Quantum chromodynamics

Quantum Chromodynamics

Volumn , Issue , 2007, Pages 1-553

  Greiner, Walter ^a   Schramm, Stefan ^b   Stein, Eckart ^c  

^a FRANKFURT INSTITUTE FOR ADVANCED STUDIES   (Germany)

^b GOETHE UNIVERSITY   (Germany)

^c Maharishi University of Management   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84892265783     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-48535-3     Document Type: Book

References (138)

1. For a detailed discussion of the content of this chapter see W. Greiner and B. Müller: Symmetries (Springer, Berlin, Heidelberg 1994).
2. See the Review of Particle Physics by W.-M. Yao et al., Journal of Physics G 33 (2006) 1, and information available online at http://pdg.lbl.gov/
3. W. Greiner and B. Müller: Quantum Mechanics: Symmetries (Springer, Berlin, Heidelberg, 1994).
4. CDF collaboration (F. Abe et al. - 397 authors): Phys. Rev. Lett. 73, 225 (1994);
5. Phys. Rev. D50, 2966 (1994);
6. Phys. Rev. Lett. 74, 2626 (1995).
7. D∅ collaboration (V. M. Abazov et al.): Nature 429, 638 (10 June 2004); the preprint hep-ex/0608032 by the CDF and D∅ collaborations gives a mass of mtop = 171.4± 2.1GeV/c2, resulting from a combined analysis of all data available in 2006.
8. For a detailed discussion see W. Greiner: Relativistic Quantum Mechanics - Wave Equations, 3rd ed. (Springer, Berlin, Heidelberg 2000)
9. see W. Greiner: Quantum Mechanics - An Introduction, 4th ed. (Springer, Berlin, Heidelberg, 2000), Exercise 13.2.
10. We use here the Heaviside-Lorentz units of electrodynamics, in contrast to Gauß units, which are used in W. Greiner and J. Reinhardt: Quantum Electrodynamics, 3rd ed. (Springer, Berlin, Heidelberg, 2003). See in particular Section 4.2 and Exercise 4.2 of this volume, where various gauges and unit systems are discussed.
11. see W. Greiner and J. Reinhardt: Quantum Electrodynamics, 3rd ed. (Springer, Berlin, Heidelberg, 2003).
12. Any vector field carries spin 1 - see W. Greiner and B. Müller: Quantum Mechanics: Symmetries (Springer, Berlin, Heidelberg, 1994).
13. see, e. g., W. Greiner and J. Reinhardt: Quantum Electrodynamics, 3rd ed. (Springer, Berlin, Heidelberg, 2003).
14. see, e. g., W. Greiner and B. Müller: Quantum Mechanics: Symmetries (Springer, Berlin, Heidelberg, 1994).
15. For a discussion, see M. Jones, R.H. Dalitz, and R.R. Hougan: Nucl. Phys. B 129, 45 (1977).
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17. and T.A. De Grand: Ann. Phys. 101, 496 (1976).
18. see, e. g., W. Greiner and J. Reinhardt: Quantum Electrodynamics, 3rd ed. (Springer, Berlin, Heidelberg, 2003).
19. In the literature one may also find the following definition for ν: ν = P ?q/MN. It differs from our definition by the factor 1/MN. We shall use the definition (3.19) throughout this book. It is the one standardly used in connection with the operator product expansion and the DGLAP equations (see Chap. 5).
20. The proof of this relation can be found in Exercise 2.4 of W. Greiner and B. Müller: Gauge Theory of Weak Interactions, 3rd ed. (Springer, Berlin, Heidelberg 2000).
21. Here and in the following we omit the parton index i on the mass and momentum variables.
22. See also W. Greiner and B. Müller: Quantum Mechanics - Symmetries, 2nd ed., (Springer, Berlin, Heidelberg 1994)
23. P. Hasenfratz, J. Kuti, Phys. Rep. 40 C, 75 (1978).
24. See also W. Greiner and J. Reinhardt: Field Quantization (Springer, Berlin, Heidelberg 1996)
25. and W. Greiner: Relativistic Quantum Mechanics - Wave Equations, 3rd ed. (Springer, Berlin, Heidelberg 2000).
26. W. Greiner and J. Reinhardt: Field Quantization (Springer, Berlin, Heidelberg 1996).
27. Deformed bags are discussed in D. Vasak, R. Shanker, B. Müller and W. Greiner: J. Phys. G 9, 511 (1983) in connection with the study of fissioning bags as a form of overcritical quark-antiquark production.
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32. See also W. Greiner and B. Müller: Quantum Mechanics - Symmetries, 2nd ed., (Springer, Berlin, Heidelberg 1994)
33. P. Hasenfratz, J. Kuti, Phys. Rep. 40 C, 75 (1978).
