On the Mass Difference between pion and rho meson using a Relativistic Two-Body Model

TL;DR

This paper uses a relativistic two-body Dirac equation approach with a modified Richardson potential to explain the significant mass difference between pion and rho mesons, highlighting the role of spin-dependent interactions.

Contribution

It applies a relativistic constraint dynamics framework to quark-antiquark systems, providing a detailed explanation of the pion-rho mass difference through spin interactions.

Findings

Cancellation of Darwin and spin-spin terms in pion mass

Wave functions are non-singular at short distances

Relativistic approach captures spin-dependent effects accurately

Abstract

The big mass difference between the pion and rho meson possibly originates from the spin-dependent nature of the interactions in the two states since these two states are similar except for spin. Both pi and rho are quark-antiquark systems which can be treated using the two-body Dirac equations (TBDE) of constraint dynamics. This relativistic approach for two-body system has the advantage over the non-relativistic treatment in the sense that the spin-dependent nature is automatically coming out from the formalism. We employed Dirac's relativistic constraint dynamics to describe quark-antiquark systems. Within this formalism, the 16-component Dirac equation is reduced to the 4-component 2nd-order differential equation and the radial part of this equation is simply a Schroedinger-type equation with various terms calculated from the basic radial potential. We used a modified Richardson potential for quark-antiquark systems which satisfies the conditions of confinement and asymptotic freedom. We obtained the wave functions for these two mesons which are not singular at short distances. We also found that the cancellation between the Darwin and spin-spin interaction terms occurs in the pi mass but not in the rho mass and this is the main source of the big difference in the two meson masses.