vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2021-57-1-46-63vestifm-567Research ArticleФИЗИКАPHYSICSМезонные резонансы в релятивистской кварковой моделиМeson resonances in the relativistic quark modelСергеенкоМ. Н.SergeenkoМ. N.

Сергеенко Михаил Николаевич – доктор физико- математических наук

ул. Советская, 104, 246019, г. Гомель

Mikhail N. Sergeenko – Dr. Sc. (Physics and Mathematics)

104, Sovetskaya Str., 246019, Gomel

msergeen@mail.ruГомельский государственный университет им. Ф. СкориныFrancisk Skorina Gomel State University2021010420215714663Copyright © Сергеенко М.Н., 20212021Сергеенко М.Н.Sergeenko М.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/567

Релятивистская кварковая модель развивается для изучения мезонов и резонансов как квази-связанных состояний кварков. Анализируется классический аналог бесспинового уравнения Солпитера. Показано, что потенциал для консервативной изолированной системы двух частиц является лоренц-скалярной функцией расстояния между кварками и может быть включен в массу частиц, что приводит к координатно-зависимой массе кварков. Потенциал типа воронки модифицируется с учетом зависимости постоянной сильной связи αS от расстояния. Развивается концепция свободного движения частиц в связанном состоянии. Задача на собственные значения связанного состояния определяется релятивистским квазиклассическим волновым уравнением для скалярного потенциала. Получены два точных асимптотических решения этого уравнения для кулоновской и линейной частей потенциала в аналитическом виде; на этой основе записана комплексная массовая формула для мезонов и резонансов. Эффективность модели демонстрируется в сравнении результатов расчетов с данными для масс ρ и D мезонов.

In this paper, the relativistic quark model is developed for the study of mesons and resonances as quasi-bound quark states. A classic analogue of the spinless Salpeter equation is analyzed. It is shown that the potential for a conservative isolated two-particle system is the Lorentz-scalar function of the distance between quarks and can be included into the particle mass, which leads to the position-dependent quark mass. The funnel-type potential is modified with taking into account the dependence of the strong coupling αS on the distance. The concept of free motion of particles in a bound state is developed. The eigenvalue problem for the bound state is defined by the relativistic quasiclassical wave equation for the scalar potential. Two exact asymptotic solutions of the equation for the Coulomb and linear parts of the potential are obtained analytically; on this basis, the complex-mass formula for mesons and resonances is written. The efficiency of the model is demonstrated by comparison of the calculation results with the data for the masses of ρ and D mesons. 

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The authors declare that there are no conflicts of interest present.