Petr Zavada | Searcharxiv

arXiv2023

Kinematics of the Milky way from the statistical analysis of the Gaia Data Release 3

The aim of the analysis of data from the Gaia Space Observatory is to obtain kinematic parameters of the collective motion of stars in a part of our galaxy. This research is based on a statistical analysis of the motion of {$55,038,539$} stars selected in different directions from the Sun up to a distance of 3--6 kpc. We developed statistical methods for the analysis working with input data represented by the full astrometric solution (five parameters). Using the proposed statistical methods, we obtained the local velocity of the Sun $\left( U_{\odot}% ,V_{\odot},W_{\odot}\right) =(9.58,16.25,7.33)\pm(0.05,0.04,0.02)_{stat}% \pm(0.7,0.9,0.1)_{syst}$ km/s and the rotation velocity of the galaxy at different radii. For the Sun's orbit radius, we obtained the velocity of the galaxy rotation$\ V_{c}\approx234\pm4$ km/s. Collective rotation slows down in the region under study linearly with distance from the disk plane: $\Delta V/\Delta Z\cong33.5~\mathrm{km\,s}^{-1}\mathrm{kpc}^{-1}$. We showed that the different kinematic characteristics and distributions, which depend on the position in the galaxy, can be well described in the studied 3D region by a simple Monte Carlo simulation model, representing an axisymmetric approximation of the galaxy kinematics. The optimal values of the six free parameters were tuned by comparison with the data.

astro-ph.GA↗

arXiv2021

Catalogue of wide binary, trinary and quaternary candidates from the Gaia data release 2 (region $\left\vert b\right\vert >25\,°$)

The occurrence of multiple stars, dominantly binaries, is studied using the \textit{Gaia}-ESA DR2 catalogue. We apply the optimized statistical method that we previously developed for the analysis of 2D patterns. The field of stars is divided into a mosaic of small pieces, which represent a statistical set for analysis. Specifically, data input is represented by a grid of circles (events) with radius $0.02\,°$ covering the sky in the field of galactic latitude $\left\vert b\right\vert >25\,°$. The criteria for selecting candidates for multiple stars are based on two parameters: angular separation and collinearity of proper motion. Radial separation, due to limited accuracy, is used only as a weaker supplementary constraint. Due attention is paid to the accurate calculation of the background, which is a necessary input for evaluating the quality of the candidates. Our selection algorithm generates the catalogue of candidates: $900,842$ binaries, $5,282$ trinaries and $30$ quaternaries.

astro-ph.GA↗

arXiv2020

Spin structure of hadrons and minimum energy of bound systems

The spin of a composite particle, like a nucleus or a hadron, is generated by the composition of angular moments (consisting of spins and orbital angular moments) of the constituents. The composition of two angular moments is done by the standard way with the use of Clebsch-Gordan coefficients. However, if there are more than two constituents, the composition must be done in a hierarchical way, which admits more ways leading to the same resulting spin state |J, J_{z}>. Different composition patterns can generate states with the same spin quantum numbers, but which may vary in the contributions of different kinds of the constituents. We will discuss which composition patterns could be preferred in the hadrons from the viewpoint of minimal energy of the bound system. In this context, particular attention is paid to the role of gluons or quark orbital angular momentum in the proton spin.

hep-ph↗

arXiv2019

Statistical analysis of binary stars from the Gaia catalogue DR2

We have developed a general statistical procedure for analysis of 2D and 3D finite patterns, which is applied to the data from recently released Gaia-ESA catalogue DR2. The 2D analysis clearly confirms our former results on the presence of binaries in the former DR1 catalogue. Our main objective is the statistical 3D analysis of DR2. For this, it is essential that the DR2 catalogue includes parallaxes and data on the proper motion. The analysis allows us to determine for each pair of stars the probability that it is the binary star. This probability is represented by the function \b{eta}(Δ) depending on the separation. Further, a combined analysis of the separation with proper motion provides a clear picture of binaries with two components of the motion: parallel and orbital. The result of this analysis is an estimate of the average orbital period and mass of the binary system. The catalogue we have created involves 80560 binary candidates.

