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V. A. Karmanov

Publications and source records attributed to V. A. Karmanov.

At least 37 records · Page 2Linked to original sources
arXiv2016

Zero energy scattering calculation in Euclidean space

We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe-Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe-Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.

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arXiv2015

Ab Initio Approach to the Non-Perturbative Scalar Yukawa Model

We report on the first non-perturbative calculation of the scalar Yukawa model in the single-nucleon sector up to four-body Fock sector truncation (one "scalar nucleon" and three "scalar pions"). The light-front Hamiltonian approach with a systematic non-perturbative renormalization is applied. We study the $n$-body norms and the electromagnetic form factor. We find that the one- and two-body contributions dominate up to coupling $α\approx 1.7$. As we approach the coupling $α\approx 2.2$, we discover that the four-body contribution rises rapidly and overtakes the two- and three-body contributions. By comparing with lower sector truncations, we show that the form factor converges with respect to the Fock sector expansion.

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arXiv2015

Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach

The transition form factor for electrodisintegration of a two-body bound system is calculated in the Bethe-Salpeter framework. For the initial (bound) and the final (scattering) states, we use our solutions of the Bethe-Salpeter equation in Minkowski space which were first obtained recently. The gauge invariance, which manifests itself in the conservation of the transition electromagnetic current Jq = 0, is studied numerically. It results from a cancellation between the plane wave and the final state interaction contributions. This cancellation takes place only if the initial bound state BS amplitude, the final scattering state and the operator of electromagnetic current are strictly consistent with each other, that is if they are found in the same dynamical framework. A reliable result for the transition form factor can be obtained in this case only.

hep-ph↗
arXiv2015

Non-Perturbative Calculation of the Scalar Yukawa Theory in Four-Body Truncation

The quenched scalar Yukawa theory is solved in the light-front Tamm-Dancoff approach including up to four constituents (one scalar nucleon, three scalar pions). The Fock sector dependent renormalization is implemented. By studying the Fock sector norms, we find that the lowest two Fock sectors dominate the state even in the large-coupling region. The one-body sector shows convergence with respect to the Fock sector truncation. However, the four-body norm exceeds the three-body norm at the coupling $α\approx 1.7$.

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arXiv2014

Current conservation in electrodisintegration of a bound system in the Bethe-Salpeter approach

Using our solutions of the Bethe-Salpeter equation with OBE kernel in Minkowski space both for the bound and scattering states, we calculate the transition form factors for electrodisintegration of the bound system which determine the electromagnetic current J of this process. Special emphasis is put on verifying the gauge invariance which should manifest itself in the current conservation. We find that for any value of the momentum transfer q the contributions of the plane wave and the final state interaction to the quantity J.q cancel each other thus providing J.q=0. However, this cancellation is obtained only if the initial Bethe-Salpeter amplitude (bound state), the final one (scattering state) and the current operator are strictly consistent with each other. A reliable result for the transition form factor can be found only in this case.

hep-ph↗
arXiv2014

Solving Bethe-Salpeter scattering state equation in Minkowski space

We present a method to directly solving the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators and Bethe-Salpeter amplitude itself. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange is computed for the first time.

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arXiv2013

Critical stability of few-body systems

When a two-body system is bound by a zero-range interaction, the corresponding three-body system -- considered in a non-relativistic framework -- collapses, that is its binding energy is unbounded from below. In a paper by J.V. Lindesay and H.P. Noyes it was shown that the relativistic effects result in an effective repulsion in such a way that three-body binding energy remains also finite, thus preventing the three-body system from collapse. Later, this property was confirmed in other works based on different versions of relativistic approaches. However, the three-body system exists only for a limited range of two-body binding energy values. For stronger two-body interaction, the relativistic three-body system still collapses. A similar phenomenon was found in a two-body systems themselves: a two-fermion system with one-boson exchange interaction in a state with zero angular momentum J=0 exists if the coupling constant does not exceed some critical value but it also collapses for larger coupling constant. For a J=1 state, it collapses for any coupling constant value. These properties are called "critical stability". This contribution aims to be a brief review of this field pioneered by H.P. Noyes.

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arXiv2013

Nonperturbative calculations in truncated Fock space in LFD

A non-perturbative approach based on the Fock decomposition of the state vector and its truncation is discussed. In order the non-perturbative renormalization procedure after truncation could eliminate infinities, it should be the sector dependent. We clarify the meaning of this procedure in a toy model. Then we demonstrate stability, relative to the increasing cutoff, of the anomalous magnetic moment found using the sector dependent renormalization scheme in Yukawa model.

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arXiv2013

Present status of the Bethe-Salpeter approach in Minkowski space

Recently developed methods allowing to find the solutions of the Bethe-Salpeter equations in Minkowski space, both for the bound and scattering states, are reviewed. For the bound states, one obtains the bound state mass and the corresponding BS amplitude. For the scattering states, the phase shifts (complex above the meson creation threshold) and the half-off-shell BS amplitude are found. Using these solutions, the elastic and transition electromagnetic form factors are calculated.

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arXiv2012

Scattering states in Bethe-Salpeter equation

The off-mass shell scattering amplitude, satisfying the Bethe-Salpeter equation for spinless particles in Minkowski space with the ladder kernel, is computed for the first time.

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arXiv2012

Three different approaches to the same interaction: the Yukawa model in nuclear physics

After a brief discussion of the meaning of the potential in quantum mechanics, we examine the results of the Yukawa model (scalar meson exchange) for the nucleon-nucleon interaction in three different dynamical frameworks: the non-relativistic dynamics of the Schrodinger equation, the relativistic quantum mechanics of the Bethe-Salpeter and Light-Front equations and the lattice solution of the Quantum Field Theory, obtained in the quenched approximation.

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arXiv2012

Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model

We present a coherent and operational strategy to calculate, in a nonperturbative way, physical observables in light-front dynamics. This strategy is based on the decomposition of the state vector of any compound system in Fock components, and on the covariant formulation of light-front dynamics, together with the so-called Fock sector dependent renormalization scheme. We apply our approach to the calculation of the electromagnetic form factors of a fermion in the Yukawa model, in the nontrivial three-body Fock space truncation, for rather large values of the coupling constant. We find that, once the renormalization conditions are properly taken into account, the form factors do not depend on the regularization scale, when the latter is much larger than the physical masses. We then extend the Fock space by including antifermion degrees of freedom.

hep-th↗
arXiv2010

Solutions of the Bethe-Salpeter equation in Minkowski space and applications to electromagnetic form factors

We present a new method for solving the two-body Bethe-Salpeter equation in Minkowski space. It is based on the Nakanishi integral representation of the Bethe-Salpeter amplitude and on subsequent projection of the equation on the light-front plane. The method is valid for any kernel given by the irreducible Feynman graphs and for systems of spinless particles or fermions. The Bethe-Salpeter amplitudes in Minkowski space are obtained. The electromagnetic form factors are computed and compared to the Euclidean results.

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arXiv2010

Relativistic descriptions of few-body systems

A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in three-body observables are demonstrated. The three-body forces of relativistic origin are also discussed.

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arXiv2010

Solving Bethe-Salpeter equation for two fermions in Minkowski space

The method of solving the Bethe-Salpeter equation in Minkowski space, which we developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original Bethe-Salpeter amplitudes. The numerical solutions for the J=0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. The stability of the scalar and positronium states without vertex form factor is discussed. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.

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