Multiplicity fluctuations in one- and two-dimensional angular intervals compared with analytic QCD calculations

Multiplicity fluctuations in rings around the jet axis and in off-axis cones have been measured by the DELPHI collaboration in e⁺e⁻ annihilations into hadrons at LEP energies. The measurements are compared with analytical perturbative QCD calculations for the corresponding multiparton system, using the concept of Local Parton Hadron Duality. Some qualitative features are confirmed by the data but substantial quantitative deviations are observed.     

Chromodynamics and jet acollinearity in e+e− annihilation: Determining the Quark-Gluon coupling

Acollinearity of the quark and antiquark jets produced in e⁺e^? collisions is an obvious signature of gluon emission. We discuss the computation of acollinearity distributions in perturbative QCD and compare the results with recent data. Teh measurements provide us with a direct determination of the running coupling constant α_S.     

Heavy quark correlations ine + e − annihilations

In heavy quark jets the quark mass acts as a regulator of collinear singularities, making the quark momentum an infra-red safe variable in perturbative QCD. This allows a direct comparison of measured heavy hadron momentum spectra with perturbative calculations. We exploit the factorisation of heavy quark fragmentation to derive QCD predictions for momentum correlations between heavy hadrons produced ine ⁺ e ^? annihilations. We study the practical feasibility and model sensitivity of our approach using Monte Carlo simulations. Higher order perturbative corrections and contributions from non-perturbative effects are found to be at the level of 10%.     

Low energy QCD predictions from non perturbative methods

We show that by using lattice results about the euclidean ?-propagator, it is possible to give theoretical predictions on the low energy behavior of thee ⁺ e ^?→had. cross section. Furthermore, we present a comparison of perturbative QCD results (plus certain sum rules corrections) with non perturbative results from the lattice in the intermediate energy region.     

Fluctuations and anomalous dimensions in QCD cascades

A recently proposed multiplicity measure is used to study the properties of QCD cascades. We show that it is possible to define anomalous dimensions locally in rapidity space for the QCD cascade ine ⁺ e ^–-annihilation events and in deep inelastic lepton scattering. In this way it will be possible to differentiate between different suggested models for multiple gluon emission. We also show that the properties of an event are to a surprisingly large degree deterimined by the first one or two gluons. Thus e.g. the multiplicity fluctuations ine ⁺ e ^–-annihilation at theZ ⁰-pole are to about 90% determined by the hardest gluon. This implies that it may be principally difficult to make a distinct separation between the hard perturbative phase and the soft hadronization phase.     

Experimental investigation of the energy dependence of the strong coupling strength

The energy dependence of the relative production rate of three-jet events is studied in hadronic e⁺e⁻ annihilation events at center of mass energies between 22 and 46.7 GeV. Three-jet events are defined by a jet finding algorithm which is closely related to the definition of resolvable jets used in O(α_s²) perturbative QCD calculations, where the relative production rate of three-jet events is roughly proportional to the size of the strong coupling strength. The production rates of three-jet events in the data decrease significantly with increasing centre of mass energy. The experimental rates, which are independent of fragmentation model calculations, can be directly compared to theoretically calculated jet production rates and are in good agreement with the QCD expectations of a running coupling strength. The hypothesis of an energy independent coupling constant can be excluded with a significance of four standard derivations.     

Simulation of QCD jets: The choice of the cutoff

In view of the simulation ofe ⁺ e ^? annihilation events corresponding to QCD multi-jet final states, we examine the dependence of the results on the value of the cutoff, which delimits the perturbative from the non-perturbative regimes. We do this by studying in some detail related effects for the lowest order perturbative contributions (including single gluon emission). We conclude that event simulation is considerably affected by the choice of the cutoff. Up to energies where only two and three jet configurations are dominant, though, this does not prevent from having quantitative tests of QCD, if suitable kinematical cuts are applied.     

Nonperturbative corrections in resummed cross sections

We show that the resummation of large perturbative corrections in QCD leads to ambiguities in high energy cross sections that are suppressed by powers of large momentum scales. These ambiguities are caused by infrared renormalons, which are a general feature of resummed hardscattering functions in perturbative QCD, even though these functions are infrared safe order-by-order in perturbation theory. As in the case of the operator product expansion, the contributions of infrared renormalons to coefficient functions may be absorbed into the definition of higher-dimensional operators, which induce nonperturbative corrections that are power-suppressed at high energies. The strength of the suppression is determined by the location of the dominant infrared renormalon, which may be identified explicitly in the resummed series. In contrast to the operator product expansion, however, the relevant operators in factorized hadron-hadron scattering and jet cross sections are generally nonlocal in QCD, although they may be expressed as local operators in an effective theory for eikonalized quarks. In this context, we verify and interpret the presence of 1 /Q corrections to the inclusive Drell-Yan cross section with Q the pair mass. In a similar manner, we find exp (-b² In Q) corrections in the impact parameter space of the transverse momentum distributions of the Drell-Yan process and e⁺6^- annihilation. We also show that the dominant nonperturbative corrections to cone-based jet cross sections behave as 1 /(Qδ), with δ the opening angle of the jet and Q the center of mass energy.     

