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ON THE FIELD-THEORETICAL FORMULATION OF THE LOW-ENERGY PION-NUCLEON SCATTERING PROBLEM
http://lt-jds.jinr.ru/record/59769
A. I . MachavarianiTue, 30 Oct 2012 11:40:04 GMThttp://lt-jds.jinr.ru/record/59769Joint Inst. Nucl. Res.1989On the relativistic field-theoretical three dimensional equations for the coupled Nd-3N systems with and without quark-gluon degrees of freedom
http://lt-jds.jinr.ru/record/59088
Machavariani, A.I.Thu, 02 Aug 2012 10:37:28 GMThttp://lt-jds.jinr.ru/record/59088Current conservation, screening and the magnetic moment of the Delta resonance. 1. Formulation without quark degrees of freedom
http://lt-jds.jinr.ru/record/29757
The pion-nucleon bremsstrahlung $\pi+N\Longrightarrow\gamma'+\pi'+N'$ is studied in a new form of current conservation. According to this condition, the internal and external particle radiation parts of the $\pi N$ radiation amplitude have opposite signs, i.e., they contain terms which must cancel each other. Therefore, one has a screening of the internal and external particle radiation in the $\pi N$ bremsstrahlung. In particular, it is shown that the double $\Delta$ exchange diagram with the $\Delta-\gamma' \Delta'$ vertex cancel against the appropriate longitudinal part of the external particle radiation diagrams. Consequently, a model independent relation between the magnetic dipole moments of the $\Delta^+$ and $\Delta^{++}$ resonances and the anomalous magnetic moment of the proton $\mu_p$ is obtained, where $\mu_{\Delta}$ is expressed by $\mu_p$ as $\mu_{\Delta^+}={{M_{\Delta}}\over {m_p}} \mu_p$ and $\mu_{\Delta^{++}}={3\over 2}\mu_{\Delta^+}$ in agreement with the values extracted from the fit for the experimental cross section of the $\pi^+ p\to\gamma'\pi^+ p$ reaction.Machavariani, A.I.Fri, 29 Oct 2010 08:42:58 GMThttp://lt-jds.jinr.ru/record/29757Current conservation, screening and the magnetic moment of the Delta resonance. 2. Formulation with quark degrees of freedom 3. Magnetic moment of the Delta-degree and Delta- resonances
http://lt-jds.jinr.ru/record/29525
Our previous paper \cite{MFNEW} is generalized within the field theoretical formulation with the quark degrees of freedom \cite{HW,H,N,Z}, where pions and nucleons are treated as the bound systems of quarks. It is shown that relations generated by current conservation for the on shell $\pi N$ bremsstrahlung amplitude with composite nucleons and pions have the same form as in the usual quantum field theory \cite{IZ,BD} without quark degrees of freedom \cite{MFNEW}. Consequently, the model independent relations for the magnetic dipole moments of the $\Delta^+$ and $\Delta^{++}$ resonances in \cite{MFNEW} remain be the same in the quantum field theory with the quark degrees of freedom. These relations are extended for the magnetic dipole moments of the $\Delta^o$ and $\Delta^-$ resonances which are determined via the anomalous magnetic moment of the neutron $\mu_n$ as $\mu_{\Delta^o}={{M_{\Delta}}\over {m_p}} \mu_n$ and $\mu_{\Delta^{-}}={3\over 2}\mu_{\Delta^o}$.Machavariani, A.I.Fri, 29 Oct 2010 08:40:43 GMThttp://lt-jds.jinr.ru/record/29525Screening in the bremsstrahlung reactions and determination of the magnetic moment of the Delta resonance
http://lt-jds.jinr.ru/record/29362
Machavariani, A.I.Fri, 29 Oct 2010 08:39:46 GMThttp://lt-jds.jinr.ru/record/29362Ward-Takahashi identity, soft photon theorem and the magnetic moment of the Delta resonance
http://lt-jds.jinr.ru/record/29109
Starting from the Ward-Takahashi identity for the radiative $\pi N$ scattering amplitude a generalization of the soft photon theorem approach is obtained for an arbitrary energy of an emitted photon. The external particle radiation part of the $\pi N\to\gamma'\pi'N' $ amplitude is analytically reduced to the double $\Delta$ exchange amplitude with the $\Delta\to\gamma'\Delta'$ vertex function. We have shown, that the double $\Delta$ exchange amplitudes with internal $\Delta$ radiation is connected by current conservation with the corresponding part of the external particle radiation terms. Moreover according to the current conservation the internal and external particle radiation terms with the $\Delta-\gamma'\Delta'$ vertex have a opposite sign i.e. they must cancel each other. Therefore we have a screening of the internal double $\Delta$ exchange diagram with the $\Delta-\gamma' \Delta'$ vertex by the external particle radiation. This enables us to obtain a model independent estimation of the dipole magnetic moment of $\Delta^+$ and $\Delta^{++}$ resonances $\mu_{\Delta}$ through the anomalous magnetic moment of the proton $\mu_p$ as $\mu_{\Delta^+}={{M_{\Delta}}\over {m_p}} \mu_p$ and $\mu_{\Delta^{++}}={3\over 2}\mu_{\Delta^+}$ in agreement with the values obtained from the fit of the experimental cross section of the $\pi^+ p\to\gamma'\pi^+ p$ reaction.Machavariani, A.I.Fri, 29 Oct 2010 07:22:56 GMThttp://lt-jds.jinr.ru/record/29109On Relationship between conformal transformations and broken chiral symmetry
