Emergence of the rho resonance from the HAL QCD potential

TL;DR

This paper uses the HAL QCD method to study the rho resonance by calculating the pi-pi potential at a specific pion mass, determining the resonance pole, and comparing results with Lüscher's method.

Contribution

First to determine the non-local I=1 pi-pi potential at N2LO of the derivative expansion using HAL QCD for rho resonance analysis.

Findings

Successfully obtained the rho resonance pole from the HAL QCD potential.

Determined the non-local I=1 pi-pi potential at N2LO.

Compared results with previous Lüscher's method calculations.

Abstract

In this article, we report the $\rho$ resonance study using the HAL QCD method. We calculate the $I=1$ $\pi \pi$ potential at $m_{\pi} \approx 0.41$ GeV by a combination of the one-end trick, sequential propagator and covariant approximation averaging (CAA). Thanks to those techniques, we determine the non-local $I=1$ $\pi \pi$ potential at the next-to-next-to-leading order (N$^2$LO) of the derivative expansion for the first time and obtain the pole of the S-matrix corresponding to the $\rho$ resonance. We also discuss the comparison between our result and a previous calculation, done by L\"uscher's method.