arXiv subjects

S. Kondratyuk

Publications and source records attributed to S. Kondratyuk.

At least 19 recordsLinked to original sources

arXiv2009

Interpretation of the neutron quantum gravitational states in terms of isospectral potentials

The recently observed quantum states of neutrons bound in a gravitational field are analyzed in the framework of one-parameter isospectral hamiltonians. Potentials isospectral to the usual Newton potential are explicitly constructed for the first time, then constrained using measured properties of the neutron gravitational states. The corresponding wave functions and the neutron fluxes are also calculated and analyzed in a simple model, including the ground state and the excited state contributions. The constructed isospectral potentials are discussed as candidates for a possible modification of Newton's law at a submillimetre scale. Our results indicate that significant deviations from the Newtonian gravity at submillimetre distances could be compatible with experiment.

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arXiv2007

Connection between the high energy-scale evolution of the P- and T-odd $πN N$ coupling constant and the strong $πN N$ interaction

The large energy-scale behaviour of the parity and time-reversal violating (PTV) pion-nucleon coupling constant is analyzed in a model combining renormalization-group techniques and the dressing of the PTV vertex with a pion loop. With the strong $πN N$ vertex as a mixture of the pseudovector and pseudoscalar couplings, we show that depending on the admixture parameter, two qualitatively distinct types of behaviour are obtained for the PTV coupling constant at high energy scales: an asymptotic freedom or a fixed-point. We find a critical value of the admixture parameter which delineates these two scenarios. Several examples of the high-energy scale behaviour of the PTV $πN N$ constant are considered, corresponding to realistic hadronic models of the strong pion-nucleon interaction.

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arXiv2007

Contribution of spin 1/2 and 3/2 resonances to two-photon exchange effects in elastic electron-proton scattering

We calculate contributions of hadron resonances to two-photon exchange effects in electron-proton scattering. In addition to the nucleon and P33 resonance, the following heavier resonances are included as intermediate states in the two-photon exchange diagrams: D13, D33, P11, S11 and S31. We show that the corrections due to the heavier resonances are smaller that the dominant nucleon and P33 contributions. We also find that there is a partial cancellation between the contributions from the spin 1/2 and spin 3/2 resonances, which results in a further suppression of their aggregate two-photon exchange effect.

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arXiv2006

P- and T-violating $πN N$ form factor

The form factor of the parity and time-reversal violating (PTV) pion-nucleon interaction is calculated from one-loop vertex diagrams. The degrees of freedom included in the effective lagrangian are nucleons, pions, $η$, $ρ$ and $ω$ mesons. We show that by studying the form factor one can constrain the PTV meson-nucleon coupling constants. We evaluate the mean square radius associated with the PTV $πN N$ vertex. Using the mean square radius, we estimate the effect of the PTV $πN N$ vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisation group $β$ function and use it to discuss evolution of the PTV $πN N$ coupling constant beyond the hadronic mass scale.

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arXiv2006

Calculation of two-photon exchange effects for $Δ$ production in electron-proton collisions

We present an evaluation of a two-photon exchange correction to the cross section for unpolarized $Δ$ isobar production in electron-proton collisions, using a relativistic, crossing symmetric and gauge invariant approach. The calculated box and crossed-box diagrams include nucleon and $Δ$ intermediate states. We find a relation between the angular nonlinearity of the two-photon exchange contribution and the value of the $γΔΔ$ coupling constant.

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arXiv2005

$Δ$ resonance contribution to two-photon exchange in electron-proton scattering

We calculate the effects on the elastic electron-proton scattering cross section of the two-photon exchange contribution with an intermediate $Δ$ resonance. The $Δ$ two-photon exchange contribution is found to be smaller in magnitude than the previously evaluated nucleon contribution, with an opposite sign at backward scattering angles. The sum of the nucleon and $Δ$ two-photon exchange corrections has an angular dependence compatible with both the polarisation transfer and the Rosenbluth methods of measuring the nucleon electromagnetic form factors.

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arXiv2005

Ratio of the proton electromagnetic form factors from meson dressing

The Dressed K-matrix Model, developed previously for low- and intermediate-energy Compton scattering, is generalized to calculate the photon-nucleon vertex with a virtual photon and an off-shell nucleon. Using this model, the ratio of the proton electromagnetic form factors is computed. The calculated ratio is in excellent agreement with the ratio measured in polarized electron-proton scattering.

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arXiv2004

The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules as probes of constraints from analyticity and chiral symmetry in dynamical models for pion-nucleon scattering

The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules are calculated within a relativistic, unitary and crossing symmetric dynamical model for pion-nucleon scattering using two different methods: 1) by evaluating the scattering amplitude at the corresponding low-energy kinematics and 2) by evaluating the sum-rule integrals with the calculated total cross section. The discrepancy between the results of the two methods provides a measure of the breaking of analyticity and chiral symmetry in the model. The contribution of the $Δ$ resonance, including its dressing with meson loops, is discussed in some detail and found to be small.

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arXiv2003

In-medium meson properties and field transformations

Since the existing calculations of the effective meson mass in nuclear medium involve approximations, it is important to examine whether they satisfy the general requirement of the equivalence theorem that the physical observables should be independent of the choice of field variables. We study here consequences of nucleon field transformations. As an illustrative case we consider the in-medium effective pion mass calculated for the s-wave pion-nucleon interaction in the linear density approximation. We demonstrate that it is necessary to include the Born term explicitly in order that the effective pion mass should obey the equivalence theorem.

