@DESY) ee -> qqg 20 Gluons RB, RG, BG, BR, GR, GB, (RR-BB)/√2, (RR+BB-2GG)/√6 gluon quark B G B time G quark 21 Gluons can do “self interaction/coupling” because they have color charges. This is different from photons. BR GB GR time 22 Quark Confinement (クォークの閉じ込め) • Only color-neutral particles are observed/observable. – Baryons (RBG, …) – Mesons (RR, …) 23 QED (Quantum electrodynamics) VEM r    ex)    1 / 137 r QCD (Quantum Chromodynamics) 4 S VQCD r     kr 3 r ex)  S ~ 0.2, k  1GeVfm -1 24 Running constants and Asymptotic freedom 25 “Running” coupling constants Force strength changes as energy because of quantum effect. 1. “Radiative correction” (輻射補正) must exist. 2. “Divergence” must be treated properly. -> We can use “renormalization prescription” (繰り込み). Coupling constants are not “constant” but depend on energy scale. -> We can use “renormalization group equation (RGE)” (繰り込み群方程式). Example: measurement of electric charge “e” (QED) (=coupling ) 観測量 Tree e0 e0 e0 e0 e(Q2) 繰り込み Divergence due to loops e0 e(m2) e0 e0 e03 e05 e(m2)3 e(m2)5 26 QED coupling 2    m  Q 2    m 2   Q 2  1 log 2  3p m    1  m   137 2 e ~137 ~0.01 -> “Perturbation” works well in QED. Also, we can get “high precision” with a few higher order corrections. 27 QCD coupling 28 QCD coupling 1 b0  4p 3 2  n  5  16   f 3  <=6 (only b0) We can go to “higher orders in perturbation series…”, b1, b2, … in principal but in the reality it is too difficult. 29 Asymptotic freedom S gets smaller as energy increases. -> We call it “asymptotic freedom” (漸近的自由性) S ~ 0.1 -> We can use the perturbative theory (pQCD). But if this S value gets larger, we cannot use the pQCD. 1 2  b ln Q 0  S (Q 2 ) 1 2   b ln m 0  S (m 2 )  b0 ln L QCD 2 LQCD~200MeV 1  S (Q )  2 Q  b0 ln 2 L QCD 2 30 Quark mass Pole mass MS-scheme mass 31 “QCD” use in Experiments 32 Properties of “QCD” • Color charge by gauge bosons: 8 Gluons (massless) – Conserve quark flavor (u, d, s, c, b, t) – Conserve electric charge – Conserve P, C and T • Confinement • Asymptotic freedom etc -> Due to “Confinement”, we observed hadrons and jets in data NOT quarks/gluons. -> Due to “Asymptotic freedom”, perturbative QCD works well in high energy regions. How do we simulate/understand experimental outputs/results? Parton model Factorization Hadronization Parton shower etc Based on QCD with experiences 33 “Parton” by Deep Inelastic Scattering • Destruction of nucleus by high energy electron – Quarks and/or gluons in nucleus look like “free point-like particles”. parton = quark or gluon -> Parton model 34 “Parton” using photons (from e) Deep inelastic scattering DESY(ドイツ) HERA ep collider 1992-2007 (circumference ~ 6.3km) Ee = 27.5GeV Ep = 820, 920GeV -> Ecm = 300, 318GeV 35 SLAC-MIT experiment : ep->eX “Bjorken scale” 1969 36 37 Proton structure function (HERA ep collider at DESY) “Bjorken scaling” 38 Proton + proton -> two jets (dijets) ET~1.2TeV ~1.3TeV 39 proton Decay Fragmentation Hadronization Parton shower Perturbative QCD (Matrix element) proton 40 Pileup Z->mm candidate with 25 proton-proton collisions (ATLAS) Beamaxis “a few mm” between vertices (several cm in z) 80mb x 5 x 1033 cm-2 s-1 / 20MHz = ~ 20回/バンチ衝突 Inelastic scattering cross section (非弾性衝突の生成断面積) Instantaneous Luminosity (瞬間ルミノシティ) LHCの1秒間でのバンチ衝突回数 41 Proton の中身の解釈・理解 Parton Distribution Function (PDF) 42 陽子･陽子衝突 We cannot use all the particle energy in hardon collisions. -> A “parton” inside a proton is collided. p1  ( x1 E1 ,0,0, x1 E1 ), p2  ( x2 E2 ,0,0, x2 E2 ) sˆ  ( x1 E1  x2 E2 ) 2  ( x1 E1  x2 E2 ) 2  4 x1 x2 E1 E2 p1 p2 sˆ  x1 x2 s , s  2 E1 E2 x1、x2 … unknown parameters (we never know their values.) 