34. See W. Greiner: Quantum Mechanics - Special Chapters, 1st ed., 2nd printing (Springer, Berlin, Heidelberg, 2001).
35. See W. Greiner and J. Reinhardt: Quantum Electrodynamics, 3rd ed. (Springer, Berlin, Heidelberg, 2003).
36. See W. Greiner and B. Müller: Gauge Theory of Weak Interactions, 3rd ed. (Springer, Berlin, Heidelberg 2000).
37. W. Greiner: Relativistic Quantum Mechanics - Wave Equations, 3rd ed. (Springer, Berlin, Heidelberg 2000).
38. W. Greiner and B. Müller: Gauge Theory of Weak Interactions, 3rd ed. (Springer, Berlin, Heidelberg 2000).
39. See, e.g., W. Greiner and J. Reinhard: Field Quantization (Springer, Berlin, Heidelberg, 1996).
40. see W. Greiner and J. Reinhardt: Quantum Electrodynamics, 3rd ed. (Springer, Berlin, Heidelberg, 2003).
41. see W. Greiner and J. Reinhardt: Quantum Electrodynamics, 3rd ed. (Springer, Berlin, Heidelberg, 2003)
42. Their properties can be found, for example, in M. Abramowitz and A. Stegun: Handbook of Mathematical Functions, Chap. 22. (Dover, 1972).
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49. Note the similarity of this effect to the diving of an empty electron state into the lower continuum in the presence of a supercritical external electric field. The hole in the lower continuum is subsequently emitted as a so-called spontaneous positron (for further details of the supercritical change of the neutral vacuum into a charged vacuum due to Coulomb fields by spontaneous positron emission, seeW. Greiner, B.Müller, J. Rafelski: Quantum Electrodynamics of Strong Fields, (Springer, Berlin, Heidelberg, 1985), pp 122.
50. V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Fortsch. Phys. 32, 585 (1985).
51. See the discussion inW. Greiner and J. Reinhardt: Field Quantization (Springer Berlin, Heidelberg 1996).
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53. E. Tomboulis: Phys. Rev. D 8, 2736 (1973).
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56. O. Nachtmann: Elementary Particle Physics (Springer, Berlin, Heidelberg 1990).
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58. Usually one defines the nth moment as the expectation value of xn rather than xn1, which is commonly chosen in QCD.
59. W.W. Press, B.P. Flannery, S.A. Teukolsky,W.T. Vetterling: Numerical Recipes (Cambridge University Press 1992)
60. M. Glück, E. Reya, A. Vogt: Z. Physik C 53, 127 (1992)
61. Greiner and J. Reinhardt: Field Quantization (Springer, Berlin, Heidelberg 1996).
62. Since the explicit calculation is quite cumbersome, we refer to A. de Rujula, H. Georgi, and H.D. Politzer: Ann. Phys. 103, 315 (1977)
63. See W. Greiner and B. Müller: Gauge Theory of Weak Interactions, 3rd ed. (Springer, Berlin, Heidelberg 2000).
64. See W. Greiner and J. Reinhardt: Field Quantization (Springer, Berlin, Heidelberg 1996).
65. See B. Ehrnsperger, et al.: OPE Analysis for Polarized Deep Inelastic Scattering, Phys. Lett. B 323, 439 (1994) and references therein.
66. .A. Bardeen, A.J. Buras, D.W. Duke and T. Muta: Phys. Rev. D 18, 3998 (1978).
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73. O. Nachtmann: Nucl. Phys. B 63, 237 (1973).
74. A. De Rujula,W. Georgi,W.D. Politzer: Phys. Rev. D 15 (1997) 2495
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76. W. Greiner and B. Müller: Quantum Mechanics - Symmetries, 2nd ed., (Springer, Berlin, Heidelberg 1994).
77. B. Ehrnsperger et al.: Phys. Lett. B 150, 439 (1994)
78. S.A. Larin, J.A.M. Vermaseren: Phys. Lett. B 259 (1991) 345.
79. G. 't Hooft in The Whys of Subnuclear Physics, ed. by A. Zichichi (Plenum, New York 1977).
80. A.H. Müller: The QCD Perturbation Series in QCD - Twenty Years Later, ed. by P.M. Zerwas and H.A. Kastrup (World Scientific, Singapore, 1922), p. 162.
81. G. 't Hooft in The Whys of Subnuclear Physics, ed. by A. Zichichi (Plenum, New York 1977).
82. A.H. Müller: The QCD Perturbation Series in QCD - Twenty Years Later, ed. by P.M. Zerwas and H.A. Kastrup (World Scientific, Singapore, 1922), p. 162.
83. M. Beneke: Nucl. Phys. B 405, 424 (1993)
84. D.J. Broadhurst: Z. Phys. C 58, 339 (1993).
