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JOINT INSITUTE FOR NUCLEAR RESEARCH

Bogoliubov Laboratory of Theoretical Physics

On the copyrights of the manuscript UDK 539.126.1

ANNA ZUZANA DUBNICKOVÂ

UNIFORM ELECTROMAGNETIC STRUCTURE MODEL OF HADRONS AND SPECIFIC ELECTROMAGNETIC AND WEAK

PROCESSES

(Specialization -01.04.02-Theoretical Physics)

Dissertation for a scientific degree of doctor of phys.-math. sciences

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Contents

1 INTRODUCTION 3

1.1 The scientific novelty and a practical worth................ 6

1.2 Summary of the dissertation........................ 9

2 ELECTROMAGNETIC FORM FACTORS OF STRONGLY INTERACTING PARTICLES AND THEIR PROPERTIES 12

2.1 The electromagnetic form factors..................... 12

2.2 The analytic properties and the unitarity condition of the electromagnetic form factors............................... 16

2.3 The asymptotic behaviour of the electromagnetic form factors. ..... 18

3 UNITARY AND ANALYTIC MODEL OF ELECTROMAGNETIC FORM FACTORS OF HADRONS 19

3.1 Electromagnetic FF's of hadrons...................... 20

4 PSEUDOSCALAR MESON ELECTROMAGNETIC FORM FACTORS 24

4.1 The pion electromagnetic form factor................... 24

4.2 The kaon electromagnetic form factors .................. 29

5 OCTET 1/2+ BARYON AND DEUTERON ELECTROMAGNETIC FORM FACTORS 35

5.1 The nucleón electromagnetic structure .................. 36

5.2 Prediction of a behaviour of A-hyperon electromagnetic form factors . . 39

5.3 The naive model of electromagnetic structure of l/2+ octet of baryons . 48

5.4 Approach to a global description of the deuteron electromagnetic structure 56

6 NEW FORMULATION OF THE UNITARY AND ANALYTIC MODEL

OF THE 1/2+ OCTET BARYON EM STRUCTURE 67

6.1 An unambiguous way of estimation of the vector-meson-nucleón tensor coupling constants ............................. 69

6.2 New formulation of the unitary and analytic model of the nucleón electromagnetic structure ....................................74

6.3 Investigation of proton magnetic formfactor in the unphysical region by means of the pp —» T°e+e~ process .................... 90

6.4 The Körner -Kuroda model of octet l/2+ baryons EM structure and its unitarization................................. 97

7 HADRONIC CONTRIBUTIONS TO THE ANOMALOUS MAGNETIC MOMENTS OF CHARGED LEPTONS 111

7.1 Experimental situation................................112

7.2 Theoretical estimates............................113

8 CONSERVED-VECTOR-CURRENT HYPOTHESIS AND THE Dte~ M~M° AND T- vrM~M+ WEAK PROCESSES 126

8.1 The weak vee~ M~M° processes....................127

8.2 The tau decay into two pseudoscalar mesons............... 136

9 CONCLUSION 142

Chapter 1

INTRODUCTION

An observation of the proton electromagnetic (EM) structure in the elastic electron scattering experiments [1, 2] was in the physics of elemerxtary particles really revolutionary.

For the first time it was apparently demonstrated, that one of the building stones of the Universe, the proton, is nonpoint-like. The latter stimulated theoretical investigations in the framework of which the concept of a nonpoint-like nature of the proton was extended also to other hadrons, what was again confirmed in subsequent experiments.

An immediate theoretical explanation of data on the proton EM structure has led to new ideas, like a postulation of the existence of isoscalar [3] and isovector [4] vector mesons, leading to the so-called vector-meson-dominance (VMD) model [5, 6], which up to now is only the successful approach in a global description of the data on the EM structure of hadrons.

