Laplace Sum Rules in Quantum ChromoDynamics

TL;DR

This paper reviews the use of Laplace sum rules in QCD to determine fundamental parameters and hadron properties, illustrating with rho and pi meson examples.

Contribution

It provides a concise overview of Laplace sum rules applications in QCD, connecting them to other spectral sum rules and detailing specific meson cases.

Findings

Effective extraction of QCD parameters like $\alpha_s$ and condensates.

Determination of meson masses and decay constants.

Connections between Laplace sum rules and other spectral sum rules.

Abstract

We shortly review some applications of the (inverse) Laplace (LSR) transform sum rules in Quantum ChromoDynamics (QCD) for extracting the fundamental QCD parameters (coupling constant $\alpha_s$, quark and gluon condensates) and the hadron properties (masses and decay constants). Links of LSR to some other forms of QCD spectral sum rules are also discussed. As prototype examples, we discuss in detail the $\rho$ and $\pi$ meson sum rules.