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

Abstract

We investigate the I = 1 ππ interaction using the HAL QCD method in lattice QCD. We employ the (2+1)-flavor gauge configurations on 32 3 × 64 lattice at the lattice spacing a ≈ 0.0907 fm and m π ≈ 411 MeV, in which the ρ meson appears as a resonance state. We find that allto-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 non-local I = 1 ππ potential is determined at the nextto-next-to-leading order (N 2 LO) of the derivative expansion for the first time, and the resonance parameters of the ρ meson are extracted. The obtained ρ meson mass is found to be consistent with the value in the literature, while the value of the coupling g ρππ 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 N 2 LO 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.

HAL QCD potentials with non-zero total momentum and an application to the $I=2$ $\pi\pi$ scattering

“…The HAL QCD method works well, in particular for two baryon interactions (see [8] and references therein), thanks to the time-dependent method [7] and multi-channel extension [9]. Recently, resonances such as the ρ meson have been investigated in the HAL QCD method, by various improvements for all-to-all propagators [10][11][12][13][14]. If we extend the HAL QCD method to systems having the same quantum numbers of the QCD vacuum such as the σ meson, a serious obstruction appears.…”