Phenomenologically, the EM structure of hadrons is taken into account by an introduction of scalar functions, so-called EM form factors (FF's) Fh(t), which depend on the four-momentum squared t = q2 = — Q2 to be transferred by the virtual photon. These EM FF's appear as coefficients in a decomposition of a matrix element of the EM current of the hadron according to a maximal number of linearly-independent

covariants to be constructed from spin-parameters and four-momenta of the hadron. Here the Lorentz and gauge invariance (also other symmetries as well) are taken into account.

A behaviour of EM FF's as a function of t is a matter of predictions of a dynamical theory of the strong interactions. It is well known that on the role of such a theory the quantum chromodynamics (QCD), the gauge-invariant local quantum field theory of interactions of quarks and gluons, is pretending. But as a consequence of its asymptotical freedom, the QCD in the framework of the perturbation theory is able to reproduce just the asymptotic behaviour [7]—[13] of EM FF's, which earlier has been predicted by the quark counting rules [14, 15] up to the logarithmic corrections. In the framework of the nonperturbative QCD sum rules [16] a prediction [17, 18] of a behaviour of hadron EM FF's in a restricted interval of the space-like region is achieved. The chiral perturbation theory approach [19, 20], which is equivalent to the QCD at low energies where the strong coupling constant takes large values and the perturbative QCD is non-applicable, describes a behaviour of EM FF's of hadrons around the point t = 0.

So, till now there are no quantitative predictions of QCD for EM FF's of hadrons in the region t0 < t < 4GeV2 (t0 is the lowest possible threshold) which in principle is setting the hadron EM FF behaviour in the space-like region and in the time-like region as well. Here the EM FF's are complex functions of their argument and the electron-positron annihilation experiments into hadron-antihadron pairs exhibit a nontrivial behaviour of cross-sections, which is caused by a creation of various unstable vector-meson states.

We would like to note, that more complex QCD description of the EM FF's of hadrons, especially in the resonant time-like region, where various nontrivial structures appear, will require a detailed understanding of the long-distance phenomena in QCD, which, however, is still far-away from its solution.

Therefore, for the present, an appropriate phenomenological approach based on the experimental fact of a creation of vector-meson resonances in electron-positron

annihilation processes and on the well-established analytic properties is still the most reasonable way of a global theoretical reconstruction of EM FF's of hadrons.

The aim of the submitted dissertation is just to elaborate and to manifest in specific electromagnetic and weak processes the uniform phenomenological unitary and analytic model of the EM structure of hadrons, which has been initiated by our investigations in original papers [21]—[23] to be devoted to the pion. This model appears to be the most successful synthesis of all known properties of the hadron EM FF's, like creation of vector-meson-resonances in electron-positron annihilation processes, the correct analytic properties and the asymptotic behaviour as predicted by the quark model of hadrons.

The subject is topical as there is a lot of data obtained on existing electron accelerators and electron-positron colliders, and there is no accomplished dynamical theory describing these all data simultaneously. On the other hand, having such an uniform global model of the EM structure of hadrons one can investigate a lot of new problems of the physics of elementary particles.

The idea consists in the following. The analytic model depends on a number of free parameters with clear physical meaning, like masses, widths and coupling constants of vector-mesons, which can be fixed in a comparison of a constructed model with data.

So, in principle, one can look for a new vector-meson states to be created in electron-positron annihilation processes into hadrons by means of the proposed model and to interpret them in a framework of predictions of various quark-bound state models.

If a satisfactory description of existing data is achieved, then by an interpolation and an extrapolation of the model one can predict a behaviour of corresponding EM FF's in the unphysical region and simultaneously to verify the quark model predictions of the asymptotic behaviour of EM FF's for different hadrons, respectively.

Because the asymptotic behaviour of the EM FF's in view of the analyticity has to be the same in both, in the space-like and in the time-like, regions, by means of the proposed unitary and analytic model of the EM structure of hadrons the time-like

region behaviour of the EM FF's of nuclei is predicted to a certain degree, what is completely new idea for nuclear physicists.