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86. J. Brodsky, G.P. Lepage, P.B. Mackenzie: Phys. Rev. D 28, 228 (1983).
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90. For a general overview on renormalons see: M. Beneke: Phys. Rept. 317, 1 (1999).
91. F. Block and A. Nordsieck: Phys. Rev. 52, 54 (1937)
92. See M. Chen: Int. J. Mod. Phys. A 1, 669 (1986).
93. See W. Greiner and B. Müller: Gauge Theory of Weak Interactions, 3rd ed. (Springer, Berlin, Heidelberg, New York 2000).
94. R.K. Ellis, W. Furmanski, and R. Petronzio: Nucl. Phys. B 207, 1 (1982);
95. Nucl. Phys. B 212, 19 (1983)
96. J. Qiu, G. Sterman: Nucl. Phys. B 353, 105 (1991).
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98. See also C. Itzykson and J.-B. Zuber: Quantum Field Theory (McGraw-Hill, New York, 1978).
99. L.V. Gribov, E.M. Levin, M.G. Ryskin: Phys. Rept. 100, 1 (1983)
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102. See, for example, P.D.B. Collins: An Introduction to Regge Theory and High-Energy Physics (Cambridge University Press, Cambridge 1977).
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109. V. Fadin and L. Lipatov: Phys. Lett. B 429, 127 (1998)
110. G. Camici and M. Ciafaloni: Phys. Lett. B 430, 349 (1998).
111. W. Greiner and J. Reinhardt: Field Quantization (Springer, Berlin, Heidelberg 1996).
112. P.A.M. Dirac: Physikalische Zeitschrift der Sowjetunion 3, 64 (1933).
113. Also see the monograph by R. P. Feynman and A. R. Hibbs: Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).
114. It is customary to remove the factor i in front of (7.10) from the definition of the action. The Euclidean action SE is defined as SE =iS(t =iτ).
115. Some care has to be taken with the ordering of the operators when the Hamiltonian contains mixed products of position and momentum operators.
116. Note that all the colored quantities, the gauge field Aμ, the field strength Fμν, the link variable Uμ, and the gauge rotation g are 3×3 matrix-valued fields. To prevent cluttering of the text with too many symbols, we will suppress the ̂ symbol in the formulae.
117. A plane is defined by two axes. There are four directions on the lattice, therefore there exist six independent planes.
118. The coefficient in front of the sum is usually denoted as β = 6/g2 for SU(3), or in general β = 2N/g2 for a SU(N) gauge group. It is the only free parameter of the theory.
119. The relevant original references are T. Banks, S. Raby, L. Susskind, J. Kogut, D.R.T. Jones, P.N. Scharbach, and D.K. Sinclair: Phys. Rev. D 15, 1111 (1977);
120. L. Susskind, Phys. Rev. D 16, 3031 (1977).
121. For a more extended discussion of this point, see W. Greiner and J. Reinhardt: Field Quantization (Springer, Berlin, Heidelberg 1996).
122. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller: J. Chem. Phys. 21, 1087 (1953).
123. e.g. see M. Abramowitz, I.A. Stegun: Handbook of Mathematical Functions (Dover 1968) Formula (9.6.10).
124. see e.g. P. Weisz: Phys. Lett. B 100, 330 (1981).
125. M. Creutz: Phys. Rev. D 21, 2308 (1980).
126. Greiner, H. Stöcker, L. Neise: Thermodynamics and Statistical Mechanics (Springer Berlin, Heidelberg 1995).
127. See B. Svetitsky, L.G. Yaffe: Nucl. Phys. B 210, 423 (1982).
128. See M.A. Shifmann, A.I. Vainshtein, and V.I. Zakharow: Nucl. Phys. B 147, 385 and 448 (1979).
129. L.J. Reinders, H. Rubinstein and S. Yazaki: Phys. Rep. 127, 1 (1985).
130. V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov: Fortsch. Phys. 32, 585 (1985).
131. See J. Ambjørn and P. Olesen: Nucl. Phys. B 170, 60 (1980).
132. See S.G. Matinyan and G.K. Savvidy: Yad. Fiz. 25, 218 (1977).
133. See Hagedorn: Suppl. Nuov. Cim. 3, 147 (1965).
134. For a review see, e.g.,W. Greiner, H. Stöcker, and A. Gallmann (Eds.): Hot and Dense Nuclear Matter, NATO-ASI SERIES B-Physics (Plenum Press, 1994).
135. See W. Scheid, H. Müller and W. Greiner: Phys. Lett. 13, 741 (1974).
136. See B. Witten: Phys. Rev. D 30, 272 (1984).
137. See E. Farhi and R.L. Jaffe: Phys. Rev. D 30, 2319 (1984).
138. See C. Greiner, P. Koch, and H. Stöcker: Phys. Rev. Lett. 58, 1825 (1987).