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Deep Inelastic Lepton-Hadron Interactions at High Energies

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Deep Inelastic Lepton-Hadron Interactions at High Energies DEEP INELASTIC LEPTON-HADRON INTERACTIONS AT HIGH ENERGIES V.A. Matveev Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, USSR. PREFACE The purpose of these lectures - to state the main ideas and elements of theoretical tools in studying the deep inelastic processes of high energy lcpton-hadron interactions. This field of elementary particle physics has achieved in the last years great successes both experimental and theoretical. About ten years ago M. Markov put forward an idea on point-like behaviour of total cross sections of inelastic neutrino reactions. The first SLAC-MIT experi• ments on deep inelastic scattering of electrons on proton v/ere performed in 19C8 and the foregoing DESY experiments supported this idea. A similar point-like picture of in• elastic neutrino-nucleon interactions has been observed in the CEBN experiments. More over, the experiments on deep inelastic electro- production reveal a remarkable regularity - the inelastic form factors of this process are determined asymptotically by functions of dimensionless ratios of kinematical varia• bles and do not depend on any dimensional parameters.Such a phenomena - called usually the Bjorken scaling - has stimulated many theoretical investigations. There are now a number of different approaches and models - more or less sophysticated - which are trying to explain the main regu• larities of various processes of high energy lepton-hadron internctions ( Feynman's pnrton model, the current algebra behaviour was also observed in pure hadronic inclusive and li/rht-cone analysis, dual-resonance model and other). reactions, for the first time on the Serpuhov machine and It is the principle of automodelity, proposed in 1969 then on the ISR and NAL. The theoretical studying of the by Ii. Murodynn, A.Tavkhelidze and the author, which state inclusive processes was initiated by pioneer's work3 of the scale invariant behaviour to be a universal model- A.A. Logunov and Collaborators. independent property of all the deep inelastic processes An extension of the automodelity hypothesis to determining by the physical similarity laws and the dimen• relativistic nucleus collisions has led A. Baldin to a sional analysis. A similar approach which uses the dimen• prediction of the so-called commulative production effect, sional analysis was recently proposed by T.D. Lee. confirmed in 1970 in Bubna. As it was noticed by N.N. Dogolubov, the automodel or It will be extremely hard task to give a full history scale invariant behaviour of the inelastic form factors of of development of physics of deep inelastic interactions. deep inelastic processes is in an intimate analogy with This course of lectures is only an introductory the so-called automodel solutions of a problem of strong review and does not pretend to represent all of the vari• point explosion in hydrodynamics, well-known for a long ous aspects of the physics of deep inelastic lepton-hadron time. interactions at high energies. There are many excellent The successful applications of the automodelity reviews on this field to which we may refer the readers. principle to the analysis of the muon pair production experiments performed in Brookhaven by the Columbia Uni• 1. INTRODUCTION. versity group and the recent experiments on the inclusive hndron electroproduction show the fruitfulneas of this 1.1. Deep inelastic lepton-hadron processes as a tool for studying the elementary hypothesis in studying deep inelastic processes. particle structure. The recent fundamental investigations by N. Bogolubov, A. Tavkhelidze and V. Vladimirov on automodel asymptotics In the recent, years the main interest in studying in quantum field theory have provided a rigorous basis high energy interactions of particles have shifted from for the light-cone analysis, developed by R. Brandt, the field of elastic and quasielastic interactions to H. and others. Leutwyler that of essentially inelastic multiparticle processes. The Notice, that the automodel or scale invariant reason is that in studying elastic processes one deals, in essense, with global properties of particles ( effec• structureless particles. tive radii, "transperance", etc.) whereas in studying the The"point-like" nature of lepton-hadron interactions inelastic multiparticle interactions one gets a possibility at high energies has led to an idee on automodel or scale- to investigate the local structure of particles. In essen• invariant behaviour of the deep inelastic differential tially inelastic processes when extremely large number of cross sections. channels are openning, we deal, in some sense, not with The automodelity principle consists in an assumption properties of individual