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Quarks, Colors, and Confinement

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Presentation on theme: "Quarks, Colors, and Confinement"— Presentation transcript:

1 Quarks, Colors, and Confinement
ChoeJo YeolLin Dept. of Physics, KAIST Fall KAIST PH489 1

2 Introduction Baryons, Mesons, and Quarks Fall KAIST PH489 2

3 Fall KAIST PH489 3

4 Historical Backgrounds
1961 The Eightfold Way 1935 Yukawa’s Meson 1949 Quantum Electrodynamics 1949 Quantum Electrodynamics 1947 Discovery of Strange Particle 1928 Dirac Equation Fall KAIST PH489 4

5 Quantum Chromodynamics
1975- The Standard Model 1974 Discovery of J/ψ Meson 1964 The Quark Model Quantum Chromodynamics Deep Inelastic Scattering Experiments Fall KAIST PH489 5

6 Color Charge Fall 2017 KAIST PH489 6
Fall KAIST PH489 6

7 Color Confinement Fall 2017 KAIST PH489 7
Fall KAIST PH489 7

8 Review: QED Symmetry and Formalisms of Quantum Electrodynamics
Fall KAIST PH489 8

9 Quantum Electrodynamics
Fall KAIST PH489 9

10 QED Lagrangian ℒ= 𝜓 𝛾 𝜇 𝑝 𝜇 𝜓−𝑚 𝜓 𝜓 Dirac Lagrangian
ℒ= 𝜓 𝛾 𝜇 𝑝 𝜇 𝜓−𝑚 𝜓 𝜓 Dirac Lagrangian ℒ=𝑖 𝜓 𝛾 𝜇 𝜕 𝜇 𝜓−𝑚 𝜓 𝜓− 𝑞 𝑒 𝜓 𝛾 𝜇 𝜓 𝐴 𝜇 − 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈 ℒ= 𝜓 𝛾 𝜇 𝑝 𝜇 − 𝑞 𝑒 𝐴 𝜇 𝜓−𝑚 𝜓 𝜓 Free fermion Lagrangian (Dirac) Interaction term Free photon Lagrangian Fall KAIST PH489 10

11 The Feynman Rule Fall 2017 KAIST PH489 11
Fall KAIST PH489 11

12 The Feynman Rule Interaction term − 𝑞 𝑒 𝜓 𝛾 𝜇 𝜓 𝐴 𝜇 Vertex factor
− 𝑞 𝑒 𝜓 𝛾 𝜇 𝜓 𝐴 𝜇 Vertex factor −𝑖 𝑞 𝑒 𝛾 𝜇 Fall KAIST PH489 12

13 The Feynman Rule 𝑢 𝑐 𝑝 𝑐 −𝑖 𝑞 𝑒 𝛾 𝜇 𝑢 𝑎 𝑝 𝑎
𝑢 𝑐 𝑝 𝑐 −𝑖 𝑞 𝑒 𝛾 𝜇 𝑢 𝑎 𝑝 𝑎 ℳ LO = 𝑢 𝑐 𝑝 𝑐 −𝑖 𝑞 𝑒 𝛾 𝜇 𝑢 𝑎 𝑝 𝑎 − 𝑖 𝑔 𝜇𝜈 𝑞 𝑢 𝑑 𝑝 𝑑 −𝑖 𝑞 𝑒 𝛾 𝜈 𝑢 𝑏 𝑝 𝑏 − 𝑖 𝑔 𝜇𝜈 𝑞 2 𝑗 𝜇 𝑗 𝜈 𝑢 𝑑 𝑝 𝑑 −𝑖 𝑞 𝑒 𝛾 𝜈 𝑢 𝑏 𝑝 𝑏 Fall KAIST PH489 13

14 The Feynman Rule Corrections to the QED matrix element
ℳ 𝑓𝑖 =𝛼 ℳ LO + 𝛼 2 𝑗 2 ℳ 2, 𝑗 𝛼 3 𝑗 3 ℳ 3, 𝑗 𝛼 4 𝑗 4 ℳ 4, 𝑗 4 +… ℳ 𝑓𝑖 2 = 𝛼 2 ℳ LO 2 +𝑂 𝛼 3 +𝑂 𝛼 4 +… Fall KAIST PH489 14

