PoS - Proceedings of Science
Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Hadron Spectroscopy and Interactions
Three-pion effects in $K^0-\bar{K}^0$ mixing
A. Jackura*, R. Briceno and M. Hansen
Full text: pdf
Pre-published on: January 27, 2023
Published on: April 06, 2023
The rate of mixing between a neutral kaon and an anti-kaon ($K^0-\bar{K}^0$) is given, in part, by a long-range matrix element, defined with two insertions of the weak Hamiltonian separated by physical, Minkowski time evolution. For physical quark masses, the kaon mass lies above the two- and three-pion thresholds and, as a result, this long-range matrix element receives contributions from intermediate on-shell $2\pi$ and $3\pi$ states. These contributions cannot easily be captured in a finite Euclidean spacetime, meaning that such matrix elements are not directly accessible via lattice QCD. In this talk, we present a strategy for combining quantities that can be extracted in numerical lattice QCD calculations in order to reproduce the physical, infinite-volume long-range amplitude for $K^0-\bar{K}^0$. The key novelty relative to published work is that we fully include the effects of three-particle states that were previously neglected. The strategy is built on existing formalism for long-range matrix elements with two-particle intermediate states, together with the relativistic-field-theory finite-volume formalism for extracting three-hadron weak decays.
DOI: https://doi.org/10.22323/1.430.0062
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