The Relation between the Perturbative QCD Scale $\Lambda_s$ and Hadronic Masses from Light-Front Holography

TL;DR

This paper establishes a theoretical link between the perturbative QCD scale and hadronic masses using light-front holography, enabling predictions of hadron masses from the QCD scale and vice versa.

Contribution

It introduces a novel analytic relation connecting the QCD scale 1 to hadronic masses, utilizing light-front holography to bridge short- and large-distance QCD regimes.

Findings

Predicted 1 in 5 scheme agrees with experiments.

Derived analytic form of 1 at small Q^2.

Predicted light hadron masses from 1 value.

Abstract

QCD is well understood at short distances where perturbative calculations are feasible. Establishing an explicit analytic connection between the short-distance regime and the large-distance physics of quark confinement has been a long-sought goal. A major challenge is to relate the scale $\Lambda_{s}$ underlying the evolution of the QCD coupling in the perturbative regime to the masses of hadrons. We show here how new theoretical insights into the behavior of QCD at large distances leads to such a relation. The resulting prediction for $\Lambda_{s}$ in the $\overline{MS}$ scheme agrees well with experimental measurements. Conversely, the relation can be used to predict the masses of hadrons composed of light quarks with the measured value of $\Lambda_{s}$ as the sole parameter. We also use "light-front holography" to determine the analytic form of $\alpha_s(Q^2)$ at small $Q^2$.