As the proposed model of the EM FF's of hadrons is unitary, i.e. it predicts a behaviour of the imaginary part of the EM FF's starting correctly to be nonzero just above the first threshold, one can investigate polarization effects in the electron-positron annihilation processes to hadron-antihadron pairs with nonzero spins.

The hadronic vacuum-polarization contributions to the anomalous magnetic moment of charged leptons can be expressed by the integral over the total cross-section of the electron-positron annihilation processes into hadrons, including also the hadron-antihadron pairs in the final states. The latter are completely described by the corresponding EM FF's represented by the unitary and analytic models, which allow to evaluate the dominant hadronic contributions with a high accuracy.

Finally, based on the conserved-vector-current (CVC) hypothesis and the unitary and analytic model of the EM FF's of pions and kaons one can describe the t-lepton weak decays and the antineutrino-electron annihilation processes into two pseudoscalar mesons.

1.1 The scientific novelty and a practical worth

A new approach to a global description of the deuteron EM structure was developed on the basis of a modification of the well known VMD model of EM interactions of hadrons by incorporating the true deuteron FF analytic properties, non-zero vector meson widths and the correct power asymptotic behaviour as predicted by QCD. In principle the method provides a possibility to reconstruct theoretically all three EM FF's of deuteron from data on two structure functions.

An unambiguous way of estimation of the vector-meson-nucleon tensor coupling constants is proposed by requiring only QCD asymptotics and normalization for VMD parametrization of isoscalar and isovector parts of the Pauli nucleon EM FF's. An

unexpected agreement of obtained results for ground state vector mesons with phe-nomenological estimates of other authors led to a new formulation of the unitary and analytic VMD model of nucleón EM structure with a remarkable reduction of the number of free parameters. Even it led to a construction of a quite reasonable model of EM structure of the whole octet of l/2+ baryons.

On the other hand, having a model for the nucleón EM structure the rate of EM corrections to the dominant direct hadronic decay in the J/^ —> NN processes and a behaviour of the polar angle asymmetry parameters for e+e~ —> NÑ are predicted.

By using the method of an incorporation of a two-cut approximation of correct FF analytic properties and nonzero vector-meson widths to be elaborated in the case of nucleons, the Korner-Kuroda model of EM structure of octet l/2+ baryons was unitarized, providing in this manner a better agreement of predicted behaviours with existing data.

Utilizing old and new formulation of the unitary and analytic model of the nucleón EM structure, which both give a good description of existing data, polarization effects in e+e~ —> NÑ processes were investigated in detail. An explicit form of components of the vector polarization of the created nucleón were calculated explicitly, which depend on the real and imaginary parts of the product of the electric and magnetic FF's of nucleons, however, to be different in behaviours depending wether old or new formulation of the nucleón EM structure model is used. In principle, by a measurement of components of the vector polarization of the created nucleón one could reveal, which of the two nucleón EM structure models is preferable.

However, the latter approach will say nothing to the behavior of the nucleón EM FF's below the nucleon-antinucleon threshold, where two formulations of the nucleón EM structure models give different predictions for the absolute values of FF's. In order to solve the latter problem, the annihilation of very slow antinucleons on nucleons at rest into pion and lepton pairs were investigated theoretically in detail. For the process pp —»■ 7T°Z+I~ it has been shown that its amplitude, calculated in the framework of the

tree-diagram approximation, is completely described by the magnetic form factor of the proton in that unphysical region.

By using more accomplished models for a description of the pion and kaon EM structure, more complete data on some exclusive processes and the revised (due to a new value of the coefficient of the third power of as) QCD formula for R = atot(e+e~ —► hadrons)/crioi(e+e~ —> ¡x~) with electroweak corrections, up to now the most precise evaluation of the hadronic contributions to the anomalous magnetic moment of charged leptons was carried out.

Based on the conserved-vector-current (CVC) hypothesis and the unitary and analytic models of the EM structure of pion and kaon FF's a behaviour of the weak pion and kaon FF's is obtained. Then cross-sections of the weak i/ee~ —► 7T~7r° and vee~ —>• K~K° processes are predicted theoretically for the first time and the effective mass spectra of mesons and the widths of the r~ i/TM~M° decays are calculated explicitly.