15 The Feynman Rule Mandelstam Variables Value of 𝑞 2 𝑠= 𝑝 1 + 𝑝 2 2
𝑠= 𝑝 1 + 𝑝 2 2 𝑡= 𝑝 1 − 𝑝 3 2 𝑢= 𝑝 1 − 𝑝 4 2 Fall KAIST PH489 15

16 Color SU(3) and QCD Symmetry and Formalisms of Quantum Chromodynamics
Fall KAIST PH489 16

17 Quantum Chromodynamics
Fall KAIST PH489 17

18 Color SU(3) 𝜓′= 𝐴 11 𝐴 12 𝐴 13 𝐴 21 𝐴 22 𝐴 23 𝐴 31 𝐴 32 𝐴 33
𝜓′= 𝐴 11 𝐴 12 𝐴 13 𝐴 21 𝐴 22 𝐴 23 𝐴 31 𝐴 32 𝐴 33 𝜓= 𝜓 𝑟 𝜓 𝑔 𝜓 𝑏 = 𝜓 𝑟 ′ 𝜓 𝑔 ′ 𝜓 𝑏 ′ Fall KAIST PH489 18

19 Color SU(3) 𝐴 𝜇 = 1 2 𝛌∙ 𝐀 𝜇 = 1 2 𝑗=1 8 𝜆 𝑗 𝐴 𝜇 𝑗 𝐴 𝜇 →
𝐴 𝜇 = 1 2 𝛌∙ 𝐀 𝜇 = 1 2 𝑗=1 8 𝜆 𝑗 𝐴 𝜇 𝑗 𝐴 𝜇 𝐀 𝜇 = 𝐴 𝜇 1 𝐴 𝜇 2 ⋮ 𝐴 𝜇 8 𝐹 𝜇𝜈 𝐹 𝜇𝜈 = 𝜕 𝜇 𝐴 𝜈 − 𝜕 𝜈 𝐴 𝜇 +𝑖 𝑞 𝑐 𝐴 𝜇 , 𝐴 𝜈 𝛌= 𝜆 1 𝜆 2 ⋯ 𝜆 8 Fall KAIST PH489 19

20 QCD Lagrangian ℒ=𝑖 𝜓 𝛾 𝜇 𝜕 𝜇 𝜓−𝑚 𝜓 𝜓− 𝑞 𝑐 𝜓 𝛾 𝜇 𝜓 𝐴 𝜇 − 1 4 𝐹 𝜇𝜈 𝐹 𝜇𝜈
ℒ=𝑖 𝜓 𝛾 𝜇 𝜕 𝜇 𝜓−𝑚 𝜓 𝜓− 𝑞 𝑐 𝜓 𝛾 𝜇 𝜓 𝐴 𝜇 − 𝐹 𝜇𝜈 𝐹 𝜇𝜈 ℒ= 𝜓 𝛾 𝜇 𝑝 𝜇 − 𝑞 𝑐 𝐴 𝜇 𝜓−𝑚 𝜓 𝜓 Free fermion Lagrangian Quark-gluon interaction term Gluon Lagrangian Fall KAIST PH489 20

21 QCD Lagrangian 𝐹 𝜇𝜈 = 𝜕 𝜇 𝐴 𝜈 − 𝜕 𝜈 𝐴 𝜇 +𝑖 𝑞 𝑐 𝐴 𝜇 𝐴 𝜈 − 𝐴 𝜈 𝐴 𝜇
𝐹 𝜇𝜈 = 𝜕 𝜇 𝐴 𝜈 − 𝜕 𝜈 𝐴 𝜇 +𝑖 𝑞 𝑐 𝐴 𝜇 𝐴 𝜈 − 𝐴 𝜈 𝐴 𝜇 ⇒ 𝐹 𝜇𝜈 𝐹 𝜇𝜈 =𝑂 𝐴 𝜇 𝐴 𝜈 +𝑂 𝐴 𝜇 𝐴 𝜈 𝐴 𝜉 +𝑂 𝐴 𝜇 𝐴 𝜈 𝐴 𝜉 𝐴 𝜊 Fall KAIST PH489 21

