Emergence of the ρ resonance from the HAL QCD potential in lattice QCD

We investigate the I = 1 pi pi interaction using the HAL QCD method in lattice QCD. We employ the (2 + 1)-flavor gauge configurations on 32(3) x 64 lattice at the lattice spacing a approximate to 0.0907 fm and m(pi) approximate to 411 MeV, in which the rho meson appears as a resonance state. We find that all-to-all propagators necessary in this calculation can be obtained with reasonable precision by a combination of three techniques, the one-end trick, the sequential propagator, and the covariant approximation averaging (CAA). The nonlocal I = 1 pi pi tor potential is determined at the next-to-next-to-leading order ((NLO)-L-2) of the derivative expansion for the first time, and the resonance parameters of the p meson are extracted. The obtained rho meson mass is found to be consistent with the value in the literature, while the value of the coupling g(rho pi pi) turns out to be somewhat larger. The latter observation is most likely attributed to the lack of low-energy information in our lattice setup with the center-of-mass frame. Such a limitation may appear in other P-wave resonant systems and we discuss possible improvement in future. With this caution in mind, we positively conclude that we can reasonably extract the (NLO)-L-2 potential and resonance parameters even in the system requiring the all-to-all propagators in the HAL QCD method, which opens up new possibilities for the study of resonances in lattice QCD.