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V. A. Karmanov

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

At least 19 recordsLinked to original sources
arXiv2026

Helium-3 relativistic wave function in light-front dynamics

The relativistic wave function of $^3$He nucleus is calculated in the framework of Light-Front Dynamics. It is determined by 32 spin-isospin components, each of which depends on five scalar variables. For NN interaction, the one-boson exchange model is assumed, but without a potential approximation. The relativistic effects manifest themselves in deviation of the relativistic components from the non-relativistic input, in the appearance of the components absent in the non-relativistic limit, and in dependence of solutions on specific variables that don't exist in the non-relativistic wave function.

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arXiv2025

Relativistic $^3$He light-front wave function

The relativistic light-front (LF) wave function of $^3$He is determined by the three-body LF equation for the Faddeev components in the momentum space. As an interaction, we take the one-meson exchange kernels, without the potential approximation. Within the explicitly covariant formulation of LF dynamics, we calculate the full relativistic $^3$He LF wave function, comprising 32 spin-isospin components. In the non-relativistic domain, five of these components dominate and closely resemble their non-relativistic counterparts. Relativistic effects manifest themselves in deviations in relativistic domain of these components from the non-relativistic ones and in appearance of new components.

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arXiv2024

Abnormal states with unequal constituent masses

The Bethe-Salpeter equation for system of two oppositely charged particles not only reproduces the Coulomb spectrum, but, for enough large coupling constant ${\cal C}>\fracπ{4}$, predicts additional levels not predicted by the Schrödinger equation. These relativistic states (called abnormal), in contrast to the normal ones, are dominated, for more than 90-99 percent, by Fock states involving the exchange particles - the photons, whereas contribution of two massive charged particles themselves is rather small (1-10 \%). Since the carrier of a large (positive) charge is a heavy ion, and the negative charge is provided by electron, the masses of two constituents are very different. It is shown that in a system with so different masses the abnormal states still exist. Moreover, the effect of unequal masses is attractive. The balance between photons and charged constituents is weakly sensitive to the mass ratio, so the photons still predominate.

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arXiv2023

On cancellation of non-adiabatic and off-shell effects in the antiproton annihilation in deuteron

As known, some approximate approaches to the hadron scattering from nuclei work rather well far beyond the limits of their applicability. This was explained by cancellation of the contributions (non-adiabatic and off-shell effects) omitted in these approaches. Moreover, in some cases (in particular, for the reaction $\bar{p}d \to e^+e^-n$) this cancellation allowed to derive rather simple analytical formula for the reaction amplitude. Solving the Faddeev equations, we confirm numerically this formula and, hence, the cancellations.

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arXiv2022

Systems Dominated by Exchange Particles

As well known, the spectrum of a non-relativistic two-body system interacting by the Coulomb potential is the Balmer series $E_n=\frac{α^2m}{4n^2}$ produced by the Schrödinger equation. In 1954, Wick and Cutkosky have found, in the Bethe-Salpeter equation framework, that for $α>\fracπ{4}$ the relativistic effects result in new levels (in addition to the Balmer series). However, the physical nature of these new states remained unclear and therefore their existence was being questioned. We have recently shown that these extra states are dominated by the exchange (massless) particles, moving with speed of light. That's why they did not appear in the non-relativistic (Schrödinger) framework.

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arXiv2022

Abnormal Bound Systems

It is taken for granted that bound systems are made of massive constituents that interact through particle exchanges (charged particles interacting via photon exchanges, quarks in elementary particles interacting via gluon exchanges, and nucleons in nuclei interacting via meson exchanges). However, as was recently theoretically found, there exist systems dominated by exchange particles (at least for the zero exchange masses). In these systems, the contribution of massive constituents is negligible. These systems have a relativistic nature (since they are mainly made of massless particles moving at the speed of light), and therefore, they cannot be described by the Schroedinger equation. Though these results were found so far in the simple Wick--Cutkosky model (spinless constituents interacting via the ladder of spinless massless exchanges), the physical ground for their existence seems to be rather general.

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arXiv2021

New form of kernel in equation for Nakanishi function

The Bethe-Salpeter amplitude $Φ(k,p)$ is expressed, by means of the Nakanishi integral representation, via a smooth function $g(γ,z)$. This function satisfies a canonical equation $g=Ng$. However, calculations of the kernel $N$ in this equation, presented previously, were restricted to one-boson exchange and, depending on method, dealt with complex multivalued functions. Although these difficulties are surmountable, but in practice, they complicate finding the unambiguous result. In the present work, an unambiguous expression for the kernel $N$ in terms of real functions is derived. For the one-boson scalar exchange, the explicit formula for $N$ is found. With this equation and kernel, the binding energies, calculated previously, are reproduced. Their finding, as well as calculation of the Bethe-Salpeter amplitude in the Minkowski space, become not more difficult than in the Euclidean one. The method can be generalized to any kernel given by irreducible Feynman graph. This generalization is illustrated by example of the cross-ladder kernel.