22 QCD Lagrangian Interaction term − 𝑞 𝑐 𝜓 𝛾 𝜇 𝜓 𝐴 𝜇
− 𝑞 𝑐 𝜓 𝛾 𝜇 𝜓 𝐴 𝜇 =− 1 2 𝑞 𝑐 𝜓 𝛾 𝜇 𝜆 𝑗 𝜓 𝐴 𝜇 𝑗 Vertex factor − 1 2 𝑖 𝑞 𝑐 𝜆 𝑗 𝛾 𝜇 Fall KAIST PH489 22

23 QCD Lagrangian QED fermion current 𝑗 𝜇 = 𝑢 3 𝑝 3 −𝑖 𝑞 𝑒 𝛾 𝜇 𝑢 1 𝑝 1
𝑗 𝜇 = 𝑢 3 𝑝 3 −𝑖 𝑞 𝑒 𝛾 𝜇 𝑢 1 𝑝 1 QCD fermion current 𝑗 𝜇 = 𝑢 3 𝑝 3 𝑐 𝑛 † − 1 2 𝑖 𝑞 𝑐 𝜆 𝑗 𝛾 𝜇 𝑐 𝑚 𝑢 1 𝑝 1 Fall KAIST PH489 23

24 Running of Coupling Constant
Fall KAIST PH489 24

25 Running of Coupling Constant
Effective photon propagator 𝑃 0 = 𝑒 0 𝑞 2 ⇒𝑃= 𝑃 0 + 𝑃 0 𝜋 𝑞 2 𝑃 0 + 𝑃 0 𝜋 𝑞 2 𝑃 0 𝜋 𝑞 2 𝑃 0 +⋯= 𝑃 −𝜋 𝑞 2 ≡ 𝑃 − 𝑒 0 2 Π 𝑞 2 ≡ 𝑒 2 𝑞 2 𝑞 2 Fall KAIST PH489 25

26 Running of Coupling Constant
𝑃= 𝑒 2 𝑞 2 𝑞 2 = 𝑒 𝑞 − 𝑒 0 2 Π 𝑞 2 𝛼 𝑞 2 = 𝑒 2 𝑞 2 4𝜋 = 𝛼 𝜇 2 1−𝛼 𝜇 𝜋 ln 𝑞 2 𝜇 2 ⇒ 𝑒 2 𝑞 2 = 𝑒 − 𝑒 0 2 Π 𝑞 2 , 𝑒 2 𝜇 2 = 𝑒 − 𝑒 0 2 Π 𝜇 2 ⇒ 𝑒 2 𝑞 2 = 𝑒 2 𝜇 2 1− 𝑒 2 𝜇 2 Π 𝑞 2 −Π( 𝜇 2 ) = 𝑒 2 𝜇 2 1− 𝑒 2 𝜇 𝜋 2 ln 𝑞 2 𝜇 2 Fall KAIST PH489 26

27 Running of Coupling Constant
Fall KAIST PH489 27

28 Running of Coupling Constant
QED coupling constant QCD coupling constant (𝑛=3 in our QCD) 𝛼 𝑠 𝑞 2 = 𝛼 𝑠 𝜇 𝐵 𝛼 𝑠 𝜇 2 ln 𝑞 2 𝜇 2 𝛼 𝑞 2 = 𝛼 𝜇 2 1− 1 3𝜋 𝛼 𝜇 2 ln 𝑞 2 𝜇 2 𝐵= 1 4𝜋 11∙ 1 3 𝑛−2 𝑁 𝐹 Gluon-gluon coupling Fermion Fall KAIST PH489 28

29 Running of Coupling Constant
Fall KAIST PH489 29

30 Running of Coupling Constant
Fall KAIST PH489 30

31 Asymptotic Freedom Fall KAIST PH489 31

32 Asymptotic Freedom Fall KAIST PH489 32

33 Color Confinement Fall 2017 KAIST PH489 33
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34 Color Confinement Fall 2017 KAIST PH489 34
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35 Color Confinement in Hadrons
Structures of Mesons, Baryons, Tertaquarks, and Pentaquarks Fall KAIST PH489 35

