Effects of finite volume on the $K_L$-$K_S$ mass difference

Abstract

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher, and Lellouch and Lüscher, which determine the leading order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second order mixing of the $K^0$ and $\overline{K^0}$ states. We extend the methods of Kim, Sachrajda and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the $K_L$-$K_S$ mass difference $\Delta M_K$ and the CP violating parameter ${\epsilon }_K$ are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.

19 pages, 2 figures; v2: a typo in Eq. (27) corrected

References in corpus (1)

• $K_L-K_S$ mass difference from lattice QCD

Cited by in corpus (49)

• FLAG Review 2019
• FLAG Review 2021
• Scattering processes and resonances from lattice QCD
• A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
• From deep inelastic scattering to heavy-flavor semi-leptonic decays: Total rates into multi-hadron final states from lattice QCD
• FLAG Review 2024
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Double-$\beta$ Decay Matrix Elements from Lattice Quantum Chromodynamics
• The isotensor axial polarisability and lattice QCD input for nuclear double-$\beta$ decay phenomenology
• Exploratory Lattice QCD Study of the Rare Kaon Decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$
• The $\pi \gamma \to \pi \pi$ transition and the $\rho$ radiative decay width from lattice QCD
• The role of the Euclidean signature in lattice calculations of quasi-distributions and other non-local matrix elements
• Form factors of two-hadron states from a covariant finite-volume formalism
• The role of boundary conditions in quantum computations of scattering observables
• Finite-volume effects due to spatially non-local operators
• Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions
• Prospects for a lattice computation of rare kaon decay amplitudes II $K\to \pi \nu \bar{\nu }$ decays
• Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report
• Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays
• Anatomy of ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• The path from lattice QCD to the short-distance contribution to $0\nu \beta \beta$ decay with a light Majorana neutrino
• Light-Neutrino Exchange and Long-Distance Contributions to $0\nu 2\beta$ Decays: An Exploratory Study on $\pi \pi \to ee$
• Lattice QCD study of the rare kaon decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ at a near-physical pion mass
• Short-distance matrix elements for $D^0$-meson mixing for $N_f=2+1$ lattice QCD
• Opportunities for lattice QCD in quark and lepton flavor physics
• Consistency checks for two-body finite-volume matrix elements: II. Perturbative systems
• Exploratory lattice QCD study of the rare kaon decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$
• Finite-volume formalism in the $2\stackrel{H_I+H_I}{\to }2$ transition: an application to the lattice QCD calculation of double beta decays
• Lattice QCD Inputs for Nuclear Double Beta Decay
• Dual QCD Insight into BSM Hadronic Matrix Elements for $K^0-{\bar{K}}^0$ Mixing from Lattice QCD
• On-shell representations of two-body transition amplitudes: single external current
• Variations on the Maiani-Testa approach and the inverse problem
• Two-neutrino double-beta decay in pionless effective field theory from a Euclidean finite-volume correlation function
• Emerging lattice approach to the K-Unitarity Triangle
• Updated evaluation of ${\epsilon }_K$ in the Standard Model with lattice QCD inputs
• Finite-volume effects in long-distance processes with massless leptonic propagators
• Lattice QCD calculation of $K\to \ell {\nu }_{\ell }{\ell }^{\prime +}{\ell }^{\prime -}$ decay width
• Two-current transition amplitudes with two-body final states
• Radiative corrections to leptonic decays using infinite-volume reconstruction
• Prospects for a lattice calculation of the rare decay ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$
• Another SMEFT Story: $Z^{\prime }$ Facing New Results on ${\epsilon }^{\prime }/\epsilon$, $\Delta M_K$ and $K\to \pi \nu \bar{\nu }$
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• Effect of correlations on routing and modeling of Time Varying Communication Networks
• Progress on the exploratory calculation of the rare Hyperon decay ${\Sigma }^{+}\to p{\ell }^{+}{\ell }^{-}$
• Neutrinoless double-beta decay in a finite volume from relativistic effective field theory
• Calculation of the $K_L-K_S$ mass difference for physical quark masses
• Long-distance contributions to flavour-changing processes
• Results for the mass difference between the long- and short- lived K mesons for physical quark masses
• Kaon physics overview