Perturbative quantum chromodynamics

A large variety of modern perturbative aspects of QCD is critically reviewed from a theoretical as well as phenomenological point of view. The first part of this review is devoted to the classical more formal approach of summing leading logs: After a brief discussion of the basic concepts of renormalization theory, we review the renormalization group and its predictions for the effective (running) coupling constant in any field theory (asymptotic freedom as well as ‘fixed point’ theories). Using, in addition, the operator product expansion for deep inelastic scattering we calculate scaling violations of structure functions and show how to compare these results with experiment. Furthermore, dynamical calculations of parton distributions are discussed, as well as σ_L/σ_T, jets in leptoproduction and subleading corrections. We then proceed to show how these renormalization group improved results can be also derived using a simple perturbative language (Kogut-Susskind; Altarelli-Parisi) or by summing parton (Bethe-Salpeter) ladders. The universal validity (process independence) of the resulting Q² dependencies of parton distributions is emphasized and their factorization from the uncalculable non-perturbative piece (infrared divergences) is discussed. These latter results enable us to make rather unambiguous predictions for processes other than deep inelastic scattering, to which the remainder of this review is devoted. The hard scattering processes discussed indetail include hadronic (Drell-Yan) production of lepton pairs as well as their transverse momenta, the hadronic production of heavy quark flavors, semi-inclusive processes and fragmentation functions, high-p_T reactions and some recent topics and problems of jet production in e⁺e^? annihilation.     

Condensates in quantum chromodynamics

The paper presents a short review of our knowledge today on vacuum condensates in quantum chromodynamics (QCD). The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determining physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of the quark condensate, connected to the existence of baryon masses, is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic τ decay. In theoretical analysis, the terms of perturbation theory (PT) up to α _s ³ are accounted for; in the operator product expansion (OPE), those up to dimension 8. The total probability of the decay τ → hadrons (with zero strangeness) and of the τ-decay structure functions are best described at α _s (m _τ ² )=0.330±0.025. It is shown that the Borel sum rules for τ-decay structure functions along the rays in the q ²-complex plane are in agreement with experiment, having an accuracy of ～2% at the values of the Borel parameter |M ²|>0.8 GeV². The magnitudes of dimension 6 and 8 condensates were found, and the limitations on gluon condensates were obtained. The sum rules for the charmed-quark vector-current polarization operator were analyzed in three loops (i.e., in order α _s ² ). The value of the charmed-quark mass (in an \(\overline {MS} \) regularization scheme) was found to be \(\bar m_c (\bar m_c^2 ) = 1.275 \pm 0.015\) GeV, and the value of gluon condensate was estimated as 〈0|(α _s/π)G ²|0〉=0.009±0.007 GeV⁴. The general conclusion is that the QCD described by PT + OPE is in good agreement with experiment at Q ²?1 GeV².     

Charmed baryons in quantum chromodynamics

We consider a three-phase model of strongly interacting matter, treating each phase as an ideal gas modified by a simple phenomenological interaction feature. For nuclear matter, we take into account the baryonic repulsion; for the quark-gluon plasma, we include the bag pressure; the constituent quark phase has a non-zero effective quark mass as well as an independent bag pressure. By studying which phase dominates thermodynamically in what region of temperature and baryon number density, we obtain a phase diagram for strongly interacting matter and gain some insight on the relation between deconfinement and chiral symmetry restoration.     

Lattice quantum chromodynamics and baryon-baryon interactions

After briefly reviewing the theoretical concepts and numerical methods in lattice QCD, recent simulation results of the hadron masses and hadron interactions with nearly physical quark masses are presented. Special emphasis is placed on the baryon-baryon interactions on the basis of the HAL QCD method where the integro-differential equation for the equal-time Nambu–Bethe–Salpeter amplitude plays a key role to bridge a gap between the multi-baryon correlation and the scattering observable such as the phase shift.     

Scaling violations and perturbative quantum chromodynamics

We try to understand the meaning of the recent data on scaling violations of the moments of the structure function F₃ measured in ν and $\text{ν}$ deep inelastic scattering, and their relevance as a test of QCD. We do this by reducing to the minimum the theoretical machinery and prejudices and stressing the perturbative nature of the problem. We are led to a definition of the perturbation coupling constant σ_S(Q = 2.5 GeV) = 0.61 ± 0.06, in termas of which the corrective terms for all quantities computed so far turn out to be relatively small.     