http://lt-jds.jinr.ru/record/28025
Starting with the conformal transformations in the momentum space, the nonlinear $\sigma$-model and the standard model with the spontaneous broken $SU(2)\times U(1)$ symmetry are reproduced. The corresponding chiral Lagrangians are given in the five dimensional form because for the conformal transformations of the four-momentum $q_{\mu}$ ($q'_{\mu}=q_{\mu}+h_{\mu}$, $q'_{\mu}=\Lambda^{\nu}_{\mu}q_{\nu}$, $q'_{\mu}=\lambda q_{\mu}$ and $q'_{\mu}=-M^2q_{\mu}/q^2$) the equivalence rotations in the 6D space were used. The derived five dimensional Lagrangians consists of the parts defined in the two different region $q_{\mu}q^{\mu}\pm q_5^2=\pm M^2$ which are connected by the inversion $q'_{\mu}=-M^2 q_{\mu}/q^{2}$, where $M$ is a scale parameter. For the $\sigma$-model $M$ is determined by the pion mass $M^2= m_{\pi}^2/2$. For the 5D Lagrangian with the spontaneous broken $SU(2)\times U(1)$ symmetry the scale parameter $M^2$ is defined by the Higgs particle mass $8m^2_{Higgs}=9M^2$. Unlike to the usual four-dimensional formulation in the present approach the chiral symmetry breaking terms are obtained from the conformal transformations and it is demonstrated, that the corresponding interaction parts of Lagrangians have the opposite sign in the regions $q^{\mu}q_{\mu}>M^2$ and $0\le q^{\mu}q_{\mu}<M^2$.Machavariani, A.I.Fri, 29 Oct 2010 07:19:08 GMThttp://lt-jds.jinr.ru/record/28025Conformal group of transformations of the quantum field operators in the momentum space and the five dimensional Lagrangian approach
http://lt-jds.jinr.ru/record/27696
Conformal group of transformations in the momentum space, consisting of translations $p'_{\mu}=p_{\mu}+h_{\mu}$, rotations $p'_{\mu}=\Lambda^{\nu}_{\mu}p_{\nu}$, dilatation $p'_{\mu}=\lambda p_{\mu}$ and inversion $p'_{\mu}= -M^2p_{\mu}/p^2$ of the four-momentum $p_{\mu}$, is used for the five dimensional generalization of the equations of motion for the interacting massive particles. It is shown, that the ${\cal S}$-matrix of the charged and the neutral particles scattering is invariant under translations in a four-dimensional momentum space $p'_{\mu}=p_{\mu}+h_{\mu}$. In the suggested system of equations of motion, the one-dimensional equations over the fifth coordinate $x_5$ are separated and these one dimensional equations have the form of the evaluation equations with $x_5=\sqrt{x_o^2-{\bf x}^2}$. The important property of the derived five dimensional equations of motion is the explicit separation of the parts of these equations according to the inversion $p'_{\mu}=-M^2 p_{\mu}/p^{2}$, where $M$ is a scale constant.Machavariani, A.I.Thu, 28 Oct 2010 18:39:56 GMThttp://lt-jds.jinr.ru/record/27696Propagator of the Delta resonance and determination of the magnetic moment of the Delta+ from the gamma p ---> gamma pi0 p reaction
http://lt-jds.jinr.ru/record/27459
Machavariani, A.I.Thu, 28 Oct 2010 18:39:18 GMThttp://lt-jds.jinr.ru/record/27459Field theoretical three body relativistic equations for the multichannel pi N <---> gamma N <---> pi pi N <---> gamma pi N reactions
http://lt-jds.jinr.ru/record/26180
A new kind of the relativistic three-body equations for the coupled $\pi N$ and $\gamma N$ scattering reactions with the $\pi \pi N$ and $\gamma \pi N$ three particle final states are suggested. These equations are derived in the framework of the standard field-theoretical $S$-matrix approach in the time-ordered three dimensional form. Therefore corresponding relativistic covariant equations are three-dimensional from the beginning and the considered formulation is free of the ambiguities which appear due to a three dimensional reduction of the four dimensional Bethe-Salpeter equations. The solutions of the considered equations satisfy the unitarity condition and are exactly gauge invariant even after the truncation