astro-ph.IM↗

arXiv2018

A statistical analysis of two-dimensional patterns and its application to astrometry

Here we develop a general statistical procedure for the analysis of finite two-dimensional (2D) patterns inspired by the analysis of heavy-ion data. The method is used in the study of publicly available data obtained by the Gaia-ESA mission. We prove that the procedure can be sensitive to the limits of accuracy of measurement, and can also clearly identify the real physical effects on the large background of random distributions. As an example, the method confirms the presence of binary and ternary star systems in the studied data. At the same time, the possibility of the statistical detection of the gravitational microlensing effect is discussed.

astro-ph.IM↗

arXiv2015

Role of gluons and the quark sea in the proton spin

The real, interacting elementary particle always consits of a 'bare' particle and a cloud of virtual particles mediating a self-interaction and/or the bond inside a composite object. In this letter we discuss the question of spin content of the virtual cloud in two different cases: electron and quark. Further, the quark spin is discussed in the context of proton spin, which is generated by the interplay of quarks and virtual gluons. We present a general constraint on the gluon contribution and make a comparison with the experimental data.

hep-ph↗

arXiv2014

On the role of quark orbital angular momentum in the proton spin

We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark spins and orbital angular momenta, which collectively contribute to the proton spin. The spin structure functions $g_{1}$ and $g_{2}$ corresponding to the many-quark state $J=1/2$ are studied and it is shown they satisfy constraints and relations well compatible with the available experimental data including proton spin content $ΔΣ\lesssim1/3$. The suggested Lorentz invariant 3D approach for calculation of the structure functions is compared with the approach based on the conventional collinear parton model.

hep-ph↗

arXiv2014

Spin-orbital composition in relativistic many-fermion systems

The interplay of spins and orbital angular moments of the fermions play an important role for the structure of the many-fermion systems like atoms, nuclei, nucleons (baryons) or mesons. We start our study from the one-fermion eigenstates of angular momentum represented by the spinor spherical harmonics. Afterwards we study the properties of many-fermion states resulting from a multiple angular momentum composition of the one-fermion states, giving the total angular momentum $J=\left\langle L\right\rangle+ \left\langle S\right\rangle $, which is identified with the spin of the composite particle. We demonstrate how the composition rules affect the relativistic interplay between the sums of the spins $\left\langle S\right\rangle $ and orbital angular moments $\left\langle L\right\rangle $ of the constituents, which collectively generate the spin of composite particle. It is suggested that in a relativistic case, when the masses of the constituent fermions are much less than their energy (in the rest frame of the composite particle), then the spin of the composite particle is dominated by the orbital angular moments $\left\langle L\right\rangle $ of the constituents, while $\left\vert \left\langle \mathbb{S}\right\rangle \right\vert \leq$ $J/3$. A special attention is paid to the case $J=1/2$ that is related to the spin of proton generated by the composition of spins and orbital angular moments of the quarks.

hep-ph↗

arXiv2013

Proton spin in leading order of the covariant approach

We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark spins and orbital angular momenta, which collectively contribute to the proton spin. The spin structure functions $g_{1}$ and $g_{2}$ corresponding to the many-quark state $J=1/2$ are studied and it is shown they satisfy constraints and relations well compatible with the available experimental data including proton spin content $ΔΣ\lesssim1/3$. The suggested Lorentz invariant 3D approach for calculation of the structure functions is compared with the approach based on the conventional collinear parton model.

hep-ph↗

arXiv2012

Kinematics of deep inelastic scattering in leading order of the covariant approach

We study the kinematics of deep inelastic scattering corresponding to the rotationally symmetric distribution of quark momenta in the nucleon rest frame. It is shown that rotational symmetry together with Lorentz invariance can in leading order impose constraints on the quark intrinsic momenta. Obtained constraints are discussed and compared with the available experimental data.

hep-ph↗

arXiv2011

Generalized Cahn effect and parton 3D motion in a covariant approach

The Cahn effect and the unintegrated unpolarized parton distribution function $f_{1}^{q}(x,\mathbf{p}_{T})$ are studied in a covariant approach. The Cahn effect is compared with some other effects due to the parton intrinsic motion. The comparison suggests that the present understanding of parton transverse momenta and intrinsic motion in general is still rather incomplete. The new relation for $f_{1}^{q}(x,\mathbf{p}_{T})$ is obtained in the framework of the covariant parton model from which a prediction for this distribution function follows.

