Einstein-Podolsky-Rosen State of Neutral Mesons: The Entangled Partner of K_L Is Not K_S

TL;DR

This paper clarifies the quantum state projections of entangled neutral kaons in EPR pairs, revealing that the partner of a detected $K_L$ is orthogonal to $K_L$, which impacts the interpretation of experimental parameters and symmetry violations.

Contribution

It corrects the understanding of entangled kaon states in EPR pairs, affecting the analysis of symmetry violations in kaon experiments.

Findings

The partner of a detected $K_L$ is orthogonal to $K_L$, not $K_S$.

Re-tagging alters the values of parameters related to CPT and Lorentz violation.

Implications for interpreting semileptonic charge asymmetries in kaon experiments.

Abstract

In a $\phi$ factory, neutral kaons are produced in Einstein-Podolsky-Rosen (EPR) states, furthermore, a $K_S$ is tagged if its entangled partner is detected as $K_L$, and vice versa. Here we point out that upon its detection as $K_L$, one of the EPR-entangled particles is projected into one of the orthogonal basis states, consequently the other particle should be projected to the state orthogonal to $K_L$, denoted as $K_{\perp L}$, rather than $K_S$, because $K_S$ is not orthogonal to $K_L$. Therefore the semileptonic charge asymmetry of what was previously regarded as $K_S$ is really that of $K_{\perp L}$. Based on this re-tagging, we modify the experimentally determined values of several parameters, including the one describing the violation of $\Delta S = \Delta Q$ rule, the one describing CPT violation for $\Delta S = \Delta Q$ transitions, and the time-like CPT- and Lorentz-violating coefficient for the two valence quarks in a kaon.