of the of the multiparticle ($n>3$) intermediate states. Moreover the form of these three-body equations does not depend on the choice of the model Lagrangian and it is the same for the formulations with and without quark degrees of freedom. The effective potential of the suggested equations is defined by the vertex functions with two on-mass shell particles. It is emphasized that these INPUT vertex functions can be constructed from experimental data. Special attention is given to the construction of the intermediate on shell and off shell $\Delta$ resonance states. These intermediate $\Delta$ states are obtained after separation of the $\Delta$ resonance pole contributions in the intermediate $\pi N$ Green function. The resulting amplitudes for the $\Delta\Longleftrightarrow N\pi$: $\Delta\Longleftrightarrow N\gamma:$ $% \Delta^{\prime}\Longleftrightarrow \Delta\gamma$ transition have the same structure as the vertex functions for transitions between the on mass shell particle states with spin 1/2 and 3/2.Machavariani, A.I.Thu, 28 Oct 2010 11:42:19 GMThttp://lt-jds.jinr.ru/record/26180Relativistic field-theoretical equations for the three-body multichannel pi N and gamma N scattering reactions and propagator of the Delta-resonance
http://lt-jds.jinr.ru/record/26093
Machavariani, A.I.Thu, 28 Oct 2010 11:42:06 GMThttp://lt-jds.jinr.ru/record/26093Relativistic field theoretical formulation of the three-dimensional equations for the three fermion system
http://lt-jds.jinr.ru/record/25980
A new kind of the relativistic three-body equations for the three fermion systems are suggested. These equations are derived in the framework of the standard field-theoretical $S$-matrix approach in the time-ordered three dimensional form. Therefore corresponding relativistic covariant equations are three-dimensional from the beginning. The solutions of the considered equations satisfy automatically the unitarity condition and for the leptons these equations are exactly gauge invariant even after the truncation over the multiparticle ($n>3$) intermediate states. Moreover, the form of these three-body equations does not depend on the choice of the model Lagrangian and it is the same for the formulations with and without quark degrees of freedom. The effective potential of the suggested equations is defined by the vertex functions with two on-mass shell particles. It is emphasized that these INPUT vertex functions can be constructed from experimental data. Special attention is given to the comparison with the three-body Faddeev equations. Unlike to these equations, the suggested three-body equation have the form of the Lippmann-Schwinger-type equations with the connected potential. In addition, the microscopical potential of the suggested equations contains the contributions from the three-body forces and from the particle creation (annihilation) mechanism on the one external particles. The structure of the three-body forces, appearing in the considered field-theoretical formulation, is analyzed.Machavariani, A.I.Thu, 28 Oct 2010 11:41:51 GMThttp://lt-jds.jinr.ru/record/25980Field theoretical description of the multichannel gamma p scattering reaction in the delta resonance region and determination of the magnetic moment of the delta+ resonance
http://lt-jds.jinr.ru/record/25710
The cross-sections of the $\gamma p-\gamma' N'$, $\gamma p-\pi' N'$ and $\gamma p-\gamma'\pi' N'$ reactions are calculated in the framework of the field-theoretical one-particle ($\pi,\omega,\rho$-mesons, nucleon and $\Delta$-resonance) exchange model. Unlike the other relativistic approaches, our resulting amplitudes of the $\gamma p$ multichannel reactions require one-variable covariant vertex functions as input ingredient and every diagram of these amplitudes satisfies the current conservation condition in the Coulomb gauge. The complete set of the model independent skeleton diagrams for the ${\gamma} p\to\gamma'\pi'N'$ reaction is presented. The separable model of the $\pi N$ interaction is generalized to construct the spin 3/2 particle propagator of the $\Delta$-resonance. This procedure allows to obtain the $\pi N-\Delta$ form factor and $\Delta$ propagator directly from the $\pi N$ $P_{33}$ phase shifts. The numerical calculation of the differential cross section of the $\gamma p-\gamma' N'$, $\gamma p-{\pi^o}' N'$ and $\gamma p-\gamma'{\pi^o}'N'$ reactions are performed with two different separable models of