Description of Heavy Quark $\overline{MS}$ Mass by Lippmann Schwinger Equation

TL;DR

This paper calculates the $ar{MS}$ masses of heavy quarks by solving the Lippmann-Schwinger equation with the Martin potential, fitting heavy quarkonium spectra, and extracting quark masses consistent with experimental data.

Contribution

It introduces a method to determine heavy quark $ar{MS}$ masses using the Lippmann-Schwinger equation and the Martin potential, providing results aligned with existing literature.

Findings

Mass spectra for $b\bar{b}$ and $c\bar{c}$ fit experimental data

Extracted heavy quark $ar{MS}$ masses agree with literature

Method avoids relativistic and spin corrections for spectra

Abstract

Quark masses are of great prominence in high-energy physics. In this paper, we have studied the heavy meson systems via solving the Lippmann-Schwinger equation by using the Martin potential for heavy quark masses. We have also attempted to use Martin potential to find an acceptable mass spectrum for heavy quarkonia. We obtained this spectrum via minimal phenomenological model (M. Melles, Phys. Rev. D \textbf{62}: 074019 2000). The mass spectra for $b\bar{b}$ and $c\bar{c}$ are calculated without taking into account the relativistic corrections and spin-dependent effects. The obtained mass spectra turn out to fit the experimental findings. By using the conventional spectrum, we extract the pole mass of heavy quarks and use it along with the relation between $\overline{MS}$ mass (modified minimal subtraction scheme) and the on-shell quark mass to find $\overline{MS}$ mass for these quarks. The obtained results for $\overline{MS}$ mass are in good agreement with corresponding values reported in the literature.