Gösta Gustafson

Parton fragmentation and string dynamics

While muchhasbeenlearnedrecentlyaboutquark andgluon interactionsin theframeworkof perturbativeQuantumChromodynamics,the relationbetweencalculatedpartonpropertiesandobservedhadrondensitiesinvolves modelswhere dynamicsandjet empincal ruleshaveto be combined.Thepurposeof this article is to describea presentlysuccessful approachwhich is basedon a cascadejet model usingStringdynamics.It can readily lead to Monte Carlo jet programmesof greatuse when analyzingdata. Production processesin an iterative cascadeapproach,with tunneling in a constantforce field, arereviewed. Expecteddifferencesbetweenquark and gluon jets are discussed.Low transversemomentum phenomenaare alsoreviewed with emphasison hyperon polarization. In so far as this approachusesa fragmentationschemebasedon String dynamics,it wasdeemedappropriateto alsoincludeunderthesamecovera specialreport on theClassicaltheoryof relativisticStrings,seenasthe classicallimit of theDual Resonancemodel. TheEquationsof motion and interactionamongstringsarepresented. Single ordersfor this issue PHYSICSREPOR1’S(Review Sectionof PhysicsLetters)97, Nos.2 & 3 (1983)31—171. Copies of this issue may be obtainedat the price givenbelow. All ordersshouldbe sentdirectly to the Publisher.Ordersmust be accompaniedby check. Single issuepriceDfl. 79.00, postageincluded. 34 B. Andersson et a!., Patton fragmentation and siring dynamics testsof the theory,in particularof the perturbativeQCD structure,containse.g.nonscalingdeviations from the partonmodel. There are at this point already some difficulties becauseit is well-known that any finite energy hadronicdistributionwill containnonscalingcontributions,sometimesto an evenlargerdegreethanthe inherent scale breaking effects of the theory. Further the pencilsharpenergyand momentumdistributions from the single partonsareessentiallydistorted, widenedin transversedirectionsandeven the basicquantumnumberslike chargeandstrangeness etc.seemto havebeentransportedsometimes ratherfar away in longitudinal rapidity space.It has thereforebecomeincreasinglyobvious over the yearsthat in order to compareexperimentto basictheory,it is necessaryto havereliabledescriptionsof the transferfrom the partonicstageto the hadronicone,i.e. to haveconsistentmodelsfor the process of partonfragmentation. Suchmodelsmayon the onehandbe lookedupon solely as phenomenological parametrizationsand rulesof thumb in order to obtain a translationfrom onelanguageto another.As such theyare useful for analysis of experiment as well as for the planning. On the other hand one may as always in connectionwith phenomenologytry to obtain a dynamicalframeworkthat servesas a motivation anda generalizingprinciple for theconstructions. It shouldbekept in mind, however,that thereareno easilyavailablemeasuresof the successof such a venture.As Bacontold us a long time ago,it is actuallyonly possibleto learnthat oneis wrong by a comparisonbetweenmodel calculationsand experimentalfindings. If the predictionagreesthereis no reassurancethat one is evenworking in the right basicdirection (althoughthereis evidentlya possible reasonto feelsomeconfidence!). A modestmeasureof successwould be a demandthat the numberof phenomenological parameters andthe variation in size of their valuesare nonincreasingfunctionsof time as well as the numberof independent experimentalfindings. It is alsoof evidentinterestthat thesamebasicschemeis applicable in different contextssuch as different partonic processesand different parts of phase-space. Several schemeswith a more or less profound theoreticalfoundationhavebeensuggestedbut we will in this review be concernedonly with iterative cascadejet modelsbasedupon string dynamics.The present experiencefrom thesemodelsshowsthat at leastthe above-mentionedcriteriafor successarefulfilled. We will in this reviewmostlydiscussa possibledynamicalframeworkbehindthe modelsandwe will only usecomparisonsto datain order to demonstratemattersof principle.One of the nice featuresof the models is their stochasticstructurewhich readily lends itself to an implementationin terms of computergeneration.Severalsuch MonteCarlojet programsareavailable[21for the interestedreader to makemuchmore detailedcomparisons. Our approachwill primarily be of a semi-classicalnature,i.e. we will at most placesmakeuseof a classicaldynamicalframeworkfor our considerations. We will, however,at all necessaryplacespoint to the basicquantummechanicalconstraints. It is well-known that by meansof a careful choice of dynamicalvariablesit is often possibleto circumvent such constraints.As an example we note that it is in general not possible to give independentvaluesto canonicallyconjugatevariablessuch as momentum(p) andposition(x) dueto Heisenberg’suncertaintyprinciple:

