Борис Лазаревич Иоффе (к восьмидесятилетию со дня рождения), Бьеркен Дж.Д., Вагнер А., Гешкенбейн Б.В., Гинзбург В.Л., Гуревич А.В., Дрёмин И.М., Кайдалов А.Б., Кондратюк Л.А., Ледерман Л.М., Майани Л., Субботин В.И., Шарков Б.Ю.

The magnitudes of gluon and four-quark condensates are found from the analysis of vector mesons consisting of light quarks (the families of rho and omega mesons) in the three-loops approximation. The QCD model with an infinite number of vector mesons is used to describe the function R(s). This model describes well the experimental function R(s). Polarization operators calculated with this model coincide with the Wilson operator expansion at large Q(2). The improved perturbative theory, such that the polarization operators have correct analytical properties, is used. The result is <0|(alpha(s)/pi)G(2)|0>=0.062+/-0.019 GeV4. The electronic widths of rho(1450) and omega(1420) are calculated.

The hadronic vacuum-polarization contribution to the muon anomalous magnetic moment a_{mu}(hadr) and to the value of the eleectromagnetic coupling constant at q^2 = M^2_z are determined more precisely in connection with a new more exact value of the electronic width of rho-meson. The QCD model with infinite number of vector mesons is used. The more precisely determined results are: a_{mu}(hadr) = 678(7)*10^{-10}, δα_{hadr}(M^2_z) = 0.02786(6).

The contribution of the muon anomalous magnetic moment aμ(hadr) to the vacuum polarization and electro-magnetic coupling constant α(q2) for q2=M z 2 is refined by using a new, more accurate value of the ρ-meson width. The values aμ(hadr)=678(7)×10−10 and δα(M z 2 =0.02786(6) were obtained in a QCD model with an infinite number of vector mesons.

The ALEPH data on hadronic tau-decay is throughly analysed in the framework of QCD. The perturbative calculations are performed in 1-4-loop approximation. The analytical properties of the polarization operators are used in the whole complex q^2 plane. It is shown that the QCD prediction for R_{tau} agrees with the measured value R_{tau} not only for conventional Lambda^{conv}_3 = (618+-29) MeV but as well as for Lambda^{new}_3 = (1666+-7) MeV. The polarization operator calculated using the renormgroup has nonphysical cut [-Lambda^2_3, 0]. If Lambda_3 = Lambda^{conv}_3, the contribution of only physical cut is deficient in the explanation of the ALEPH experiment. If Lambda_3 = Lambda^{new}_3 the contribution of nonphysical cut is very small and only the physical cut explains the ALEPH experiment. The new sum rules which follow only from analytical properties of polarization operators are obtained. Basing on the sum rules obtained, it is shown that there is an essential disagreement between QCD perturbation theory and the tau-lepton hadronic decay experiment at conventional value Lambda_3. In the evolution upwards to larger energies the matching of r(q^2) (Eq.(12)) at the masses J/psi, Upsilon and 2m_t was performed. The obtained value alpha_s(-m^2_z) = 0.141+-0.004 (at Lambda_3 = Lambda^{new}_3) differs essentially from conventional value, but the calculation of the values R(s) = sigma(e+e- ->hadrons)/sigma(e+e- ->mu+mu-), R_l = Gamma(Z ->hadrons)/Gamma(Z ->leptons), alpha_s(-3 GeV^2), alpha_s(-2.5 GeV^2) does not contradict the experiments.

The thorough analysis of the ALEPH data on hadronic tau decay is performed in the framework of QCD. The perturbative calculations are performed in three- and four-loop approximations. The terms of the operator product expansion (OPE) are accounted for up to the dimension D=8. The value of the QCD coupling constant alpha (S)(m(tau)(2))=0.355 +/-0.025 is found from the hadronic branching ratio R-tau. The V+A and V spectral functions are analyzed using the analytical properties of the polarization operators in the whole complex q(2) plane. Borel sum rules in the complex q2 plane along the rays, starting from the origin, are used. It is demonstrated that QCD with OPE terms is in agreement with the data for a coupling constant close to the lower error edge alpha (S)(m(tau)(2))=0.330. The restriction on the value of the gluonic condensate was found to be <(alpha (S)/pi )G(2)> =0.006 +/-0.012 GeV2. The analytical perturbative QCD is compared with the data. It is demonstrated to be in strong contradiction with experiment. The restrictions on the renormalon contribution are found. The instanton contributions to the polarization operator are analyzed in various sum rules. In the Borel transformation they appear to be small, but not in the spectral moment sum rules.

The problem of determining the pion electromagnetic form factor F(q(2)) in the spacelike region from the value of its modulus in the timelike region is solved by form factor analyticity. If F(q(2)) has no zeros in the complex plane then the form factor in the spacelike region is determined uniquely. If F(q(2)) has zeros in the complex plane q(2) it can be obtained in the spacelike region within narrow limits using experimental data from the timelike region. The form factor phase phi(s) which coincides with the P-wave phase delta(1)(1)(s) of pi pi scattering is calculated. The value of the pion radius has been improved.

The problem of determining the pion electromagnetic formfactor $F(q^2)$ in the space-like region from the value of its modulus in the time-like region is solved by the formfactor analyticity. If $F(q^2)$has no zeroes in the complex plane then the formfactor in the space-like region is determined uniquely. If $F(q^2)$has zeroes in the complex plane $q^2$ it can be obtained in the space-like region within narrow limits using experimental data from the time-like region. The formfactor phase $\phi(s)$ which coincides with the $P$-wave phase $\delta^1_1(s)$ of the $\pi\pi$ scattering is calculated. The value of the pion radius has been improved.

