Hadronization, spin, and lifetimes

Measurements of lifetimes can be done in two ways. For very short lived particles, the width can be measured. For long lived ones, the lifetime can be directly measured, for example, using a displaced vertex. Practically, the lifetime cannot be extracted for particles with intermediate lifetimes. We show that for such cases information about the lifetime can be extracted for heavy colored particles that can be produced with known polarization. For example, a $t$-like particle with intermediate lifetime hadronizes into a superposition of the lowest two hadronic states, $T^*$ and $T$ (the equivalent of $B^*$ and $B$). Depolarization effects are governed by time scales that are much longer than the hadronization time scale, $\lqcd^{-1}$. After a time of order $1/\Delta m$, with $\Delta m \equiv m(T^*)-m(T)$, half of the initial polarization is lost. The polarization is totally lost after a time of order $1/\Gamma_{\gamma}$, with $\Gamma_{\gamma}= \Gamma(T^*\to T\gamma)$. Thus, by comparing the initial and final polarization, we get information on the particle's lifetime.