rpp2010-rev-qcd - 9. Quantum chromodynamics 1 9. QUANTUM...

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9. Quantum chromodynamics 1 9. QUANTUM CHROMODYNAMICS Written October 2009 by G. Dissertori (ETH, Zurich) and G.P. Salam (LPTHE, Paris). 9.1. Basics Quantum Chromodynamics (QCD), the gauge feld theory that describes the strong interactions oF colored quarks and gluons, is the SU(3) component oF the SU(3) × SU(2) × U(1) Standard Model oF Particle Physics. The Lagrangian oF QCD is given by L = X q ¯ ψ q,a ( μ μ δ ab g s γ μ t C ab A C μ m q δ ab ) ψ q,b 1 4 F A μν F Aμν , (9 . 1) where repeated indices are summed over. The γ μ are the Dirac γ -matrices. The ψ are quark-feld spinors For a quark oF flavor q and mass m q , with a color-index a that runs From a =1to N c =3 , i.e. quarks come in three “colors.” Quarks are said to be in the Fundamental representation oF the SU(3) color group. The A C μ correspond to the gluon felds, with C running From 1 to N 2 c 1=8 , i.e. there are eight kinds oF gluon. Gluons are said to be in the adjoint representation oF the SU(3) color group. The t C ab correspond to eight 3 × 3 matrices and are the generators oF the SU(3) group (cF. the section on “SU(3) isoscalar Factors and representation matrices” in this Review with t C ab λ C ab / 2). They encode the Fact that a gluon’s interaction with a quark rotates the quark’s color in SU(3) space. The quantity g s is the QCD coupling constant. ±inally, the feld tensor F A μν is given by F A μν = μ A A ν ν A A μ g s f ABC A B μ A C ν [ t A ,t B ]= if ABC t C , (9 . 2) where the f ABC are the structure constants oF the SU(3) group. Neither quarks nor gluons are observed as Free particles. Hadrons are color-singlet ( i.e. color-neutral) combinations oF quarks, anti-quarks, and gluons. Ab-initio predictive methods For QCD include lattice gauge theory and perturbative expansions in the coupling. The ±eynman rules oF QCD involve a quark-antiquark- gluon ( q ¯ qg ) vertex, a 3-gluon vertex (both proportional to g s ), and a 4-gluon vertex (proportional to g 2 s ). A Full set oF ±eynman rules is to be Found For example in ReF. 1. UseFul color-algebra relations include: t A ab t A bc = C F δ ac ,where C F ( N 2 c 1) / (2 N c )= 4 / 3 is the color-Factor (“Casimir”) associated with gluon emission From a quark; f ACD f BCD = C A δ AB where C A N c = 3 is the color-Factor associated with gluon emission From a gluon; t A ab t B ab = T R δ AB T R =1 / 2 is the color-Factor For a gluon to split to a q ¯ q pair. The Fundamental parameters oF QCD are the coupling g s (or α s = g 2 s 4 π ) and the quark masses m q . K. Nakamura et al. ,JPG 37 , 075021 (2010) (http://pdg.lbl.gov) July 30, 2010 14:57
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2 9. Quantum chromodynamics This review will concentrate mainly on perturbative aspects of QCD as they relate to collider physics. Related textbooks include Refs. 1–3. Some discussion of non-perturbative aspects, including lattice QCD, is to be found in the reviews on “Quark Masses” and “The CKM quark-mixing matrix” of this Review . Lattice-QCD textbooks and lecture notes include Refs. 4–6, while recent developments are summarized for example in Ref. 7. For a review of some of the QCD issues in heavy-ion physics, see for
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rpp2010-rev-qcd - 9. Quantum chromodynamics 1 9. QUANTUM...

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