Cornell Interaction in the Two-body Pauli-Schr\"odinger-type Equation Framework: The Symplectic Quantum Mechanics Formalism

TL;DR

This paper explores the quantum behavior of quark-antiquark systems under magnetic fields using symplectic quantum mechanics, revealing enhanced non-classicality and confinement effects, with implications for heavy-ion collision experiments.

Contribution

It introduces a symplectic formulation approach to analyze quark-antiquark bound states in magnetic fields, incorporating phase space methods and Bohlin mapping.

Findings

Magnetic field increases non-classicality of the Wigner function.

Confinement observed in phase space structure.

Estimated magnetic field strength aligns with heavy-ion collision data.

Abstract

We investigate the quantum behavior of a quark-antiquark bound system under the influence of a magnetic field within the symplectic formulation of quantum mechanics. Employing a perturbative approach, we obtain the ground and first excited states of the system described by the Cornell potential, which incorporates both confining and non-confining interactions. After performing a Bohlin mapping in phase space, we solve the time-independent symplectic Pauli-Schr\"odinger-type equation and determine the corresponding Wigner function. Special attention is given to the observation of the confinement of the quark-antiquark, that is revealed in the phase space structure. Due to the presence of spin in the Hamiltonian, the results reveal that the magnetic field enhances the non-classicality of the Wigner function, signaling stronger quantum interference and a departure from classical behavior. The experimental mass spectra is used to estimate the intensity of the external field, leading to a value that is in order of the transient magnetic field measured in non-central heavy-ion collisions at RHIC and LHC.