On de-globalization in quantum chromodynamics

The recent discovery and resummation of a class of single logarithmic effects (non-global logs), has a significant impact on several QCD observables ranging from the classic Sterman-Weinberg jet definition to currently studied event shapes and rapidity gap observables. The discovery of the above effects overturns, for example, the common wisdom that hadronic energy flow in limited inter-jet regions is dictatedprimarily by the colour flow of the underlying hard partonic subprocess. We discuss some features of non-global logs and the rapid progress being made in estimating and controlling such corrections.     

Multijet structure in quantum chromodynamics

Field theories naturally give rise to multiple jets of hadrons in short-distance processes, such as e⁺ e^? annihilation. In particular, a low-energy jet of hadrons distributed in some cone of opening angle δ would be naively expected to evolve at high energies into multiple jets within the angle δ. We explore to what extent this will happen in quantum chromodynamics.     

The quark-nucleon phase diagram and quantum chromodynamics

The temperature dependence of a conjectured first-order phase transition between nuclear matter and quark-gluon matter is calculated for temperatures below T = 200 MeV. On the nuclear side a rather successful meson-nucleon mean field theory is applied while quark-gluon matter at large densities and finite temperatures is described perturbatively by quantum chromodynamics. Outside the finite volume of hot and dense quark-gluon matter the physical vacuum is characterized, by the newly determined bag parameter Λ_B = 235 MeV. We observe a dramatic drop in the density of nuclear matter at the phase transition point as the temperature increases, if the scale parameter Λ of QCD is chosen as Λ = 100 MeV. For larger values of Λ the effect is less pronounced. Further work is required to settle this problem.     

A construction of two-dimensional quantum chromodynamics

We present a sketch of the construction of the functional measure for theSU(2) quantum chromodynamics with one generation of fermions in two-dimensional space-time. The method is based on a detailed analysis of Wilson loops.     

The static potential in quantum chromodynamics

The effective interaction between a static quark-antiquark pair is computed within the framework of 〈G_μv^aG_a^μv〉 ≠ 0. Due to the static approximation the interaction takes the form of a potential, which is in striking agreement with phenomenological potentials.     

Large sea polarisation in quantum chromodynamics

The spin structure of sea quarks and gluons is obtained by using QCD evolution equations and the angular momentum sum rule. Several consequences of the predicted large polarisations are enumerated.     

Infrared regularization in two-dimensional quantum chromodynamics

Using 2-dimensional quantum chromodynamics as an example, it is shown that the gauge-invariant fields formalism allows one to avoid the difficulties related to the choice of an infrared regularization, and leads to confinement of both single quarks and quark-antiquark pairs.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 74–78, May, 1990.     

Semileptonic b-quark decay in quantum chromodynamics

We compute real and virtual one-gluon corrections to the charged lepton energy distribution in the following reaction: $\text{b}\text{→}\text{c}\text{+ ?}{}^{\mathrm{?}}\text{+}\text{v}{}_{\mathrm{?}}$ for arbitrary quark masses.     

Gauge invariance structure of quantum chromodynamics

Perturbative QCD may be subdivided into separately gauge-invariant sectors according to the projection of non-abelian color weights onto linearly independent basis elements. We exploit the general Lie group structure of the theory to give an algorithm for finding these gauge-invariant sets and present several examples of its use. The planar sector and the systematics of the non-planar corrections are defined for any gauge theory. Our gauge set classification has implications for QCD bound states, finite order perturbative QCD calculations, the study of QCD infrared singularities and for the question of convergence of the perturbation series.     

Quark confinement physics from quantum chromodynamics

We show the construction of the dual superconducting theory for the confinement mechanism from QCD in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. We find that essence of infrared abelian dominance is naturally understood with the off-diagonal gluon mass m_off ≈- 1.2GeV induced by the MA gauge fixing. In the MA gauge, the off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon phase tends to be random. As the mathematical origin of abelian dominance for confinement, we demonstrate that the strong randomness of the off-diagonal gluon phase leads to abelian dominance for the string tension. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system. We investigate the monopole-current system in the MA gauge by analyzing the dual gluon field B_μ. We evaluate the dual gluon mas as m_B = 0.4 0.5GeV in the infrared region, which is the lattice-QCD evidence of the dual Higgs mechanism by monopole condensation. Owing to infrared abelian dominance and infrared monopole condensation, QCD in the MA gauge is describable with the dual Ginzburg-Landau theory.