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

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.