Internal States of Hadrons in Relativistic Reference Frames

Authors

  • N. O. Chudak Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • K. K. Merkotan Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • D. A. Ptashynskyy Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • O. S. Potiyenko Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • M. A. Deliyergiyev Institute of Modern Physics, Department of High Energy Nuclear Physics
  • A. V. Tikhonov Universit´e de Gen´eve, D´epartement de Physique Nucl´eaire et Corpusculaire
  • G. O. Sokhrannyi Jozef Stefan Institute, Department of Experimental Particle Physics
  • O. V. Zharova Odesa National Polytechnic University, Chair of Higher Mathematics and Modeling Systems
  • O. D. Berezovs’kyi Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • V. V. Voitenko Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • Yu. V. Volkotrub Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • I. V. Sharph Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics
  • V. D. Rusov Odesa National Polytechnic University, Chair of Theoretical and Experimental Nuclear Physics

DOI:

https://doi.org/10.15407/ujpe61.12.1033

Keywords:

hadrons, reference frame, bound states of quarks, hadron scattering, state transformation

Abstract

The internal state of an aggregate of a few bound particles and its transformation, when changing from the reference frame, where this combined particle is at rest, to a reference frame, where it moves relativistically, have been considered. It is supposed that the internal state of the combined particle in its rest frame can be considered in the non-relativistic approximation. This internal state is shown to remain the same, when changing from one inertial reference frame to another one. In other words, a particle that is spherically symmetric in its rest frame does not change its form in any other reference frame and does not undergo the Lorentz contraction in the direction of motion of any reference frame with respect to the rest one. A possible application of the results obtained to describe the scattering of hadrons considered as bound states of quarks has been discussed.

References

I.V. Sharf, A.V. Tikhonov, G.O. Sokhrannyi, K.V. Yatkin, M.A. Deliyergiev et al. Description of hadron inelastic scattering by the Laplace method and new mechanisms of cross-section growth. Ukr. Fiz. Zh. 56, 1151 (2011). 1046 ISSN 2071-0194. Ukr. J. Phys. 2016. Vol. 61, No. 12 Internal States of Hadrons in Relativistic Reference Frames

I. Sharph, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan et al. On the role of longitudinal momenta in high energy hadron-hadron scattering. Central Eur. J. Phys. 10, 858 (2012) https://doi.org/10.2478/s11534-012-0056-5

I.V. Sharph et al. The new method of interference contributions accounting for inelastic scattering diagrams. arXiv: 1509.04329 (2015).

I.V. Sharf, K.K. Merkotan, N.A. Podolyan, D.A. Ptashynskyy, A.V. Tykhonov et al. Gluon loops in the inelastic processes in QCD. arXiv:1210.3490 (2012).

Yu.V. Volkotrub et al. Multiparticle field operators in quantum field theory. arXiv:1510.01937 (2015).

N. Chudak, M. Deliyergiyev, K. Merkotan, O. Potiyenko, D. Ptashynskyi, Y. Shabatura, G. Sokhrannyi, A. Tykhonov, Y. Volkotrub, I. Sharph, V. Rusov. Multiparticle quantum fields. Phys. J. 2, 181 (2016) [http://www.aiscience.org/journal/pj

R.P. Feynman. Photon-Hadron Interactions (Benjamin, 1972).

M. Diehl, D. Ostermeier, A. Schafer. Elements of a theory for multiparton interactions in QCD. J. High Energy Phys. 1203, 089 (2012) https://doi.org/10.1007/JHEP03(2012)089

M. Strikman. Transverse structure of the nucleon and multiparton interactions. Prog. Theor. Phys. Suppl. 187, 289 (2011). https://doi.org/10.1143/PTPS.187.289

A.P. Kobushkin, V.P. Shelest. Relativistic equations for bound quark systems. Teor. Mat. Fiz. 31, 156 (1977).

R.N Faustov. Relativistic wavefunction and form factors of the bound system. Ann. Phys. 78, 176 (1973) https://doi.org/10.1016/0003-4916(73)90007-9

E.E. Salpeter, H.A. Bethe. A Relativistic equation for bound state problems. Phys. Rev. 84, 1232 (1951) https://doi.org/10.1103/PhysRev.84.1232

A.A. Logunov, A.N. Tavkhelidze. Quasi-optical approach in quantum field theory. Nuovo Cimento 29, 380 (1963) https://doi.org/10.1007/BF02750359

S.J. Brodsky, H.-C. Pauli, S.S. Pinsky. Quantum chromodynamics and other field theories on the light cone. Phys. Rept. 301, 299 (1998) https://doi.org/10.1016/S0370-1573(97)00089-6

T. Heinzl. Light Cone Dynamics of Particles and Fields. PhD thesis (Regensburg Univ., 1998) [http://alice.cern.ch/format/showfull?sysnb=0300475

M.V. Terent’ev. On the structure of wave functions of mesons as bound quark states. Yad. Fiz. 24, 207 (1976).

P.A.M. Dirac. Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392 (1949) https://doi.org/10.1103/RevModPhys.21.392

N.N. Bogoliubov, D.V. Shirkov. Introduction to the Theory of Quantized Fields (Wiley, 1980).

F.A. Berezin. The Method of Second Quantization (Academic Prfess, 1966).

M.A. Deliyergiyev, A.G. Kotanzhyan, K.K. Merkotan, N.O. Podolian, O.S. Potiyenko et al. Transformation of the nonrelativistic quantum system under transition from one inertial reference frame to another. arXiv:1307.2280v5 (2013).

I.M. Gelfand, G.E. Shilov Generalized Functions (Academic Press, 1964–1968).

V.A. Karmanov. Relativistic composite systems in the light front dynamics. Fiz. Elem. Chast. At. Yadra 19, 525 (1988) (in Russian).

L.H. Ryder, Quantum Field Theory (Cambridge Univ. Press, 1985).

Xiangdong Ji. Generalized parton distributions. Ann. Rev. Nucl. Part. Sci. 54, 413 (2004) https://doi.org/10.1146/annurev.nucl.54.070103.181302

C. Alexandrou, C.N. Papanicolas, M. Vanderhaeghen. Colloquium: The shape of hadrons. Rev. Mod. Phys. 84, 1231 (2012) https://doi.org/10.1103/RevModPhys.84.1231

I.M. Dremin. Elastic scattering of hadrons. Usp. Fiz. Nauk 183, 3 (2013) https://doi.org/10.3367/ UFNr.0183.201301a.0003

R. Conceicao, J. Dias de Deus, M. Pimenta. Proton–proton cross-sections: The interplay between density and radius. Nucl. Phys. A 888, 58 (2012) https://doi.org/10.1016/j.nuclphysa.2012.02.019

I.V. Sharph et al. The state of nonrelativistic quantum system in a relativistic reference frame. arXiv:1403.3114 [hep-ph] (2014).

A.A. Duviryak. Application of two-particle Dirac equation in meson spectroscopy. Zh. Fiz. Dosl. 10, 290 (2006).

UJP 2016 V610 #12uk

Downloads

Published

2016-12-15

Issue

Vol. 61 No. 12 (2016)

Section

Fields and elementary particles

License

Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine

The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:

1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.

2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.

3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.

4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.

5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.

6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.

How to Cite

Internal States of Hadrons in Relativistic Reference Frames. (2016). Ukrainian Journal of Physics, 61(12), 1033. https://doi.org/10.15407/ujpe61.12.1033

Most read articles by the same author(s)