Non-exponential decay in quantum field theory and in quantum mechanics: the case of two (or more) decay channels

摘要

We study the deviations from the exponential decay law, both in quantum fieldtheory (QFT) and quantum mechanics (QM), for an unstable particle which candecay in (at least) two decay channels. After a review of general properties ofnon-exponential decay in QFT and QM, we evaluate in both cases the decayprobability that the unstable particle decays in a given channel in the timeinterval between $t$ and $t+dt.$ An important quantity is the ratio of theprobability of decay into the first and the second channel: this ratio isconstant in the Breit-Wigner limit (in which the decay law is exponential) andequals the quantity $\Gamma_{1}/\Gamma_{2}$, where $\Gamma_{1}$ and$\Gamma_{2}$ are the respective tree-level decay widths. However, in the fulltreatment (both for QFT and QM) it is an oscillating function around the meanvalue $\Gamma_{1}/\Gamma_{2}$ and the deviations from this mean value can besizable. Technically, we study the decay properties in QFT in the context of asuperrenormalizable Lagrangian with scalar particles and in QM in the contextof Lee Hamiltonians, which deliver formally analogous expressions to the QFTcase.