$\pi\pi$ scattering at Large $N_\text{c}$

TL;DR

This paper investigates how pion-pion scattering amplitudes scale with large N_c in a four-flavor QCD setting, comparing lattice regularizations and matching to chiral perturbation theory to understand low-energy couplings.

Contribution

It provides the first detailed lattice study of N_c scaling in pion-pion scattering for N_f=4, including discretization effects and chiral perturbation theory matching.

Findings

Significant discretization effects observed in the AA channel.

Results consistent with theoretical N_c scaling expectations.

Constraints on low-energy couplings from chiral perturbation theory matching.

Abstract

We study the Large $N_\text{c}$ scaling of pion-pion scattering amplitudes for $N_\text{f}=4$ degenerate quark flavors. We focus on the standard isospin-2 channel and the adjoint-antisymmetric (AA) representation. The latter only exists for $N_\text{f}\geq 4$ and a representative state is $\frac{1}{\sqrt{2}}(|D_s^+\pi^+\rangle-|D^+ K^+\rangle)$. We compare the results obtained for two regularizations (Wilson and twisted-mass fermions) and three values of the lattice spacing, and observe significant discretization effects in the AA channel. Finally, we match our results to NLO SU(4) and NNLO U(4) Chiral Perturbation Theory and constrain the $N_\text{c}$ scaling of the relevant low-energy couplings.