Emergence of the rho resonance from the HAL QCD potential

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 Lüscher's method.

Comments: 9 pages, 4 figures, talk presented at the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26th-30th July 2021, Zoom/Gather@Massachusetts Institute of Technology, United States