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Emergence of the rho resonance from the HAL QCD potential

In this article, we report the ρ resonance study using the HAL QCD method. We calculate the I = 1 ππ potential at mπ ≈ 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 nonlocal I = 1 ππ potential at the next-to-next-to-leading order (N2LO) of the derivative expansion for the first time and obtain the pole of the S-matrix corresponding to the ρ resonance. We also discuss the comparison between our result and a previous calculation, done by Lüscher’s method.