The obtained theoretical results essentially extend a knowledge about the EM structure of strongly interacting particles. The elaborated methods of this dissertation are used by other authors in theoretical calculations and in analyses of experimental data as well. Results of some predictions are considered to be taken into account in a preparation of new experiments.

Approbation of the dissertation

The main results of this dissertation were presented at the seminars of the Laboratory of Theoretical Physics, JINR (Dubna), Department of Theoretical Physics Come-nius University in Bratislava, International Centre for Theoretical Physics in Trieste, Institute for Theoretical Physics in Vienna University, Rudjer Boskovic Institute in Zagreb, Institute of Theoretical Physics of Eôtvôs University in Budapest, Laboratori Nazionali di Frascati (Roma), Dipartimento di Fizica University di Padova, Dipartimento di Fisica University di Ferrara, Dipartimento di Fisica Teorica University degli Studi di Torino, Institute of Nuclear Physics Krakow and Institute for Particle Physics

of ETH Zurich in Villigen.

Besides the latter they have been presented at many International Conferences and Symposia, including VI. Conference of Czechoslovak Physicists in Ostrava (1979), the 3-rd Adriatic Summer Meeting on Particle Physics in Dubrovnik (1980), the VIII. Conference of Czechoslovak Physicists in Bratislava (1985). the International Seminar "QUARKS'82"in Suchumi (1982 USSR), the International Seminar "QUARKSW (1990, Georgia), the International Triangle Workshop JINR-CERN-IHEP in Dubna

(1991), the XXVI. Rencontre de Moriond in Les Arcs (1991), the Hadron Structure'91 Conference in Starâ Lesnâ (1991), the Hadron Structure'92 Conference in Starâ Lesnâ

(1992), the VII. International Seminar QUARK'92 in Zvenigorod (1992), the Hadron Structure'94 Conference'94 in Kosice (1994), the Int. Europhysics Conference on High Energy Physics, July 27-August 2, 1995, Brussels, Session PA01 and PA04.

Publications

The materials contained in the dissertation were published in 27 scientific papers.

1.2 Summary of the dissertation

The presented dissertation consists of the introduction (first chapter), the seven CHAPTERS of the main contents of the investigated subject and summaries.

In the second chapter a general concept of the electromagnetic form factor and its fundamental properties are reviewed.

Since one of the main contributions into the dissertation is an uniform approach in a description of the EM structure of strongly approach in a description of the EM structure of strongly interacting particles, in the third chapter the basic idea of a construction of the unitary and analytic model of the hadron EM structure is presented. The fourth chapter contains models of the pseudoscalar meson EM FF's. The fifth chapter is devoted to a description of the EM structure of the l/2+ octet of baryons and also to a completely new approach in a description of the deuteron EM

structure. A special attention is paid to a construction of the unitary and analytic model of the nucleon EM structure and to a global realistic model of the A- hyperon EM FF's.

In the sixth chapter more specific problems are discussed. First, parametrizing the nucleon Pauli FF's by means of the canonical VMD model and requiring explicitly normalization and asymptotic behaviour as predicted by the quark model of hadrons, the unambiguous way of an estimation of the corresponding vector-meson-nucleon tensor coupling constants is achieved. Moreover, the obtained numerical values are very consistent with results obtained by a completely different way. The latter led then to a new formulation of the unitary and analytic model of the nucleon EM structure with a remarkable reduction of the number of free parameters in a comparison with the previous formulation in the chapter fifth.

As a result, there are now two formulations of the unitary and analytic model of the nucleon EM structure which almost equally well are describing the existing experimental data in both, the space-like and the time-like regions. However, they diifer in a behaviour for energies of the unphysical region t0 < t < Am2N. In order to clarify which of there two models is more realistic, we investigate the nucleon-antinucleon annihilation processes into pion and di-lepton pairs by means of which practically a behaviour of the nucleon EM FF's in unphysical region can be obtained. Finally, the existing Korner-Kuroda model of the octet l/2+ baryons EM structure is unitarized by our method developed in previous chapters.

