Binary systems in QM and in QFT: CPT

TL;DR

This paper explores the differences between Quantum Field Theory and Quantum Mechanics in describing quasi-degenerate neutral systems like kaons, highlighting the implications for CP violation and TCP symmetry without assuming a simple mass matrix.

Contribution

It analyzes the phenomenological consequences of QFT versus QM treatments of neutral meson systems, emphasizing the role of spurious states and the limitations of the mass matrix approximation.

Findings

QFT reveals tiny differences in CP violating parameters without TCP violation.

Spurious states with zero norm influence the pole structure.

Semi-leptonic asymmetry does not indicate TCP violation.

Abstract

Quasi-degenerate neutral systems like a (K, \bar{K}) type are investigated in Quantum Field Theory (QFT). A constant mass matrix as the one used in Quantum Mechanics (QM) can only be introduced as a linear approximation to QFT. We study the phenomenological consequences of the differences between the QFT and QM treatments. The role of ``spurious'' states with zero norm at the poles is emphasized. The K_L-K_S mass splitting triggers a tiny difference between the CP violating parameters \epsilon_L and \epsilon_S, without any violation of TCP. Non-vanishing semi-leptonic asymmetry delta_S - \delta_L does not signal TCP violation (usual claims not withstanding), while A_{TCP} keeps vanishing when TCP is good symmetry.