The quark mass dependence of the pion mass at infinite N

TL;DR

This paper explores how the pion mass depends on quark mass in planar QCD, revealing a quadratic relation derived from a one-dimensional Schrödinger problem that aligns with four-dimensional numerical data.

Contribution

It introduces a novel quadratic relation for pion mass dependence on quark mass derived from a nonlocal eigenvalue equation in two-dimensional planar QCD.

Findings

Quadratic relation for pion mass and quark mass in 2D QCD

Compatibility of the 2D model with 4D numerical data

Reconstruction of nonlocal eigenvalue structure from the quadratic relation

Abstract

In planar QCD, in two space time dimensions, the meson eigenvalue equation has a nonlocal structure interpretable as resulting from hidden degrees of freedom. The nonlocality can be reconstructed from the functional form of the pion mass dependence on quark mass within an expansion starting from a special one dimensional Schroedinger problem. The one dimensional problem makes the pion mass depend on the quark mass through a simple quadratic relation which is shown to be compatible also with numerical data obtained in four dimensions.