In chapter seven the most precise estimation of the hadronic contribution to the anomalous magnetic moment of charged leptons is achieved, which is very important in connection with the new g — 2 muon Brookhaven National Laboratory (BNL) E821 experiment to be realized in near future.

Another practical application of the constructed realistic hadron EM structure models is carried out in chapter eighth. Here the weak processes of the antineutrino-electron annihilation and the r- decay into two pseudoscalar mesons are investigated. They are

completely described by the weak pseudoscalar meson FF's for which neither experimental data nor suitable phenomenological models exist. However, by means the Conserved-Vector-Current (CVC) hypothesis one can find relations between the corresponding weak and EM FF's. By using the unitary and analytic models of the pseudoscalar mesons the abovementioned weak processes are then completely described.

In the conclusion (ninth chapter) the main results of the presented dissertation are reviewed.

Chapter 2

ELECTROMAGNETIC FORM FACTORS OF STRONGLY INTERACTING PARTICLES AND THEIR PROPERTIES

2.1 The electromagnetic form factors

The electromagnetic (EM) form factors (FF's) are scalar functions of one variable the momentum transfer squared t = — Q2, by means of which the non-pointlike EM structure of strongly interacting particles is taken into account, e.g. at the elastic scattering of charged leptons on hadrons, or at a creation of hadron-antihadron pairs at the electron - positron annihilation processes.

These processes are caused by the EM interactions and as a result the matrix element, let us say, of the elastic electron-hadron scattering, M(e~h —» e~h), at the lowest order according to the fine structure constant a & 1/137, can be represented in

the following form

M(e~h -> e~h) = J^y^ihhMh) < P2\U0)\Pi >, (2-1)

where eu{k2)~fpu(ki) is the matrix element of the electron EM current, QM is the photon momentum transfer and < P2\J^)\P\ > is the matrix element of the hadron EM current, which due to the non-pointlike nature of the hadron is unknown.

However, if a maximally possible set of linearly independent covariants Rfx{pi,p2) is constructed from spin parameters and four-momenta P1.P2 of the hadron, then one can parametrize the matrix element of the hadron EM current as follows

<P2\JM\Pl>=Y^Kfa'P2)Ftf)> (2-2)

i

where Fi(t) are EM FF's of the hadron. Let us consider the most topical cases. We start with the nonet of pseudoscalar IX1CSOI1S 7T .7T , Since they have spin to be zero, in a construction of covariants (p2 — and (p2 only two four-momenta, pi and p2, are used. By an application of the gauge invariance of the EM interactions one comes to the following final parametrization

< P*\JM\Pi >= eFP(t)(p1+p2)fi (2.3)

only with one EM FF Fp(t) completely describing the EM structure of any member of the nonet of pseudoscalar mesons. Moreover, making use of transformation properties of the EM current operators J^x) and the one-particle state vector with regard to the all three discrete C,P,T transformations simultaneously, one finds that

FP(t) = -FP(t) (2.4)

from where it follows that for true neutral pseudoscalar mesons 7r0,??,^' the EM FF's are equal to be zero for all —oo < t < +oo. The pseudoscalar meson EM FF's normalized to the charge at t = 0.

A consideration of the nonzero value of the isospin of the pion does not enlarge a number of EM FF's. The FT(t) is proportional to the third component of the isovector, by means of which the pion charge is determined.

A complete different situation is with kaons. The K+ and K° belong to the same isomultiplet with J = 1/2. Therefore instead of the neutral kaon one can introduce the EM current of the kaon and to investigate what isotopic structure it has. One can show, that it splits on a sum of isotopic scalar and isotopic vector. In connection with the latter the isoscalar F^\t) and isovector F^\t) FF's of the kaon are introduced to be expressed by Ffc+(t) and FKo(t) as follows

m) = + (2.5)

W) = liW) - FKo(t)}.

