Curve collapse for the isospin-2 pion scattering length from QCD with 3, 4, and 5 colors

TL;DR

This paper compares pion-pion scattering lengths across QCD theories with 3, 4, and 5 colors, confirming the expected 1/Nc scaling from large Nc arguments through lattice simulations.

Contribution

It provides the first comparative lattice study of the isospin-2 pion scattering length for different numbers of colors in QCD.

Findings

Scattering length scales as 1/Nc, consistent with theoretical predictions.

Lattice results support large Nc counting arguments.

Demonstrates the feasibility of simulating multiple Nc values in QCD.

Abstract

I show comparisons of the pion - pion scattering length in the isospin - two channel from simulations of of QCD with $N_c = 3$, 4 and 5 colors and $N_f = 2$ flavors of degenerate mass fermions. The scattering length varies as $1/N_c$, as expected from large $N_c$ counting arguments.