On Goldstone bosons decoupling from high-lying hadrons

In this paper, we discuss a decoupling of the Goldstone bosons from highly excited hadrons in relation to the restoration of chiral symmetry in such hadrons. We use a generalised Nambu-Jona-Lasinio model with the interaction between quarks in the form of an instantaneous Lorentz-vector confining potential. This model is known to provide spontaneous breaking of chiral symmetry in the vacuum via the standard selfenergy loops for valence quarks. For highly excited hadrons, where the typical momentum of valence quarks is large, the loop contributions represent only a small correction to the chiral-invariant classical contributions and asymptotically vanish. Consequently the chiral symmetry violating Lorentz-scalar dynamical mass of quarks vanishes. Then the conservation of the axial vector current in the chiral limit requires, via the Goldberger-Treiman relation, that the valence quarks decouple from the Goldstone boson. As a consequence, the whole hadron decouples from the Goldstone boson as well, which implies that its axial constant also vanishes.Comment: RevTeX4, 21 pages, 5 Postscript figures, uses epsfig.sty, new chapter with numerical estimates added, to appear in Phys.Rev.

Chiral symmetry restoration in excited hadrons, quantum fluctuations, and quasiclassics

In this paper, we discuss the transition to the semiclassical regime in excited hadrons, and consequently, the restoration of chiral symmetry for these states. We use a generalised Nambu-Jona-Lasinio model with the interaction between quarks in the form of the instantaneous Lorentz-vector confining potential. This model is known to provide spontaneous breaking of chiral symmetry in the vacuum via the standard selfenergy loops for valence quarks. It has been shown recently that the effective single-quark potential is of the Lorentz-scalar nature, for the low-lying hadrons, while, for the high-lying states, it becomes a pure Lorentz vector and hence the model exhibits the restoration of chiral symmetry. We demonstrate explicitly the quantum nature of chiral symmetry breaking, the absence of chiral symmetry breaking in the classical limit as well as the transition to the semiclassical regime for excited states, where the effect of chiral symmetry breaking becomes only a small correction to the classical contributions.Comment: RevTeX4, 20 pages, 4 Postscript figures, uses epsfig.sty, typos correcte

Vibrating the QCD string

The large distance behaviour of the adiabatic hybrid potentials is studied in the framework of the QCD string model. The calculated spectra are shown to be the result of interplay between potential-type longitudinal and string-type transverse vibrations.Comment: LaTeX2e, 9 pages, 2 Postscript figures, final version to appear in Yad.Fi

QCD string in light-light and heavy-light mesons

The spectra of light-light and heavy-light mesons are calculated within the framework of the QCD string model, which is derived from QCD in the Wilson loop approach. Special attention is payed to the proper string dynamics that allows us to reproduce the straight-line Regge trajectories with the inverse slope being 2\pi\sigma for light-light and twice as small for heavy-light mesons. We use the model of the rotating QCD string with quarks at the ends to calculate the masses of several light-light mesons lying on the lowest Regge trajectories and compare them with the experimental data as well as with the predictions of other models. The masses of several low-lying orbitally and radially excited heavy--light states in the D, D_s, B, and B_s meson spectra are calculated in the einbein (auxiliary) field approach, which has proven to be rather accurate in various calculations for relativistic systems. The results for the spectra are compared with the experimental and recent lattice data. It is demonstrated that an account of the proper string dynamics encoded in the so-called string correction to the interquark interaction leads to an extra negative contribution to the masses of orbitally excited states that resolves the problem of the identification of the D(2637) state recently claimed by the DELPHI Collaboration. For the heavy-light system we extract the constants \bar\Lambda, \lambda_1, and \lambda_2 used in Heavy Quark Effective Theory (HQET) and find good agreement with the results of other approaches.Comment: RevTeX, 42 pages, 7 tables, 7 EPS figures, uses epsfig.sty, typos corrected, to appear in Phys.Rev.

QCD string and the Lorentz nature of confinement

We address the question of the Lorentz nature of the effective long-range interquark interaction generated by the QCD string with quarks at the ends. Studying the Dyson-Schwinger equation for a heavy-light quark-antiquark system, we demonstrate explicitly how a Lorentz-scalar interaction appears in the Diraclike equation for the light quark, as a consequence of chiral symmetry breaking. We argue that the effective interquark interaction in the Hamiltonian of the QCD string with quarks at the ends stems from this effective scalar interaction.Comment: LaTeX2e, 5 pages, uses jetpl.cls (included), to appear in JETP Let

Spectroscopy of Baryons Containing Two Heavy Quarks in Nonperturbative Quark Dynamics

We have studied the three quark systems in an Effective Hamiltonian approach in QCD. With only two parameters: the string tension sigma and the strong coupling constant alpha_s we obtain a good description of the ground state light and heavy baryons. The prediction of masses of the doubly heavy baryons not discovered yet are also given. In particular, a mass of 3620 MeV for the lightest (ccu) baryon is found by employing the hyperspherical formalism to the three quark confining potential with the string junction.Comment: 8 pages, LaTe