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arXiv2002

Pion-nucleon amplitude near threshold: the sigma-term and scattering lengths beyond few loops

The pion-nucleon amplitude is considered in the vicinity of the elastic scattering threshold within a relativistic dynamical model dressing the pi N N and pi N Delta vertices self-consistently with an infinite number of meson loops. The dressing is formulated as solution of a system of coupled integral equations incorporating unitarity, crossing symmetry and analyticity constraints. The calculated scattering lengths and the sigma-term agree with recent data analyses. The dressing is important in this model both below and at threshold. The contribution of the Delta resonance is discussed, including effects of the consistent dressing of the pi N Delta vertex. A comparison with the approaches of chiral perturbation theory and the Bethe-Salpeter equation is outlined.

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arXiv2002

Compton Scattering on the Proton

A microscopic coupled-channels model for Compton and pion scattering off the nucleon is introduced which is applicable at the lowest energies (polarizabilities) as well as at GeV energies. To introduce the model first the conventional K-matrix approach is discussed to extend this in a following chapter to the "Dressed K-Matrix" model. The latter approach restores causality, or analyticity, of the amplitude to a large extent. In particular, crossing symmetry, gauge invariance and unitarity are satisfied. The extent of violation of analyticity (causality) is used as an expansion parameter.

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arXiv2001

Low-energy Compton scattering on the nucleon and sum rules

The Gerasimov-Drell-Hearn and Baldin-Lapidus sum rules are evaluated in the dressed K-matrix model for photon-induced reactions on the nucleon. For the first time the sum $α+β$ of the electric and magnetic polarisabilities and the forward spin polarisability $γ_0$ are explicitly calculated in two alternative ways -- from the sum rules and from the low-energy expansion of the real Compton scattering amplitude -- within the {\em same} framework. The two methods yield compatible values for $α+β$ but differ somewhat for $γ_0$. Consistency between the two ways of determining the polarisabilities is a measure of the extent to which basic symmetries of the model are obeyed.

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arXiv2001

The equivalence theorem and the Bethe-Salpeter equation

We solve the Bethe-Salpeter equation for two-particle scattering in a field-theoretical model using two lagrangians related by a field transformation. The kernel of the equation consists of the sum of all tree-level diagrams for each lagrangian. The solutions differ even if all four external particles are put on the mass shell, which implies that observables calculated by solving the Bethe-Salpeter equation depend on the representation of the theory. We point out that this violation of the equivalence theorem has a simple explanation and should be expected for any Bethe-Salpeter equation with a tree-level kernel. Implications for dynamical models of hadronic interactions are discussed.

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arXiv2001

Compton scattering on the nucleon at intermediate energies and polarizabilities in a microscopic model

A microscopic calculation of Compton scattering on the nucleon is presented which encompasses the lowest energies -- yielding nucleon polarizabilities -- and extends to energies of the order of 600 MeV. We have used the covariant "Dressed K-Matrix Model" obeying the symmetry properties which are appropriate in the different energy regimes. In particular, crossing symmetry, gauge invariance and unitarity are satisfied. The extent of violation of analyticity (causality) is used as an expansion parameter.

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arXiv2000

Compton scattering in a unitary approach with causality constraints

Pion-loop corrections for Compton scattering are calculated in a novel approach based on the use of dispersion relations in a formalism obeying unitarity. The basic framework is presented, including an application to Compton scattering. In the approach the effects of the non-pole contribution arising from pion dressing are expressed in terms of (half-off-shell) form factors and the nucleon self-energy. These quantities are constructed through the application of dispersion integrals to the pole contribution of loop diagrams, the same as those included in the calculation of the amplitudes through a K-matrix formalism. The prescription of minimal substitution is used to restore gauge invariance. The resulting relativistic-covariant model combines constraints from unitarity, causality, and crossing symmetry.

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arXiv2000

Dressing the nucleon in a dispersion approach

We present a model for dressing the nucleon propagator and vertices. In the model the use of a K-matrix approach (unitarity) and dispersion relations (analyticity) are combined. The principal application of the model lies in pion-nucleon scattering where we discuss effects of the dressing on the phase shifts.

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arXiv1999

Non-perturbative model for the half-off-shell γN N vertex

Form factors in the nucleon-photon vertex with one off-shell nucleon are calculated by dressing the vertex with pion loops up to infinite order. Cutting rules and dispersion relations are implemented in the model. Using the prescription of minimal substitution we construct a γπN N vertex and show that it has to be included in the model in order that the Ward-Takahashi identity for the γN N vertex be fulfilled. The vertex is to be applied in a coupled-channel K-matrix formalism for Compton scattering, pion photoproduction and pion scattering. The form factors show a pronounced cusp structure at the pion threshold. As an illustration of a consistent application of the model, we calculate the cross section of Compton scattering. To provide gauge invariance in Compton scattering, a four-point γγN N contact term is constructed using minimal substitution.

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arXiv1998

Consistent off-shell $πN N$ vertex and nucleon self-energy

We present a consistent calculation of half-off-shell form factors in the pion-nucleon vertex and the nucleon self-energy. Numerical results are presented. Near the on-shell point the pion-nucleon vertex is dominated by the pseudovector coupling, while at large nucleon invariant masses we find a sizable pseudoscalar admixture.

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