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arXiv2020

Three-boson bound states in Minkowski space with contact interactions

The structure of the three-boson bound state in Minkowski space is studied for a model with contact interaction. The Faddeev-Bethe-Salpeter equation is solved both in Minkowski and Euclidean spaces. The results are in fair agreement for comparable quantities, like the transverse amplitude obtained when the longitudinal constituent momenta of the light-front valence wave function are integrated out. The Minkowski space solution is obtained numerically by using a recently proposed method based on the direct integration over the singularities of the propagators and interaction kernel of the four-dimensional integral equation. The complex singular structure of the Faddeev components of the Bethe-Salpeter vertex function for space and time-like momenta in an example of a Borromean system is investigated in detail. Furthermore, the transverse amplitude is studied as a mean to access the double-parton transverse momentum distribution. Following that, we show that the two-body short-range correlation contained in the valence wave function is evidenced when the pair has a large relative momentum in a back-to-back configuration, where one of the Faddeev components of the Bethe-Salpeter amplitude dominates over the others. In this situation a power-law behavior is derived and confirmed numerically.

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arXiv2020

Structure and EM form factors of purely relativistic systems

The Bethe-Salpeter equation for two massive scalar particles interacting by scalar massless exchange has solutions of two types, which differ from each other by their behavior in the non-relativistic limit: the normal solutions which turn into the Coulomb ones and the "abnormal" solutions. The latter ones have no non-relativistic counterparts and disappear in the non-relativistic limit. We studied the composition of all these states. It turns out that the normal states, even for large binding energy, are dominated by two massive particles. Whereas, the contribution of the two-body sector into the abnormal states, even for small binding energy, is of the order of 1% only; they are dominated by an indefinite number of the massless particles. The elastic electromagnetic form factors for both normal and abnormal states, as well as the transition ones between them, are calculated.

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arXiv2019

Bound states of relativistic nature

Bethe-Salpeter equation, for massless exchange and large fine structure constant $α>π/4$, in addition to the Balmer series, provides another (abnormal) series of energy levels which are not given by the Schrödinger equation. So strong field can be created by a point-like charge $Z>107$. The nuclei with this charge, though available, they are far from to be point-like that weakens the field. Therefore, the abnormal states of this origin hardly exist. We analyze the more realistic case of exchange by a massive particle when the large value of coupling constant is typical for the strong interaction. It turns out that this interaction still generates a series of abnormal relativistic states. The properties of these solutions are studied. Their existence in nature seems possible.

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arXiv2019

Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.

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arXiv2018

Equation for the Nakanishi weight function using the inverse Stieltjes transform

The bound state Bethe-Salpeter amplitude was expressed by Nakanishi in terms of a smooth weight function g. By using the generalized Stieltjes transform, we derive an integral equation for the Nakanishi function g for a bound state case. It has the standard form g= Vg, where V is a two-dimensional integral operator. The prescription for obtaining the kernel V starting with the kernel K of the Bethe-Salpeter equation is given.

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arXiv2017

Bound state equation for the Nakanishi weight function

The bound state Bethe-Salpeter amplitude was expressed by Nakanishi using a two-dimensional integral representation, in terms of a smooth weight function $g$, which carries the detailed dynamical information. A similar, but one-dimensional, integral representation can be obtained for the Light-Front wave function in terms of the same weight function $g$. By using the generalized Stieltjes transform, we first obtain $g$ in terms of the Light-Front wave function in the complex plane of its arguments. Next, a new integral equation for the Nakanishi weight function $g$ is derived for a bound state case. It has the standard form $g= N g$, where $N$ is a two-dimensional integral operator. We give the prescription for obtaining the kernel $ N$ starting with the kernel $K$ of the Bethe-Salpeter equation. The derivation is valid for any kernel given by an irreducible Feynman amplitude.

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arXiv2017

Three-body bound states with zero-range interaction in the Bethe-Salpeter approach

The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe-Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: ({\it i}) For weak enough two-body interaction the three-body system is unbound. ({\it ii}) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. ({\it iii}) For even stronger two-body interaction this state becomes unphysical with a negative mass squared. However, another physical (excited) state appears, found previously in light-front calculations. The Bethe-Salpeter approach implicitly incorporates three-body forces of relativistic origin, which are attractive and increase the binding energy.

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arXiv2017

Euclidean to Minkowski Bethe-Salpeter amplitude and observables

We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude -- or alternatively the Light-Front wave function -- as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function.

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arXiv2016

Bound state structure and electromagnetic form factor beyond the ladder approximation

We investigate the response of the bound state structure of a two-boson system, within a Yukawa model with a scalar boson exchange, to the inclusion of the cross-ladder contribution to the ladder kernel of the Bethe-Salpeter equation. The equation is solved by means of the Nakanishi integral representation and light-front projection. The valence light-front wave function and the elastic electromagnetic form factor beyond the impulse approximation, with the inclusion of the two-body current, generated by the cross-ladder kernel, are computed. The valence wave function and electromagnetic form factor, considering both ladder and ladder plus cross-ladder kernels, are studied in detail. Their asymptotic forms are found to be quite independent of the inclusion of the cross-ladder kernel, for a given binding energy. The asymptotic decrease of form factor agrees with the counting rules. This analysis can be generalized to fermionic systems, with a wide application in the study of the meson structure.

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arXiv2016

Direct Bethe-Salpeter solutions in Minkowski space

We review a method to directly solve the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the many singularities which appear in the kernel and propagators. The off-mass shell scattering amplitude for spinless particles interacting by a one boson exchange was computed for the first time. Using our Minkowski space solutions for the initial (bound) and final (scattering) states, we calculate elastic and transition (bound to scattering state) electromagnetic form factors. The conservation of the transition electromagnetic current J.q=0, verified numerically, confirms the validity of our solutions.

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