ПРОГНОЗУВАННЯ РІВНЯ ІНВЕСТИЦІЙНОГО ЗАБЕЗПЕЧЕННЯ РОЗВИТКУ СІЛЬСЬКОГО ГОСПОДАРСТВА

Assessment of the formation of the level of investment ensure and its impact on the indicators of agricultural development requires the use of mathematical methods of parametric forecasting. The methodological approaches have been substantiated and methodical approach to forecasting the level of investment ensuring of agricultural development has been developed in the paper. Investment ensure for agriculture has been proposed to be considered simultaneously as a result of the influence of internal and external factors, as well as a factor affecting the parameters of the industry’s development. The use of gross value added in agriculture as an indicator of the efficiency of investment ensuring and the parameter of agricultural development has been substantiated. The methodical approach to the analysis of investment ensure based on time factor has been improved. Multi-factor econometric model has been developed for assessing the influence of factors (profitability level, volume of lending, state support, foreign direct investment) on the level of investment ensure for agriculture. Indicators of investment ensure of agricultural development have been forecast on the basis of econometric model using data extrapolation method by linear, logarithmic, polynomial and exponential mathematical functions for each factor. An econometric model for assessing the impact of the level of investment ensure on gross value added in agriculture has been developed and used to predict the level of agricultural development. The projected values of investment and gross value added in agriculture in Ukraine have been calculated in an optimistic, realistic and pessimistic scenario. The need to increase the efficiency of agricultural producers, the volume of lending and state support to achieve the appropriate parameters of investment ensure for agricultural development has been substantiated.Оцінка формування рівня інвестиційного забезпечення i його впливу на показники розвитку сільського господарства потребує використання математичних методів параметричного прогнозування. Oбґрунтовано методологічні засади i розроблено методичний підхід до прогнозування рівня інвестиційного забезпечення розвитку сільського господарства. Запропоновано інвестиційне забезпечення сільського господарства розглядати одночасно як результат впливу внутрішніх i зовнішніх факторів та як фактор, що впливає на параметри розвитку галузі. Обґрунтовано, що показником ефективності інвестиційного забезпечення і параметра розвитку сільського господарства доцільно використовувати валову додану вартість у сільському господарстві. Удосконалено методичний підхід до аналізу інвестиційного забезпечення на основі урахування фактору часу. Розроблено багатофакторну економетричну модель для оцінки впливу факторів (рівня рентабельності, обсягів кредитування, державної підтримки, прямих іноземних інвестицій) на рівень інвестиційного забезпечення сільського господарства. Спрогнозовано показники інвестиційного забезпечення розвитку сільського господарства на основі економетричної моделі з використанням методу екстраполяції даних за лінійною, логарифмічною, поліноміальною та степеневою математичними функціями для кожного фактору. На основі розробленої економетричної моделі оцінки впливу рівня інвестиційного забезпечення на валову додану вартість у сільському господарстві розраховано прогнозні значення інвестицій та валової доданої вартості в сільському господарстві України за оптимістичним, реалістичним і песимістичним сценаріями. Обґрунтовано потребу підвищення ефективності діяльності виробників, нарощування обсягів кредитування та державної підтримки для досягнення відповідних параметрів інвестиційного забезпечення розвитку сільського господарства

Interplay of quark and meson degrees of freedom in near-threshold states: A practical parametrisation for line shapes

We propose a practical parametrisation for the line shapes of near-threshold states compatible with all requirements of unitarity and analyticity. The coupled-channel system underlying the proposed parametrisation includes bare poles and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting formulae are general enough to be used for a simultaneous analysis of the data in all available production and decay channels of the (system of) state(s) under consideration for a quite wide class of reactions. As an example, we fit the experimental data currently available for several decay channels for the charged $Z_b^{(\prime)}$ states in the spectrum of bottomonia and find a good overall description of the data. We find the present data to be consistent with the $Z_b(10610)$ as a virtual state and with the $Z_b(10650)$ as a resonance, both residing very close to the $B\bar{B}^*$ and $B^*\bar{B}^*$ threshold, respectively.Comment: LaTeX2e, 19 pages, 10 figures, version published in Phys.Rev.

Ground-state baryons in nonperturbative quark dynamics

We review the results obtained in an Effective Hamiltonian (EH) approach for the three-quark systems. The EH is derived starting from the Feynman--Schwinger representation for the gauge-invariant Green function of the three quarks propagating in the nonperturbative QCD vacuum and assuming the minimal area law for the asymptotic of the Wilson loop. It furnishes the QCD consistent framework within which to study baryons. The EH has the form of the nonrelativistic three-quark Hamiltonian with the perturbative Coulomb-like and nonperturbative string interactions and the specific mass term. After outlining the approach, methods of calculations of the baryon eigenenergies and some simple applications are explained in details. With only two parameters: the string tension $\sigma=0.15 GeV^2$ and the strong coupling constant $\alpha_s=0.39$ a unified quantitative description of the ground state light and heavy baryons is achieved. The prediction of masses of the doubly heavy baryons not discovered yet are also given. In particular, a mass of $3660 MeV$ for the lightest $\Xi_{cc}$ baryon is found by employing the hyperspherical formalism to the three quark confining potential with the string junction.Comment: 25 pages, 4 figures included, LaTeX 2e; to be published in Phys. Atom. Nuc

Two-photon decays of hadronic molecules

In many calculations of the two--photon decay of hadronic molecules, the decay matrix element is estimated using the wave function at the origin prescription, in analogy to the two-photon decay of parapositronium. We question the applicability of this procedure to the two-photon decay of hadronic molecules for it introduces an uncontrolled model dependence into the calculation. As an alternative approach, we propose an explicit evaluation of the hadron loop. For shallow bound states, this can be done as an expansion in powers of the range of the molecule binding force. In the leading order one gets the well-known point-like limit answer. We estimate, in a self-consistent and gauge invariant way, the leading range corrections for the two-photon decay width of weakly bound hadronic molecules emerging from kaon loops. We find them to be small. The role of possible short-ranged operators and of the width of the scalars remains to be investigated.Comment: LaTeX2e, 26 pages, new figure and additional appendix added, version to appear in Phys.Rev.