Abstract
We investigate the $I=1$ $\ensuremath{\pi}\ensuremath{\pi}$ interaction using the HAL QCD method in lattice QCD. We employ the ($2+1$)-flavor gauge configurations on ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice at the lattice spacing $a\ensuremath{\approx}0.0907\text{ }\text{ }\mathrm{fm}$ and ${m}_{\ensuremath{\pi}}\ensuremath{\approx}411\text{ }\text{ }\mathrm{MeV}$, in which the $\ensuremath{\rho}$ 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 $I=1$ $\ensuremath{\pi}\ensuremath{\pi}$ potential is determined at the next-to-next-to-leading order (${\mathrm{N}}^{2}\mathrm{LO}$) of the derivative expansion for the first time, and the resonance parameters of the $\ensuremath{\rho}$ meson are extracted. The obtained $\ensuremath{\rho}$ meson mass is found to be consistent with the value in the literature, while the value of the coupling ${g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}$ 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 ${\mathrm{N}}^{2}\mathrm{LO}$ 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.
Highlights
Understanding the hadronic resonances from the firstprinciple lattice QCD simulation is one of the most important subjects in particle and nuclear physics
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)
We successfully determine the potential in this channel at the N2LO of the derivative expansion for the first time and calculate the resonance parameters of the ρ meson
Summary
Understanding the hadronic resonances from the firstprinciple lattice QCD simulation is one of the most important subjects in particle and nuclear physics. The HAL QCD method directly constructs inter-hadron potentials from spatial and temporal correlation functions calculated in lattice QCD. There exists, a practical challenge in the HAL QCD method when expanding the scope to many other resonances, since the expensive computations of all-to-all quark propagators are necessary in most cases To overcome this difficulty, we have previously explored two different all-to-all techniques, the LapH method [24] and the hybrid method [25]. We have previously explored two different all-to-all techniques, the LapH method [24] and the hybrid method [25] It turned out [26,27] that the LapH smearing on sink operators with a small number of LapH vectors enhances nonlocality of the HAL QCD potential and the systematic errors associated with the truncation of the derivative expansion. Some details on the N2LO analysis, namely the assumption in the potential fit and behavior of our N2LO potential in terms of energy-dependent local manner, are given in Appendix D and E
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
