Lattice determination of $I=0$ and 2 $\pi \pi$ scattering phase shifts with a physical pion mass

Abstract

Phase shifts for $s$-wave $\pi \pi$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\to \pi \pi$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calculation \cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $\pi \pi$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $\pi \pi$ interpolating operators including a scalar bilinear "$\sigma$" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

v3: Add a subsection "Higher partial wave correction", and correct the unit of scattering length. 88 pages and 14 figures v2: 1). Add reference 29 as an example of pipi scattering calculation above 4mpi threshold. 2). Modify the wording on page 3 for the footage. 3). Correct the σoperator on page 17

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Cited by in corpus (6)

• FLAG Review 2021
• 50 Years of Quantum Chromodynamics
• FLAG Review 2024
• Quark mass dependence of $\pi \pi$ scattering in isospin 0, 1, and 2 from lattice QCD
• Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions