Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

On nonperturbative and relativistic corrections to the highly resonant hadronic bound states

Document Type : Original Article

Author
Arezu Jahanshir
1-Department of Physics and Engineering Sciences, Buein Zahra Technical University, Iran, 2- Department of Physics, Kazakh National University, Kazakhstan
10.30511/ttmp.2025.2065578.1059
Abstract
In this article, we suggest a method for calculating the mass spectrum of a bound state with relativistic corrections. In standard calculations of mass spectra that consider the nonperturbative nature of interactions, researchers typically consider only the lowest-order term in v/c, the ratio of a particle’s velocity inside the bound state to the speed of light. Using a theoretical framework based on specific mathematical techniques, we go beyond the lowest-order term in v/c approximation and define the structure of relativistic nonperturbative interaction potential by summing an infinite series in powers of v/c. Furthermore, we introduce and characterize a relativistic mass correction formulated through the current-current correlated tensor associated with two charged scalar particles in an external gauge field, where the fields obey Gaussian statistics. This two-point correlation function describes the correlation of polarization function components of the current across different spacetime points in a 4D Euclidean spacetime coordinate frame. Under relativistic conditions, this correlation structure contributes to the formation of bound states, which provide a basis for defining the constituent or relativistic mass of the particle in the bound state. Our analysis is carried out within the frameworks of quantum field theory and quantum mechanics.
Keywords
Bottomonium
Gaussian gauge field
Green&rsquo
s function
Path integral
Polarization function
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Transactions in Theoretical and Mathematical Physics
Volume 2, Issue 3
Summer 2025
Pages 148-159

  • Receive Date 12 July 2025
  • Accept Date 28 August 2025
  • First Publish Date 28 August 2025
  • Publish Date 01 August 2025