the $\Delta$ propagator and with the propagator of Breit-Wigner shape. It is demonstrated that the numerical description of these reactions in the $\Delta$-resonance region are very sensitive to the form of the $\Delta$-propagator. The sensitivity of the cross-sections of the $\gamma p\to\gamma'{\pi^o}'p'$ reaction to the magnitude of the $\Delta^+$ magnetic moment is examined and the most convenient kinematical region for the determination of the magnetic moment of the $\Delta^+$-resonance from the forthcoming data is indicated.Machavariani, A.I.Thu, 28 Oct 2010 11:41:11 GMThttp://lt-jds.jinr.ru/record/25710Relativistic field theoretical approach to the inverse scattering problem
http://lt-jds.jinr.ru/record/25610
The inverse scattering problem for the relativistic three-dimensional equation $\Bigl(2E_{\bf p'}-2E_{\bf p}\Bigr)<{\bf p'}|\Psi_{\bf p}>= -\int V(t)d^3{\bf p''}<{\bf p''}|\Psi_{\bf p}>$ with $E_{\bf p}=\sqrt{m^2+{\bf p}^2}$ and $t=\Bigl(E_{\bf p'}-E_{\bf p''}\Bigr)^2 -\Bigl({\bf p'}-{\bf p''}\Bigr)^2$ is considered. The field-theoretical potential $V(t)$ of this equation is constructed in the framework of the old perturbation theory. It contains all contributions of diagrams with intermediate off-mass shell particles. In particular, this potential reproduces the OBE Bonn model of the $NN$ potential exactly.For the $\pi N$ scattering it is generated by $\sigma,\rho, \omega$-meson exchange diagrams. The inverse scattering problem is solved by reduction of these relativistic equations to the standard Schr\odinger equations $\Bigl(\Delta_{\bf r}+{\bf k}^2\Bigr)<{\bf r}|\phi_{\bf p}>= - v({\bf r})<{\bf r}|\phi_{\bf k}>$ with $E_{\bf p}={\bf k}^2/2m+m$. The relation between the relativistic potential $V(t)$ and its nonrelativistic representation $v({\bf r})$ is obtained.Machavariani, A.I.Thu, 28 Oct 2010 11:40:57 GMThttp://lt-jds.jinr.ru/record/25610Relativistic field-theoretical representation of the Schroedinger equation and field-theoretical generalization of the inverse scattering method
http://lt-jds.jinr.ru/record/25460
Machavariani, A.I.Thu, 28 Oct 2010 11:40:37 GMThttp://lt-jds.jinr.ru/record/25460Determination of the magnetic moment of the Delta+ resonance in the gamma* p - gamma pi N reactions
http://lt-jds.jinr.ru/record/24776
Machavariani, A.I.Thu, 28 Oct 2010 09:45:20 GMThttp://lt-jds.jinr.ru/record/24776Separation of meson and quark gluon degrees of freedom in hadron interactions
http://lt-jds.jinr.ru/record/23836
Machavariani, A.I.Thu, 28 Oct 2010 09:43:22 GMThttp://lt-jds.jinr.ru/record/23836Field-theoretical description of electromagnetic Delta resonance production and determination of the magnetic moment of the Delta+(1232) resonance by the e p --> e' N' pi' gamma' and gamma p --> N' pi' gamma' reactions
http://lt-jds.jinr.ru/record/23517
Machavariani, A.I.Thu, 28 Oct 2010 07:48:26 GMThttp://lt-jds.jinr.ru/record/23517Three-dimensional field-theoretical construction of the nucleon nucleon potential from quark degrees of freedom
http://lt-jds.jinr.ru/record/21554
Machavariani, A.I.Wed, 27 Oct 2010 15:05:05 GMThttp://lt-jds.jinr.ru/record/21554A chiral quark model and the spin observables in nucleon nucleon scattering
http://lt-jds.jinr.ru/record/20794
Entem, D.R.Wed, 27 Oct 2010 13:21:29 GMThttp://lt-jds.jinr.ru/record/20794Field-theoretical construction of the nucleon nucleon potential with quark degrees of freedom
http://lt-jds.jinr.ru/record/20677
Machavariani, A.I.Wed, 27 Oct 2010 13:21:18 GMThttp://lt-jds.jinr.ru/record/20677Conserved currents for e d ---> e-prime N N, e d ---> e-prime d-prime and gamma d ---> N N reactions in the framework of three-dimensional field theoretical formulation
http://lt-jds.jinr.ru/record/19655
Machavariani, A.I.Wed, 27 Oct 2010 11:27:41 GMThttp://lt-jds.jinr.ru/record/19655Equal time commutators and field-theoretical three-dimensional equations for the deuteron electromagnetic reactions
http://lt-jds.jinr.ru/record/19197
Machavariani, A.I.Wed, 27 Oct 2010 11:27:02 GMThttp://lt-jds.jinr.ru/record/19197Formulation of three-dimensional field theoretical equations for two particle scattering reactions
http://lt-jds.jinr.ru/record/17365
Machavariani, A.I.Wed, 27 Oct 2010 10:36:38 GMThttp://lt-jds.jinr.ru/record/17365ON THE FIELD THEORETICAL FORMULATION OF THE LOW-ENERGY PION - NUCLEON SCATTERING PROBLEM
http://lt-jds.jinr.ru/record/16184
Machavariani, A.I.Tue, 26 Oct 2010 11:35:34 GMThttp://lt-jds.jinr.ru/record/16184