DYNAMICAL SYMMETRY BREAKINGS IN QUANTUM CHROMODYNAMICS

Dynamical symmetry breakings in quantum chromodynamics （QCD） are investigated by means of the renormalization-group equations and the Dyson equations. It is shown that: （1） The electromagnetic （and weak） interactions can not be neglected in studying those nonperturbative problems as dynamical symmetry breakings for type-A models in QCD. （2） When the electromagnetic interactions between stratons are taken into account in the weak coupling approximation, dynamical symmetry breakings in QCD occur for many realistic models （type-A models） with QCD asymptotically free. This conclusion may hold beyond the weak coupling approximation of the electromagnetic interactions if there can still be a self-consistent solution of Johnson-Baker-Willey in quantum electrodynamics or β_e has an UV-stable fixed point. e_∞≠0 （a simple zero of β_e） and e_∞is not too large.     

Perturbative QCD and the exclusive decay of heavy quarkonium into a photon and two mesons

We consider the radiative decays of the ³S₁ ground state Q$\text{Q}$ into a real photon and two light pseudoscalar or vector mesons. For sufficiently large mass of the heavy quark Q, the decay, e.g. ? → γππ, can be calculated in perturbative QCD, provided that the photon does not carry away a predominant fraction of the available energy. We present differential and integrated Dalitz plot distributions and, for quarkonium states produced with transverse polarization in e⁺e^? annihilation, angular distributions of the orientation of the decay triangle relative to the beam direction.     

Hump-backed QCD plateau in hadron spectra

New data on inclusive energy distribution of hadrons from quark jets ine ⁺ e ^? annihilation are shown to agree with the quantitative predictions of perturbative QCD, supporting the hypothesis of local parton-hadron duality.     

Conformal couplings and “azimuthal matching” of QCD pomerons

Using the asymptotic conformal invariance of perturbative QCD we derive the expression of the coupling of external states to all conformal spin p components of the forward elastic amplitude. Using the wave function formalism for structure functions at small x, we derive the perturbative coupling of the virtual photon for , which is maximal for linear transverse polarization. The non-perturbative coupling to the proton is discussed in terms of “azimuthal matching” between the proton color dipoles and the configurations of the photon. As an application, the recent conjecture of a second QCD pomeron related to the conformal spin-1 component is shown to rely upon a strong azimuthal matching of the component in –proton scattering. Received: 25 October 1999 / Revised version: 19 January 2000 / Published online: 14 April 2000     

Search for large-rapidity-gap events in e+e− annihilation

We investigate the cross section for the production of a low-mass colour-singlet cluster ine ⁺ e ^? annihilation with a large rapidity gap between the colour-singlet cluster and the other jets. It is argued that such events are the cross-channel analogue of large-rapidity-gap events in deep-inelastic scattering, and therefore could in principle be used to investigate the analytic continuation of the BFKL pomeron to the positive-t kinematic regime, where one would expect the trajectory to pass through glueball states. The cross section can be calculated in perturbative QCD, so that the infrared scale arising from non-perturbative effects, which prevents an exponential fall-off with rapidity gap in the case of deep-inelastic scattering, is absent ine ⁺ e ^? annihilation. Correspondingly, the cross section for such events decreases rapidly with increasing rapidity gap.     

QCD at lowQ 2—A correspondence relation for moments of structure functions

The precocious validity of QCD predictions in deep inelastic lepton nucleon scattering ande ⁺ e ^? annihilation is interpreted as a signal for an underlying “correspondence principle” relating perturbative and nonperturbative physics on theQ ² average. Correspondence relations for nonsinglet moments of deep inelastic structure functions are formulated, discussed and successfully tested against experiment. The relations provide an independent determination of the QCD ?-parameter from lowQ ² data in perfect agreement with results from largeQ ² analyses.     

Perturbative expansions in QCD and analytic properties of α s

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties and contain, in particular, infrared-generated Landau ghost poles and cuts. As an outcome, a rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In the limiting case of large N _c, where QCD amplitudes contain only pole singularities, the strong coupling constant α _s(Q ²) is shown to be a meromorphic function of external momenta as well. Some simple models and examples are given where nonperturbative β function and α _s(Q ²) can be written explicitly. The general form of amplitudes at large N _c is given in the framework of background perturbation theory, and its correspondence with standard perturbation theory at highmomenta is demonstrated in the example of e ⁺ e ^? annihilation. For timelike momenta, the background coupling constant differs drastically from the standard one, but the background series averaged over energy intervals has the same (AF) behavior at high momenta in the Euclidean and in the Minkowskian region.     

Quark-hadron duality and production of charmonia and doubly charmed baryons in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> anninhilation

The cross sections for the production of charmonia and doubly charmed baryons in e ⁺ e ^? annihilation at an interaction energy of \(\sqrt s \) = 10.6 GeV are predicted under the assumption of quark—hadron duality. The method used is shown to remove some contradictions between experimental data and perturbative QCD.     

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.