particles, but with those of that the asymptotic behaviour of deep inelastic processes "hsdron matter" ( an excitation of continium occurs). is independent of any dimensional quantities, such as Processes of essentially inelastic lepton-hadron masses, "elementary lengths", etc.; therefore the struc• interactions at high energies and large momenta transfered ture functions or form factors of these processes arc from leptons to hadrons, accompanied by the secondaries functions of the invariant kinematical variables, the gene• production, are usually called the deep inelastic pro• ral form of which is defined by the dimensional analysis. cesses. Due to the local nature of weak and electromag• A number of approaches to the theoretical interpreta• netic interactions, deep inelastic lepton-hadron scatter• tion of automodelity or scale invariance for deep inelas• ing is an unique tool for studying the local properties tic scattering do exist. In what follows we will discuss of particlea, i.e. a behaviour of "hadron matter" at only some of them, which are based on the very attractive small distances. from the physical viewpoint idea on hadrons as composite As experiment reveals one of the typical properties extended objects with internal degrees of freedom. Among of all the deep inelastic lepton-hadron processes is their such model heuristic approaches there is the parton' model "point-lile" character. The essence of this property which is treating, in some sense, hadrons as a gas, of consists in the following. In the limit of high energies elementary constituents - partons. The parton model and large momentum transfers, the total deep inelastic allows one to obtain relations between cross sections and cross sections, having been summed over all open channels form factors of various deep inelastic processes, starting probability of each of them is considerably suppressed from concrete assumptions about a type of partons (valent, because of form factors of strongly interacting particles, quarks, quark-antiquart pairs, glyons., etc.) and on a are comparable by magnitude with those of point-like degree of compositeness of hadrons. The other more or less traditional approach of quantum field theory to studying To the second class one can assign the process of deep inelastic processes are developing such as vector electron-positron pairs annihilation into hadrons: dominance, model, current algebra and analysis of singula• 3. t~-*> battrons , rities of current commutators on the light cone ( "physics and the procesa of the muon-pair production in proton- on the light cone") and some other methods which will be nucleon collisions: mentioned in these lectures only in passing. 2. The kinematics of deep inelastic processes. 4. p>+ N-*> jtt*+ fjT+ battrons • 2.1. The clasflification of deep inelastic lepton- To the last process there is closely related the hadron processes. process of the charged lepton pairs production via, as one usually believe, the generation of the In respect with that whether the four-dimensional intermediate charged fir -mesons: momentum ^, trensfered from leptons to hadrons is space- jfc . like ( g <r 0 ) or time like ( f}> O ), all the deep 5. p+ N¥V + neutrons inelastic processes of the lepton-hadron interactions can be separated into two classes: 1. Í <-° :"excitation" of hadrons by leptons; In the last years there arises a special logic in 2. £ >0 ; annihilation and production lepton pairs studying pure hadronic inelastic reactions, namely, inclu with participation of hadrons. sive experiments, i.e. the multiparticle production To the first class such processes as the inelastic electro- processes in high energy hadron collisions when one or production or neutrino/antineutrino production on nucléons more particles in the final state are identified while belong the rest being undetected. The classic deep inelsstic 1. ¿~+N-t eT+ herons, processes of the types 1, and 2 are in fact, the inclu• sive type processes when a secondary lepton is identified 2. + M -*) ^ + hadrona, in final states ( so called " one arm" experiment). y# +. { + hadrons, / = e~ f*~ . An extension of inclusive description on hadron The studying of these processes put basis of the system in the final states of deep inelastic lepton theory of deep inelastic reactions. hadron collisions leads to a special type of deep 2.2. Inelastic electroproduction on nucleón inelastic processes, for example, an inclusive electro- or neutrino/antineutrino/ - production on nucléons: The matrix element of deep inelastic electroproduc• tion on nucleón £ .• • « corresponding to the 6. •£ +tV-> €~+ Á¿+ ÁActroHS : diagramm, pictured on Fig. i , or a process of inclusive annihilation of electron- ELECTRON t FINAL HADRON positron pairs into hadrons: STATE PROTON FIG. 4. ro where  j - is some particular hadron. is determined by
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