Transverse momentum of jets in electroproduction from quantum chromodynamics

Detailed predictions of QCD on transverse momentum distributions of jets in leptoproduction are presented. The average p_⊥² is found to be asymptotically proportional to W² (the hadronic invariant mass squared) with a coefficient function that depends little on x and y. Contributions from gluons in the nucleon are relatively smaller than for σ_L/σ_T.     

Quantum chromodynamics and charm photoproduction

It is shown that charm photoproduction can be consistently described within an asymptotically free field theory. Quantum chromodynamics is used to derive sum rules for the total cross section σ_c^γ which includes both production of mesons with hidden charm (J/ψ, ψ′ and so on) and of charmed particles (pairs $\text{D}\text{D}$, $\text{F}\text{F}$ and so on). An estimate of σ_c^γ as a function of energy is given and fast growth is discovered up to energies ～ 1000 GeV. In this energy range σ_c^γ turns out to be equal to several μb. It is argued that measurements of charm photoproduction would give the most direct information on the gluon distribution within a nucleon. All the results are generalized to production of heavier particles containing new quarks. In particular, a simple rescaling law is derived connecting the cross sections for charm and beauty.     

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.     

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.     

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.     

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 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.     

Pions in large N quantum chromodynamics

An effective field theory of quarks, gluons, and pions, with the number N of colors treated as large, is proposed as a basis for calculations of hadronic phenomena at moderate energies. The qualitative consequences of the large N limit are similar though not identical to those in pure quantum chromodynamics, but because constituent quark masses appear in the effective Lagrangian, the 't Hooft coupling in the effective theory need not be strong at moderate energies. To leading order in 1/N the effective theory is renormalizable, with only a finite number of terms in the Lagrangian.     

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.     

Masses of light quarks in quantum chromodynamics

We try to determine light quark masses by considering sum rules for the vacuum expectation value of the time-ordered correlation function of two divergences of the axial vector current. The evaluation is carried out at momenta high enough for the non-perturbative contributions to be negligible. We find that the average mass of the up and down quark at a momentum of 1 GeV lies between 3.3 and 7.9 MeV while that for the strange quark lies between 84 and 212 MeV. The ranges of values reflect predominantly the uncertainty in the absorptive part in the low energy region (?1.7 GeV).