A model for low-pT hadronic reactions with generalizations to hadron-nucleus and nucleus-nucleus collisions

Abstract We present a model for hadronic low transverse momentum transfer reactions based upon a phenomenological treatment of a hadron as a vortex line in a colour superconducting medium. The predictions of the model are in agreement with the earlier successful model for the quantum number flows in the hadronic fragmentation regions while the present model also provides a number flows in the hadronic fragmentation regions while the present model also provides a consistent treatment of the central rapidity region. The model can also be applied to hadron-nucleus and nucleus-nucleus collisions.

Dipole formulation of QCD cascades

Abstract The formulation of a QCD parton cascade in terms of colour dipoles or colour antennae is applied to e + e − -annihilation. In this formulation the destructive interference for soft-gluon emission has a very natural interpretation, and it is easy to construct a Monte Carlo simulation program. At PEP and PETRA energies the results agree very well with experimental data, and thus also with results from conventional parton cascades. However, at higher energies observable differences emerge, which can discriminate between the models.

Dual description of a confined colour field

Abstract The result of perturbative QCD can be formulated in two dual or complementary ways, either in terms of quarks and gluons or in terms of colour dipoles. The relation between the two description in similar to that between a lattice and its dual lattice. If the confined field behaves like a vortex line in a superconductor, then the dipoles form a chain along the vortex line.

A General Model for Jet Fragmentation

We present a general condition on quark fragmentation which gives a hadron distribution satisfying Lorentz invariance and causality. The hadronization can be described as an iterative cascade process, symmetric with respect to iteration from the quark and the antiquark ends. The possible particle distributions are strongly restricted, with few free parameters related to the total multiplicity and corelations in rapidity. These parameters can be given an appealing interpretation in terms of the expected area and perimeter dependence of Wilson loop integrals.

How to Find the Gluon Jets in e+ e- Annihilation

Abstract We point out an asymmetry in the combined multiplicity aand angular distributions of the final state mesons in a quark-antiquark-gluon fragmentation event from e + e − annihilation. The asymmetry is characteristics for the gluon jet in the model for soft hadronisation of coloured objects which we have developed based on the semiclassical treatment of a string-like colour force field (a stretched-out bag) without excited transverse modes.

The Linked dipole chain model for DIS

Abstract The Linked Dipole Chain Model provides an interpolation between the regions of high Q 2 (DGLAP) and low x moderate Q 2 (BFKL) in DIS. It is a reformulation and a generalization of the results obtained by Ciafaloni, Catani, Fiorani and Marchesini, and it gives a unified treatment of “normal DIS”, boson-gluon fusion events and hard subcollisions in resolved photon-proton scattering. Thus the formalism provides a complete picture which incorporates all hard or semihard hadronic interactions in a simple way, which is suitable for a Monte Carlo treatment of both structure functions and final state properties. We also discuss non-leading effects which significantly reduce the increase of the structure function for very small x -values.

Coherence Effects in Deep Inelastic Scattering

We present a framework for deep inelastic scattering, with bound state properties in accordance with a QCD force field acting like a vortex line in a colour superconducting vacuum, which implies some simple coherence effects. Within this scheme one may describe the results of present energies very well, but one obtains an appreciable depletion of gluon radiation in the HERA energy regime.

A semiclassical model for the polarization on inclusively produced Λ0-particles at high energies

Abstract We present a semiclassical model for inclusive Λ 0 -production which is able to explain the observed polarization effect in proton-proton collisions. It is well known that hard scattering processes, when calculated in perturbative QCD, do not give rise to large polarization effects. The mechanism producing the polarization in this model is basically a soft process, where quark-antiquark pairs are produced by a tunneling process in the colour field and where perturbatice QCD is not applicable.

A Model for Baryon Production in Quark and Gluon Jets

Experiments at e+e− storage rings show a non-negligible production of baryons, although a detailed structure, in particular the correlation between a baryon and an antibaryon, has not been clarified. We formulate here a simple model for baryon-antibaryon production which is in good agreement with present e+e− inclusive data. We also present a set of predictions of the model that can be tested when more experimental data are available. One interesting property of the model is that the leading particle is more often a baryon or antibaryon in a gluon jet than in a quark jet.