A method of improving perturbation theory in QCD is developed which can be applied to any polarization operator. The case of the polarization operator Π( q 2 ), corresponding to the process e + e − → hadrons, is considered in detail. By the use of the analytical properties of Π( q 2 ) and a perturbation expansion of Π( q 2 ) for q 2 <0, the function ImΠ( q 2 ) at q 2 >0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R ( q 2 )= σ ( e + e − →hadrons)/( e + e − → μ + μ − ) is improved. After substitution of R ( q 2 ) into the dispersion relation an improved Adler function D ( q 2 ) is obtained, having no infrared pole and a frozen α s ( q 2 ). Good agreement with experiment is achieved.

Vasil'evich Terent'ev, a talented theoretical physicist Ð an irreplaceable loss for science and for all those who knew him. Mikhail Vasil'evich was born into the family of a civil servant in 1935. Until his last day, his career was nonseparable from the Institute of Theoretical and Experimental Physics (known as ITEF for short in Russian). He was assigned there in 1959 immediately after he had graduated from the Moscow Engineering Physics Institute where he studied under Vladimir Borisovich Berestetski|̄. In 1962, Mikhail Vasil'evich presented his dissertation, Some Aspects of Dispersion Techniques in Perturbation Theory, for which he obtained a candidate of sciences degree. Among other things, it reproduced in dispersion techniques the result for the anomalous magnetic moment of the electron in two loops. In 1973, he was awarded a doctorate for his doctoral dissertation, Studies of the Electromagnetic Properties of Elementary Particles, where he described the scattering amplitudes of particles at low energies. Mikhail Vasil'evich found special attraction in challenging difficult problems Ð he devoted all of himself to them and solved them. It would have taken too much time and space to list all the results he obtained. We will touch only a few. In 1963, he proved the nonrenormalization of the vector coupling constant. This result was re-discovered byAdemollo and Gatto a year later. As early as 1965, Mikhail Vasil'evich (with V S Vanyashin) discovered a `wrong' sign in the contribution of charged vector bosons to the vacuum polarization of the electromagnetic field, thus anticipating the theoretical discovery of asymptotic freedom in nonAbelian gauge theories. Using the anomalous Ward identities, he obtained classic results in the physics of soft pions. Equally widely known are his results on the relativistic quark model. In his last years, Mikhail Vasil'evich turned to supergravity. From 1976, he was the executive secretary of the journal Yadernaya Fizika (Sov. J. Nucl. Phys.). More recently, already severely ill, Mikhail Vasil'evich took to lecturing on the physics of elementary particles at the Moscow Engineering Physics Institute, and did this with enthusiasm. From 1990 to 1994, he was the secretary of the Scientific and Technical Council of the ITEF's theoretical laboratories. He took a deep interest in ecology and environmental protection. He wrote a remarkable book on the evolution of the physical notion of a vacuum (which he entitled The Theory of Emptiness). Undoubtedly, it is among the best pieces of science history. Unfortunately, the book has not yet found a publisher. Mikhail Vasil'evich was an extremely gentle and kind man. High moral standards and untainted honesty of him were combined with extraordinary tact and kindness. At the time of the last farewell, someone said he had been the conscience of the ITEF's theoretical department. It is not customary to say such words while a person is alive, but it is our firm belief that although they had not been spoken aloud earlier, Mikhail Vasil'evich felt our love and respect. Mikhail Vasil'evich is not with us any longer, but he will remain alive in our memories and in our hearts, and his works have become part of the golden fund of science. He liked to quote the poet Boris Pasternak: ``The aim of one's creative activity is to give up all of oneself, and not a lot of talk nor a race for success...''. Mikhail Vasil'evich's life was a confirmation of the truth of these words.

We investigate restrictions on the hadronic contribution to the muon $(g-2)$ factor and to the pion electromagnetic formfactor from the analytical properties of the pion formfactor and the experimental data of the pion formfactor in the space-like [1] region. The values of the pion formfactor of [1] have been improved (see Table 1) and the values of the pion formfactor have been calculated at 20 additional points (see Table 2).

The magnitude of gluon condensate is found from analysis of the families of vector mesons consisting of light quarks (the families of rho, omega, and phi mesons). The result is [0/(alpha(s)/pi)G(2)/0] = 0.061 +/- 0.019 GeV4, which agrees with the magnitude obtained from analysis of the families of J/psi and gamma [Geshkenbein, B.V. Yad. Fit., 1990, vol. 51, p. 1121; Geshkenbein, B.V. and Morgunov, V.L., Yad. Fiz., 1995, vol. 58, p. 1873]. The magnitude of the four-quark condensate is calculated. The electronic widths of rho(770), rho(1450), omega(1420), and phi(1680) mesons are refined and the phi(2000) mass is calculated.

The hadronic vacuum-polarization contributions to the muon anomalous magnetic momentum a(mu)(hadr.) and to the value of the electromagnetic coupling constant at q(2) = M(z)(2) are calculated with the record accuracy. A QCD model with an infinite number of vector mesons suggested by one of the authors is used. In this model the non-perturbative effects are included automatically. The results are: a(mu)(hadr.) = 670(7) x 10(-10), a(mu)(theor.) = 11659153(7) x 10(-10), delta alpha(hadr), (M(z)(2)) = 0.02780(6)and alpha(M(z)(2)) = (128.921(8))(-1).