In the case of the octet l/2+ baryons p, n, A, £+, E°, E°, E~ covariants Rn{p-i,p2) are constructed by the four-momenta pi, p2, Dirac matrices and bispinors. The final result for a parametrization of the matrix element of the EM current of the octet l/2+ baryons takes the form

(P2M0)\Pl) = j^-3u(P2)h,FlB(t) + -p^F2B{t)}u(Pl), (2.6)

where Fib, F2b are so-called the Dirac and Pauli FF's, respectively and mg is the baryon mass.

From practical point of view it is more suitable to describe the EM structure of the octet l/2+ baryons by means of Sach's FF's [24], defined through Dirac and Pauli FF's by means of the following expressions

GfCO = F1B(t) + ¿rF2B(t) (2.7)

<?&(<) = FlB(t) + F2B(t).

There is a special coordinate system (the Breit reference frame), in which GB(t) and Gfrf(t) describe a distribution of the charge and magnetic moment of the baryon. Hence

they are called the electric Cf (t) and magnetic Gff(t) FF's to be normalized to the charge and magnetic moment of the baryon, respectively, for t = 0.

Similarly to kaons one can consider instead of the EM current of every member of the octet l/2+ baryons electromagnetic currents of the corresponding isomultiplets and to look for their splitting into isoscalar and isovector parts. As a result one finds the following decomposition of the nucleon and A-, £- and E- hyperon electric and magnetic FF's into isoscalar and isovector parts of the Dirac and Pauli FF's

GpE(t) = [Fm(t) + F?N(t)} + -¿¿[FUt) + (2.8)

Gpu(t) = [F?n( t) + F?N(t)} + [F*N(t) + F2y*)]

Gm = [FfN(t) - F?„{t)] + ^\F!N(t) - FlK(t)] (2.9)

Gm = lFfN(t) - F^(t)] + - F?N(t)]

G&t) = F?A(t) + ^~-FiA(t)

GM(<) = + FL(t) (2.10)

Gf(t) = [F^t) + F^(t)] + + F^(t)}

<?£*(*) = [F?x(t) + F?t(t)) + {Fk(t) + F^(t)} Gf(t) = F^(t) + ^/Ut)

G$(t) = *fz(t) + FfzW (2-11)

Gl°(t) = [F?B(t) + F&t)] + ^rlF^t) + F&t)]

G^(t) = [F?3(t) + FUt)) + [Fk(t) + FUt)] (2.12)

Gfi(<) = lFUt)-FUt)} + {FUt)-FUt)}.

15

Covariants R^pi^) for EM FF's of the nonet of vector mesons p~,

K*°, K'°, K*~, 4>, oj and also of the deuteron are constructed by the four-momenta pu p2 and polarization vectors. Then a parametrization of the matrix element of the EM current of vector-particles takes the following form

(2p012p02)^(p2\J,mPi) = -e{Gi(i)(£'*-04.+ (2.13)

+ * <?) ~■ iI)] -

where £ and are polarization vectors for incoming and autgoing particles of four-momenta p1 and p2, respectively, = (py +p2)fi and qM = (pt - p2)^. The polarization vectors fulfil conditions as follows

(t'-P2) = 0, f'3 = -l, (2-14)

W-Pi) = 0, £2 = 1.

Practically, it is convenient to describe the EM structure of vector particles by an analogue of the Sach's FF's for nucleons

Gc(t) = (2-15)

GM(t) = G2(t)

GQ(t) = G^t) - G2(t) + (I --^)G3(t)

the names of which charge, magnetic and quadrupole FF are derived from the fact that their static values correspond to the charge, magnetic and quadrupole moment of the vector particle.

2.2 The analytic properties and the unitarity condition of the electromagnetic form factors.

There is a general belief that EM FF's are analytic functions in the complex plane of the momentum transfer squared t besides a cut from the lowest branch point t0 on the

real axis to +00.

