Speaker
Description
We present a systematic study of the finite-volume spectrum of isospin-zero two-pion scattering using lattice QCD with physical quark masses and G-parity boundary conditions. This is a reanalysis of the data used for the 2020 RBC&UKQCD calculation of $\epsilon’$. Our main focus is the extraction of the ground-state energy, which is critical for computing the $I=0$ $K \to \pi \pi$ decay amplitude with physical kinematics, which combined with the $I=2$ amplitude gives $\epsilon’$, a measure of the Standard Model direct CP-violation in the kaon system. Our analysis employs the generalized eigenvalue problem to isolate finite-volume energy levels using 3 and 2 operators. We further compare the standard GEVP approach with a “rebased” GEVP procedure. Obtaining precise and robust results for this system is challenging because of noisy disconnected diagrams, nearby excited-state contamination, the rapid decay of the signal-to-noise ratio and fit choices. Our results provide a systematic assessment of these methodologies and challenges.