Quantum Chromodynamics

Abstract

Aimed at graduate students and researchers in theoretical physics, this book presents the modern theory of strong interaction: quantum chromodynamics (QCD).The book exposes various perturbative and nonperturbative approaches to the theory, including chiral effective theory, the problems of anomalies, vacuum tunnel transitions, and the problem of divergence of the perturbative series. The QCD sum rules approach is exposed in detail. A great variety of hadronic properties (masses of mesons and baryons, magnetic moments, formfactors, quark distributions in hadrons, etc.) have been found using this method. The evolution of hadronic structure functions is presented in detail, together with polarization phenomena. The problem of jets in QCD is treated through theoretical description and experimental observation. The connection with Regge theory is emphasized. The book covers many aspects of theory which are not discussed in other books, such as CET, QCD sum rules, and BFKL. B . L . I O FF E is Head of the Laboratory of Theoretical Physics at ITEP, Moscow. He discovered the origin of baryon masses in QCD, the light-cone dominance in deep inelastic scattering. He predicted that parity violation in weak interactions should be accompanied by violation of charge symmetry or time reversal invariance, and the observation of parity violating spin-momentum correlations would mean the charge symmetry violation. He has won several prizes, including the Alexander von Humboldt Award. V. S . FA D I N is Head of the Theoretical Department of the Budker Institute of Nuclear Physics. He is one of the authors of the BFKL equation for parton distributions, which gives the most common basis for the theoretical description of semi-hard processes. He is also one of the discoverers of the coherence effect in gluon emission, which is crucial for inclusive spectra of hadrons in their soft region. L . N . L I PAT OV is Director of the Theoretical Physics Department at the Institute for Nuclear Physics, St. Petersburg. He is one of the authors of the DGLAP and BFKL equations for the parton distributions used in the theoretical description of the deep inelastic ep scattering and other processes in QCD. He has been awarded prizes from the ITEP and FIAN institutes for outstanding scientific achievements.

Sum rules for CP-violating operators of Weinberg type

“…where m q Λ QCD 0.3 GeV denotes the constituent quark mass andρ 1/(0.6 GeV) is the average instanton size. Notice that for the quoted values of m q andρ one finds qq −(0.25 GeV) 3 in agreement with the standard value for the quark condensate [67,68,75].…”

“…To determine the OPE correlator (4.3) corresponding to the dimension-eight Weinberg-type operator O 8 , we also need values for the two condensates in (5.25). The only estimates that exist at present are based on the instanton liquid model [68,[87][88][89][90]. One obtains [86] qiγ 5 qg 2 sG · G = 64 5ρ 4 qq , qt A iγ 5 qg 2 s d ABCG B · G C = 32 15ρ 4 qq .…”

“…In this section, we derive the phenomenological form Π phen of the correlator (2.1) following the argument presented in [35,37,60,61]. An often considered approach for the phenomenological side of two-point correlators is the use of dispersion relations [62][63][64][65][66][67][68]. Since we are interested in the correlator of two nucleon currents η in an external EM field, we are, however, effectively dealing with a three-point correlation function.…”

“…They do not have definite signs due to the lack of positivity constraints of the considered correlator [61]. Applying the Borel transformation defined in Appendix B, one finds that the numerically leading contributions of the Borel transforms of the three terms in (3.15) are given by , (3.17) where we have used the values m n ' 0.94 GeV and m N 0 ' 1.44 GeV [68] for the mass of the neutron and its lightest excitation to obtain the quoted numerical prefactor. Under the assumption that | f N 0 | ' | f N 0 N 00 | ' 2 m n d n and setting M = 2⇤ QCD ' 0.6 GeV with ⇤ QCD the QCD scale, the mixed ground-state and exited-state (excited-states only) contributions therefore naively amount to relative corrections of the order of 30% (5%).…”

“…with qq −(0.25 GeV) 3 [67,68,75] the quark condensate. The effective operator O 6 can be perturbatively inserted into the quark propagator [40].…”