The latter is confirmed by an exact proof [25] of the analytic properties of the pion EM FF in the framework of axiomatic quantum field theory and also by an investigation of the analytic properties of Feynman diagrams [26, 27] representing separate terms of a formal series of EM FF's obtained in the framework of quantum field perturbation theory.

As a consequence of the hadron EM current to be Hermitian all EM FF's are real on the real axis for t < to. Then by an application of the Schwarz reflection principle to EM FF's one finds the so-called reality condition

F*h(t) = Fh(t*) (2.16)

reflecting the reality of the EM FF's on the real axis below i0 and the relation of values of EM FF's on the upper and lower boundary of the cut

F*h(t-+ie) = Fh(t*-ie), e<l (2.17)

automatically.

The discontinuity across the cut is given by the unitarity condition

1{(M|J„(0)|0) - (0|J,(0)|hi)*} = (2.18)

n

where the sum in (2.18) is carried out over a complete set of intermediate states allowed by various conservation laws and T+ means Hermitian conjugate amplitudes.

Moreover, the unitarity condition (2.18) tells us that there is an infinite number of branch points on the positive real axis between i = f0 and +00, which always correspond to a new allowed intermediate state n in (2.18). In order to fulfil the reality condition (2.16), the cuts associated with these branch points are chosen to extend to +00 along the real axis.

2.3 The asymptotic behaviour of the electromagnetic form factors.

One of the basic properties of the EM FF's of strongly interacting particles is their asymptotic behaviour. However, until the discovery of the quark-gluon structure of hadrons the latter was unknown theoretically and only polynomial bounds were always assumed to be fulfilled.

According to the quark model the large momentum transfer behaviour of the hadron EM FF is related to the number of constituent quarks of hadron by the expression as follows

(2.19)

This is a prediction of a dimensional counting rule and some simple assumptions which are based on the case of an underlying scale-invariant theory [14, 15].

The asymptotic behaviour (2.19) was proved (up to the logarithmic correction) in the framework of the perturbative QCD for some special cases like mesons [7]-[9], baryons [10, 11] and deuteron [12, 13]. It is consistent with existing experimental data.

Chapter 3

UNITARY AND ANALYTIC MODEL OF

ELECTROMAGNETIC FORM FACTORS OF HADRONS

As we have emphasized in the Introduction the main aim of the presented dissertation is a further elaboration of the uniform approach in a description of the electromagnetic structure of strongly interacting particles. The latter is achieved by the unitary and analytic model of the EM FF's which is based on the synthesis of the analyticity with an experimental fact of a creation of vector-mesons in the electron-positron annihilation processes and the asymptotic behaviour (2.19) as predicted by the quark model of hadrons.

The experimental fact of a creation of vector-mesons in the electron-positron annihilation processes is well taken into account by the vector-meson dominant (VMD) model, which has been originated by the description analysis of the data on nucleon EM FF's. Here Y. Nambu, investigating a difference between the EM radii of the

proton and neutron, was enforced to assume [3] an existence of the isoscalar vector-meson w(783) and later on Frazer and Fulco [4] have even predicted parameters of the isovector P-wave two-pion resonance state />(770). Both of these resonances were discovered experimentally in the papers [28] and [29], respectively.

3.1 Electromagnetic FF's of hadrons

At the present there is a lot of neutral vector-mesons [30] with quantum numbers to be identical with photon. They have the isospin either 0 or 1.

On the other hand the EM current of hadrons is by a rotation in the isospinspace transformed like the sum of isospin scalar and the third component of isovector. The latter transformation properties reflect well known fact of non-conservation of the isospin in the EM interactions and lead automatically to a phenomenon, observed experimentally, that at the absorption and creation of virtual photon by hadron the isospin value can be changed by 1. Therefore the photon can be considered to be a superposition of states with isospin value 0 (the isoscalar pho