43 Parton Density Function (PDF) • 前ページのx1、x2がこれ。 • 陽子は単純にuudではなく、実際には gluonや他のクォークも存在。 – uやdはvalence quark+see quark – その他のクォークはsee quark (g->qq) – Gluonも存在 • x=0.3付近でuとdが大きくなる。 -> uud(valence)を反映している。 • Q2を大きくするとlow xが増える。 44 実効衝突エネルギー • √s = √(x1x2) √s なので対象とする物理現象によって必要となるx1,x2が異なる。 – √s=8TeVで125GeVのヒッグスなら、 • √(x1x2) = 125/8000 = 0.016 ~ O(10-2) x1 ~ x2 ~ O(10-2) -> Gluon-gluonからの生成がメイン – √s=13TeVで2TeVのSUSYなら（ペアなので4TeV）、 • √(x1x2) = 4/13 = 0.31 ~ O(10-1) x1 ~ x2 ~ O(10-1) -> Gluonのみならず、valence quarkからも生成。 45 PDF CT10 (NLO) http://hepdata.cedar.ac.uk/pdf/pdf3.html Q2=(10GeV)2 Q2=(100GeV)2 As Q2 increases, valence quarks get smaller. Also, contributions in low-x get larger. Q2=(1000GeV)2 46 LHC用のPDF • この図の意味 – √s=14TeVにおいて、ある（M,y）の事象を起こしたい場合、x1とx2は自動的に決まる。 DGLAP extrapolation • PDF for LHC (or future hadron colliders) might not be measured. • 既存の実験で求めた陽子の分布を DGLAP方程式を使って、LHCの領域まで発展させる。 – Dokshitzer–Gribov–Lipatov– Altarelli–Parisi equation – Altarelli-Parisi equation 47 事象の生成@計算機: モンテカルロ・シミュレーション qq  g  tt  W  bW b  qqbqqb どうする？ 48 事象の生成@計算機: モンテカルロ・シミュレーション Factorization Theorem m（factorization scale）でハードプロセスから切り離して実験結果を適切に説明できる。 PDF+PS+… ハードプロセス +… PDF+PS+… mより小さいscaleはすべてPDFに押し付けてしまう。 PDFのscale mまで発展していく過程の中でクォークやグルーオンを出す。この手法をパートンシャワー（Parton shower, PS）と呼び、それらのクォークやグルーオンはInitial state radiation（ISR）によって生成されたという。 m ~Qにとると断面積などはデータと合っているように見えるが、あまり根拠がないので 0.5倍, 2倍して不定性を見積もることが多い。 49 qq  g  tt  W  bW b  qqbqqb 50 qq  g  tt  W  bW b  qqbqqb ハードプロセスはまじめに計算する。 Matrix Element（ME） 51 qq  g  tt  W  bW b  qqbqqb ハードプロセスから切り離して PDFとPatron showerにおまかせする。 52 qq  g  tt  W  bW b  qqbqqb 検出器シミュレーションへハードプロセスから切り離してPatron showerにおまかせして QCDのスケール（～200MeV）になったらハドロン化する。（Final state radiation + Fragmentation/Hadronization） 53 qq  g  tt  W  bW b  qqbqqb すべてのオーダーの計算をしないため、結合定数sのスケールが大事になる。（全部やれば原理的にはスケールに依存しない。） -> 途中で止めた計算結果でも十分正しいスケールがあれば便利。考えているプロセスの典型的なエネルギースケールがそれに相当。 54 LOの生成断面積計算結果はscaleの選び方に強く依存する。  本当は依存してほしくないが、計算を途中で止めている以上仕方ない。計算のオーダーを上げるとスケールの依存性はなくなるので、経験的には NLOやNNLOの計算をして、交差するところがscaleとして「いい点」（職人技？）いろいろなプロセスの計算結果を総合すると、経験的には s-channel -> √s、 t-channel -> pT の付近がよい。 TevatronでのTopの生成断面積生成断面積の依存性はsの依存性。高次の計算をすると不定性はなくなっていく。（全部計算すれば依存しなくなる。） LOとNLOの断面積の比をk-factor （NNLOとの比でもOK） k-factor = σ(NLO)/σ(LO) Q 55 Jet 56 Proton + proton -> two jets (dijets) ET~1.2TeV ~1.3TeV 57 Jet Reconstruction “Jets” are reconstructed from energy deposits in calorimeters and/or tracks. In this lecture, we focus on “jet” algorithm used in hadron colliders. 58 “Good” Jet Algorithm E 1-z Eg ~ (1-z)E z Eq ~ zE q Splitting function q -> 0 … “collinear” z -> 1 … “soft” Gluon emission probability -> infinity If a jet algorithm used is proper, our measurements should be insensitive to such collinear/soft gluons. Collinear- and infrared-safe: - “Collinear” splitting should not change jets. - “Soft” emission should not change jets. Typical “cone” type algorithms are not “collinear- and infrared-safe”. kT, anti-kT type algorithms are “collinear- and infrared-safe”. 59 “kT” algorithms JHEP04(2008)063 dij is the smallest -> merge diB is the smallest -> Particle i is set to “a jet”. kti, yi and fi are transverse momentum, rapidity and azimuth of particle i. p=1 … kT p=0 … Cambridge/Aachen p=-1 … anti-kT 1 E  pz 1 E  pz E  pz 1  E  pz y  ln  ln  ln 2 E  p z 2 E  p z E  p z 2  mT Massless -> pseudo rapidity h 2  E  pz   ln mT  h   ln tan q 2 60 JHEP04(2008)063 Anti-kT is geometrically also good. 61 Gluon spin 62 3-jet events TASSO experiment at DESY using PETRA (e+e- experiment) PLB 97 (3-4), 453 Gluon spin = 1 63 Others 64 QCD in low energy regions “Non-perturbative” -> Use Lattice QCD with super computers. 65 Short Report I 忘れずに！ 66