hep-ph↗

arXiv2007

Parton distribution functions and quark orbital motion

Covariant version of the quark-parton model is studied. Dependence of the structure functions and parton distributions on the 3D quark intrinsic motion is discussed. The important role of the quark orbital momentum, which is a particular case of intrinsic motion, appears as a direct consequence of the covariant description. Effect of orbital motion is substantial especially for polarized structure functions. At the same time, the procedure for obtaining the quark momentum distributions of polarized quarks from the combination of polarized and unpolarized structure functions is suggested.

hep-ph↗

arXiv2007

Proton structure functions and quark orbital motion

Covariant version of the quark-parton model is studied. Dependence of the structure functions on the 3D quark intrinsic motion is discussed. The important role of the quark orbital momentum, which is a particular case of intrinsic motion, appears as a direct consequence of the covariant description. Effect of orbital motion is substantial especially for polarized structure functions. At the same time, the procedure for obtaining the quark momentum distribution from the structure functions is suggested.

hep-ph↗

arXiv2005

Spin of the proton and orbital motion of quarks

Effect of the quark intrinsic motion on the proton spin structure functions is demonstrated. It is shown, that the covariant version of the quark-parton model taking into account the orbital motion gives the consistent picture of the proton spin structure, which is based on the valence quarks. This picture is supported by the recent data, which indicate, that the spin contributions from the sea quarks and gluons are compatible with zero.

hep-ph↗

arXiv2004

Proton transversity and intrinsic motion of the quarks

The spin structure of the system of quasifree fermions having total angular momentum $J=1/2$ is studied in a consistently covariant approach. Within this model the relations between the spin functions are obtained. Their particular cases are the sum rules Wanzura - Wilczek, Efremov - Leader - Teryaev, Burkhardt - Cottingham and also the expression for the Wanzura - Wilczek twist 2 term $g_{2}^{WW}$. With the use of the proton valence quark distributions as an input, the corresponding spin functions including transversity are obtained.

hep-ph↗

arXiv2004

Proton spin structure and intrinsic motion of the constituents

The spin structure of the system of quasifree fermions having total angular momentum $J=1/2$ is studied in a consistently covariant approach. Within this model the relations between the spin functions are obtained. Their particular cases are the sum rules Wanzura - Wilczek, Efremov - Leader - Teryaev, Burkhardt - Cottingham and also the expression for the Wanzura - Wilczek twist 2 term $g_{2}^{WW}$. With the use of the proton valence quark distributions as an input, the corresponding spin functions are obtained. The resulting structure functions $g_{1}$ and $g_{2}$ are well compatible with the experimental data. Comparison with the basic formulas following from the standard quark-parton model reveals the importance of the quark intrinsic motion inside the target for the correct evaluation of the spin structure functions.

hep-ph↗

arXiv2004

Transversity and intrinsic motion of the constituents

The probabilistic model of parton distributions, previously developed by one of the authors, is generalized to include the transversity distribution. When interference effects are attributed to quark level only, the intrinsic quark motion produces the transversity, which is about twice as large as the usual polarized distribution. The applicability of such a picture is considered and possible corrections, accounting for interference effects at the parton-hadron transition stage are discussed.

hep-ph↗

arXiv2002

Proton spin structure and valence quarks

The spin structure of the system of quasifree fermions having total angular momentum $J=1/2$ is studied in a consistently covariant approach. Within this model the relations between the spin functions are obtained. Their particular cases are the sum rules Wanzura - Wilczek, Efremov - Leader - Teryaev, Burkhardt - Cottingham and also the expression for the Wanzura - Wilczek twist 2 term $g_{2}^{WW}$. With the use of the proton valence quark distributions as an input, the corresponding spin functions are obtained. The resulting structure functions $g_{1}$ and $g_{2}$ are well compatible with the experimental data.

hep-ph↗