36 Mesons 1 quark, 1 antiquark 𝜓 𝑐 = 1 3 𝑟 𝑟 +𝑔 𝑔 +𝑏 𝑏
- Bosonic particle with spin 𝑠=0 or 1 - Baryon number 𝐵=0 𝜓 𝑐 = 𝑟 𝑟 +𝑔 𝑔 +𝑏 𝑏 - Quark and antiquark carry opposite color Fall KAIST PH489 36

37 Baryons 3 quarks 𝜓 𝑐 = 1 6 (𝑟𝑔𝑏−𝑟𝑏𝑔 +𝑔𝑏𝑟−𝑔𝑟𝑏 +𝑏𝑟𝑔−𝑏𝑔𝑟)
- Fermionic particle with spin 𝑠=1/2 or 3/2 𝜓 𝑐 = (𝑟𝑔𝑏−𝑟𝑏𝑔 - Baryon number 𝐵=1 - 3 quarks carry 3 different colors +𝑔𝑏𝑟−𝑔𝑟𝑏 +𝑏𝑟𝑔−𝑏𝑔𝑟) Fall KAIST PH489 37

38 Tetraquarks 2 quarks, 2 antiquarks 𝑑 𝑢 𝑐 𝑐 - Bosonic particle
- Baryon number 𝐵=0 𝑢 𝑐 𝑐 Fall KAIST PH489 38

39 Pentaquarks 4 quarks, 1 antiquark 𝑐 𝑑 𝑐 𝑢 𝑢 - Fermionic particle
- Baryon number 𝐵=1 𝑐 𝑢 𝑢 Fall KAIST PH489 39

40 QCD Matter Brief Introduction to Non-Hadronic Quark Matter States
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41 QCD Matter Fall 2017 KAIST PH489 41
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42 QCD Matter Fall 2017 KAIST PH489 42
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43 Quark-Gluon Plasma Fall 2017 KAIST PH489 43
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44 Quark-Gluon Plasma Fall 2017 KAIST PH489 44
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45 References [1] Thomson, M. (2013). Modern Particle Physics. Cambridge University Press. [2] Griffiths, D. (2008). Introduction to Elementary Particles. John Wiley & Sons. [3] Greiner, W., Schramm, S., & Stein, E. (2007). Quantum Chromodynamics. Springer Science & Business Media. [4] Halzen, F., Martin, A. D. (1984). Quarks and Leptons. [5] Ryder, L. H. (1996). Quantum Field Theory. Cambridge university press. [6] Greiner, W., & Reinhardt, J. (2012). Quantum Electrodynamics. Springer Science & Business Media. [7] Yoo, J. H. (2017). KAIST 2017 Spring Undergraduate Physics Course Lecture Series PH450 Particle Physics [8] Riordan, M. (1992). The Discovery of Quarks. Science, 256(5061), [9] Ollitrault, J. Y. (2015). The Littlest Liquid. Physics, 8, 61. [10] Instituto de Física Corpuscular, Lattice QCD, the numerical approach to the strong force [11] Walsh, K. M. (2016). Tracking the transition of early-universe quark soup to matter-as-we-know-it. Brookhaven National Laboratory's Relativistic Heavy Ion Collider News, Web, 4 Fall KAIST PH489 45

46 References (For Further Readings)
[12] Aaij, R., Adeva, B., Adinolfi, M., Affolder, A., Ajaltouni, Z., Albrecht, J., ... & Cartelle, P. A. (2014). Observation of the resonant character of the 𝑍 − state. Physical review letters, 112(22), [13] Aaij, R., Adeva, B., Adinolfi, M., Affolder, A., Ajaltouni, Z., Akar, S., ... & Alkhazov, G. (2015). Observation of 𝐽/𝜓𝑝 Resonances Consistent with Pentaquark States in 𝛬 𝑏 0 →𝐽/𝜓 𝐾 − 𝑝 Decays. Physical review letters, 115(7), [14] Park, W., & Lee, S. H. (2014). Color spin wave functions of heavy tetraquark states. Nuclear Physics A, 925, [15] Ruester, S. B., Werth, V., Buballa, M., Shovkovy, I. A., & Rischke, D. H. (2005). Phase diagram of neutral quark matter: Self-consistent treatment of quark masses. Physical Review D, 72(3), Fall KAIST PH489 46

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